Semiconductor superlattices and quantum wells for infrared optoelectronics

Semiconductor superlattices and quantum wells for infrared optoelectronics

Prog. Quant. Electr. 1993, Vol. 17, pp. 93-164 0079-6727]93 $24.00 © 1993 Pergamon Press Ltd Printed in Great Britain. All rights reserved. SEMICON...

4MB Sizes 6 Downloads 105 Views

Prog. Quant. Electr. 1993, Vol. 17, pp. 93-164

0079-6727]93 $24.00 © 1993 Pergamon Press Ltd

Printed in Great Britain. All rights reserved.

SEMICONDUCTOR SUPERLATTICES A N D Q U A N T U M WELLS FOR I N F R A R E D OPTOELECTRONICS F. F. S 1 z o v * a n d A . ROGALSKI~" *Institute of Semiconductors of the Academy of Sciences of the Ukraine, pr. Nauki 45, 252650 Kiev, Ukraine tInstitute of Technical Physics, WAT, 01-489 Warsaw, Poland CONTENTS Abbreviations 1. Introduction 2. Semiconductor Superlattices, Quantum Wells and n-i-p-i-Structures 2.1. Types of structure 2.2. Quantum well and superlattice energy levels 2.2.1. Confined electrons 2.2.2. Multiple quantum wells and superlattices 2.3. Band-offset and material considerations 2.4. Optical properties of QWs and SLs 2.4.1. Interband transitions 2.4.2. Intersub-band (intraband) transitions 3. Intersub-band GaAs/A1GaAs and Related Quantum Wells Infrared Photodetectors 3.1. Intersub-band absorption 3.2. Intersub-band relaxation times 3.3. Intersub-band multiple quantum well GaAs/A1GaAs photodetectors 3.4. Other III-V material system intersub-band detectors 3.5. Si~_xGe~/Si intersub-band detectors 3.6. GaAs/AIGaAs MQW photovoltaic and hot-electron transistor detectors 3.7. Intersub-band MQW IR detector arrays 3.8. Performance aspects of intersub-band infrared detectors 4. Interband Type II Infrared SL Photodetectors 4.1. InSb/InAs~_xSbx strained layer superlattices 4.2. InAs/Gat_xlnxSb strained layer superlattices 4.3. Strained layer supperlattice photodiodes 5. HgTe/CdTe and Related Superlattices 6. Doping Superlattices 7. IV-VI Superlattices and Quantum Wells 8. Conclusions References

ABBREVIATIONS ALE BLIP CBE D* Ec Es

Ev EWFA FPAs HWT Ic IE IR LAE Lb Lw Lz LGLL

Atomic layer epitoxy Background limited infrared photodetector Chemical beam epitaxy Detection efficiency Conduction band Band-gap Valence band Envelope wave function approximation Focal plane arrays Hot-wall technique Collector dark currents Emitter dark currents Infrared Laser assisted evaporation Barrier thickness Well thickness Period of structure Larger band-gap and larger lattice constant 93

94 97 98

99 I00 103 103 107 108 109 111 113 118 119 125 125 127 129 131 134 137 140 143 145 150 154 156 157

F . F . SIZOV and A. ROGALSKI

94

LO LWIR MBE MOV PE MQWs MWIR

QW QWIP SGSL SLs SLSs VPE w

Longitudinal optical Long-wavelength infrared Molecular beam epitaxy Metalorganic vapour phase epitaxy Multiple quantum wells Medium-wavelength infrared Quantum well Quantum well infrared photodetector Small band-gap and small lattice constant Superlattices Stained-layer superlattices Vapour phase epitaxy Integrated probability

1. I N T R O D U C T I O N

Within intrinsic photon detectors used at present for detection of IR radiation at wavelengths of/l = 3-20 pm in the absence of III-V alloys with long-wavelength cutoff, there is the unique position of Hgl _xCdxTe narrow-gap semiconductors. The longest wavelength III-V system (InAsSb) only has a 9 # m cutoff at T = 77 K and cannot be used for long-wavelength detector applications via interband (valence to conduction band) electron transitions, though at room temperature InAs0.36Sb0.64 has the band-gap Eg - 0.1 eV. The Hg~_ xCdxTe alloy now is one of the most thoroughly studied semiconductors. During the 1970s another alloy technique for IR detector applications, namely Pbt_xSnxTe, was advancing rapidly. However the advantages of HgCdTe and considerable improvements in its technology shifted the attention to HgCdTe devices for the production of IR imaging detector arrays at the end of 1970s. HgCdTe has, however, the most serious technological problems of any semiconductor material in mass production. In spite of achievements in material and device quality, difficulties still exist due to lattice, surface and interface instabilities. Present HgCdTe focal plane arrays (FPAs) are limited by the yield of arrays, which increase their cost. The difficulties with this material have made it desirable to examine other material systems to see whether the performance of infrared (IR) arrays can be improved. In the group of alternative materials, three classes of IR detectors have been recently developed: (i) photoemissive metal silicide Schottky barriers, (ii) intrinsic detectors made from ternary alloy systems such as InAsSb, HgZnTe and HgMnTe, (iii) quantum well IR detectors. The last class of detectors has emerged from the large amount of research activity initiated by the proposal of Esaki and Tsu (l) and the advent of molecular beam epitaxy (MBE). The interest in semiconductor superlattices (SLs) and quantum well (QW) structures has continued to increase over recent years, driven by technological challenges, new physical concepts and phenomena, as well as promising applications including IR optoelectronics. The developments in IR optoelectronics connected with FPAs has led to demands for new device concepts, connected with uniformity, controllability and yield. It seems unlikely that these requirements will be resolved in the near future using unstable, and difficult to apply, ternary HgCdTe-like alloys, but perhaps might be resolved on the basis of band-gap engineering concepts (2) which take into account the possibility of constructing the SL and QW optoelectronic structures with u!trathin layers of different semiconductors.* Several *High uniformity, controllability and yield in FPAs are possible too for the region 2 < 8 # m with Pt:Si Shottky-barrier photodetectors (see, e.g. Ref. 3).

4.2 7.2

PV PC

PV PC PC

PC PV PV

InAsSb/InSb SiGe/Si PbTe-nipi

HgCdTe HgCdTe PbSnTe

8.6 12.1 10.0 8.6 5.8 4.7 11.0 10.3 10.3

2.7

PC

PC

7.6

PC

8.9 4.1

9.8 10.0 7.9 13.2

PC PC PC PC

PC, PV PC

8.3

PC

Mode

lnGaAsP/InP

lnGaAs/InP

GaAs/AIGaAs InGaAs/lnAlAs

GaAs/AIGaAs

Type

2p (gm)

77 50 77 77 77 140 77 77 77

77

77

77 77

68 4 77 77 6O 50 77 77

77

T (K)

0.3

0.51 0.3

0.014

1.2

0.05 0.039

1.0

1.2

0.42

R (A/W)

10 .° 10 t3 10 I° 109 109 l0 w 1012

× 1010

x x x × x x x

x

10 I°

5.3 x 1.3 x 1.0 x 1.0x 8.0 x 5.0 x 7.0 x 1.7 x 1.0 x l 0 II

109 109 10 I° 109 10 I° 10t° 10 n 10 zl

3.0 x 10 I°

9.0

1.6 x 10=° 2.3 x I0 t°

2.0 >3.0 4.0 1.0 6.3 3.3 1.1 3.1

1.0 x 10 I°

D* (cm Hz I/2 W -l) Comments

0 FOV 0.5 ~ FOV 60o FOV

MBE, detector uses indirect A1GaAs barriers MBE, valence band intersub-band absorption MBE, band-to-miniband transitions MBE, lattice-matched multiquantum wells, BLIP performance up to 120K M O M B E , lattice-matched multiquantum wells, D* larger than equivalent GaPdAs/GaAs one M O M B E , lattice-matched p-doped multiquantum wells, normal incidence M O M B E , lattice-matched multiquantum wells MBE, strained-layer superlattices MBE, possiblity of monolithic FPAs HWE, BaF 2 substrates

MBE, 2o = 14.7 # m N E A T = 0 . 0 2 K at 6OK

MBE, conduction band intersub-band absorption, first bound-to extended state absorption detector MBE, NE A T = 0.01 K at 68 K

TABLE I. Performance of q u a n t u m well infrared detectors

21 22 23

18 19 20

17

16

15

13 14

11 12

10

9

8

Reference

o

ga

96

F.F. S1zovand A. ROGALSKI

propositions of semiconductor SLs and QWs for IR optoelectronics were made with III-V ~4'5) and II-VI <6) systems or elemental semiconductors (Sil _xGex/Si). ~7) Introduction of these new types of structures, accompanied by advanced growth techniques for their fabrication, allowed new physical concepts and has led to significant advances in IR optoelectronic applications. Table 1 summarizes the performance of different materials and types of superlattices and multiple quantum well (MQW) IR detectors. The parameters of HgCdTe and PbSnTe detectors are also presented. The difference between MQW and SL structures is that the thickness Lb of the barrier in the former one is large enough to prevent tunneling from the wells of the thickness Lw. In this paper we focus on physical effects and devices which involve IR excitation of carriers in QWs. A distinguishing feature of these devices is that they can be implemented in chemically stable wide band-gap materials, as a result of use of intraband (intersub-band) processes. On account of this it is possible to use such material systems as GaAs/A1GaAs, InGaAs/InAIAs, InAs/GalnSb and SiGe/Si, as well as other systems, although most of the work has been carried out with GaAs/A1GaAs. These materials have fewer processing problems than HgCdTe and monolithic FPAs can also be achieved. Some of the devices are sufficiently advanced that there exists the possibility of them being incorporated into high-performance integrated circuits. High uniformity of epitaxial growth over large areas shows promise for the production of large area (e.g. 512 × 512) two-dimensional arrays. In addition, flexibility associated with control over composition during epitaxial growth can be used to tailor the response of QW devices to particular IR bands or multiple bands. There is now considerable activity, both theoretical and experimental, in these directions. This new type of detector technology would benefit firstly from the potential advantages of integration with the large scale integrated technology for FPA detector applications. Also much higher quality substrates are available and behaviour and stability of dopants are much better grounded compared to HgCdTe or PbSnTe; to say nothing of the bond strength and material stability. Still, there are a lot of problems to resolve and science to be done, both fundamental and applied. At the beginning of the 1980s studies on semiconductor II-VI, III-V and IV-VI lowdimensional systems, such as n-i-p--i-, QW and SL structures, and a little bit later from elemental semiconductors, have revealed a number of mechanisms for obtaining the cut-off wavelengths of 2 - 5-20/~m. The above interest has been driven by technological challenges, new physical phenomena as well as promising applications. At present the most developed and most promising low-dimensional systems for mid- and long-wavelength IR detectors are those based on heterostructures between GaAs and GaA1As. Also the III-V strained layer quantum well structures are now promising, though there are severe metallurgical problems with alloys suitable for these aims. Strained-layer Sil_xGex/Si SLs (lattice mismatch between Ge and Si is 4.17% at room temperature) have created a great deal of interest due to the potential integration with silicon VLSI technology for FPA detector applications. Development of a new class of devices was possible owing to a powerful technique called molecular beam epitaxy (MBE). Today, several subcategories of beam epitaxy and vapour phase epitaxy (VPE) have been developed to routinely produce artificially layered semiconductors of high structural perfection, for fundamental research and device applications. The fundamentals of several modern epitaxial methods for growth of III-V compounds, including metalorganic vapour phase epitaxy (MOVPE) and the various subcategories of gas-source MBE have been recently described in this journal (Gobel and Ploog(24)). The above techniques give one the ability to control and vary the composition at the level of successive atomic layers during epitaxial deposition. Steady improvements in growth techniques during the last decade have made possible high-quality heterostructures having designed potential profiles and impurity distributions

Infrared optoelectronics

97

with dimensional control close to interatomic spacing and with virtually defect-free interfaces, particularly in a lattice-matched case such as GaAs/AIGaAs. The semiconductor SL structures have been grown with III-V, II-VI and IV-VI compounds, and elemental semiconductors (e.g. SiGe/Si), as well as amorphous materials. In addition to MBE and MOCVD, new or unconventional techniques such as GS (gas-source) MBE, LO (low pressure) MOCVD, CBE (chemical beam epitaxy), HWE (hot wall epitaxy), ALE (atomic layer epitaxy) and LAE (laser assisted evaporation) have been explored for this purpose. The performance of long-wavelength QW IR detectors is inferior in comparison with HgCdTe and related photodetectors operating at the same temperatures (see Table 1). A number of questions must be resolved regarding, for example, dark currents and noise or the values of quantum efficiencies in SL or MQW photodetectors. So, the key challenge in the development of SL and MQW structures for long-wavelength detector applications in many cases aims at demonstrating competitive performance or the ways of its achievement in such kind of detectors. For IR semiconductor laser applications in the spectral region of 2 - 3-20 #m, the basic role plays SLs and MQWs from IV-VI semiconductors. The goal of the design of IV-VI SL and QW devices in application to IR optoelectronics lies in obtaining more effective devices operating at elevated temperatures compare to the liquid nitrogen temperature, which is now the operating temperature of IV-VI diode lasers. This paper is devoted to physical properties and applications of quantum well structures for infrared optoelectronics, mainly infrared detectors and lasers. It is difficult to cover such topics since the technology of the above devices is rapidly developing and new concepts are constantly being proposed. It is assumed, that the basic phenomena and materials are well-known by the reader. More information can be found in excellent review articles which have been published within the last few years covering fundamental aspects, (25-27) technology,<2s)electrical and transport properties, <29-33)linear and nonlinear optical properties, ~34'35)as well as device applications32'36-3s) For scientists not specialized in the field but interested in recent developments in semiconductor microstructure physics, papers written by Weisbuch,~39) Gobel and Ploog(24) are recommended. This paper is divided into seven sections. The second section shortly describes different types of quantum wells and their electronic and optical properties. Attention is made on band-offset considerations. The next six sections are devoted to different types of QW IR detectors dependent on physical principals, which are utilized to directly shift response of microstructures into the IR region, and dependent on type of materials. The last chapter concerns IV-VI SLs and QWs applied to both IR detectors and semiconductor lasers. The main efforts in this direction are shifted to obtain more effective devices operating at elevated temperatures.

2. SEMICONDUCTOR SUPERLATTICES, QUANTUM WELLS AND n - i - p - i - S T R U C T U R E S The research on semiconductor SLs was initiated in 1969 with the proposal by Esaki and Tsu °) for a solid state system with an effective one-dimensional periodic potential which resulted from alternating ultrathin semiconducting layers. It should be noticed that creation of a similar one-dimensional potential in solids by the use of acoustic waves, was firstly proposed by Keldysh<4°)as eary as 1962. Since the proposal by Esaki and Tsu, the interest in semiconductor SLs and QWs has continued to increase, due to the progress in ultrathin layer technology and its control, understanding of the basic low-dimensional system properties and device concept applications.

98

F.F. SlzOV and A. ROGALSKI

2.1. Types of Structure The discontinuity at the heterointerface between the different semiconductor layers involves the discontinuity in the band structure. Therefore, the conduction- and valenceband discontinuities determine the carrier transport across the interface and so they are the m o s t i m p o r t a n t quantities that characterize a semiconductor heterojunction. According to the character o f discontinuity and ignoring the changes in the lattice constants, the local effects at the interfaces, and also the doping effects, k n o w n hetero-, Q W and SL-structures can be classified into several types: t3°) type I, type II, type III, and n - i - p - i - s t r u c t u r e s (so-called doping SLs as opposed to the three types o f compositional SLs mentioned). The types o f Q W - and SL-structures are shown in Fig. 1.

(c)

Bulk conduction

band edges

S1's energy levels t~

Bulk valence

band edges

Distance

Distance

(d)

(b)

CdTe

r,

I

Distance

*6

Distance

(e) i:

Lz

"i

? g~

Distance

FIG. 1. The various types of semiconductor SL and MQW structures: (a) Type-I structures. Lz is the period of the structure, Lb and Lware the width of the barrier (wall) and the well respectively; , E~ are the band-gaps of different semiconductors. (b) Type-II "misaligned" structures. (c) ype-II "staggered" structures. (d) Type-III structures. The schematic band diagrams of semiconductors with a positive band-gap (CdTe) and a "negative" band-gap (HgTe) are also presented near the F-point of the Brillouin zone. (e) n-i-p-i-structures (doping SL). 2V0 is the modulation potential, E~ is the effective band-gap.

~sJ

Infrared optoelectronics

99

The values for the band discontinuities of the conduction band (AEc) and the v a l e n c e b a n d (AEv) c a n n o t be obtained by simple considerations. Theoretical descriptions of types and values of discontinuity at the semiconductor heterointerface are extremely difficult due t o complexity of the real interface. There is some general agreement b e t w e e n t h e p r e s e n t experimental measurements of band discontinuities and the results of the limited number of realistic theoretical models of microscopic mechanism causing band discontinuities. These questions will be briefly discussed in Section 2.3. In type I (Fig. la) heterostructures applied, for example, to the GaAs/AIAs, GaSb/AISb, GaAs/GaP and most of II-VI and IV-VI semiconductor structures with nonzero bandgap, electrons and holes are confined in one of the semiconductors. In these kinds of SL and MQW structures one can expect lower current thresholds in injections lasers compared to heterolasers. In type II structures (Fig. lb) that are applied to so called type II "misaligned" structures (e.g. to InAs/GaSb, PbTe/SnTe) the top of the valence band of one of the semiconductors is located above the bottom of the conduction band of another semiconductor. These structures form the semimetallic QWs or SLs as the carriers from the valence band of the first semiconductor transfer to the conduction band of the second one. In type II "staggered" structures (Fig. lc) the bottom of conduction band of one of the semiconductors is above, but the top of valence band is below, the top of the valence band of another (e.g. as in the case of InAsxSbl_x/InSb, Inl_xGa~As/GaSb~_yAS:-Si/Si0.5Ge05 SLs on 5i0.75Ge0.25 buffer). In this type of structure the lowest conduction and the highest valence bands are located in different layers and so there is spatial separation of confined electrons and holes and such structures can potentially be used as effective photodetectors since photoinduced nonequilibrium carriers would be spatially separated. Type III structures (see Fig. ld) are formed from the semiconductors, one of which is a semiconductor with positive band-gap Eg = Err - Er8 > 0 (e.g. CdTe or ZnTe) and another is a semiconductor with a "negative" band-gap E 8 = Err - Ers < 0 (HgTe-type semiconductors). At all temperatures the HgTe-type semiconductors behave as semimetals, as there are no activation energies between the light- and heavy-hole states of Fs band. The "negative" band-gap Eg changes its value with the temperature. In n-i-p-i-structures (doped SLs) the constituents are made from the same semiconductor, but the layers are doped by different impurities or doping levels. The band-gaps of the layers do not depend on the z-coordinate, but the value of the effective potential 2V0 (Fig. le) and effective band-gap E ~ depend on the doping levels, the values of the dielectric constants and the thicknesses of the layers. These structures are also potential effective photodetectors due to the spatial separation of photoinduced carriers. 2.2. Quantum Well and Superlattice Energy Levels* The energy spectrum of MQWs and SLs can quite easily, and with the insight into the problems, be described by the envelope wave function approximation (EWFA) (see e.g. Refs 26, 39, 41-43) based on the effective-mass approximation and with the envelope function slowly varying on the atomic lengths. The EWFA does not break down until layer thicknesses in SLs of 6-8 monolayers<44'45)at least in predicting the values of energy levels. At thinner layers the physical processes underlying the formation of SL states may not be fully accounted for by this method and the electron spectra may be calculated using, f o r instance, the tight binding semiempirical approach o r p s e u d o p o t e n t i a l calculations.(~7,46) The simple one-band Kronig-Penny model is quite adequate for the higher-lying III-V semiconductors heavy-hole energy states stemming from a high degree of parabolicity of the *For more familiar acquaintance with the description of the electron spectra in low-dimensional semiconductor systems one can use, for example, the excellent reviews published by Bastard ~) and Weisbuch. (39)

100

F . F . Sizov and A. ROrALSK1

bulk heavy-hole bands. This model is less adequate for the conduction and light-hole bands as these bands states are constructed from the bulk components of different bands. (46) 2.2.1. Confined electrons. The most simple situation is that of the electron confinement by a one-dimensional rectangular potential of a well with an infinite wall height. In this infinite-well model many results can be obtained analytically and although they are not applicable quantitatively in many cases, the insights gained for such a model are transferable to the finite-well case. The wave functions that are vanishing at the boundaries in the infinite-well model are: (47'48)

cb.(z) = (2/Lw) t/z sin n ~ z ,

(1)

for odd integers n = 2, 4, 6 . . . and

~m(z ) = (2/Lw)'/2 cos(m -~w Z ),

(2)

for even integers m = l, 3, 5 . . . . The confinement energy is given by

E, = (n2h2/2rn *L 2 )n 2,

(3)

where the quantum number n = 1, 2, 3 . . . and m* is the electron effective mass. In the other two directions the electrons are not confined and so the energy of the two-dimensional (2D) free electrons is

E2t, = E. + (h2/2m*)(k] + key).

(4)

The free electron wavefunctions are combined plane waves in x- and y-directions and even or odd harmonic functions in z-direction:

~2.D= (2/L )exp(tkxx)exp(tkyy)(2/Lw)'iz { S~71k~nmZ))} = A expOk± r±)X(z).

(5)

Here k± and r± are two-dimensional wave and position vectors respectively: k . = (kx, ky),

r. = (x,y) and kz = nT~/Lw, and L is the system dimension in x,y directions. Taking into account the periodicity of the crystal lattice the electron wave function of a semiconductor well is the product of the function (5) and a Bloch function, which is periodic with the atomic lattice spacing

Fi(n, k, r) =

2DUik (r) = A Uik (r)exp(ik± rl ) X ( z ) Ach i.

(6)

where Utk(r) is the periodic part of the Bloch function for " i " band and X(z) is the envelope function which describes the motion of the particle in z-direction. The 3D-density of states g3D(E) defined per volume V = 1 cm 3 in the case of parabolic dispersion law by the expression

2i/2

g3o = - -

tm *~3t2~1/2

7~2h 3V'"

#

~

,

(7)

Infrared optoeloctronies

~ 1 ~

101

4

1

f2

//lIE1 E2 ¢9 .~,

! E3! E4 , ~ ', ' 1/4 112 Energy (Eg) FIG. 2. 2D-density of states (2, 4) in comparison with 3D-density of states (1, 3) in parabolic one-band approximation (1, 2) and nonparabolic two-band approximation (3, 4).

changes in 2D-case to the staircase one per S = V/Lw (Fig. 2): m'S_

g2D = ~

(8)

)Z O.(E - E.),

T

where O ( E - E,,) is the step function: 1, E > E . , O ( E - E,,) = O, E < E,, " It means that the density of states of a given quantum state E, is independent of energy E. The nonparabolicity of the dispersion law, many-valley band structure and finite heights of the walls (barriers) change the equations essentially, although in many cases they are qualitatively the same. For instance, in the case of two-band Kane nonparabolicity that is a good approximation of the conduction band dispersion law in the most of III-V and II-VI semiconductors,~26)the 2D density of states is given by gin(e)=

m*(O)S "1

n---~--t + 2 E / E g ) ~ _ O . ( E - E . )

(9)

n

where m*(O) is the electron effective mass at the band-edge. In the large-gap semiconductor structures (e.g. GaAs/GaA1As QWs), the band nonparabolicity plays a minor role, but it must be taken into account in the evaluations of the electron- and light-hole confinement energies in semiconductor SLs formed from semiconductors with the band-gaps Eg < 0.5 eV, e.g. in such structures as GaSb/A1Sb, GaSb/InAs, IV-VI and HgTe/CdTe-like MQWs and SLs. In the case of many-valley semiconductors (e.g. IV-VI semiconductors with the band structure like n-Ge) with two-band nonparabolic dispersion law, the density of states for the valley with the main axis oriented at the angle 4> relatively to the z-direction, is given by the expression .~. g 2 D ~,17")

S F mt (O)mt~(O) = ,,,, 2 L , , , ,"o'sz , ,,, 2 -z ' 'cos

2

-]la 4>" (1 + 2 e / e . ) _ E

J

0(e - e,).

(io)

0.05

O. 1 0

0.15

1 O0

50

W e l l w i d t h (,/~)

I

I

Ex

kJ

E2

nffil

n=2

n=3

o

o

0.05

0.10

0.15

--

--

(b)

I

-50

J

50

D i s t a n c e (,~)

I00

150

~ exp (-Kz Z)

U 0 = 0.15eV

FIG. 3. First three b o u n d energy levels and wave functions in an infinitely deep q u a n t u m well (a) and finite q u a n t u m well (b) with the barrier height Uo = 0.15 eV. Effective mass m * = 0.1 mo and the well width Lw = 100 A.

eJ

>.

0.25

0.30

(a)

r~

S

.-n

Infrared optoelectronics

103

Here mt (O) and ml (O) are the transverse and the longitudinal electron effective masses at the band-edge, respectively. The nonparabolicity of the many-valley structure essentially changes the electron confinement energies compared to parabolic dispersion laws, even in the wells with infinitely high barriers. In the finite-well case the position of the levels is also considerably different compared to the infinite-well case, even for the parabolic dispersion law. The electron wave functions do not vanish at the boundaries, but penetrate into the walls (the amplitudes drop exponentially in the walls); this is the basis for the formation of SLs in the case of periodic structures with overlapping well potentials. Figures 3a and b show the positions of the first three levels in separate infinite wells and in the finite one. Also shown are the wave functions of these states for both cases. Figure 4 shows the dependence of the integrated probability, W, on the well thickness for finding the electron in the barrier of a square quantum well in the ground bound state for two values of barrier heights and two values of the electron effective masses. We can see that the penetration of the particle into the barrier increases essentially with decreasing well width, barrier height and effective mass. 2.2.2. Multiple quantum wells and superlattices. In isolated QW the discrete energy levels are narrow (the sub-band dispersion is fiat) and the value of the effective mass in z-direction is infinite, as the electron on the level oscillates back and forth in the well and therefore there is no macroscopic current along the z-axis. The presence of a sequence of QWs separated by the barriers with the overlapping well wave functions leads to quantum well levels broadening to form the SLs sub-bands (see Fig. 5). The SL potential changes the 2D-density of the states character, destroying the stairlike form of p(E). The minibands divided by minigaps arise and, for example in tight-binding, description of the superlattice sub-bands, the inverse effective mass in the z-direction, and also the band width are proportional to the modulus of the transfer matrix element that comes from the wave function overlap in neighbouring wells of the chain. 2.3. Band-offset and Material Considerations In a bulk semiconductor the transport and optical properties are basically determined by the parameters of the uppermost valence band and the lowest conduction band that are

1.0 0.5

0.2 ~

0.1 0.05

¢h O.02 0.01

0

I

I

I

I

I

50

1O0

150

200

250

Well width (~) FIG. 4. The dependences of the integrated probability on quantum well thickness for finding the electron in the ground state of the well. l--U0--0.15eV, m*ffi0.1m0; 2 - - U o f 0 . 1 5 e V , m* = 0.05 too; 3--Uo= 0.05 eV, rn* = O.05mo.

104

Slzov and A . ROGALSKI

F.F.

2.0

1,4

G a l . x AIxA s

1.2 --

AEcB: AEvB = 0 . 6 4 : 0 . 3 6

1.0

////~ 0.8

o

200

o.6

0

r~ 0.4

-bm @ L

F¢2+(5E) D - - @ ~

, ,,,

• m



~> 0

0.2

I00

0 -0.2 X=0.3 LA = L B

o

-0.4

I

I

1 O0

200

d

(~)

FXG. 5. Supcrlattice band structure for electrons in GaAs/Ga0.vAl0.3As superlattices versus the period L Z (after Rcf. 26). The allowed energy states arc hatched.

-0.6

0.2

0.4

0.6

0.8

1.0

C o m p o s i t i o n parameter ( x ) FIG. 6. G a ~ _ x A l x A s band edges measured relative to

the Fe acceptor level, which was taken as a reference level independent of x (after Ref. 57).

separated by the band gap E8. In MQWs and SLs electrical and optical properties are mostly governed by the band discontinuities at the heterointerface, i.e. the band alignment, of course taking into consideration the band structure of the semiconductor (the band structure of semiconductors will not be discussed here except the cases need to explain the peculiarities of the SLs or MQWs properties). Modern epitaxial techniques such as MBE (for a review see Refs 24 and 49), metalorganic chemical vapour deposition (MOCVD) (24) for growth of III-¥ and II-VI compounds and laser-induced evaporation (5°) in application to II-VI and IV-VI semiconductors, have made it technologically possible to grow artificially layered semiconductors of high structural perfection at the interface for fundamental research and applications. An important requirement for high-quality MQWs and SLs is the matching of the lattice constants of the constituents. But in pseudomorphic systems (so called strained-layer SLs) internal mechanical strain due to lattice constants mismatch, can be used for additional, to the effect of confinement, band engineering. °2,5t) Recently there have been considerable efforts to theoretically understand the interface phenomena and to experimentally measure the band-offset at semiconductor interfaces/52~1) To obtain the values of the band-offsets several different experimental methods have been used that are based on optical experiments,(62'63)electrical measurements of device characteristics64'65,photoemission ~66,67)and photovoltaic ~6s)experiments. Also inelastic light scattering ~m and electron-beam-induced current measurements~69'7°)are used with this aim in mind. It must be taken into account that electrical and optical methods do not measure the band-offsets themselves, but quantities associated with the electronic structure of the

Infrared optoelectronics

105

heterojunction. The determination of the band-offset values from these experiments requires an appropriate theoretical model. For a band-offset value used in testing any band-discontinuity model, the device quality is of primary importance concerning the junction abruptness, lack of chemical composition purity and the impurity concentration distribution. A number of different theoretical models have been proposed to predict the band-offsets in semiconductor heterojunctions. These models can be divided into two different categories: t58) (i) "linear" models that attempt to predict band offsets from differences between quantites which are intrinsic to the bulk semiconductors; (ii) models, that seek to determine band-offsets for a particular interfacial geometry from a self-consistent determination of the electronic potential shift. It is interesting to note that in a lot of cases there is a general agreement among the different predictions. The earliest model of the first category is the affinity rule model, that was introduced by Anderson35~) This model is usually formulated in terms of conduction band-offsets (AEc), when the conduction band discontinuity is equal to the difference in the electron affinities of semiconductors in contact. But in direct gap III-V and II-VI semiconductors the conduction band contribution to the density of states is negligibly small in comparison to the valence-band density of states and its theoretical energy position is affected by many factors. Harrison ~53)has proposed a theoretical model in which the valence band-offset is equal to the difference of the valence-band maxima of the two semiconductors, as calculated in a tight-binding approximation using atomic term values. The weaknesses of this atomic orbital model are the assumption that the atomic term values are carried over from atom to solid and the inherent inaccuracies of the tight-binding approximation method. Based on this model follows the so called "common anion rule" according to which t55) the band-offset should be small in the case of semiconductor junction with the same anion. In many cases this model fails in description of the band-offset values (e.g. the case of HgTe/CdTe heterojunction, see Section 5). Other approaches in this class of models (see, e.g. Ref. 54 and for analysis see Refs 56, 71, 72) use screening arguments to determine a mid-gap charge neutrality level in each semiconductor which would be aligned when an interface is formed. The valence band-offset is taken to be equal to the difference in the neutrality levels. Although the physical origin of the charge neutrality levels is unclear, models postulating the existence of such levels were reasonably successful in predicting band discontinuities. In Ref. 57 it was postulated that deep transition impurity levels can be used as the reference levels for obtaining the valence band-offsets in heretojunctions. This was successfully demonstrated for some isovalent lattice-matched heterojunctions: GaAs/Ga~_xAlxAs, InP/In~_xGaxAsyP~_y, GaAs/In~_xGaxP, and HgTe/Hg~_xCdxTe. In such a reference transition impurity model a valence band discontinuity is given by the difference in the energy level positions of a transition metal impurity in two semiconductors forming a heterojunction. In Fig. 6 a full Gal _xAlx band diagram is presented, in which the Fe acceptor level was taken as the reference level independent of " x " . The position dependence of the Fe level on the valence band edge position EvB is described by the expression: ~57) EFt -- Eva = 0.516 + (0.453 _ 0.01)x, eV,

(11)

and the conduction band offset (at x < 0.4) can also be described by linear dependence AEcB = (0.79 _ 0.02)x, eV.

(12)

106

F . F . Sizov and A. ROGALSKI

0.2 0.1

&

0

~ , 0.3ev

-I

f HgSe

I

I

I

I

0.2

0.4

0.6

0.8

fr"

%

Composition

HgTe

CdTe

FIG. 7. Evolution of the zero-gap crossing points in HgTe t _xSex and their relative position to the valence-band edge of CdTe as obtained by taking the Fe 2+ energy level (0) as a reference level (after Ref. 57).

Very attractive from the practical point of view for IR detector applications seemed lattice-matched III-type SLs composed of zero-gap and wide-gap semiconductors, like HgTe/CdTe SLs. Analysis of the position of valence bands in HgTe~ _xSex compounds and in CdTe (see Fig. 7) confirms the large band-offset AEv = 0.3 eV obtained in photoemission experiments(67) and supported by recent theoretical results. (73'74) The "common-anion rule", predicting almost zero value of AEv in HgTe/CdTe heterojunctions, is not applicable in this case. The second category of theoretical descriptions of the band discontinuity are based on self-consistent pseudopotential calculations in which the electrons are allowed to adjust to the environment created by the interface.(6°'75-77) The interface is taken as an ideal structure in which the bulk crystalline structure is followed by an abrupt change of material at the interface. The valence band discontinuity is taken to be equal to either the difference in energy of atomic c o r e levels(7t,76) or the difference in some average potential in the bulk and at heterojunction.(6°,77) These self-consistent approaches require a different calculation for each separate system. Taking into account the evidence that band-offsets at most nonpolar semiconductors are nearly independent of a particular surface geometry,(6°'75'76) the model for abrupt junctions formed by two intrinsic semiconductors based on "linear" models, including charge rearrangement effects at the interface, was outlined by Pollard. (58) It was shown that this model works fairly well for both polar and nonpolar semiconductors and that the band-offsets depend on the amount of strain. Comparison of the experimental valence band discontinuities and those predicted by different models are presented in Table 2. One can see that for a quite wide group of heterojunctions there is broad general agreement between the different theories and experimental results. We can also see that for many pairs presented in Table 2 the transitivity rule AE~2 + A E 23+AE~ = 0 '

works well enough.

31

(13)

Infrared optoelectronics

107

TABLE2.Comparison of experimental and calculated valence band discontinuities (in eV) (after Rcf. Heterojunction AIAs/GaAs AIAs/Ge GaAs/Ge GaAs/InAs GaP/Si GaP/Ge InAs/GaSb AISb/GaSb

InSb/Si Si/Ge InP/Ge InP/Si InSb/Ge ZnSe/Ge ZnSe/GaAs ZnSe/Si CdS/Si CdS/Ge CdS/InP CdSe/Si CdSe/Ge GaAs/Si GaSb/Ge InAs/Ge InAs/Si

Data

ot °s)

0.42 0.95 0.56 0.52 0.80 0.85 0.38 0.39 0.25 0.18 0.64 0.36 0.12 1.57 0.92 1.26 1.47 1.75 1.31 1.27 1.37 0.21 0.30 0.34 0.50

P s e u d o p o t e n t i a l (~°~ 0.37 1.05 0.63 -0.61 -0.38 0.49 -----2.17 1.59 -----------

,

58)

Harrison model (7~)

Tersoff model (x)

Experiment

0.12 0.78 0.66 0.13 0.69 0.98 0.42 0.18 0.31 0.29 ---2.01 1.35 ----1.37 ------

0.37 0.87 0.32 0.00 0.45 0.63 0.43 0.38 0.35 0.18 0.58 0.40 0.17 1.52 1.20 1.34 1.56 1.74 1.16 1.05 1.23 0.14 0.21 0.32 0.14

0.40 0.95 0.56 0.17 0.80 0,88 0,51 0.45 0.1)6 0.17 0.64 0.57 0.06 1.52 0.96 1.25 1.55 1.75 1.63 1.20 1.39 0.05 0.15 0.33 0.15

Here some results of band discontinuities between semiconductor heterojunctions composed of III-V and II-VI semiconductors that are of recent theoretical and experimental interest were briefly discussed. There exists some other theoretical models of band discontinuities in semiconductor heterojunctions (for analysis see, e.g. Refs 55, 58, 59, 61, 72) but their agreement with experimental values of band discontinuities are worse. The particular case of IV-VI semiconductor junction band-offsets will be discussed in Section 7. 2.4. Optical Properties of Q Ws and SLs A few optical properties on the base of a very simplified model concerning interband and intraband dipole optical transitions will be discussed in this section. The particular cases of optical absorption in QWs and SLs will be analyzed separately. Here only some general features of the optical absorption in QWs and SLs will be considered. For an analysis of optical transitions in zinc-blend structure semiconductors one can see Refs 26, 31. As in this paper the properties of QWs and SLs are reviewed only for mid- and long-IR spectral regions, the exeitonic absorption will not be discussed. For a review of this kind of absorption one can see for example Ref. 24. In optical absorption experiments one measures the attenuation of a light that is passing through the sample of thickness L. The attenuation of a light is determined by an absorption coefficient a (hco), which according to Fermi's Golden Rule for transition probability per unit time neglecting the spontaneous emission is defined by an expression: <47) 1

~(~, co) ffi B , j ~ (F,I ~ I~> 2 ~(Ej- E , - h~)[f(E,) -f(Ej)l,

(14)

where ~ is the polarization vector which is perpendicular to a propagation vector q of an electromagnetic wave of frequency co, p is the electrical dipole moment, f(E~)= JPQE 1712--B

108

F . F . SIZOV and A. ROGALSKI

{l+exp(E~k-EF/T)} -~ is the Fermi occupation function of the state E~, EF is the chemical potential. Wave function, in this case, is defined by expression (6). To obtain the absorption coefficient values one needs to calculate the dipole matrix element CP,~ = ( F i 1¢/~ [ F y ) .

(15)

Because here there is a rapid variation of the periodic part of the Bloch functions U~,(r) on the elementary cell length and a slowly varying envelope function X~(z), one can represent (15) by (16) where [2 is the volume of the elementary cell and V = SL is the sample volume. From the analysis of (16) one can see that the allowed optical transitions are split into two classes. There are: (i) interband transitions which take part between QW subbands originating from different band extrema i, j and defined by atomic-like dipole matrix elements (Uv, I#lUjk); and (ii) intersub-band (i = j ) optical transitions which are defined by dipole matrix elements between the envelope functions of the same band. 2.4.1. Interband transitions. The interband dipole optical transitions are defined by the first part of the right side of the Eqn. (16), as for interband transitions (Uv, IUjk) = 0 due to the different parity of Bloch functions. For interband transitions the selection rules associated with the wave polarization and also the part associated with the envelope functions overlap must be taken into account. The interband optical absorption for type I structures, in which the electrons and holes are confined in the same layers, will be stronger than in type II structures, where electrons and holes are spatially separated. An analysis of the periodic part of the Bloch functions determines the selection rules for the electromagnetic wave polarization and depends on the symmetry of the band states. For zinc-blende semiconductors for optical transitions between F6-states (En) and F8 heavy-hole (hh) and light-hole (lh) states are summarized in Table 3. For additional selection rules one needs to evaluate (Xi, IXjm), and at this point there is a difference between the type I and type II structures. Type I structures. A simple analysis can be made for a situation of the rectangular infinite well model with the envelope wave functions (5). In this model the integral (X~ IXjm) is nonzero only if An = n - m = 0. For superlattices the superlattice quasimomentum kz also has to be preserved: Akz = 0. The intensity of interband optical transitions, and therefore the

TAnLE 3. Relative I ( Uc.k(r,) I~01 Uv,k(rh)) d u c t o r with b a n d different polarization

strength o f the dipole matrix element [ P ~ I 2 = 12 for different Q W transitions of a zinc-blende semiconextrema at F - p o i n t of the Brillouin zone and o f the light (after Ref. 26). Only transitions from Fs to F 6 states are taken into account

Polarization

Propagation

E[Ix

Elly

EIIz

Type o f transitions

q Ilz q [[x q IlY

3 -3

3 3 --

-0 0

h h n =*. E m hh n ~ E m hhn =~ Em

q [[z q [[x q Ily

1 -1

1 I --

-4 4

lh a =~ E m lhn =~ Em lhn ~ Em

Infrared optoelectronics

109

absorption coefficient in QWs, will be of the same order as in the bulk semiconductor if (Xi, [Xjm) ~ 1 and so to observe the absorption in MQWs with Lw = 102A, in separate QW one needs to have a structure with at least about 10 identical QWs. The finite-well case diminishes the intensity of optical interband transitions as the envelope wave functions partly penetrate into the barriers. For higher lying states the intensity of optical transitions diminishes due to increased penetration of the wave functions into the barriers and broadening of the excited sub-band states (see Fig. 3b). Because in type I QWs the absorption has a staircase-like shape, as it is expected from the density of states in two-dimensional structures, the interband optical absorption has a blue shift compared with the absorption in a bulk semiconductor. In nonrectangular QWs the selection rule An = 0 may not be fulfilled and other, but much weaker (compare to An = 0) transitions, are possible. The interband optical absorption in SLs is to a certain degree qualitatively changed, although the optical absorption is often analyzed in terms of isolated QW even for rather thin (Lb < 80/1,) barriers, when due to the overlap of the wave functions in neighbouring QWs, the minibands are formed. In SLs the relative spatial localization of electron and hole wave functions play a major role in evaluating the selection rules, also the dispersion relations along the SL axis should be taken into account. Type H structures. In such a kind of structure the electrons and holes are spatially separated. We restrict ourselves to the case when the energy of photons is lower than the band gaps of constituents (hco < Eg~) to ensure the IR absorption in the system composed of wide gap materials. In this case the optical absorption is only possible due to the overlap of the conduction and valence band envelope functions exponentially decaying in the neighbouring layers. In type II structures the integral (Xi, [Xj,,) should increase with increased numbers of the states in QWs, as the envelope functions penetrate deeper into the barriers. 2.4.2. Intersub-band (intraband) transitions. In bulk semiconductors the intraband optical transitions within the same band are forbidden and may only be induced by phonons or impurities to provide the momentum conservation. From the analysis of the second part of the right side of the expression (16) it is seen that for evaluating the intersub-band optical transitions in QWs or SLs one needs to calculate (X~, [q~ IX~,) as (U~ I Ujk) ~ 0 for the same band. The dipole optical transitions for electromagnetic waves with polarization Ellx, y are allowed if only the initial and final states coincide (hco = 0). For these polarizations at hco ~ 0 the intersub-band transitions in QWs or SLs are only possible for the free carrier absorption mechanisms that is an analog of free carrier absorption in bulk semiconductors. But the in-plane propagation of the wave with the electric field vector polarization Ellz leads to allowed optical transitions between the sub-bands. The optical intersub-band absorption between square quantum well states can readily be calculated and the peculiarities of the process understood using the electron wave functions (5) for the well with the infinite wall height. The interaction term in the Hamiltonian can be taken in the form W = e ( E r ) , (78'79) where E is the electric field of the electromagnetic wave and e is the electron charge. So the dipole matrix element

(n I(Er)lm> = f~/2 X~*(Er)X. dz,

(17)

d -L~/2

that defines the intensity of the optical transitions, will not be equal to zero only for the case of the wave functions of opposite parity and for nonzero Ez-electric field component. The intensity of intersub-band optical transitions will be proportional to cos2 q~, where ~ is the angle between the plane of QW and the electromagnetic wave electric field vector.

II0

F.F. $1zov and A. ROGALSKI

A dipole matrix element between any two states of opposite parity is defined by

8

mn

( z ) = ( n I z [ m ) = ( - 1)(" - m + l)/2L, ~ 2 ( m 2 _ n 2)"

(18)

For a QW with Lw = 50/~, the matrix element ( z ) ~ 10/~ and does not depend on the band parameters of the semiconductor. For the oscillator strength of the corresponding transition it follows

2 2 ( z ) 2 2/.,pz) ~ 64 rn0 2mo09,~ mn f'~ = h = m0hco,m - rc2 m* (m 2 - n2)3'

(19)

where ( P z ) = ( n l P z l m ) , to.m= (Em-E,)lh, the energies E,,m in the well are defined by expression (3), and m0 is the free electron mass. From the above considerations it follows that for intersub-band transitions the Bloch states remain constant and the dipole transitions are between the envelope states. This situation differs from the interband valence to conduction band optical dipole transitions, which occur between the Bloch states. Moreover, the intersub-band transitions are only possible for the component of the electric field which is perpendicular to the QW or SL plane. These considerations are well applied to n-type III-V semiconductors with c-band extrema at F-point of the Brillouin zone. Also they are applied to p-type III-V and SiGe/Si SLs and MQWs for optical transitions between quantum states of the same hole band. <7) In this case transitions between two different hole bands are also possible, but their intensity is smaller than the transitions between two quantized states in the same band due to the p-like character of the Bloch functions. It must be taken into account that the intersub-band transitions in QW or SL will be possible if only their initial states are occupied by carriers, so that the photodetectors with intersub-band transitions are extrinsic in nature. To receive a component of polarization normal to the QW or SL plane to enhance a field in the well, the grating may be used (s~3) as it is shown in Fig. 8. Also angled facets and edge illumination are utilized o°'u'sS) that is schematically illustrated in Fig. 9. For p-type III-V QWs with hole intersub-band absorption selection rules intrinsically allow normal incidence absorption/s6,sT) For indirect gap semiconductors, such as silicon and A1GaAs, with large AlAs content (the conduction and valence band extrema are anisotropic) several authors (s8-9°)have argued that normal incidence radiation could also excite carriers out of QWs.

E ,

~

/ "~ /

4oooA

"GaAs ~

Al°'4Ga°'eAs GaAs Alo.2Gao.sAs

~

~ FIG. 8. Use of gratingto producediffractedwaveswitha polarizedcomponentperpendicularto a GaAsQW IR detector (after Ref. 82). -

Vp

+

Infraredoptoelectronics

111

cOhmic ontacts

X

/

Mq w ---~/'///////////////////~v//////////./.,,//.,,,////////~///A...... ~ / ~ I Irn~id~in2n J ~ = 45~

Substrate !

FIG. 9. GaAs/A]G~s quantumwell photoconductorand illmnination geometry(after Ref. |0). The oscillator strength (19) has the property to increase linearly with the quantum number " m " for m--* (m + 1) transitions. From the most practical point of view of intersubband photo-detectors (m = 1~ m = 2 transitions) the oscillator strength f~2 =0.96mo/m*. For example, for GaAs m* = 0.067m0 and so for this case fl2 = 14 (in the infinite high wall approximation). The finite-well case changes the situation, to a certain degree, as the wave functions in the well penetrate into the barriers, especially for higher lying states that diminish oscillator strength. But still large dipole matrix elements for intersub-band optical transitions ((p~)--- 1.5 x 10-SeVcm at typical (z)-values ( z ) = 15/~) are only a few times less than the dipole matrix elements for interband dipole optical transitions, which are about 9 x 10-SeVcm for III-V semiconductors. This determines large intersub-band optical absorption, which will be delta-like due to congruent in-plane dispersion relations of the initial and final sub-bands. Nonparabolicity, the well's and wall's width nonconservation and other effects, the final values of relaxation times of the excited states' would change the delta peak into a spectral line of final width. 3. INTERSUB-BAND GaAs/A1GaAs AND RELATED QUANTUM WELL INFRARED PHOTODETECTORS IR photodetectors based on HgCdTe ternary alloys seem not to be very reliable or uniform in two-dimensional matrices and so are rather difficult to apply in the large focal plane arrays. It has been anticipated by Schulman et a136'9° that HgTe/CdTe superlattices would have several advantages over bulk HgCdTe for these applications due to: (i) possible higher degree of uniformity because of using binary compounds; (ii) smaller leakage currents due to suppression of tunneling because of larger effective masses of carries in SLs; (iii) lower recombination rates because of splitting of the light- and heavy-hole bands and increasing of effective masses of carriers. Earlier attempts to realize HgTe/CdTe SLs as IR effective photodetectors were unsuccessful partly because of the difficulties associated with epitaxial growth of stable superthin HgTe and CdTe layers, although there exist basic problems associated with the band structure of HgTe/CdTe-type SLs. More recently several authors t4'5) have proposed some new modes of possible IR SL and MQW detectors based on III-V semiconductor mature technology. One such proposition is based on the intersub-band-like optical excitation of the carriers in quantum well.w'92~This

112

F.F. SIZOV and A. ROGALSKI

new IR detector concept, based on the mature GaAs and related materials technologies, as well on the potential for monolithic integration with high speed GaAs FET (field effect transistor) or CCD (charge coupled devices) electronic devices, might be preferable in the 10 #m range compared to the narrow-gap ternary alloys infrared detector concept, although this type of detector is extrinsic in nature and has been shown by Kinch and Yariv ¢93)to be limited to performance inferior to that of intrinsic HgCdTe detectors. The second approach was proposed by Osbourn ~,94) for III-V strained layer SLs, where the changes in band-gap and band splittings lead to superlattice electronic structure that can be used for design of IR detector applications. Among different types of QW detectors the technology of GaAs/AIGaAs MQW photodetectors is the most developed. Recently, rapid progress has been made in the performance of these detectors and now 128 x 128 FPAs with long-wavelength (2 = 10 #m) performance comparable to that of HgCdTe have been fabricatedfl5.96) GaAs/AIGaAs and related materials MQW IR detectors are based on intersub-band (intraband) absorption. In this type of detector the carriers are excited from the filled ground state to the upper lying state in the well or from the ground state to the extended ("virtual") states in the continuum. In one such photoemissive d e v i c e (92'97'98) carriers trapped in the well are photoexcited into the upper states--a sub-band that lies slightly above the top of the well (Fig. 10). The ground state of a GaAs well is replenished, e.g. by tunneling through the AIGaAs barrier from a highly doped region. This new IR detector concept (the electric field polarization E llz) was soon expanded by Bell's Laboratory group ~99-~°t,1°2) that demonstrated several quantum well detector designs. This concept is based on the possibility of realization of a strong IR intersub-band absorption in doped GaAs/A1GaAs and related QW structures with electromagnetic wave electric field vector polarization perpendicular to the QW plane. In Refs 103, 104 the case of electric field polarization in the x , y plane of QW was considered to produce photoconductivity. This one would be much less than that in the previous case0°5) though for this electric field polarization in Ref. 106 the rather high responsivity of 0.05 A / W at T = 15 K was observed in GaAs/A10.24Ga0.76As MQW structure, that it seems to be due to the hot-electron bolometric effect. 1.0

Conduction band

~ ,

First excited state

_

"~

o.8

~

0.6

"-,,.

0

r, o.4 G r o u n d state

-

I

~ o.2

0

I

I

I

20

40

60

,'b.

,

80

A n g l e o f polarization (deg)

I AlxGat_xAs

I GaAs

AlyGa1_yAs

FIG. I0. Photoemissive device structure (after Ref. 98).

Fro. ! 1. Integrated absorbanc~ (A = -log(transmission)) at O = 73 ° and a sample temperature of 10K (Ga0.47In0.53As/AIo.~In0.s2As MQW) as a function of the angle ~6. The integrated absorbance is normalized to the value at ~ = 0 ° (after Ref. 119).

Infrared optoelectronics

113

3.1. Intersub-band Absorption The study of intersub-band optical transitions in doped MQWs was motivated by possibilities of realizing high-speed sensitive IR photodetectors and fast modulators on the base of optical transitions between the states of quantum well. West and Eglash~9) were the first who demonstrated that the oscillator strengths and dipole matrix elements of such transitions, which occur between the envelope states in the GaAs/Alo.3Gao.7As MQWs, are very large. Since that publication other groups have studied intersub-band optical transitions in GaAs/A1GaAs and related MQWs: GaAs/AlxGat_~As0°7-115), In0.s3Gao.47As/In0.52Alo.48As,016-119) In~Gal_~As/Alo.4Gao.6As,°2°) InGaAs/InP~m) and Sil_xGex/Si37's4) Similar in nature, intersub-band optical transitions in the accumulation layers of the interfaces of Si, InAs, InSb, HgCdTe were observed earlier, tTs'79:°7,H3) The observed dependences of the polarized light absorption on the angle ~ between the plane of incidence and the polarization vector (the angle of incidence was kept fixed at Brewster's angle 0 = 73° for GaAs) clearly confirmed~79:°7,"9) the normal component electric field selection rule. The absorption is maximum for tk = 0 and is vanishing for ~b = 90° (see Fig. 11). The experiments with the angle of incidence changing from 0 = 0 (normal incidence) to 0 = 80° (glancing incidence) also showed°°T) that the absorption drops as 0 decreases toward the normal incidence. The oscillator strength (19) has the property to increase linearly with quantum number m for m - , (m + 1) transitions. The growth of f23 oscillator strength compared to f12 (the ratio fE3/f~2 = 2.32 is close to that calculated from the (19) value off23/f~2 = 1.94) was observed by Asai and Kawamura°~7) in InGaAs/InA1As MQWs with large conduction band discontinuity (AEc = 500 meV) though the values off~2 were less than expected for the infinite well case. The finite well case changes, to a certain degree, the situation as the wave functions in the well penetrate the barriers. This penetration does not considerably change the dipole matrix elements and the oscillator strengths which for different MQWs are in the range of fiE ~---(1 1"--20) (79'107'109'119) (GaAs/AIGaAs and Gao.47Ino.53As/Alo.4sIno.52AsMQWs) though for some cases they are lower (f~2 = 4.24 for InxGat _xAs/Al0.4Gao.6As).°2°) These measurements of optical absorption confirmed the strong dependence of the absorbance (A =-lOglo(transmission)) on the angle of the electric field to the plane of GaAs/AIGaAs and related MQWs (see Fig. l l) and demonstrated large oscillator strengths and dipole matrix elements ( ( z ) - 10-20/]k (79'99'107'112'119)) and, even larger ((z> =27A)31°9) This was even though the net absorption in one-pass experiments is rather small and does not exceed the value of 3--50/0; (79'96'107'117"120) because of the experimental configuration (QWs are put to the light beam at Brewster's angle 0 = 73 ° for GaAs) the fraction of light absorbed is small due to the large value of the refraction index in the semiconductors under question (for GaAs n =3.2) though the absorption coefficient per one GaAs well achieves (1-4) 103 cm- 1.(102,122,123) In order to increase the small one-pass net absorption a multipass waveguide was produced by polishing a 45 ° angle on both edges of the substrate. °°2:°7'12°) In this case absorption enhancement of up to 102 times was reached. The absorption enhancement can also be achieved using textured interfaces,°24) a waveguide with a grating coupler°25) and metal grating, o3) The waveguide transmission spectrum for GaAs/AIAs MQW structure (50GaAs (71 + 2 A) wells with the center 51 A doped N = 6 x 1017cm -3 and (30 + 1 ,~) barriers of undoped AlAs) is shown in Fig. 12. The energy difference between the ground and the first excited state is hco = 152 meV.

114

F.F. SIzov and A. ROGAI.,SKI 100

m

80 --

6o

.2 m m

"~

40

~

2O

o 2000

1800

1600

1400

1200

1000

800

P h o t o n e n e r g y v (cm -1) FIG. 12. Measured waveguide transmission versus photon energy. The geometry is indicated in the insert (after Ref. 107).

At room temperature absorption coefficients have a typical maximum value of 0 t - 7 x 102cm -1 (N ~ 10~Scm-3). At lower temperatures this peak absorption coefficient increases. It appears that the peak of 0t at 77 K can be determined from the room temperature values by multiplying them by the factor 1.3. (126) As it was shown by Goossen et aL ~m) at such values of absorption coefficients the quantum efficiency of single QW is only about 1%. An unpolarized double-pass quantum efficiency (at a 45 ° angle of incidence) is defined by the expression 1 - e x p ( - 2~1) ~/=

2

'

(20)

where l = NL,~ is the total active SL length. The factor of 2 in the exponent of Eqn. (20) and the factor of 2 in the denominator accounts for the double pass and the unpolarized beam, respectively. For typical SL active lengths of l = 50 x 50/~, ct = 800 cm -3 and a 45 ° polished double-pass geometry, the quantum efficiency is about 20% that necessary to provide an efficient operation of intersub-band photodetectors. At this optical configuration the detectors at the facet edge can only be effectively illuminated, giving-rise to one dimensional (linear) arrays. The absorption coefficient in intersub-band transitions is defined by doping levels in the ground state. For T = 77 K and 45 ° geometry the peak absorption coefficients increase with doping levels and are equal to % = 110, 220 and 830 cm -1 for electron concentrations at the ground state Na = 4.7 x 1016cm -3, 1.2 x 1017cm -3 and 1.9 x 10 js cm -3 respectively. The integral absorption strength (i.e. the area under the absorption spectrum) is proportional to % times the fractional bandwidth A2/2 and is expected to scale with doping as A2 ~v -'~" "~ Nd.

(21)

From the results of Ref. 126 it follows that in spite of varying doping by a factor of 30, the normalized absorption coefficient g ( A 2 / 2 ) / N a is constant to within a factor of 2. It results in a weak dependence of detectivity D* on the doping level Nd. Recently, considerable attention, both theoretical and experimental, was paid to "bound-to extended" state absorption M Q W detectors, (97:°5'12s'129) experimentally realized at first by

Infrared optoelectronics

115

Levine et al. (85) In such a photodetector the electrons are excited by IR radiation (polarized similarly to intersub-band photodetectors) from the ground symmetric state in the well to an antisymmetric extended state pushed slightly out of the well. The rapid progress in this direction is caused by the conditions that: (i) bound-to extended state devices require substantially less biases to observe a photosignal and there exists a linear relation between responsivity and the bias voltage in contrast to bound-to bound state devices; (ii) the barrier thickness in bound-to extended state devices can be greatly increased, thereby substantially lowering the dark current. For the square quantum well the wave functions and so the matrix dipole elements for such bound-to extended state transitions have maximum values only in the case: t¢:°s'ng)

[ 2 m * ( U o + E ) ] '/2

~_~

~h = (2n - 1)-~-,

n = 1,2,3 . . . .

(22)

where the energy of electron above the well E--, 0. Figure 13 shows the dependence of the ionization probability of bound-to extended optical transitions on the photon energy. For example, for GaAs/A10.3~Ga0.69As MQWs (barrier height AEc = 250meV) with n = 1 (the number of the state above the well) E corresponds to a few meV for the well with Lw = 40/~. The matrix element, and therefore the intensity of the optical transitions for this case (the absorption coefficient may reach 5 x 103 c m - 1 ) 028) will be close to the intensity of intersub-band transitions although the absorption curves will be rather different, transforming from the nearly Lorenzian shape to the asymmetric one with a high energy tail.O2s,129) Linewidth in the intersub-band absorption. Experiments on intersub-band optical absorption in GaAs/AIGaAs and related MQWs showed that the half width (full width at halfheight of the absorption curve) of the absorption lines, which have a Lorenzian-like shape, as a rule do not exceed Av - 100cm -~ (AE ~ 12 m e V ) a t 2 ~ 1 0 # m and T = 3 0 0 K . (79'113'117'119'123) In some cases (e.g. GaAs/A1As MQWs) the half width is noticeably broader (AE - 19 meV at T = 300 K as it was shown in Ref. 107) than can be connected with the inhomogeneity of

0.15

0.10

21

0.05

0

0.05

0.10

Photon enrgy, E -- (~m-Eo)/U o FIG. 13. Dependence of the photoionization probability for the bound-to extended optical transitions from QW on photon energy E = [(hoJ - Eo)/Uo], where E 0 is the energy o f the bound state, and U0 is the well depth. I--L~/22 = ~/2; 2--1.47; 3--1.37; 4 - - I .27, where 2 = [h/(2me U0) ~/2] (after Ref. 128).

116

F . F . Sizov and A. ROGAkSKI

the layers and not with the lifetime of the excited states. At the temperature of liquid helium the half widths of the absorption lines are at least twice as narrowY j3,uT'ug) In the case of the parabolic dispersion law and the long lifetime limit of the upper states of the homogeneous wells, the intersub-band absorption spectra would consist of one or more delta peaks associated with the optical transitions between different sub-bands. The broadening of the absorption lines may be caused by several mechanisms:~79'N3'~3°) (i) different in-plane curvature of the sub-bands, due to nonparabolicity of the conduction band; (ii) the final lifetimes of the states of the upper sub-bands that determine the operating frequency of MQW devices; (iii) the inhomogeneities of the wells' widths and composition of the wells and the walls. A lineshape intersub-band absorption analysis of yon Allmen e t alJ u3) for GaAs/A10.35Ga0.65As MQWs showed that at T = 4.2 K the theoretical absorption coefficient for different kp-models, when taking into account the nonparabolicity of the conduction band, can be fitted satisfactorily to the experimental curve only by adjusting the optical transition time Top, the peak position and the amplitude. At T = 300 K the theoretical curve is much more asymmetric than the experimental one and the low-energy side can not be adjusted without effective mass renormalization though the high energy side of the absorption line is entirely determined by Top (Top- 0.9 ps as a lower limit). Experimentally peak positions decrease as the temperature i n c r e a s e s (79'1°2'H2'113:2°) a s is shown in Fig. 14. Nonparabolicity only slightly changes the peak position towards the low energy region in GaAs/A1GaAs QWs (1-3 meV for 80/~ GaAs wells)~°2) compared to parabolic dispersion law case, although the shift can be larger in heavily doped and narrower wells. An exchange interaction for the ground state, as it was shown in Refs 114, 131 and the change of the barrier height with temperaturd ~°2) are necessary to account for the temperature peak position shift. Exchange interaction is opposite in sign to direct Coulomb interaction and is not large for typical electron densities (N < 10~7-10~scm -3) for intersub-band MQW photodetectors operating in the wavelength region 2 ~< 10/~m, as it was shown by Bandara et aL (132'133) It appears that exchange induced shifts become more pronounced when the states in the well

0.5 F l

In0 IGa09As/ A10",Oa0" 6As

L 04 |

8K

'

II ~,, lsoz

0.3

0.2

0.1

or--- i 1900

1800

"

I

I

I"

I

1700

1600

1500

1400



1300

W a v e n u m b e r (cm -1) FIG. 14. Temperature dependent intersub-band absorption spectra of Ino.tGa0.gAs/Alo.4Ga0.6As MQW. The sample is fabricated as a single-pass, multiple internal reflection waveguide with a wedge angle of 45 °, a thickness of 0.466 mm and a length of 9.5 mm (after Ref. 120).

Infrared optoelectronics

117

3530! D e t e c t o r e

f ff J

g i2, ~

/

o

/

~,~

~5

*



"1

10

I

I

I

I

15 20 25 30 Wavelength (microns)

I

35

omitting exchange interactions

FIG. 15. The effect of exchangeinteractions on the IR photocurrent response. For each design wavelengtha differentbarrier heightis used to optimizeresponseby maintainingthe excitedstate near the threshold for escape from the well (after Ref. 134). are separated at AE~2< 0.1 eV. Figure 15 quantitatively indicates that exchange interaction is appreciable in the long IR wavelength region. The analysis of the lineshape temperature dependences show that nonparabolicity is not the major reason of the lineshape broadening with temperature,<99,u3,uT'~34) which is mainly caused by a decrease in the upper state lifetime, that is governed by the process of longitudinal optical (LO) phonon scattering. The experimental linewidths used (Av - 5 0 - 1 2 0 cm - ~ - 6-15 meV) to calculate the transition time of carriers from the upper to lowest states correspond to the intersub-band relaxation time z2~ = (0.2-0.9)ps. (113'12°'123) In Refs 8, 85, 135 MQW GaAs/AIGaAs photodetectors with bound-to extended states absorption was demonstrated. By decreasing the size of a QW that contains two bounded states, it is possible to push the excited state out of the well conserving strong bound-to extended state absorption comparable to bound-to bound state absorption. Figure 16 shows the measured and calculated absorption spectra at T = 300K of 50 period of a 45 A GaAs MQW (N = 1.5 x 10~s)cm -3 with 140 A undoped Al0.2Ga0.sAs barriers. For this structure the QW has only one state in the well at El = 84meV below the top of the barrier (the height of the barrier AEc = 160 meV). As in the case of bound-to bound optical transitions, the absorption of bound-to bound extended states transitions was also highly polarized with an electric wave-field vector along the MQW axis. The absorption curves of the excited states, with extended nature, are a few times broader than the intersub-band transitions, c~°2'~35'~36) A sharp rise in the theoretical spectrum at 680cm -~ in Fig. 16 corresponds to a long-wavelength IR absorption threshold band between the bound and extended continuum states. The peak absorption corresponds to an energy AE = 19meV above the top of the barrier. At higher energies there is a decrease of ~t(hco), since the extended continuum states become more similar to free electrons and the intensity of optical transitions decreases due to decreases of the matrix element (z}, although it is only slightly lower ( ( z } = 16.2/~) 035) than in the case of bound-to bound transitions, corresponding to an oscillator strength f = 7.5.

118

F. F. Slzov and A. ROGALSKI E n e r g y above b a r r i e r AE ( m e V ) 0 20 40 60 80 100 I~ I I I I

1400 1200

.

1000



/~

~

/

Experiment

1/\\

600 "~

400

O

-~ 200 < o 600

I

I

I

I

800

1000

1200

1400

1600

P h o t o n e n e r g y v (era -1) FIe;. 16. Measured and calculated absorption spectrum at T = 300 K of a GaAs/Al0.2 Gao.s MQW for bound-to extended states optical transitions (after Ref. 135).

3.2. lntersub-band Relaxation Times There was a considerable interest in the direct determination of an intersub-band relaxation time as that time determines the operating frequency of MQW devices (but not the efficiency of the stationary photoconductivity which is proportional to T/~ - constant, where/~ is the carder mobility above the barriers). If LO-phonons play an important role in such transitions, then the intersub-band relaxation time in MQW structures will depend much on the situation when the energy separation between the sub-bands is not equal to the LO-phonons energy (e.g. the GaAs LO-phonon mode is equal to hoo~= 36.7 mV). If separation between the states in the well AEt2 < hoot, the LO-optical phonons would not play any role in relaxation processes and the lifetime of the excited carriers may be rather long. This situation was observed in the experiments on picosecond time-resolved Raman spectroscopy. The intersub-band relaxation times of several hundred ps at T = 5 K between the states with AEt2 = 26.8 meV < hoot = 36.7 meV were detected by Oberly et al. (137) in 215/~, GaAs wells (GaAs/Alo.3Ga0.TAs MQWs). These rather long lifetimes were explained by longitudinal acoustical phonon scattering of the carders in the upper state. For narrower wells (Lw = 116/~, Et2 = 64.2 meV > hool), where LO-phonons play a dominant role in relaxation processes, the intersub-band relaxation time z2t was too short to be measured with the resolution of about 8 ps of the technique used. Other experiments on intersub-band relaxation time determination within the conditions Et2 > boo showed (lt°'t22't30'138-140)that in this case rather short times of intersub-band relaxation were also observed in GaAs and related MQWs. The experiments using an infrared bleaching technique by Seilmeier et al. (u°'139) with a resolution better than 2ps in GaAs/AlxGal_xAs (0.30 < x < 0.35) MQWs at T = 300K, or experiments determining the decay time after optical saturation of intersub-band absorption in GaAs/Alo.aGa0.TAS MQWs at T = 300 K by Julien et al/122) showed that the relaxation time has a value of z > 8 ps, which is much longer than the theoretical times of "~2t < 1 p s . (t4t't42)

Lifetimes of the upper limit less than z2. < 3 ps were observed in G8.0.47111o.53 As/Alo.~ Ino.52As MQWs by Elsaesser et al. (t3°'las) by picosecond spectroscopy at T = 10 K. In such MQWs large conduction band offset (AEc = 500 meV) takes place and poor confinement of the n = 2 band is avoided contrary to narrow GaAs/A1GaAs wells.

Infrared optoelectronics

119

The discrepancy between the experimental results mentioned above and the theory was attributed to the poor confinement of electrons in the upper sub-band °43) or to the combined effects of LO-phonon screening, inter-valley F - L scattering and hot phonons. °~) At the same time direct measurements of the intersub-band scattering rate by Tatham et aL ~14°)in a 60 period GaAs/A10.35Gao.65As MQW (146 ,~/157 A with AEt2 = 52meV) at T = 30 K by subpicosecond time-resolved anti-Stokes Raman scattering gave ~2~ in the range of 0.36-0.63 ps with good agreement with theoretical predictions. In contrast to the above mentioned experiments this one was performed at low photoexcited carrier densities (NED < 3 X 101°cm -2) to avoid the effects of intersub-band carrier-carrier scattering, screening and hot phonons. Also, due to wider wells being used than in the other experiments, poor confinement of the upper sub-band is avoided and in this experiment F - L and X - L inter-valley scattering was not allowed. All the experiments fulfilled on the intersub-band relaxation time determination in GaAs and related MQWs are consistant with the model in which the polar LO-phonons scattering is the most relevant relaxation mechanism to explain the absorption curve broadening in intersub-band transitions with temperature. However, in many experiments with high photoexcited carrier densities at the upper sub-bands the decay times are longer than theoretically predicted or obtained in the experiments with low photoexcited carrier densities. In the case of bound-to extended state transitions the lifetime of the extended states depends much on the localization of the wave function above the wall and is an oscillating function of the well's width. °45) In the case of high localization the states are resonantly transparent for low energy free electrons and as it was shown by Schick et al. °°5) the lifetime is about z = (zLO/~(E))(L/Lw) where

~(E) =

E

E+~U0 sin2{[2~/2m *(Uo + E) Lw]/2h }

--- 1

(23)

for highly localized states (e.g. n = 1 in formula (22)) and so in this case the value is approximately the lifetime of the excited localized state. But if condition (22) is not fulfilled, the lifetime of the extended states may be much longer. Experimentally observed by Levine et aL,~s5'146) response times of QWlP with bound-to extended states transitions were circuit limited and were less than 5 ns, °~) allowing realization of a 200/~m device of 300 ps speed. From transit time considerations it is expected to achieve the device speed of 30 ps in 50/zm diameter detectors. The absorption line shape in QWs with bound-to extended states transitions is not Lorentzian-like, although its half-width is mainly determined by the lifetime, as in the ease of intersub-band transitions. The line shape is strongly asymmetric02s.129,147A~) and possesses a high energy tail due to the level broadening. Moreover the depolarization effect in doped wells can substantially reduce the height and the half-width of the absorption curve, shifting the peak absorption position to the higher energy region. 3.3. lntersub-band Multiple Quantum Well GaAs/AIGaAs Photodetectors The operation of the intersub-band GaAs/GaAIAs and related MQW IR photodetectors can be understood from Fig. 17 where the n-doped GaAs/AlxGal_xAs (x--0.25) MQW with two confined states in the wells is schematically shown. The infrared radiation resonant with the intersub-band transition between the localized (doped N = 1.4 × 10m8cm -3) ground state El and first excited state E2 (E2- El = 124 meV, the barrier height AEc ffi 200 meV) excites electrons to the state E2 where they can tunnel in the electric field out of the well

120

F . F . Slzov and A. ROGALSKI

V////A. FIG. 17. Photoconductivity produced by absorption of intersub-band radiation followed by tunneling out of the well (after Ref. 99).

through the thin tops of the barriers. These photogenerated hot electrons (with mobilities different to those in the wells) then travel a mean free path L and thereby generate a photocurrent before being recaptured by one of the wells. In the first such demonstrated by Levine e t a/. (99'149'~5°) novel high-speed IR photodetector, based on intersub-band absorption and sequential resonant tunneling, the responsivity of 0.52 A/W (T -- 15 K) at 2m~ = 10.8 t~m was achieved with a rather narrow bandwidth of A2/2 ~ 10%. (99) In such intersub-band MQW photodetector the responsivity spectra follow the intersub-band absorption spectra at different temperatures and biases. The intersub-band photoconductive detector mentioned consisted of a 50 period SL of 65 ]k GaAs n-doped only in the center 50 ,~ wells to reduce the possibility of interface states and 95 .~ A10.25Ga075As barriers. The excited state lifetime estimated from the halfwidth AE = 97 cm- l was equal to z = 0.11 ps. This small value of z is due to the high degree of well homogeneity and the almost congruent dispersion curves of El and E2 sub-bands in the x, y directions of GaAs wells and is consistent with the LO-phonons scattering mechanisms. The QW GaAs/A1GaAs structures are mainly grown by the MBE technique on semiinsulating GaAs substrate. However, excellent QW structures can also be grown using M O C V D . (12s'lsl'152) These structures consist of a periodic array of Si-doped (No ~ 10~sc m -3) GaAs quantum wells of thickness Lw separated by undoped AlxGal_ xAS barriers of thickness Lb. The heavy n-type doping in the wells assured that freeze-out would not occur at low temperatures and that a sufficient number of electrons would be available to absorb the IR radiation. For operation at 2 = 7 - 1 1 # m , typically wells with Lw~40/~, Lb------500/~, x = 0.25-0.30 and 50 periods are grown. In order to shift the intersub-band absorption to longer wavelength region the x-value is decreased to x ---0.15 and in addition, in order to maintain the strong optical absorption and reasonably sharp line shape, the QW width is increased to 50-60 ~. This optimization allows the same bound state to reach the excited continuum state optical absorption and efficient hot electron transport and collection. The active structures are sandwiched between about 1 gm thick heavily doped (also

Infrared optoelectronics

121

Nd -- 10 Is cm -3) GaAs contact layers. The photoconductive detectors are then fabricated by etching mesas through the MQW. To improve the optical coupling, the gratings (see Fig. 8) and 45 ° polished edge samples (see Fig. 9) are usually used. Initial efforts with MQW photoconductive detectors showed appreciable dark currents which involve three relevant mechanisms: tunneling, phonon assisted tunneling and thermionic emission out of quantum wells. In Fig. 18 individual current contributions for devices with area A = 2 × 10 -5 cm 2 at bias Va ~<0.05 V are shown as a function of temperature. One can see that tunneling is the dominant dark current mechanism in the low temperature region, while thermionic emission limits the performance at high operating temperatures. Thermionic emission generally limits 10/~m photoconductive type MQW detectors to operating temperatures less than about 70 K (Fig. 19). There is no evidence for a Stark shift in square wells up to 9 V bias 023) (E - 8 x 104 V/cm, N = 1.0 x l0 is cm -3 doped 76/~ GaAs wells) as such high doping screens the applied field in the square wells and results in a Stark shift (the energy difference AEI2 increases in the electric field) of AE = 1 meV. In 5 x 1017 c m -3 GaAs doped square wells the Stark shift is of the same order (1-1.3 meV), as it was shown by Harwit and Harris (t°s) in the electric field of E = 36kV/cm. In heavily doped (N = 2 . 2 x 10iScm -3) GaAs/A10.2sGa0.72As MQWs it is almost an order less. (136)Large Stark shifts of intersub-band transitions were observed in step QWs and they were more than an order (about 8 meV at E = 18 kV/cm) greater than for intersub-band transitions in square wells, as it was shown by Karunasiri e t al. (154)The reason of the energy shift AEI2 in an electric field is caused by the decrease in an electric field of the ground state while higher states only slightly depend on E. (155) The main disadvantage of bound-to bound state intersub-band photodetectors is that the barriers must be rather thin to ensure the efficient tunneling of the photoexcited 10 -3

_

.....x"

10--4 _

~

10-5

-

IO--4S

-

lo -~

_

/

I

/ t X

104

e_e~ I.

10-9

II ii i I i I

-

I

I

S S t

-

" Igt

Ith

I I

lo-tO 0

I 50

I I 100

I 150

I 200

I 250

I

300

Temperature (K) Fro. 18. Temperature dependence of the dark current at low bias for bound-to bound multiple GaAs/Al0.3eGae.~As device (50 the 70~ wells and 140/I. barriers). The subsczipt "th", "st", and "pt" refer to thermionic, tunneling, and phonon-assisted tunneling mechanisms (after Ref. 100).

122

F.F. SlZOV and A. ROGALSKI ].6

m

200 K

/

49 K

1.2 -~-"

0.8

,~

0.4

.~' m

o

•'o

-0.4

~

-0.8 -1.2

-1.6 i~~l~ -5

-3

I -1

0

I

I

I

1

2

3

V o l t a g e (V) FIG. 19. Measured temperature dependence of the current-voltage characteristics of an AlxGa~_xAs/GaAs (x =0.23) 50-well structure with 61 ,~ wells and 154A barriers (after Ref. 153).

electrons, but at the same time there would be large dark currents preventing high detection efficiency. Further rapid progress in MQW IR detectors was conditioned by the use of thinner QWs and pushing the excited state into the continuum. Schematically the performance of the bound to extended state IR photodetectors (also called LWlR-detector--long-wave length IR detector) ~82)is shown in Fig. 20 for GaAs/AIo31Ga0.69As MQW, whose responsivity peaked at 2p = 8.3 #m (T = 77 K). The spectral halfwidth of such LWlR detector was of the same value (Av/v _~ 13%) as in the case of bound-to bound state optical absorption tunneling detectors and has a high energy tail due to excitation of the electrons into the more free electron-like continuum at higher photon energies. These bound-to extended state transition detectors are also based on hot electron transport of electrons above the MQW barriers. The linear relation between responsivity and the bias voltage for these devices is completely different to the highly nonlinear photoresponse obtained for devices with bound-to bound transitions. In particular, the bound-to bound state devices require a substantial bias Vb > 0.5 V before any photosignal is observed whereas the bound-to extended detectors generate a photocurrent at a very low bias. The reason for this difference is that the bound-to bound state detector requires a large electric field to assist the tunneling escape of the

well

300 :k -J

[[~]

Alo.3zGao.69As barrier FIG. 20. Schematic conduction band diagram of the q u a n t u m well detector (after Ref. 85).

Infrared optoelectronics

123

photoexcited carriers out of the well, and thus at low bias the excited carriers cannot be collected resulting in a negligible photoresponse. Using QWs with width Lw---40/~ the IR radiation could also be effectively absorbed via bound-to extended state transitions and since photoelectrons could now be effectively collected without tunneling and enhanced detector performance could be observed. (1°'85'95'133'135:36'151'152'156-159) In addition the barrier thickness could be greatly increased (e.g. up to Lb = 500/~) thereby dramatically lowering the undesirable dark current and significantly increasing the detection efficiency. By reducing the A1 mole fraction in the AlxGa I _xAS barriers to x = 0.22057) (the barrier height is AE¢ = 180meV) it was possible to shift the maximum responsivity peak to 2p= 10.2/~m. Moreover, by pushing the excited state further up into the continuum (AE = 20 meV above the top of the barriers compared to a few meV in GaAs/Alo.3t Ga0.69As MQWs) a much broader bandwidth of the responsivity curve was achieved (Av/v -~ 36% compared to Av/v ~- 13% for x = 0.31 A1GaAs barriers). The MQWs consist of 50 periods of 38/~ wells (doped N = 2 x 1018cm -3) and 280/~, Alo.22Ga07sAs barriers. However, due to the lower barrier energy (AEc = 180 meV) the dark current in such a structure, which is a thermionic-assisted tunneling current, as it was shown by Bethea et al. ~156,16°)increased and thus detection efficiency D* decreased. By increasing the barrier width up to Lb-----500~056) (GaAs/A10.25Ga0.75As MQW, Lw = 40 .~, the barrier height AE¢ = 200 meV) the tunneling is reduced by more than an order of magnitude and the responsivity of this QWIP (quantum well infrared photodetector) at 2p = 9.8/~m and T = 77 K was five times larger than that with 280/~ A10.22Gao.TsAS barriers. The detection efficiencies obtained with the bias of 3 V at T = 50, 68 and 77 K were D* = 2 x 1011, 2 × 101° and 6 x l09 c m n z l / 2 / W respectively, which is more than an order of magnitude better than the previous results. The first infrared camera with such a QWIP structure of a 10 pixel GaAs QW array was demonstrated by Bethea et al. ~161)with high noise equivalent temperature difference sensitivity ( N E AT < 0.1°C). For QWIP with 2p = 7.9/~m and 2¢0 = 8.4 # m at T = 77 K (50 period of Lw = 40/~ and Lb = 305 A GaAs/Alo.29Ga0.71As MQW, the height of the barrier AE¢ = 235 meV) the value D* is 4 x 101°cm Hzt/2/W. These values are comparable with HgCdTe photodetectors for the same spectral regions, though for the 10/~m region the operation temperature of QWlP is still lower ( T = 68 K). Medium wavelength M Q W intersub-band infrared detectors. It has been thought that GaAs/AlxGal_ xAs is not an appropriate system for application for quantum well photodetectors in the 3-5 # m atmospheric transmission window as the maximum direct gap barrier height (conduction band discontinuity) is AE¢ = 336 meV at x = 0.45 o62) (see Fig. 6) and so at higher x-values F - X scattering would prevent effective operation of QWlP. Wavelength bands shorter than 5 # m would be impossible to achieve (with one bound state in the well or with the second bound state near the top of the well). Thus, to shift the intersub-band absorption response into the spectral region of 3-5/~m another MQW structure was used, 016'163) namely the lattice-matched In0.53Ga0.47As/Ino.s2A10.asAs MQW, that has the direct gap conduction band discontinuity of AE~o=550meV. °64) A 50 period MQW structure with 30/~ Ino.53Gao.47As quantum wells (doped N = 2 x 10 Is cm -3) and 300/~ of undoped Ino.s2A10.48As barriers was grown by MBE on InP substrates. This was demonstrated by Hasnain et al. ~163) using mediumwavelength infrared (MWlR) intersub-band photodetector with responsivity at 2p = 4.05/~m that was background limited ( F O V = 180 °) with D ' L = 2 . 3 x 101°cmHzl/2/W (D~ = 1.5 x 1012cm Hzl/2/W at temperatures up to T = 120 K). However, it is desirable to use more mature GaAs/AIGaAs systems for M W l R detectors. Levine et al. c165)demonstrated an effective operation of GaAs/A10.55Ga0.45As M W I R detector with D*(2 v = 4.2 #m) = 10 ~2cm Hz~/2/W at T = 80 K. In this indirect barrier QWlP F-valley bound-to extended transitions in GaAs wells occur and photoexcited carriers rapidly scatter JPQE 17/2---C

124

F . F . Smov and A. ROGALSKI

into X-valley states in A10.55Ga0.45As barriers where they are transported through X-barriers by the electric field. This MQW structure consisted of 50 Lw = 30/~ GaAs wells divided by 500/~ AIGaAs barriers. Another proposition of M W l R GaAs/AIGaAs detector was demonstrated by Schneider et al. °6° Large intersub-band spacing was obtained by using ultrathin AlAs barriers in either side of the GaAs QWs (50 wells with Lw = 45-50/It divided by 20 ~ AlAs barriers) followed by a 250/~ Al0.3Ga0.TAs layer. Each QW is doped N2D = 8 x 10" cm -2. Photoconductivity arises from tunneling of the photoexcited electrons out of the second sub-band, through the thin AlAs barriers, into the Al0.3Ga0.TAS layers and subsequent relaxation into the first sub-band of adjacent wells. Transport time for tunneling z = 200 fs is sufficient for tunneling of the photoexcited carriers out of the well before relaxing. The construction of the detector proposed implies a possiblity of a photovoltaic operation regime due to asymmetry of the thicknesses of AlAs barriers. Extended long-wavelength intersub-band infrared detectors. Shifting of the intersub-band absorption to longer wavelengths has been achieved by lowering the AI concentration in the GaAs/AI xGa~_ xAs barriers from the commonly used range, x = 0.25-0.30, to 0.15. Two such types of 50 period structures with Lw = 50 A and 60/~ (Lb = 500/~,, N d = 5 × 10 ~7c m - 3 ) have been grown by Zussman et a13l°) For MQWs with Lw = 50/~, the spectral response is extended to ).p = 13.3/~m (2~o= 14.7/zm) while the responsivity is still comparable to the shorter wavelength GaAs QW detectors. The bias-voltage dependence of peak responsivity (Fig. 21) for both MQWs are linear at low biases with the responsivity and gain starting to saturate at Vb = - 2 V. Temperature dependence of detection efficiency is shown in Fig. 22. Note the extremely rapid increase of D* as the temperature is reduced, from 109cmHzl/2W -l at 77K, 3 x 10t°cmHzl/2W -l at 5 0 K to more than 1012cmHzl/2W -l at 33K. This is due to the exponential decrease of the thermionic carrier emissions over the barriers. The N E AT = 4 m K at 50 K and 19 m K at 60 K have been achieved, encouraging that further research should lead to high performance GaAs/A1GaAs MQW infrared detectors having even longer wavelength response with 2co > 15 #m.

1013 _

0.6

--

Lw =

6

1012

~ L~

Vb = -2V

& ~d 0.4 --

~ L w =50]~

*~

1011

w = 60A

G o ~d

0.2

0

~

Z - ~.p

/

lolO

I

I

I

-1

-2

-3

Bias voltage Vp (V) FIo. 21. Bias-voltage dependence of the peak responsivity of 50 period GaAs/Al0asGao.ssAs MQW structures measured at the peak wavelength at T -- 10 K for two samples with L w -- 50 ~ and 60 ~ (after Ref. 10).

109 30

50

70

Temperature T (K) FIG. 22. Temperature dependence of detection efficiency

for two structures(as in Fig. 21) measured at Vb = - 2 V (after Ref. 10).

Infrared optoelectronics

125

3.4. Other I I I - V Material System Intersub-band Detectors The long-wavelength QW photodetectors have been also demonstrated using InP based material systems such as lattice matched: GaAs/Gao.sIno.sP, ct67) InP/Ino.53Gao.47As,cts'lt~) InP/InGaAsP °~9) heterosystems. The responsivities of n-doped InP/In0.53Gao.47As MQW infrared photoconductors operating at wavelengths of 7-8 #m, were in fact, somewhat larger than those obtained in equivalent GaAs/AIGaAs photoconductors. Recently long-wavelength (2~o= 13.2/~m) MQW detectors using lattice matched 1.3/~m InP/InGaAsP material systems and the first short-wavelength (2~o---2.7/~m) photodetector in p-type InP/Ga0.47Ino.53As material systems were also demonstrated by Gunapala et al. °~9~ 3.5. Si~_ x Gex/Si Intersub-band Detectors

The first observation of intersub-band IR absorption in SiGe/Si MQWs was described by Karunasiri et al. c7) The large valence-band offset of SiGe/Si heterostructures as well as the small hole effective mass, favours the hole intersub-band absorption. For IR detector applications the quantum well structures with a single bound state and the excited state close to the top of the barrier are desirable. Figure 23 shows the position of the bound and extended states of a Si0.s5Ge015 quantum well as a function of the well width calculated using effective mass approximation. In this calculation for x = 0.15, the corresponding band offset is about 130 meV and the heavy-hole effective mass along the growth direction is taken as m~ = 0.28 m0. From Fig. 23 it follows, that for a quantum well with Lw = 30 A the optical absorption near 10/zm would be possible between the ground and extended state, which is lying above the Si barrier. The MQW SiGe/Si structures have been grown in a Si/Ge MBE system on high-resistance Si(100) wafers kept at about 600°C. Such structures consist of 50 periods of 30 A-thick Si0.s5Ge0.1swells (doped p = 1019cm-3) and separated by 500 A-thick undoped Si barriers. The entire MQW is sandwiched between a doped (p = 1 x 1019 c m -3) 1/zm bottom and 0.5/~m top layers for electrical contacts, o9) For p-type SiGe/Ge MQWs normal incidence detection is also forbidden by the selection rule, followed from the expression (17), similar to n-GaAs/AIGaAs. Figure 24 shows the room-temperature absorption spectrum as a function of wavelength using a 45 ° multipass waveguide structure. The absorption is due to the transition from the heavy-hole ground state 250 f /

t

I

t

i

/ 200 I-" /

t

~.

~

Virtual qstatcs I '

tt

g x,0b

~ •

*. • ",

',

I,

It

-, *



! oo

'o F 0

, 20

40

60

80

100

W e l l w i d t h (J~) FlO. 23. Bound and extended states o f a Si/Sie.ssG%as/QW as a function o f well thickness. The barrier height is about 130 meV. The a r r o w s s h o w the bound-to bound (B.B.) and bound-to extended (B.E.) states transitions (after Ref. 19).

126

F . F . SlZOV and A. ROGALSKI 4000 --

300

K oo

3000

2000

..~. 1000

0

2

4

6

8 10 12 W a v e l e n g t h (IJ.m)

14

16

FIG. 24. Measured absorption spectra of 50 period Si/Si0.85Ge0.~5 MQW structure (Lw= 30/~, L b = 500/~, p = 1 × I019 cm -3) at 300 K as a function of wavelength using waveguide structure. The background absorption was substracted. The set of curves are for the different polarization angles of the incidence beam (after Ref. 170).

to the extended one. It appears that the light-hole ground state is about 50 meV above the heavy-hole ground state due to the splitting of the light- and heavy-hole bands in the strained Si0.s5Ge0.15 QWs. The reduction of the absorption coefficient as the polarization angle is increased is due to the decrease of the E:-electric field component. The photoresponse of the SiGe/Si MQW (200 #m in diameter mesa structures) infrared detectors with a 45 ° edged facet is shown in Fig. 25. One can see the photoresponse at 0° and 90 ° polarization at 77 K with a 2 V bias. The responsivity for an unpolarized beam with a peak near 7.5 #m is about 0.6 A/W and is approximately the sum of two polarization cases. The responsivity measured by illumination, by light normally on the backside of the devices, is shown by the dashed curve in Fig. 25. The demonstration of the normal incidence absorption in SiGe/Si MQWs indicates the possible realization of IR FPAs without using the grating couplers normally required for GaAs/AIGaAs intersub-band

Unpolarized 0 6 ' ~,

Vb

MQW

< "-" 0.4

0.2

0

5

6

7

8

9

10

II

12

13

W a v e l e n g t h (ttm) FIG. 25. Responsivitiy at 77 K of Si/Si0,gsGe0.~5 MQW structure for two polarization angles with a 2V bias voltage. Infrared illumination is illuminated on the facet in such a way that the incidence angle on the structure is 45 °, as it is shown in the insert. The dashed curve shows the responsivitiy for normal background illumination (after Ref. 170).

Infrared optoclectronics

127

photodetectors. Detailed discussion of absorption mechanisms in SiGe/Si MQW structures may be found e.g. in Ref. 7, 170, 171. The estimated detection efficiency for above nonoptimized SiGe/Si MQW IR detectors is about 1 x 109 c m H z U2 W -1 at 2 = 9.5/am. By optimizing MQW design further improvement of responsivity and detectivity is possible. 3.6. G a A s / A I G a A s M Q W Photovoltaic and Hot-Electron Transistor Detectors Much of the papers concerning QW IR detectors addressed the photoconductive mode of operation for 8-12/tin spectral region. However, these detectors are extrinsic in nature, and various alternatives have been suggested for further detectors. These alternatives include low-power and low-noise operation of MQW photovoltaic and hot-electron transistor detectors. Generally, the photovoltaic effect is obtained in asymmetrical QWs including graded-gap structures. (sl-s3'mA27'133"172-175) To reduce the dark current and to increase the operating temperature of the intersub-band detectors Choi et al. 076-17s) proposed the IR hot-electron transistor (see also Ref. 179). Theoretical calculations carried out by Goossen and Lyon(s1"172) for a photovoltaic QW detector, as schematically shown in Fig. 10, indicate that performance of such an ideal QW detector is inherently inferior to HgCdTe detectors, however the signal to noise ratio is adequate for most thermal imaging applications. The first significant photovoltaic effect (without the use of external bias) within the spectral range 3.~6.2/~m was observed by Kastalsky et al. °74) This type of detector involves excitation between two minibands in GaAs/AIGaAs SL (Fig. 26). In this device structure a 1000/~ AlxGal _xAs layer graded from x = 0 to x = 0.32 was grown on a n +-GaAs substrate followed by a SL with 55/~ GaAs wells and 40/~ Al0.4Ga0.6As barriers of total thickness about 1 #m. The structure was designed so that it has two minibands below the top of the barrier with the energy of the graded barrier being lower than the bottom of the first excited-state miniband, but much higher than the top of the ground-state miniband to block the flow of electrons (dark current) from the ground-state miniband to the collector contact layer. This idea of employing such a blocking layer in a QW IR detector first appeared by Coon et al. (a7)At the doping levels in the wells of about 1017cm -3, the lowest sub-band is filled with electrons which cannot flow through the sample because of the graded barrier, however electrons excited by radiation into the second miniband are capable of diffusion over the barrier thus creating a charge separation and hence a potential difference between the n +-GaAs contact layers. The active part of the SL structure extends only about two diffusion lengths from the barrier that makes this structure not an effective photovoltaic detector. Photovoltaic-type GaAs/AIGaAs QW IR detector in 10/~m spectral band was demonstrated by Byunsungo et al. (17~) This unoptimized Kastalsky-type photodetector operates at a significantly lower bias voltage than photoconductive QW detectors and its responsivity (5 mA/W) and detection efficiency (D* = 1.6 x 108 cm Hz/W) at T = 24 K are significantly lower than demonstrated for photoconductive MQWs detectors.

71~ I

Emitter oont.0t

I

I

I-1['1 I

I

a

i

~_~..i~i. ~14"I~I'~'I.I'~.N"HH~IIINI,~ ... J ~i

i

-.

Electron emission

Collector contact

OaAs A1OaAs/OaAs GaAs FIG. 26. PhotovoltaicIR SL detector with a graded barrier to reduce the dark current Ref. 174).

(after

128

F . F . Stzov and A. ROGALSKI

E B C FIG. 27. The band diagram o f IR hot-electron transistor under an emitter bias Vc and a collector bias Vc. M2, M 3 and M4 are the first three minibands above the barriers (after Ref. 178).

The performance of the preliminary design of Kastalsky-type SL detectors are inferior in comparison with intersub-band photoconductors. However, the signal current limitation can be improved through the use of spacially tailored termination layers at the end of SLs to optimize the transmission or reflection of miniband carriers. 08°) With modification to the blocking layer design and reduction of carrier concentration in the wells (reduction of thermionic emission), one can expect D*-values approaching 1011cm Hz I/2 W -j at 40 K in 8 - 1 2 # m spectral region. As for IR hot-electron transistor the improved one was grown on a (100) semi-insulating substrate. (17s) The first layer was a 0.6 # m thick n +-GaAs layer doped to 1.2 x 10 ~scm -3 as the emitter layer. Next, an IR sensitive 50 period GaAs/A1025GaoysAs SL structure was grown. On the top of SL structure, thin 300 A In0.15Ga0.ssAs base layer was grown, followed by a 0 . 2 # m thick A10.25Gao.75As filter and 0.1 # m thick n+-GaAs (n = 1.2 x 101Scm -3) as the collector layer. The band structure of IR hot-electron transistor is shown in Fig. 27. The detector configuration together with emitter IE and collector ID dark currents are shown in Fig. 28. Because the thin In0.15Ga0.ssAsbase layer with a large F - L valley separation improves the photocurrent transfer ratio, the detection efficiency of the transistor increases to 1.4 x 10~°cmHzl/2/W at 7 7 K with a 2co = 9.5 #m, that is two times larger than the companion state of the art GaAs M Q W detector. With further optimization of device parameters a broadband 10 # m IR hot-electron transistor with detection efficiency close to D* --'-- l0 II ~11 H z I / 2 / W should be achievable at T = 77 K. 10-3

T77K, J

10-4 A

10-5

/Eno, y

10-6

/

(

c

"~ 10-7 10-8 10-9 0

I

I

I

I

I

I

-1

-2

-3

-4

-5

-6

v s (v) FtG. 28. The emitter dark current I E and the collector dark current I~ as a function of the emitter bias VE at 77 K. The insert shows the schematic device configuration (after Ref. 178).

Infrared optoeleetronics 3.7.

129

Intersub-bandMQW IR Detector Arrays

In spite of the fact that performance of intersub-band MQW photodetectors are inferior in comparison with HgCdTe ones, these detectors with a cut-off wavelength 2~o~ 10 #m and D * = 101°cmHzl/2/W at 77K, can be used in many applications, especially in large two-dimensional FPAs. In contrast to HgCdTe, GaAs-based QW IR detector arrays, and probably SiGe/Si ones, promise high yields due to well established and highly uniform MBE growth and processing technology for large square wafers. These QW detector arrays are expected to combine the advantages of PtSi Schottky barrier arrays (high uniformity, high yield, large arrays with monolithically integrated electronics and low cost) with advantages of HgCdTe (high quantum efficiency and long-wavelength response). For large arrays the relevant figure of merit is the noise equivalent temperature difference (NE AT), the temperature change of an environment required to produce a signal equal to the rms noise. NE AT may be expressed as: (~s~)

NE AT = (4F2 +

1) x / ~

(24)

where F is the f number of the optics, t is the transmission of the optics, Af is the electrical bandwith of the system, A is the detector area, I = m × n is the number of detectors in the array and M* is a signal to noise figure of merit of individual detector used to compare the performance of detectors with different 2~o for the detector of thermal radiation over finite atmospheric paths. It is related to D* by

M*(T,L)= ~: D*(2)T(L, 2 ) ( ~ ) r d 2

(25)

where T(L, 2) is the atmospheric transmittance and W~ is the spectral radiant emittance of a blackbody target of temperature T at range L. Because of spatial nonuniformities the sensitivity of focal plane array detectors is often less than one can expect to obtain on the basis of temporal noise of the discrete photodetectors. In GaAs/AIGaAs-type MQW photodetectors with principally lower detection efficiencies compare to HgCdTe photodetectors at the same operating temperature, the appropriate NE AT value can be achieved due to high uniformities of the separate devices. In the above discussion the nonuniformity due to variation in the pixel characteristics which is often the limiting factor°a2-~sS) was ignored. If the number of electrons per pixel per frame is N = 1 0 7 (limited by the multiplexer storage capacitor), then the uniformity U (after compensation) must be better than the statistical variation N -~/2 in order not to limit performance, i.e. U < 0.03%. 057'1s4) This is extremely difficult to do with HgCdTe,0s3,1sS) but has been achieved in PtSi Schottky barrier arrays operating in 3-5 #m spectral region3 ~u) For arrays which are limited by pixel nonuniformities it follows: (t57)

(NE AT)u =

0.694 T~B2U,

(26)

where 2 is operating wavelength in cm and TBB is the temperature of black body. Using TBB= 293 K, 2 = 10/~m and U = 10 -a one obtains (NE AT)u = 0.06 K. It means, that values higher than D * = 101°cmHzt/2/W are unnecessary as for f/2 optics, 50#m pixels, and A f = 60 Hz. For cited value of D* it follows NE AT = 0.01 K (see Fig. 29). Recently Adams eta/. (IsT) have given a critical look at GaAs/AIGaAs MQW IR detectors (2 - 10 #m) for thermal imaging applications. It was shown that in this ease the dominant

F. F. Smzov and A. ROOALSKI

130 0.12 I'k

X ffi lO~tm

A - (50~m) 2

0.10 ~ ' ~

u - 0.1%

f/2 (0/2 - 14 °)

I

I

I \ ^ 0"0'V [-

0.06 I"

/

~a

z

,

0.04t

ooo

o

.

109

1010

.

.

.

.

.

.

I

.

.

.

1011

1012

D e t e c t i v i t y D* (cm ,/"Hz/W) FIG. 29. Plot o f N E A E against D* (at ~.= 10#m) showing that for D * > 10t°cmHz~/2/W performance is limited by nonuniformities even for highly uniform (U = 10 -3) arrays. The calculated curve assumes a blackbody temperature TBB = 295 K, a pixel area of (50/am)2,f/2 optics and a A f = 60 Hz bandwidth (after Ref. 95, 186).

noise term is the "thermal correlated noise" due to nonuniform dark current. Reducing dark currents is the most effective way to improve staring array performance and it follows that total dark current variations must be reduced by more than an order of magnitude to attain a practical N E AT. Adams et al. 087) have suggested several other measures that can improve N E AT: optimizing bias voltage for minimum N E A T rather than for maximum D* can improve N E A T by a factor of 2; integrated micro-optics can reduce the detector area 08s'189) reducing the pattern noise by reducing dark current; a MQW chopper can be used to improve correlation for dark current nonuniformity. After careful modeling of all relevant factors, operation at temperatures up to 80 K may be possible. Bethea e t a / . (161) have demonstrated the first long-wavelength IR camera using GaAs/AIGaAs QW IR photodetector array. They have used a commercial InSb scanning camera operating in the 3-5 spectral region and modified both the optics and electronics to allow operation in 2 - 10 #m spectral region. A 10-pixel GaAs MQW array consisting of 200 ~m 2 pixels separated by 670 #m was used. Using this unoptimized IR imaging camera (2~o= 10.7/~m) N E AT < 0.1 K has been achieved. For the first time hybrid 128 x 128 GaAs/A1GaAs MQW FPAs have been fabricated, tested and imaged by Kozlowski et a/. (96) The hybrid consisted of a 50 period GaAs/A10.27Ga0.,As 60 pm square mesa structures (Iw = 50 A, Lb = 300/~, Nd = 10Is cm -3) with peak response at 7.7 #m mated to a high performance CMOS readout with direct injection input. Optical gratings were excluded to facilitate evaluation of the basic detector technology. The FPAs were fabricated by mating of the silicon CMOS readouts to the GaAs detector arrays via indium interconnections. The GaAs/AIGaAs MQW FPAs were tested at 78 and 65 K at a background of 1.0 x 1016photons/cm2 s, corresponding t o f / l optics. At 78 K, the maximum quantum efficiency of detector was 0.15%. A mean detectivity of D* = 5.76 x 109 e r a Hzl/2/W was measured, which corresponds to 55% of BLIP (Background Limited Infrared Photodetector) for the measured quantum efficiency. Recently Levine et al. <95)have presented thermal imaging data of 128 x 128 arrays of 50 #m square GaAs/AIGaAs MQW photoconductors having peak response at 2p = 9#m. To improve the optical coupling, the grating was used. Back-side illuminated (through the flat polished substrate) configurations, identical to those usually used in HgCdTe or InSb imaging systems, were utilized. High yields (99%) of this GaAs array technology is a result of the MBE growth uniformity in thickness and the mature GaAs processing technology. After correction,

Infrared optoelectronics

131

measured nonuniformity of the array was better than 0.1%, and a NE AT of 0.01 K was observed at 60 K. These array results are far from the optima. Implementation of improvements (structure of QWs, gratings, multiplexer, proper bias voltage) should improve the performance and raise the operation temperature up to 77 K, and thus make GaAs MQWs competitive and superior in array size, cost and yield compared to present HgCdTe arrays. 3.8. Performance Aspects of Intersub-band Infrared Detectors The ultimate performance of intersub-band IR photodetectors compared to HgCdTe photodetectors, especially for the 8-12 #m spectral band, is of great importance with a view to potential applications of these structures in IR systems. Thus some basic performance characteristics will be reviewed. Responsivity. The current responsivity is given by the expression )

R~= ~ r/g,

(27)

no

where q is the electron charge, g = "rL/'fT = L/I is the photoconductive gain°9°) and where ZL is the hot-electron lifetime, zr is the transit time, L is the hot-electron mean free path, ! is the SL thickness and ~/ is the quantum efficiency. Because the confined carriers are free to move within the plane, there is no energy gap separating confined from unconfined states and the density of empty final states (satisfying energy-momentum conservation for phonon emission) is high. Consequently transitions from extended states ("above" the barriers in MQW intersub-band detectors) to confined states are very fast (if the condition (23) is fulfilled), resulting in an excited carrier lifetime of the order or less than 10 ps. MQW photoconductors are similar to conventional photoconductors where the electrons recirculate through the SL or MQW for a time ZL, and thus hot-electron mean free path can be much larger than the SL or MQW thickness, l. However, because the hot-electron lifetime ZL is very short, the photoconductive gain g > 1 may be achieved only in low-period superlattices. In Fig. 30 shown in the responsivity spectrum of GaAs/A10.25Ga075As MQW with peak responsivity of R~= 1.2 A/W at Vb = 3 V, 2p = 9.8/zm and a cutoff wavelength 2°0 = 10.7 #m. 1.2 -

/

1.0 -

~

V b = 3V

0.8 .~ 0.6 ~ 0.4 0.2 o

~ 1

6

I

7

I

I

8 9 10 Wavelength Z (p,m)

I

I

11

12

FXG. 30. Spectral dependence of responsivity for 50*period GaAs/Alo.25Gao.~sAs structure (doped Nd= 1.2 x 10Is cm -3) with L w = 4 0 ~ , Lb = 500A (after Ref. 191).

132

F . F . Slzov and A. ROGALSKI 1.4

B

1.2 1.0 o.8

[ ~

0.4

0.2 0

1

2

3

4

5

B i a s v o l t a g e V b (V) FIG. 31. Bias dependence of responsivity for the structure in Fig. 30 (after Ref. 191).

The bias dependence of responsivity in this structure is shown in Fig. 31. One can see that at low biases Ri is almost linear in voltage (see also Fig. 21) and saturates at high biases. The linearity at low biases is a result of the photoconductive gain increasing as the transit time decreases. With equation

g =

#TLVb l2 '

(28)

and plot of responsivity bias dependence (Fig. 31) it follows that #z L = 2.1 x 10 -8 cm2/V for l = 2.6 #m, and then the hot-electron lifetime is zL = 21 ps..The maximum gain is g = 0.82 and the maximum mean free path is L = 2.2 #m. As the intersub-band MQW photodetectors are extrinsic in nature, the responsivity spectra depend on the doping level. For low values of quantum efficiency, r/, the peak responsivity RpoC~p. Then from (21) it follows RpocNd(2/A2),

(29)

that is confirmed experimentally by Gunapala et al. °26) Detection efficiency. The peak detection efficiency can be determined by the expression (A A f ) ~/2 in ,

(30)

1, = (4qldg A f ) ~/2.

(31)

D~*p= Rp where the current noise

Here the bias dependent dark current is defined by the expression

Id ( V) = qn ( V)v ( V)A,

(32)

where n is the number of electrons thermally excited out of the well, A is the device area and v is the average transport velocity given by v = #F[1 + (pF/vs)2] -~/2. Here p is the mobility

Infrared optoelectronics

133

of carriers, F is the average field, and vs is the saturated drift velocity. Combining Eqs (29)-(32) one can obtain the proportionality D,

Nd(~/a~)

OC

(n)l/2

.

(33)

Because the blackbody detection efficiency, D*B = D*(A2/2),

D*BocNd

x

(n) -'/2.

(34)

Thus, the blackbody detection efficiency is proportional to the doping N d and inversely proportional to the square root of the number of carriers thermally generated out of the well. If one takes an explicit expression for n, it follows°2° P

(35)

D*WVeP- 1 '

where p is the normalized doping density equal NdTth2Lw/m*kT. This relation shows that the detection efficiency has a maximum value at 77 K of p = 1.6, what corresponds Nd = 7.4 x 1017 c m -3. In Fig. 32 the dependence of detection efficiency on doping is shown. One can see that this dependence is very weak. The broad maximum has low- and high-density half heights of p = 0.18 (Nd = 8.35 x 1016cm -3) and p = 5.1 (Nd = 2.4 x 10ts cm-3), respectively. Detection efficiency varies by a factor of 2 for a factor of 30 variation in Nd. Also the blackbody detectivity D~'B is essentially independent of doping from Nd = 4.7 x 1017 c m -3 to 1.5 X 1018cm-3. (uS) The doping independence is advantageous from a system and fabrication point of view. D* will remain highly uniform across a large two-dimensional array even with doping variations across the wafer. Additionally, using lower doped detectors with comparative detection efficiencies, substantially lower dark currents can be obtained, that are especially advantageous for large two-dimensional arrays, where filling of the charge storage wells in the multiplexer circuit by the dark current must be avoided. Despite the achievements in GaAs/A1GaAs MQW intersub-band IR detector technology, direct band-gap intrinsic semiconductors, like HgCdTe exhibit superior performance at the same cut-off wavelengths and temperatures. Recently, Kinch and Yariv m) have presented an investigation of the fundamental physical limitations of separate MQW IR detectors as compared to ideal HgCdTe detectors. This performance analysis of the intersub-band GaAs/AIGaAs MQW detector for cut-off wavelengths 89.3 #m and 10.0 #m showed that detection efficiencies, at T = 77 K, of QW GaAs/AIGaAs photodetectors are more than two 1.0

";

o.s

g o.e q~

"~ 0.4

0.2 0

Z

0

I 1

I 2

I 3

i 4

I 5

N o r m a l i z e d d o p i n g (p) FIG. 32. Normalized detection efficiency as a function of normalized doping (after Ref. 126).

F.F. SIZOV and A. ROG^LSKI

134 102

1021 --'-----

10 o

8.3 IXm GaAs 10 Itm GaAs 8.31~mngCdTe

.i /.~l ~-" ~je=

//

10-2 10--4 --

10-10 20

1019

-- 1017



I 40

~O

101'~

/'/

10-8

'~

/ // e

I/ 60

10 II [ 80

109

c~

100

T e m p e r a t u r e (K) Fio. 33. Thermal generation current vs temperature for GaAs/AIGaAs MQWs and HgCdTe alloys at 3.~o= 8.3 # m and 10/am. The assumed effective quantum efficiencies are t / = 12.5 and 70% for GaAs/A1GaAs and HgCdTe respectively (after Ref. 93).

orders lower than that of HgCdTe for the same spectral regions, this is due to the extrinsic nature of these QW doped structures. The dominant factor favouring HgCdTe in this comparison is the excess carrier lifetime, which for n-type HgCdTe is above 10 - s S at 80 K, compared to 8.5 x 10-12s for the GaAs/AIGaAs MQWs. Figure 33 compares the thermal generation current vs temperature for GaAs/A1GaAs MQWs and HgCdTe alloys at ).co= 8.3/~m and 10/zm. Calculations were carried out for a typical set of device parameters: ~ = 8.5 ps, 1 = 1.7 #m, L , = 40 A and Nd = 2 x 10 ~scm -3 for detectors with 2~o = 8.3 #m. For 2co = 10 # m detector the quantum well width was changed to Lw = 30 A, and the remaining parameters were the same. It is seen that for HgCDTe the thermal generation rate at any specific temperature and cut-off wavelength is approximately five orders of magnitude smaller than for corresponding GaAs/AIGaAs QW. Plotted on the right-hand axis of Fig. 33 is the equivalent minimum temperature of operation in the BLIP regime. At a typical background flux of 1017 photons/cm 2 s, the required temperature of operation for the 8.3 # m (10 #m) GaAs/A1GaAs QW is below 69 K (58 K) to achieve the BLIP condition. Thus, to achieve the same performance as discrete HgCdTe photodetectors, additional cooling is required. 4. I N T E R B A N D T Y P E II I N F R A R E D SL P H O T O D E T E C T O R S The constituent materials in GaAs/A1GaAs and some other III-V systems (see Section 3) are very closely lattice matched, that gives the possibility to design the electronic SL or MQW band structures by the control of layer thickness and the height of the barriers. Now it is also quite possible to grow high quality III-V strained-layer structures in which a QW layer can be controlled on the atomic scale too, but with a significantly different lattice constant to the barrier material that gives additional opportunities to design the electronic band structure as it was shown by O s b o u r n . (5'94'192'193) Lattice mismatched heterostructures can be grown without misfit dislocations if the layers are sufficiently thin. (194qgs) The lattice-constant mismatch is accommodated by a distortion of a QW layer, giving a built-in coherent strain in it. Strain changes the band gaps of the constituents and splits the degeneracy of heavy- and light-hole bands. The changes in band gap and band splittings can lead to energy level reversals in the SL electronic band structure.

Infrared optoelectronics

135

10 4

1°3

~

10 2

ee

O

".7. ..L)

I

101

I

I

I

0.5

1.0 1.5 2.0 2.5 Mismatch (%) FIG. 34. Model calculation of the critical layer thickness for absolute stability he and met&stability h i as a function of lattice mismatch (after Ref. 32). In strained-layer superlattices (SLSs) the individual materials layers must be thin enough so that the lattice mismatch between the layers does not generate dislocations at the interface. There are the critical layer thickness for absolute stable and metastable strained structures at which it is energetically favourable to form misfit dislocations. In Fig. 34 model calculations o f the critical layer thicknesses for absolute stability and metastability as a function o f the lattice mismatch for two materials are presented. Dislocations, which are not desirable for device operation above these critical values, are generated. F o r the realistic case o f a SL grown on a substrate, both the individual layers and the SL as a whole must be below critical thickness <32)if dislocation is to be prevented entirely. Strained-layer band gaps and splittings respond to stress as predicted by the bulk deformation potentials. 099-2°1) A schematic o f the fabrication o f a SLS is shown in Fig. 35. Typical structures, for example In~ _xAsxSb, consist of InSb substrates (a few hundred microns thick), an InAs~ _xSb~ buffer layer which is first grown on the substrate, and finally a SL ( 2 1 # m thick), which consists o f m a n y thin alternating strained layers, o f InASl _ x Sbx with different x. The final composition Strained-layer superlattice

(SLS)

I ''''"''' "~ II I I I I I I I

I

I I I I I I I I I

Thin, mismatched

I I I I I I I lllll J

hyers

I | I I I I I I I I I I I I II I I I

I

I III I I II IIIIIIII

I II,,,,,.

/

[ "q I

[ IIII[iI

"

......

I[ lii"'i Ill I

I

i:J

I

strata

I

II

I Graded layer

I I

I

II

I

I

I I II II i i

I I I I

I I

II

I

accommodated by

I

I

II~ Ii |l

S.orla.oo:mama.oh

Substrate

FIG. 35. Schematic of the fabrication of a SLS (after Ref. 202).

136

F.F. Smov and A. ROGAI..,SKI

of the buffer layer is chosen to be the average of the lattice constants of alloy layers to be grown as the SLS. They are shown in the upper part of the Fig. 35 in their unstrained form. All of the lattice mismatch is accommodated by strain in each thin SLS layer (tensile in one, compression in other) without generation of misfit dislocations if the individual layers are below the critical thickness for dislocation generation. If the layer thickness exceeds the critical thickness value, large densities of misfit dislocations are generated. For example, for PbTe/PbS SLS with very large difference in lattice constants (Aao/ao ~- 8.2%) the critical thickness is only about 10 A (2°3) and in layers exceeding this thickness the " w o o d " of dislocations arise at the interface. These misfit generated defects severely degrade the electronic properties of interest. For InAsSb SLS many buffer defects are seen to propagate through the SLS. At present, the properties of these defects are not yet well established, but the main effort of current work is shifted to the elimination buffer defect propagation. Some approaches include the use of graded composition buffer layers, buffers with less mismatch relative to the used InSb substrate, or alternative substrates with buffers in compression. There are several possibilities to obtain the long-wavelength band to band absorption in strained III-V SLs at 2 > 10 # m in order to use such structures in IR photoelectronics; as for bulk III-V crystals the maximum 2¢o = 9/~m is possible only for InAsSb crystals (T = 77 K). If to take a material with a small band gap and small lattice constant (SGSL) and layer it coherently with material having a larger gap and larger lattice constant (LGLL) forming a strained-layer (SGSL)p/(LGLL)q superlattice, it would be seen that layers with larger bulk lattice constants are under biaxial compression and the layers with smaller bulk lattice constants are under biaxial tension. Coherence of SGSL with L G L L then expands the lattice constant of SGSL parallel to the interface, thus lowering its conduction-band minimum. At the same time, tetragonal compression of SGSL in the perpendicular direction splits its valence-band maximum, raising the energy of the upper split components (light- and heavy-hole bands). Both effects act to reduce the band gap relative to unstrained bulk SGSL. In Fig. 36 for comparison, the corresponding unstrained QW potentials are shown at the left and right of the strained SL with type II band offset. The strain lowers the electron QW energy and rises the heavy-hole QW energy. The above approach was proposed by Osbourn (5) for SGSL = InAs0.39Sb0.61 and L G L L = InAs~ _xSbx with x > 0.61. Since quantum confinement effects at small (p, q) act in the opposite direction, increasing the band gap, relatively thick

Biaxial ; compression Unstrained

[Biaxial I tension

Unstrained

FIo. 36. Use of layer strains in a strained-layerSL to reduce the SL band-gap. The corresponding unstrained QW and barrier energies are illustrated at the right and the left sides of the SL. The full lines represent the QW potentials and barriers, the broken lines represent the resulting energy levels and the arrows represent band-to band optical transitions between QW energy levels(afterRef. 205).

Infrared optoeleetronics

137

layers are needed to achieve the maximum band gap narrowing35'2°4> But at the same time the intensity of the optical transitions diminishes due to the exponential decay of the wave functions of the states in the barriers, between which the optical transitions take place. Another possibility to form a SL of type II band offset, suitable for long wave IR fundamental absorption, is a SL with lattice matched constituents. In this type of line-up, as in the case of strained SL, there can be a smaller band gap in the structure, compared to the band gaps of either of the constituents if quantum size effects are not too large. This mechanism, based also on "type II" band offsets, is illustrated in Fig. 37. The band gap in such structures occurs between electron states localized in one type of layer and hole states localized in the remaining layers. "Type II" structures were considered by Arch et al. ~2°6) for AC = InAs and BC = GaSb. Similarly as for strained-layer SL, relatively thick layers would be required to counteract the quantum confinement effects. Also thick layers would severely deteriorate the intensity of the optical absorption due to increased separation between electron and hole states. To reduce the layer thickness needed, the principle of "strain-induced reduction" has been proposed by Smith and Mailhiot ~2°7'~°8) for AC = InAs and BC = Ga~_xlnxSb. This system was grown successfully where far-infrared absorption and photoluminescence were observed. ~2°9'2t°> 4.1. InSb /InAs l_ x Sbx Strained Layer Superlattices

The InAsl _xSbx ternary alloy does not have a small gap suitable for operation in 8-14/~m atmospheric window at 77 K, but recently work has begun intensively on III-V mismatched SLS systems. <2n'2n) Appreciable achievements in InAsSb SLSs were demonstrated by using MBE c2~3-2~7)and MOCVD ~2°4,2~8)techniques. Osbourn ~5)theoretically showed that strain effects in InAsSb SLSs were sufficient to achieve wavelength cutoffs of 12 # m at 77 K, independent of the band offsets which was unknown at that time. For InSb/InAsSb SLSs it results that InAsSb layers will be in biaxial tension, instead InSb layers will be in biaxial compression (for InAs lattice constant a0 = 6.058/~, at 300 K and for InSb a0 = 6.479/~). The effect of biaxial strain in a tetrahedrally coordinated, direct band semiconductor is illustrated in Fig. 38. The out of plane conduction, light hole, heavy-hole and split-off band energies are shown for different biaxial strain conditions. The

Biaxial [ ""--compression

Biaxial tension

E~

~Elh Ee

I Type II

Eh h Eso

offsets

FIG. 37. Type II band-offsets which can produceband-to band transition energiesless than the bulk band energies

of the layer materials. The full lines represent the QW potentials and barriers, the broken lines represent the resulting energy levels and the arrows represent band-to band optical transitions between QW energy levels (after

Ref. 205).

EIh

.fT\ Flo. 38. The biaxial strain-induced shifts of the out-ofgrowth plane energies of the valence and conduction bands (after Ref. 219).

138

F.F. SIZOV and

A. ROGALSKI

tensile strain in the small band gap component of the SLSs, InAsSb, is the sum of expansive hydrostatic and compressive uniaxial strain components. The expansive hydrostatic strain lowers the energy of the conduction band, and the compressive uniaxial strain splits the degenerate light- and heavy-hole bands by shifting the light-holes to higher energy and lowering the energy of the heavy-holes. So, the small band component, InAsSb, is decreased by strain in this SLS, and the InSb-component band gap is increased. Therefore, from the effects of strain alone, InAsSb SLSs can potentially absorb at longer wavelengths than InAsSb alloys. Calculations of the effect are shown in Fig. 39 for various InAs039Sb0.61/InAs~_~Sb~ SLSs with x > 0.61. The above calculations were carried out disregarding a quantum size effect of the SLS. The studies of properties of InAsSb SLS and their growth were mainly carried out at Sandia Laboratory,¢211'212'214'215'21s'219) North Carolina State University(2~3'22°) and Imperial College. ~21v'22z) Difficulties have been encountered in finding the proper growth conditions especially for SLSs in the middle region of composition. It is connected with severe metallurgical problems, such as formation of clusters and even phase separation in the mid-alloy range. <2~7'22~) For device applications, dislocation and crack free SLSs are necessary. InAsSb materials are very brittle and the buffer being under tension contributes to microcrack formation in the SLS. Cracking can be overcome by a severely mismatched InAs,_xSb~ layer grown directly onto the InSb substrate. The high level of strain in this layer induces the nucleation of dislocations. Subsequent buffer layers with lower As content are in compression and cracking does not occur. To obtain an unstrained buffer layer, the buffer must be thick. Gradual composition grading of buffer layers grown on InSb has proven effective in eliminating microcracks from buffers with low As contant (< 10%). This appears to be a promising technique for growing higher As content on InSb substrates. Kurtz e t al. ~2°4) for the first time observed IR absorption in high-quality InAsSb SLSs. The IR absorption spectra at 80 K for two InAs0~3Sb0.s7 SLSs are shown in Fig. 40. Surface reflection and buffer absorption have been subtracted from the spectra. The difference in

Lattice m i s m a t c h 0 1

13

0.5 I

1.0 I 1:2

12

-

-

(%)

1:1

1.5 I

260 JL InAs0.13Sb0.87/ (a) I 3 - 260 ,/~ InSb SLS o ~

7

2:1 O O O

~

/,t

2 1

(2e-hh) [ (le-Ih) (le-hh) ~...~InAs a 1~Sb,

055

100

v O

¢4 10

150

200

(b) /

{J

106 ,~ InAsn l~Sb 0 8-1/ e~ .... '5O 4 -- 106 • InSb.SLS

80~

e~

9 --

~n .O

3 -

_

(le-[~

2 s o.6o

I o.65

I o.7o

L o.~s

I o.so

o.s5

X FIG. 39. Effect of InAs0.39Sb0.61/InAsl- xSbx SLS composition on the cutoff wavelength of the strained hlAs0.39Sb0.6!layers for three different ratios of SLS layer thickness at 77 K. The corresponding lattice mismatch between the two types of SLS layers is given at the top of the figure (after Ref. 5).

1

_

~055

(1©-hh)~f '

I) f

I

100

150 200 Photon energy (meV)

FIo. 40. Infrared absorption spectra of InAs0.t3Sb0.87/ lnSb 260 J~ thick layers (a) and 106 .g. thick layers (b) SLSs (after Ref. 204).

Infrared optoelectronics

139 (a)

200 ~ i n A s 0 .o a S b 0 .94 / 80K I / 3 - 200 )~ InAso 3 S b 0 . T S L S ~

4 --

0 0 1 --

I~InA

I

055

100

s0.3Sbo. 7

II

I

150

200 (b)

400 ~ InAs0.12Sbo.88 / O 0 m e~

80K

3 -- 200/~ InAs0.4Sb0.6SLS 2

1

12°r ~

f

J J"

inAs0.4Sb0.6 I

0 55

j

|

I

II

I

100

150 200 Photon energy (meV) FIG. 41. Infrared absorption spectra of 200/~ InAso.o6Sbo.94/200.~ IBAso.3Sbo. 7 SLS and 400,~ InAso.12Sbo.ss/200/~InAso.4Sbo. 6 SLS grown on a compressed strain-reliefbuffer by MBE (after Ref. 204). layer thickness shifts the positions of the absorption edge in these spectra due to quantum size effect. It is seen that the SLSs absorb at wavelengths longer than the band gap of the InAs0.13Sb0.87 alloy (Eg = 175 meV). For higher As content the absorption was observed in far IR region of 20 # m (Fig. 41). Infrared photoluminescence measurements of Kurtz e t aL (2°9) confirm results of optical absorption providing evidence that a type II offset occurs in the InSb/InAst_xSbx SLSs for alloy compositions x > 0.6. The photoluminescence lines were much narrower than those reported in InAsSb alloy photoluminescence studies. (222) Both (e-hh) and (e-lh) transitions were resolved. The band structure of such a kind of SLS was calculated with the band offsets and strains shifts obtained from the photoluminescence data. The predicted InSb/InAs0.t3Sb0.s7 band structure is shown in Fig. 42. Both the heavy-hole and light-hole quantum wells occur in the InSb layer with energy barriers of 84 and 23 meV. InAs0.13 Sb0.87

InSb

TT

Conduction band

236 meV

I 267iev hh

168 meV ' " rneV

lh hh

V a l e n c e band

Flo. 42. Calculated band structure (77 K) of InSb/InAso.13Sbo.87SLS with equal layer thicknesses (after Ref. 209). JPQE 17/2--D

140

F . F . SIzov and A. ROGALSKI

It should be noted, that type I band offset can also occur in InAsl _xSbx SLS. In this case, the electron and hole potential wells are in the same layer, and the lowest optical transitions are between the strain-shifted states of the InAsSb layer. The performance of the photoconductive detectors fabricated from the InAsSb SLS structures are strongly affected by carrier transport along the layers. Carrier lifetimes are generally longer than the corresponding lifetimes of the materials owing to the spatial separation of the carriers by the type II offset. Very long lifetimes at low temperature can be obtained by decreasing the wavefunction overlap, by making wider the SLS layer thicknesses. Then receiving of significant photoconductive gain is possible. Kurtz et al. (223) reported gain values as large as 90 for four-layer SL with a long wavelength cutoff of 8.7/~m at 77 K. In this novel photoconductor, the gain is sensitive to the structure and composition of the SL, and the sweep-out effect is eliminated with the appropriate contacts. Photoconductive lifetimes of tens of nanoseconds have been measured in undoped InAsSb SLSs with about 200/~ layer thickness. 4.2. lnAs /Ga l_ xlnx Sb Strained Layer Superlattices The long wavelength cutoffs of InSb/InAsSb SLS have only been achieved for relatively thick (> 75 .lk) layers. As such a kind of SL confines electrons and holes in different layers, these thick layers result in small electron-hole overlap, which leads to small absorption coefficients. Furthermore, InSb/InAsSb SLs must be grown on relaxed buffer layers on InSb substrates. To avoid these disadvantages Mailhiot and S m i t h (2°7'2°s'224) have proposed strained type II SLs made of InAs/Gal _xlnxSb as a new material system for IR detectors. Like InSb/InAsSb system, far-infrared response in InAs/GalnSb SLs comes from a type II band alignment. However, unlike InAsSb materials, effects due to strain are combined with a substantial valence-band offset (AEv ~ 510 meV). As can be seen from Fig. 43, the unstrained conduction band minimum of InAs lies below the unstrained valence-band maximum of InSb or GaSb. The GaSb valence band edge lies approximately 100 meV above the InAs conduction band edge at low temperatures. Because of this ususual band alignment, the SL can have a band gap smaller than that of either constituent material. Semimetallic behaviour has been reported in the lightly strained InAs/GaSb SL (225"227) which has been studied extensively332)

(a) 1.2

(b)

C

C

-

\

0.8 H c ""

0.4

~L,H

L,H

AEv 0 _

i.~. L, H

InAs

H GaSb

-0.4

Un strained

InSb

InAs tension)

Ga0.6 In0.4Sb (compression) Strained

FIG. 43. Assumed relative energy positions for unstrained InAs, GaSb and InSb bulk semiconductors (a). Effect of lattice mismatch-induced internal strain on the energy band offset for InAs/Ga0.6In0.4Sb heterointerface is shown on the right side of the figure (after Ref. 224).

Infrared optoelectronics

141

Long wavelength IR absorption however can be achieved in InAs/GaSb SLs only for InAs layer thickness greater than approximately 100/~, resulting in comparatively poor absorption due to effective localization of electrons and holes in opposite layers of SL (electrons are localized in the InAs layers, whereas holes are localized within the GaSb layers) and large barrier heights preventing the penetration of the wave functions into barriers. As a result, the optical absorption coefficient of InAs/GaSb SL is too small in the thick-layer case where the SL band gap corresponds to long 2co. This is shown in Fig. 44, where experimental low temperature absorption of InAs/GaSb SL is compared with that in InAs0.13Sb0.s7 SLS. To obtain enhancement of IR absorption, Smith and Mailhiot suggested substituting a Gain_ xInx Sb alloy for GaSb. It allows the possibility to reach the important 12 # m IR region for thin SLs to obtain large optical absorption, as optical matrix elements in type II SLs decrease rapidly with increasing SL layer thickness. In Fig. 45 it is shown that the band gap of InAs/Ga~_xlnxSb SLs for 0 < x < 0.4 as a function of layer thickness for equally thick InAs (Ma) and Gal_xlnxSb (Nb) layers. At a fixed layer thickness, the band gap decreases significantly with increasing x. It can be seen that in InAs/GalnSb SLSs, small band gap is received at much smaller layer thicknesses than in a weakly strained InAs/GaSb superlattice. Because the optical matrix elements are reasonably large, one can achieve favourable optical absorption in InAs/GalnSb SL. Figure 46 compares the theoretically calculated optical absorption coefficient of the InAs/Ga0.6In0.4Sb SLS with the absorption coefficient of a ng0.79Cd0.21Te alloy used as a basic material for IR photodetectors. Both materials have a band gap of l l 0 m e V (2co= l l.2/~m) at 77K. These calculations demonstrate that, close to threshold, the optical absorption properties of the pointed SLS can be as good as those of the HgCdTe alloy. Electronic properties of InAs/GalnSb SLS should be superior to those of the HgCdTe alloy ~2°8) as the electron effective mass of InAs/GalnSb SLS is much larger ( m * / m o _~ 0.05 compare to m * / m o _~ 0.009 in HgCdTe alloy) and nearly isotropic. Thus, diode tunneling currents in the SL can be dramatically reduced compared to the HgCdTe alloy. 5 (a) o

4

v

o=3

2 O ,.a

o

1

aD

I 0

0.I

I 0.2

0.3

0.4

Energy (eV)

Fro. 44. Experimentallow-temperatureabsorption curves as a function of photon energy for (a) an InSb/InAs0.13Sb0.87SLS with 200 ~, and (b) InAs/GaSb SL with 102~ periods. Both of these structures have the same band-gap. The InAsSb type II structure exhibitsa sharp band edge onset with 100 .~ layer thicknessprimarilydue to the small barrier heights in this system.The InAs/GaSb type lI system exhibit large barrier heights, so that weak band edge absorption is obtained even for 51 A layer thickness (after Ref. 205).

142

F . F . Smov and A. ROGALSK! 360 --

InAs'Gal-xlnxSb [ 111 ] superlattice

320 280 240 200 160

"~

80 40 0 -40 -80 -120 --

-160

I

I

I

I

I

I

I

2

4

6

8

10

12

14

I

I

16 18

I 20

M, = N b FIG. 45. Band-gap of InAs/Gao.6Ino.4 Sb [111] SLS as a function of layer thickness for various values of x. The SL consists of equally thick InAs and GaInSb layers (after Ref. 224).

The InAs/GaInSb SLSs were examined by photoluminescence, photoconductivity, and IR optical transmission. The photoconductivity spectra were obtained under backside illumination at different applied biases (Fig. 47). As expected, a systematic decrease in the energy gap with increasing InAs layer thickness at a fixed InSb fraction x - 0.25 was observed. A photoconductive cutoff beyond 15/~m was observed in a 45 A/28/~, InAs/Gao.75In0.25Sb SL. Measured optical absorption coefficients in such a kind of SL are in excellent agreement with calculated values as it was shown by Chow et al. (229) W a v e l e n g t h (~tm) 12 I

104 T"

5 -

10 I

8 I

|

12 I

10 I

InAs-Gal_xlnxSb

Hg1_xCdx Te

X=0.4

X=0.21

8 I

J

[001] •~

10 4

[

2

2

O

o 0

~ <

103

10 3

5 -

/~

J, 100

E I = 110meV

E s = 110meV

I

I

I

I

120

140

160

100

Photon

120

140

160

energy (meV)

Fro. 46. Absorption coefficient as a function of photon energy for the InAs/Gao.~Ino.4Sb SLS and for Hg0.79Cdo.2tTe alloy (after Ref. 208).

Infrared optoelectronics

143

SLS photoeonductivity

lnAs/Gal_xlnxSb

T ,- 4.2K x -0.25 45A/28A

S

.

j

"~ g~ .~ "~

.02,

41A/25A x - 0.25 37A/25A

S

x - 0.25

--

25A/25A

I

I

x- 0 2sA/2sA

I

I

,/

I

20

10 6 4 3 Wavelength (microns) FIG. 47. Photoconductivity response of InAs/Ga~ _ ~In~Sb SLSs at 4.2 K. Nominal layer thicknesses and compositions are shown in the figure (after Ref. 228).

Preliminary studies of InAs/GaInSb SLSs on GaAs or InP substrates indicate the difficulties of receiving device-quality structures. Complications derived from mixing arsenides and antimonides within a single heterostructure and difficulties associated with the considerable lattice mismatch between InAs and Ga~_xln~Sb (22.2% for an InSb fraction x = 0.25). Growth on GaAs or InP substrates results in threading dislocations originating at the base of GaSb or InAs buffer layers and propagating through the SLs in densities of 109 cm -2. Such high dislocation density has a deleterious effect on material properties, such as carrier lifetime and mobilities, which are crucial for detector performance. Better quality InAs/GalnSb SLSs have been fabricated using (100) oriented GaSb substrate3229-233) Grown to the in-plane lattice constant of GaSb, InAs is in tension with a lattice mismatch of 0.6%, whereas Ga~ _~In~Sb is in compression, with a mismatch of 1.6% for x = 0.25. Appropriate choice of InAs and GalnSb layer thicknesses balances the alternating compressive and tensile elastic stresses within the SL, removing the driving force towards misfit dislocation formation at the base of the SL. 4.3. Strained Layer Superlattice Photodiodes The first photodiode constructed from SLS (InSb/InAsl_xSbx) was described by Kurtz et a13219'234)Such photodiodes, consisting of p-n junctions embedded in an InSb/InAs0.09Sb0.91

SLS with 130 A-thick layers, were grown using MBE. Rather low detection efficiencies in these nonoptimized devices with 2~o ~ 7/~m were observed ( D * = 3 x 109cm Hzi/2/W), In a subsequent pape~ 235) the broad spectral response of InSb/InAsj _xSbx SLS photodiodes (x = 0.82-0.85) was extended to wavelength > 10/~m, however the detection efficiency still did not exceed 1 x 109cmHz~/2/W at 2 = 10#m. To compare it with existing HgCdTe technology or photoconductive intersub-band GaAs/AIGaAs intersub-band detectors, the detection efficiency above 10t°cm Hz~/2/W should be achieved. Recently Kurtz et al. °s) have fabricated high detection efficiency InSb/InAs0.tsSb0.s5 photodiodes with D* > 10l° cm Hz~/2/W at 2 < 10/~m. The construction of this photodiode

144

F . F . S1zov and A. ROGALSKI SLS: 150/~ InAso.15Sbo.85/150/~, InSb

1.0ltm

P

SLS p (5 x 1016)

2.5~m

~

SLS "i" (3 x 1015)

1.0p.m

=

SLS n (5 x 1016)

5.0~m

~

InxGal_xSb buffer (X ffi 1.0-0.9) n(5 x 1016)

~,

InSb n-type substrate f1111111111111111111///lJ

Reflecting back contact

FIG. 48. Structure and composition of the InAsSb SLS photodiode (after Ref. 18).

grown by MBE is shown schematically in Fig. 48. The SLS was grown on thick, compositiongraded InxGal _xSb (x = 1.0~.9) strain-relief buffer on an InSb substrate. The photodiode p-i-n structure was embedded in the SL with equal 150/~-thick layers. The p- and n-dopants were Be and Se respectively. The doping level in the i-region represents the background doping level in the MBE system. The photodiodes were mesa-isolated, with an area of 1.2 x 10-3cm 2. The InGaSb buffer and n-type substrate are semi-transparent at long wavelengths and with reflecting back contact the optical path length and the quantum efficiency are substantially increased. The zero-bias resistance of such a kind of device was quite sensitive to surface treatment. Thus, the detector noise is determined by surface leakage and not by the SLS material quality. A crude surface passivation was implemented by exposing the surface to water and intense illumination with a tungsten lamp. After these procedures the resistance-area product R0A increased from 0.6 to 9 f~ cm 2 at 77 K as a result of passivation. The temperature dependence of the R0A product indicates that performance of detector is not yet limited by diffusion or the depletion region generation-recombination processes inherent to narrow-gap semiconductors and that further improvements in SLS material quality or surface treatment should further increase the responsivity and detection efficiency of the InAsSb SLS photovoltaic IR detector. Noise measurements performed before and after photodiode passivation indicated that a large 1If noise component was introduced by passivation, and alternative passivation processes must be developed in order to operate with these detectors at lower modulation frequencies. The possiblity of fabrication of p-n-junctions also in InAs/GalnSb SLS system was recently demonstratedc229) by MBE growth technique. Beryllium and silicon dopants were used. Beryllium is known to be an acceptor for all of the conventional III-V compounds. Silicon is a p-type dopant for GaSb, instead of n-type impurity for InAs. So, co-deposition of Si during growth of InAs layers should result in n-type SL. n-type doping up to levels 1018cm -3 has been observed. To date, background p-type doping in InAs/GalnSb SLSs, with carrier concentrations of approximately 5 x 1016cm -3 has been consistently observed. In such a situation, the p-n-junctions were formed by Si co-deposition. Photodiodes were fabricated by chemically etched mesas with AI contacts on both the tops of the mesas and the etched surface. The spectral response of 24 A/40/~, InAs/Ga0.75In0.25Sb backside-illuminated SLS photodiode~2~8)had a threshold near 12 #m, but its performance is inferior in comparison with HgCdTe detectors.

Infrared optoeleetronics

145

The results presented above in InAsSb SLS photodiode performance arc encouraging, and this new type of device may soon become attractive for detector applications for long-wavelength FPAs. However, one can not forscc that these materials in the near future will replace HgCdTe. Progress in the development of InAsSb SLS will depend on continued improvements in material growth, device processing and understanding of SLS electronic properties. 5. H g T e / C d T e AND R E L A T E D S U P E R L A T T I C E S HgTe/CdTe system was the first from a new class of structures for IR optoclectronics, which has received a great deal of attention. Since 1979 when this SL system was first proposed, <6'230 significant theoretical and experimental attention has been given to the study of this new SL system (sec e.g. papers of Workshops on the Physics and Chemistry of Mercury Cadmium Telluride organized in U.S.A.), <237) and papers of International Conferences on II-VI Compounds. (23s)To date however, attempts to realize HgTe/CdTe and related SLs with properties suitable for IR detection have been unsuccessful. Lack of success seems to be determined by interface instabilities of SLs due to weak Hg chemical bonding in the material, leading to large Hg diffusion coefficients, even at rather moderate temperatures, (23~-u° and also by basic problems associated with the band structure of SLs leading to the necessity of producing thin (~< 50 A) constituent layers and thus closely connected with the first problem. Therefore, only some properties of HgTc/CdTe and related SLs will be briefly discussed. HgTe/CdTe SLs belong to type III SLs (see Fig. ld). <242-245)SL type III to type I transition in Hg~_ xCdxTc/CdTe and related S Ls (e.g. Hgl_ xZn~Te/CdTe and Hg~_ xM n~Te/CdTe) was observed experimentally. (24z243)CdTe is a conventional open gap semiconductor whose band ordering is the same as in most III-V semiconductors (Fig. 49). HgTc is a symmetry-induced zero-gap semiconductor. The F6 band, which is a conduction band in most III-V and II-VI semiconductors with zinc-blende structure, is a light-hole band in HgTe. The Fs light hole band in open gap III-V or II-VI semiconductors becomes a conduction band in HgTe, degenerate at the zone centre with Fs heavy-hole band. Thus, this is the case when at the Hgl_ x CdxTe

iE

\IA

1.5

\x Z

",, ] /

i

o

-l.o

-

I

I

x \Jr s .........;~ " ~ ,r+ - - ._ 4-Ae+ ~ I i ~, ,

4,

I

.~-'> Ao

I

I r,

I

I [

r

!

<

% "--

, CdTe HgTe F,G. 49. Schematic band structure of bulk CdTe and HgTe in the vicinity of F-point of the Brilloun zone.

146

F . F . Slzov and A. ROGAL.$KI

interface of the HgTe/CdTe heterostructure the light particle changes the sign of its effective mass across the interface, being electron-like in the HgTe layers and light-hole like in the CdTe layers. The theoretical calculations(26'2~-24s) show that the wave function and thus the probability density of electrons have peaks near the HgTe/CdTe interface. Thus the interface states arise and their existence depends on the relative position of the Fs edges of the constituents. In these papers only the ideal abrupt interface was considered. Beavis e t al. (249,:5°)calculated the electronic structure of HgTe/CdTe SLs for imperfect interfaces and found that new states localized at the interface should arise. A pseudopotential calculation of the band structure of the HgTe/CdTe SLs by Jaros e t al. ~25~) showed that this system may represent an example of a failure of the particle-ina-box model, suitable for any other SL system. Still, the effective mass type approach may be effectively applied to describe the HgTe/CdTe band structure, t25:) at least to a complete description of the level energy positions, line shapes of absorption spectra and the ratio of the oscillator strengths of Hg~ _xCdxTe/CdTe SLs with open band gap. (253~ As it was shown in many theoretical calculations(254-26°) of the HgTe/CdTe SL band structure, the valence band offset between HgTe and CdTe has a crucial influence on the HgTe/CdTe SL band structure. Earlier infrared absorption, magneto-absorption and electron cyclotron measurements gave the band offset to be less than AEv~ 100meV. t26~-265) Earlier magneto-opetical measurements were performed in the Faraday configuration (q I[z) and gave AEv ~ 40 m e V (26L264) that seemed to be in agreement with the common-anion rule of lattice-matched heterojunction interfaces. Recently however experimental evidence has been o b t a i n e d (57'67'266-275) of large valence band offset (AEv ~ 350 meV) in HgTe/CdTe SLs that are in contradiction with the common-anion rule in application to the lattice-matched HgTe/CdTe and related material systems. These data are in good agreement with recent theoretical calculations of the HgTe/CdTe band offset. (74,251,256,276.277) For providing the direct measurement of heterojunction valence-band discontinuity AEv the X-ray photoemission spectroscopy (XPS) experiments seem to be the most valuable and relevant. The XPS experiments by Kowalczyk e t al. (67) showed that AE~ = 0.35 _ 0.06 eV in CdTe/HgTe (TTT) heterojunctions at room temperature. This AEv value was later confirmed by Duc e t al. C27°)by the same kind of XPS experiments. Also the value AE~ = 0.25 _ 0.05 eV was obtained for the HgTe/ZnTe heterojunction. The X-ray and ultraviolet photoemission experiments of Sporken e t al. (273) at temperatures of 50-300 K confirmed the value AEv (300 K) = 350 _ 50 meV and showed that with the uncertainty of 60 meV the 50 K AE~ value changes only by a few meV compared to room temperature data. The optical absorption measurement analysis by Cesar e t al. ~253) showed that the Hg t _ xCd~Te/CdTe (x = 0.24, 0.27) valence-band offset AE~-_ 400 meV is also independent of temperature. The in s i t u XPS experiments by Becker e t al. (275) have shown that the valence-band offset for the HgTe/CdTe heterojunction is independent of the surface (100), (110) and (111)B orientation and is equal to AEv = 0.37 _ 0.07 eV. The controversy between the earlier optical and magneto-optical data of low valence-band offset value (AE~ = 40 meV) and the large one (AE~ = 350 meV) obtained from photoemission experiments, was simply resolved by Johnson e t al. (26°'278) who showed that a large AE~-value is indeed consistent with the magneto-optical data of Berroir et al. (264'265) taking into account the particular sample chosen by Berroir e t al. Figure 50 shows the SL band structure for the 100 .~ HgTe/36 .~ CdTe (111) SL, used by Berroir e t al. as a function of band offset AE~. The wave vector k~ is along the growth axis. The zero is taken to be the value band maximum of bulk HgTe. The calculations(:76) employ the EFA with k-p-perturbation theory used to obtain the SL band structure for finite k. As one can see from Fig. 50 the heavy-hole (HH) minibands are virtually independent of AE~.

Infrared optoelectronics

\

147

C!

40 --

20

-

0

-

-20

"Eg

"~HHI 1 ~ ~ m

K° 0 d

0

~

HH1

Kj. ~.~_ d

K,,

0

HH2 I _ ~m



K, 0

Kj.

SC

40

230

350

200

300

HH2

I

SM

100

C1

J,~

SC

t~

HHI

I_

400

Band offset A E v (meV) FIG. 50. The band structures for I00/~. HgTe/36~, CdTe SL as a function of the valence band offset AEv. As A E v increases, the system changes from serniconducting (SC) to semimetallic (SM) and back to semiconducting (SC) due to the crossing and uncrossing of the CI and H H I bands (after Ref. 278).

At the same time the lowest conduction miniband (C1) and highest light-hole band (LH1) change their positions very rapidly on AEv relative to the HH1 and HH2 minibands. As a result, the C1 and HH1 bands cross at AEv = 230 meV; the HH1 electrons are transferred to the C1 band, and the SL becomes semimetallic. At AEv > 295 meV the SL becomes semiconductin~g once again as a result of the uncrossing of the C1 and HH1 bands. The 100/~ HgTe/36 A CdTe SL accidentally give similar results for small and large AE~ because of the nearly symmetrical location of the semimetallic regime between the high and low values of AEv; that explains the magneto-optical results of Berroir et aL, performed in the Faraday configuration. The angular dependence of far-IR magneto-optical experiments performed on a p-type HgTe/CdTe SL with a small band-gap (less than 5 meV) by Wagner eta/. (267'279) revealed that the hole effective mass in the growth direction is more than two orders heavier than transverse to it (m*z/m* ~-280, mz = 0.30 m0). These results are in full agreement with a large valenceband offset, when the heavy-hole band is above the light-hole one. The large valence-band offset also leads to a large electron mass anisotropy ( m * / m * ~- 40, mz = 0.10 m0) as was shown by Voos et aL (2s°) for n-type Hg~_xZnxTe/CdTe semimetallic SLs (x = 0.053) by angular dependences of IR cyclotron resonance measurements. The large anisotropy obtained is consistent with a large valence band offset (AEv _- 300 meV). For small valence-band offset it should be m z / m * _~ 1. Large differences in band structure of HgTe/CdTe, and related SLs, for different AE:values also has significant consequences on the explanation of other physical properties of these objects, as partly discussed for example by Meyer et al. (28~) The growth of HgTe/CdTe SLs was first reported in 1982 by Faurie et a13282) and subsequently has been reported by many other groups. High quality HgTe/CdTe SLs were also grown by laser assisted MBE (2s3'284) and photoassisted MBE. (285)Because Hg has both a high vapour pressure and low sticking coefficient, at the commonly used growth temperatures of about 180°C, special Hg MBE sources are required. In particular, when growing SLs of several tens of layers, it is necessary to let a significant amount of mercury vapour (as much as several litres in the liquid phase) pass through the system.

148

F.F.

S I z o v a n d A, ROGALSKI

To observe sub-band structure in the optical data, it is necessary to have homogeneous distribution throughout the HgTe and CdTe layer thickness in the SL growth direction and at abrupt interfaces. The results of Leopold e t al. (286) of optical absorption measurements in an as-grown HgTe/CdTe SLs on low-temperature substrates (Tsub = 150-170°C) and thermally annealed at T = 160-240 ° SLs, showed that to minimize interdiffusion processes, the SLs must be grown at temperatures not exceeding 170°C. The as-grown samples exhibited multiple steplike absorption edge features. In thermally annealed samples the shift of the absorption edge to higher energies, as well as broadening of sub-band absorption, were observed due to interdiffusion of the components. The value of the absorption coefficient for different HgTe/CdTe SLs approaches 104 c m - 3 in the region above the bandgap E s. The optical properties arising from fundamental absorption in HgTe/CdTe SLs makes the precise band-gap determination difficult to obtain as the small changes in the transmission spectra of the Fabry-Perot SL resonator, exhibiting interference fringes, makes the interpretation rather difficult, also taking into account the complexity of the SL band structure, its broadening and possible Burstein-Moss shift, which must be taken into account in such "narrow-gap" SLs. Interdiffusion also can considerably influence the optical spectra making the features less pronounced and the conclusions less definite, c2s7) Lansari e t a / . (272) investigated the room temperature optical properties of a series of highquality MBE grown HgTe/Hg0.15Cd0.s5Te SLs (the substrate temperature Tsub = 175°C) with no evidence of Hg interdiffusion. For these SLs the valence-band offset, on the basis of tight-binding calculations, was found to be 300 meV, which extrapolates to the HgTe/CdTe interface. Figure 51 shows a comparison between the experimental optical absorption coefficient measurements of Lansari e t a / . (272) and the theoretical fundamental absorption curves of Johnson and Ehrenreich ¢28s) for 58/~ HgTe/42,~ Hg0.15Cd0.ssTe SL at room temperature. The theoretical curve for AEv = 350 meV is in excellent agreement with the experimental data. Although the interband absorption coefficient is not very sensitive to AEv, the agreement with experimental data is better for AE~ = 350 meV. Calculations of ~t(E) above E = 0.55 eV are difficult to provide since many SL bands contribute, and a E(k) dispersion curve is required for large kll values. i

2 l_

---

Expt.

on D

Theory (total)

:/ a*

AE v = 3 5 0 m e V •~

J

AE v = 4 0 m e V

~o~

~/~" Approx, .~

HHI ''~" C 1

IE ~ _ _ I[ I - L H I " ~ C l l

0.2

/HH2--~C2

0.4 Photon

H H 3 ~ C3 ......

/

/ 0

*

,* ." & o , ~ . , ." . . . . .

energy

, 0.6

0.S

E (eV)

51. Comparison of experimental(short dashed line) of Lansari et al. <272)and theoretical(solid line) fundamental absorption coefficients a(E) as a function of photon energy E for 58.~ HgTe/42~ Hg0.,sCd0.85TeSL at T = 300 K. Dominant partial contributions are shown (long dashed lines). Theoreticalcurve above E = 0.55 eV is approximate (shown dotted). A£v is taken as 350 meV. The theoreticalabsorption curve using A£v = 40 meV is indicated by a dashed-dotted line (after Ref. 288). Fio.

Infrared optoelectronics

149

500 •

400 -

IR transmission Hgo.6?Cd0.33Te band gap

;> 300 v

200

e~ co

100

iIIII I

--

I 40

I I I I I I 120 160 200 240 280 320 Temperature (K) FIG. 52. Temperature dependence of the IR photoluminescence signal (O) from 38-40A HgTe/18-20 A CdTe SL sample. The circles indicate the energy of the peak signal while the bars indicate the energies of the half-intensity points. The triangles are the results from the transmission experiment. The solid line gives the band-gap energy for a Hg0.67Cdo.33Te alloy which is the average composition of the SL (after Ref. 289). 0

I 80

Theoretical calculations predict a narrowing o f the H g T e / C d T e SL b a n d gap c o m p a r e d to the H g C d T e alloy b a n d gap with the average composition. This prediction is illustrated by Fig. 52 where the results o f Hetzler et al. (289) on I R photoluminescence, to obtain temperature dependence o f the b a n d - g a p in H g T e / C d T e SLs, are presented. The b a n d - g a p values obtained f r o m the transmission experiments and a curve representing the b a n d - g a p energy for the average composition (for H g T e / C d T e SL) Hgo.67Cd0.33Te alloy are also shown. One can see that the energy o f luminescence for H g T e / C d T e SL is significantly lower than that for H g C d T e alloy. Possible interdiffusion in H g T e / C d T e SLs will enlarge its band-gap. It has also been predicted that the H g T e / C d T e SL band-gap will decrease as the thickness o f the H g T e layers in the SL increases and the thickness o f CdTe layers decrease; illustrated

150 -

d2(~) ^ ' 2030 50' 38/20 ~

"~

50

2K

~

-

8

\ \ 0

T =

50

00,3,

100 150 200 dr(A) FIG. 53. Variation of the band-gap of different HgTe/CdTe SLs at T = 2 K as a function of the HgTe layer thickness (dz). The experimental data are given by the solid circles; for each sample, the first number corresponds to d I and the second one to d2which is the CdTe layer thickness. The solid lines are theoretical fits for three values of d2 (&Ev= 40 meV) (after Ref. 290).

150

F.F. SlZOVand A. ROGALSKI

by the results of Fig. 53, where the values of the HgTe/CdTe SLs band-gaps deduced from the extrapolation of the peaks of the IR magneto-optical transmission experimental data to values at the magnetic field H = 0 are presented. All of these results seem to establish HgTe/CdTe SLs as important IR detector materials. Nevertheless, a potential area of concern for application of these materials to IR detectors is the interdiffusion of the constituents. Appreciable intermixing of the HgTe and CdTe layers at temperatures as low as 110°C has been observed,~29~)that prevents the realization of a low dimensional solid system in a stable form. In spite of failure of HgTe/CdTe and related SLs applications in IR optoelectronics, the studies of these SLs have been intensely continued,(2s~'292-296)considering their unique physical properties. Such narrow-gap Hg-based SLs as HgTe/ZnTe,t297)HgZnTe/CdTet243,2s°ags'299)and HgMnTe/CdTe~242'3°°-3°2) are studied. 6. DOPING SUPERLATTICES A spatial modulation of the doping in an otherwise homogeneous semiconductor lattice can produce a SL effect, i.e. a spatial modulation of the band structure (see Fig. le) which induces a reduction of the Brillouin zone and new energy sub-bands arise in the SL direction. The electrons and holes in doping SLs are spatially separated which leads, first of all, to an excess carrier recombination lifetime, which can be larger, by many orders of magnitude, than those in the host material. So far, nearly all of the experimental investigations and most of the theoretical studies on doping SLs have dealt with GaAs doping SL structures (called also "n-i-p-i-structures"). The doping SLs were first considered in the original proposal of Esaki and Tsu°) and next pursued especially by Dohler and Ploog. (29'3°3-3°5) The n-i-p-i SL concept has been known for several years but only recently has this concept been demonstrated in application to mid- and long-wavelength IR photodetectors. For equal uniform doping levels Na = Na with the thicknesses of n-type and p-type layers dn= dp = d/2 and static dielectric permittivity eo the periodic potential consists of parabolic arcs and has an amplitude:0°3)

rce2Na d 2 1Io = - 2£0

(36)

For GaAs with Na = Nd = 1018cm -3 and d = 500/~ and V0 = 400 meV. The quantized energy levels in the potential wells are approximately the harmonic oscillator levels:

E¢~,v= hog¢,v(n + ½).

(37)

(4rcNder~ 1/2 co~., \ ¢0m*, )

(38)

where

=

is the plasmon frequency of carriers. For electrons in GaAs, for instance, the sub-band separation is 40.2 meV for the above parameters. For IV-VI semiconductors, e.g. PbTe, with the band-gap Eg ~ 0.2 eV and m c - m y - 0.04too, but with much higher dielectric permittivity (E0 ~ 500) the sub-band separation and so, the change of the band-gap are, much smaller.

Infrared optoelectronics

151

The value of the effective bandgap E ~ , defined as the energy difference between the uppermost valence sub-band and lowest conduction sub-band

E ~ = E g - 2 Vo + E° + E °,

(39)

depends in most cases mainly on the value of Vo and therefore linearly on the doping concentrations, but quadratically on the thickness of the doping layers. Several types of doping SLs can be fabricated. Their details are discussed, for example, by Ploog and DohlerJ 3°a) Comprehensive theory and description of many experimental results concerning doping SLs (such as variation of the band-gap with increasing excitation, change of absorption features with light intensity, tunable excitation, nonlinear optical properties, etc.) can be found in the review articles of Dohler. (3°4"3°5) Among the intriguing aspects of doping SLs, the lifetime enhancement of electron-hole pairs due to the indirect gap in real space makes these objects interesting for high sensitivity IR detector applications. The most promising for long wave-length IR detectors fabrication are n-i-p-i structures for InSb and InAs, (3°6'3°7)or their alloys(3°8)although encouraging results were obtained with PdTe n-i-p-i structures32°'3°9) Maserjian et alJ3°6) carried out an analysis of different semiconductor materials for applications of n-i-p-i SLs as long-wavelength detector arrays. This analysis is briefly presented below. The spatial separation of the electron and hole potential minima (see Fig. le) reduce the overlap of the electron and hole wave functions giving rise to a tunneling factor P ,~ 1 which reduces the absorption coefficient = P~o

(40)

and increases the electron-hole recombination time z

To

p,

(41)

where ~t0 and To are the absorption coefficient and the minority carrier lifetime of the intrinsic semiconductor. The above effect is undesirable for ~t, but is desirable for T since it improves the detector response. In overall detector performance, which depends on the product ctT = ~t0T0, this effect tends to cancel out. However, values of P should be limited to the value that do not require unreasonable thickness d of SL. If values of P = 10 -2 and ~t0 = 104cm -t are assumed, one obtains ct = 102 cm -~ and then for good quantum efficiency d ~ 1/2~t - 50 #m. Using MBE or MOCVD growth techniques, deposition of 50 # m thick layers is possible. The peak detectivity can be obtained from D* = r/E~-l [2d(Gb q'- Gt)] -1,

(42)

where d is the total thickness of active n-i-p-i layers, and Gb, Gt a r e the rates of carrier generation per unit volume contributing to noise due to background radiation and thermal processes, respectively. For slightly n-type doped SL, the thermal generation rate at low temperatures is given by

n?e

Gt = - - ,

n'c 0

(43)

152

F . F . Sxzov and A. ROGALSKI

where n is the equilibrium electron density and n i is the intrinsic carrier density. For bulk grown InSb, ~0 = 1 0 - 7 S, and n = 4 x 10 ~3cm -3. The generation rate is expressed by

G b ~- 4F2d

(44)

in terms of the background radiation flux density ~bb and the optics f - n u m b e r F. In calculations it was accepted a = ~0, P = 26, d = 100/~m and the wavelength independent quantum efficiency q = 0.46. Figure 54 shows the theoretical dependence of detection for n-i-p--i-detector at 20 #m, assuming the above theory and parameters. We can see that transition to background limited behaviour (at Tb = 295 K) occurs at about 50 K. This transition would occur at higher temperatures with larger values of the product ~ = ~0~0, that is possible for low temperature grown n-i-p-i-structures with a low Schockley-Read centre density. Theoretical considerations of P-factor for different materials indicates that P > 10 -2 is possible for InSb and InAs. InSb doping SLs. Experimental studies of preliminary InSb n - i - p - i SLs have clearly demonstrated the viability of this new approach to the design and fabrication of large area detector structures. (3°7'31°) The technology for n-i-p-i-structures has benefitted greatly from the GaAs technology base, where very high quality structures can be grown using 6-doping approaches. (24) In this method, one stops the growth of the host crystal and deposits the dopant under an As4 background until surface concentrations of 1013cm -2 are achieved. After accumulating the appropriate level of Si or Be, growth of the host III-V is continued. Dopant concentrations equivalent to 102~cm -3 can be achieved with no degradation in the quality of the material or the nature of the growth front. InSb doping SLs have been grown on (001) InSb substrates at a temperature of 340°C, with a p-type impurity concentration of 2 x 10 ~4cm -3. Si and Be dopants have been used. Contacts to samples were formed with evaporated, annealed, 100 nm indium pads. Typical photoconductivity data for n-i-p-i-structure are presented in Fig. 55. One can see that the absorption edge of n - i - p - i SL is shifted to photon energies 60 meV below the bulk InSb absorption edge. Additionally, the peak in the n - i - p - i responsivity exceeds that of the bulk InSb photoresponse at ---2100era -~ owing to the enhanced photocarrier lifetime in the n - i - p - i layers by a factor of 13 over typical bulk values of 140 ns. The dip in the photoresponse at ---1900 cm -t is not fully understood at present. 1012

--

N

v~

lO 1°

1o 9 0

I 20

I 40

I 60

Detector

I 80

I 100

temperature

I 120 (K)

I 140

I 160

FIG. 54. Calculated detectivity of n-i-p--i SL detector at 2 0 # m wavelength. F is the optics F-number (after Ref. 306).

Infrared optoelectronics

153

9

-VII ,'

-

I 1 '°°

,

1600

1800

2000

2200

Photon w a v e n u m b e r (cm -t) FI6. 55. Calculated optical power absorbed in 1/~m thick InSb n-i-p-i SL consisting of a l0 nm doped layer at 1 x l0 is era -3 with 40 nm spacer layers (a); calculated optical power absorbed in l/~m of bulk InSb (b); measured photoconductive response of sample grown to the parameters of (a) (c); photoresponse spectra from bulk InSb (d) (after Ref. 310).

The above experiments have been done with n-i-p-i SLs slab doped at 1 x 1018 CIT1-3. More encouraging results can be achieved using 6-doping technique. (3t°) Suitable for infrared detection in the range of 8-12 #m doping SL with n- and p-type 6-doped layers on the base of the narrow-gap InAsSb alloy was propsed by Haas and Kirill. (3°8) The calculations showed that, with modest doping ( < 4 x 1012cm-2) and short periods ( < 300 A) these SLs exhibit significant optical absorption up to 12 #m at 77 K. Such a kind of device might exhibit higher performance than a device based on a compositional SL because of the smaller structural perturbation.

Theory

lO 11

_

~

e E

oo 10 lo

77K

180°FOV

\ \\\\

-- 77K

90K 140K~

109

I

I

2

4

I I 8

10

W a v e l e n g t h (~tm)

FiG. 56. Detection efficiency vs wavelength for n-/-p-i PbTe SL photoconductor (2n FOV, 800 Hz). The broken line represents the BLIP limit (after Ref. 20).

154

F.F. Slzov and A. ROGALSKI

PbTe doping SLs. PbTe doping SLs were grown epitaxially on cleaved (111) BaF2 substrates by hot-wall technique (HWT). O°9) The n- and p-layers were grown in two different H W T reactors, which were incorporated within the same vacuum chamber. Doping was achieved by adjusting the stoichiometry of the PbTe layers via Te pressure (by additional Te sources). The substrate temperature during growth in this method is typically 350°C, the source temperature---450°C, and the hot wall---550°C. Figure 56 illustrates the spectral dependence of detection on efficiency for PbTe doping SL photoconductor. For optimum bias, the blackbody response (Tb = 500 K) is close to 10a V/W at 90 K and detection efficiency reaches a value close to l0 II cm Hz~/2/W at the peak wavelength of 5.8 ktm. From the carrier lifetime measurements it was found that the observed lifetimes for PbTe doping SL are enhanced by nearly two orders of magnitude. Electronic structure and some electrical properties of these doping SLs were investigated by Bauer et al. (311"312)

7. I V - V I S U P E R L A T T I C E S A N D Q U A N T U M W E L L S I V - V I compositional SLs show a number of different properties not found in such structures made of I I I - V or I I - V I semiconductors. These properties are due to some special features of the bulk I V - V I materials connected with: (i) I V - V I semiconductors crystallize in the cubic NaCI structure; (ii) these semiconductors have direct band-gap at L point of the Brillouin zone, which gives rise to the multivalley band structure; (iii) the electron and hole effective masses are nearly equal and the surfaces of constant energy are almost mirror-like ellipsoids of revolution with the (111 ) direction as their main axis; (iv) static dielectric permittivity is high (E0 >/(102-103)) and strongly temperature dependent because of the softening of the transverse optic mode. As a consequence of these features, for example, the Coulomb scattering is inefficient in limiting the carrier mobility at low temperatures. Because of the symmetry of the cubic NaCI structure the optical absorption in the bulk I V - V I crystals does not depend on the polarization of light, though in SL it may depend very strongly on the polarization as well as on the direction of the propagation with respect to SL axes, because the constant energy ellipsoid directions can be oblique to any SL axis. (313'314) Due to the high values of ~0 there are no shallow hydrogen-like bound states in the gap, there are only deep impurity or defect states that can be both in the gap and in the conduction or valence bands. Because of the TABLE4. Types of IV-VI SL or MQW structures and the methods of their growth Growth Materials methods Type of structure References PbTe/Pb~_ xSnxTe HWE II staggered 318-320 (x ~<0.2) HWE I 321-325 FEM 326-328 PbSnTe/PbTeSe HWE II staggered 329-331 PbTe/SnTe VPE 332 HWE II misaligned 333,334 PbTe/PbI _xEuxTe HWE I 335-337 PbTe/PbEuSeTe MBE I 338-340 PbTe/CdTe ICB I 341 PbTe/PbS VPE 342-345 PbS/PbSe VPE I 345 HWE I 68 PbS/EuS VPE I 346, 347 PbSe/Pbl - xEuxSe MBE I 328,348 PbSe/Pbl _xCaxSe MBE I 328 HWE--hot-wall epitaxy, VPE--vapour-phase epitaxy, MBE--molecular beam epitaxy, ICB--ionized-cluster beam epitaxy, LAE---laser-assisted evaporatin, FEM--flash evaporation method.

Infrared optoelectronics

155

electrical activity of the metal vacancies (each gives two holes), and chalcogen vacancies (each gives two electrons), the conductivity type and the value of carrier concentrations in IV-VI constituents of a SL may, to a certain degree, be controlled by the growth temperature and the vapour pressure of the chalcogen. Several SL systems were already realized by various growth methods from IV-VI semiconductors. Some properties of IV-VI SL systems and the methods of their growth are reviewed e.g. in Ref. 315-317 (see also Table 4). Band offset in I V - V I SLs. Knowledge of the band offsets is very important for fundamental studies and practical device applications as it defines the types of the optoelectronic devices. Band-offsets have been studied in less detail in IV-VI compounds compared to III-V or II-VI materials. This study is more difficult due to narrow band-gaps of IV-VI constituents and also due to relatively large strain-related effects, as the lattice mismatch, as a rule, is rather large between IV-VI constituents and the substrates used for their growth (see Table 5). For example, for the narrow-gap PbTe/Pb~_xSnxTe system the conduction band-offset is the subject of a discussion which has not settled definitely by now. The conclusions of two leading groups dealing with these objects, obtained by the same method, are opposite (see Refs 318-320 and Refs 321-324 in Table 5, where the methods of growth and the types of IV-VI SLs are presented). For other IV-VI systems, basically type I structures are possible. Due to small values of the band gaps in IV-VI semiconductors, (e.g. in PbTe/Pb~ _xSnxTe system Eg = 0.19 and 0.08 eV at x = 0 and 0.20 respectively at T = 0 K) it is very important to take into account the strain-induced shift of the band edges. (321'323"32s'347) Moreover, one needs to take into account the large thermal expansion coefficients (about five times larger than for any other semiconductor (see Table 5)) which produces thermal strain-induced gap shifts which are of the same order as the quantum size effect. IV-VI heterojunctions have large dislocation densities except the rather rare case of relatively small lattice mismatch. The lattice mismatch appears to have a much more serious effect on devices in the PbSnTe material system than in the PbSSe one. C31s) Q W and SL IR lasers. IV-VI semiconductors are mainly used for applications in IR optoelectronics as IR-detectors for wavelengths 2 - 2-15 # m and as IR diode lasers for the region of wavelengths 2 - 3-45 #m. IV-VI laser diodes, as a rule, are used in spectroscopic applications. Only IV-VI SLs and QWs today form a real alternative for these applications in the IR region as with narrowing band-gap the stimulated emission is a dominating process of recombination in these structures in contrast, e.g. to HgCdTe-like narrow gap alloys and structures where the stimulated emission decreases with decreasing band-gap. The reason for this lies in the higher density of states and lower Fermi energies for the same injected carrier densities in IV-VI structures compared to II-VI or III-V materials and structures. This enhances the radiative recombination rate compared to the Auger one. TABLE 5. Properties of the lead chalcogenides and s o m e substrates Compound Pbo. s Sno.2Te

PbTe PbS PbSe BaFx CaF 2 KC1 KBr NaCI JIbE 17/2--E

a0, A T = 300 K

E,, eV (T = 0 K)

a, 10-rcm/K T = 300 K

(Cleavage)

6.432 6.460 5.94 6.12 6.20 5.40 6.291 6.599 5.650

0.090 0.190 0.286 0.165

20.0 19.8 20.0 19.0 18.0 19.0 44.6 37.6 39.2

(100) (100) (I00) (I00) (11 l) (11 l) (100) (100) (100)

156

F.F. S]zov and A. ROGALSKI

(a)

PbSnTe(well) I ~bSnSe( barrier ) r"

.'"

~] 7 [~PbTeS¢ ~,]PbTeSI :-

PbTe

(b) 1019

M-!

O

~

101s

"n

p-type ~

lO17

i;

2.5

I

3.7 8.9 Depth (p.m)

ii

I

1 1.7

FIG. 57. Structure of Pbl_xSnxTe MQW laser (a) and carrier concentration profile (b) (after Ref. 329).

The advantages of IV-VI QW and SL structures for IR laser applications are induced by the fact that the population inversion in these structures is more easily be obtained due to (i) the step-like density of states and effective carrier confinement, (ii) appropriate doping sequence of the constituents (see e.g. Fig. 57) and (iii) more effective mode control. These are the reasons for more effective operation even at elevated temperatures compared to diode lasers, as much lower threshold currents can be achievedJ34°,349-351) IV-VI diode lasers, depending on the wavelength of the emission 2~, as a rule can be used at temperatures T ~<80 K in CW operation, though higher temperatures of CW operation have been reported. (352) In pulsed operation they are used at T~< 120K. The current state-of-the-art work for maximum QW IV-IV lasers operating temperatures enables elevation of the temperature of CW laser operation up to 174 K (2° = 4.39 ym) and up to 270 K for pulsed operation (2° = 3.88/zm) as it was shown by Partin (33s) for lattice matched PbTe/PbEuTeSe QW laser. In PbSe/PbEuSe QW diode laser the operating temperature was as high as 220 K (2e = 4.4/~m). <35~)By Shinohara eta/. (329) PbSnTe/PbTeSe MQW lasers were obtained operating in pulsed mode up to T = 204 K (2, = 6/zm) or in CW mode up to T = 130 K (2e = 6.6 #m). Valeiko et alJ 32a) reported on stimulated emission of the PbEuSe, PbCaSe MQW structures at temperatures up to 260-280 K. Thus, from application point of view, these results mean that relatively simple and inexpensive cooling systems based on the Peltier or Joule-Thomson effect may be used at least for mid IR region IV-VI QW lasers. 8. CONCLUSIONS In this paper, semiconductor superlattice and quantum well concepts for infrared optoelectronic applications have been explored. Recent investigations on intersub-band optical transitions in chemically stable wide band-gap systems, such as GaAs/AIGaAs and related SL structures, showed that this intraband transition approach gives the opportunity to avoid the crystal growth and materials processing problems inherent to narrow-gap semiconductor compounds like HgCdTe. The initial results are promising for high uniformity MBE growth

Infrared optoclectronics

157

procedures over 3 in. wafers to produce the large area (e.g. 512 x 512) two-dimensional arrays, which can be tailored to particular IR band within 3-15 #m. Still, a real uniformity of arrays is under investigation. III-V strained layer type II SLs demonstrate severe metallurgical problems for fabrication of IR detectors, though some performance results with these systems are encouraging. In spite of the fact that the HgTe/CdTe SL system was the first from the new class of SL structures for IR optoelectronics, which stimulated a great deal of investigations in this direction, the potential area of applications of these structures is restricted mainly by interdiffusion of the components. IV-VI QW lasers form a real alternative to IV-VI diode lasers, e.g. in spectroscopic applications in 3-10 #m spectral region, due to possibility of more effective operation even at elevated (compared to 77 K) temperatures which make it possible to use more simple and inexpensive cooling systems. The performance of the single element long-wavelength SL and QW IR detectors are principally inferior in comparison with HgCdTe and related photodetectors operating at the same temperature within the same spectral range. But for large two-dimensional arrays the SL and QW concept is very promising due to high yield, uniformity and well established growth procedures. The technology and manufacture of the semiconductor SLs and MQWs for IR optoelectronics are now in the early stages of development, and there exist a number of questions that must be resolved, concerning, e.g.: optimization of high responsivity and low noise in connection with device parameters; uniformity, compositional and dimensional control, which are critically important in determining the characteristics of the device photoresponse; etc. To understand the above problems, further investigations are necessary.

REFERENCES 1. L. F.SAKI and R. TSU, IBM J. Res. Develop. 14, 61 (1970). 2. F. CAPASSO, In: Semiconductors and Semimetals, R. K. WmLARDSON and A. C. BEER (eds) Vol. 24, Academic Press, New York, p. 319 (1987). 3. M. KIMATA, M. DENDA, N. YUTANI, SH. IWADE and W. Tsu~ocm. Proc. SPIE, 930, 11 (1988). 4. D. D. Coon and R. P. G. KARUNASml, Appl. Phys. Lett. 45, 649 (1984). 5. G. C. OSBOURN, J. Vac. Sci. Technol. B2, 176 (1984). 6. J. N. SCHULMANand T. C. McGILL, Appl. Phys. Lett. 34, 663 (1979). 7. R. P. G. KARUNASIRI, J. S. PARK, K. L. WANG and LI-JEN CHENG, Appl. Phys. Lett. 56, 1342 (1990); R. P. G. KARUNASIRI, J. S. PARK, Y. J. MII and K. L. WANr, Appl. Phys. Lett. 57, 2585 (1990). 8. B. F. LEVINE, C. G. BETHEA, G. HASNAIN, J. WALKER and R. J. MAUK, Appl. Phys. Lett..f~3, 296 (1988). 9. B. F. LEwd, C. G. BEgat.A, G. HASN~dN, V. O. SX-~N,E. I~LW, R. R. AaaoTr and S. J. Hsir~, J. Appl. Phys. 56, 851 (1990). I0. A. ZUSSMAN, B. F. Lmrn~, J. M. Kuo and J. DE LONG, J. Appl. Phys. 70, 5101 (1991). 11. B. F. LEVlt~, S. D. GtmAPAL^ and R. F. KOPF, Appl. Phys. Lett. 58, 1551 (1991). 12. B. F. LEvlt~, S. D. GtmAPALA, J. M. KUO, S. S. P~I and S. HuI, Appl. Phys. Lett. 59, 1864 (1991). 13. S. Yu LARRY and S. Lt SHZNG, Appl. Lett. 59, 1332 (1991). 14. G. HASNAIN, B. L. SIvco and A. Y. Cno, Appl. Phys. Lett. 56, 770 (1990). 15. S. D. GtmAPALA, B. F. LEvn,~, D. Rn'~R, R. A. H^MM and M. B. PANlSH, Appl. Phys. Lett. 58, 2024 (1991). 16. S. D. Grin^PAL^, B. F. LEVINE, D. RATTER, R. A. HAMM and M. B. PANIStl, J. Appl. Phys. 71, 2458 (1992). 17. S. D. GtmAPALA, B. F. LFcI~, D. PdTTER, R. A. HAMM and M. B. P,u~mn, Appl. Phys. Lett. 60, 636 (1992). 18. S. R. KURTZ, L. R. DAWSON, TH. E. ZiPr.RRIAN and R. D. WHAt.EV, IEEE Electron Device Lett. 11, 54

(1990). 19. 20. 21. 22. 23.

R. P. G. KARUNASlRI, J. S. PARK and K. L. WANG, AppL Phys. Lett. 59, 2588 (1991). G. BAUER and W. J~TSCH, Proc. SPIE 943, 107 (1988). M. A. KiNCI-I, S. R. BOREI,I~O and A. SIMMONS,Infrared Phys. 17, 127 (1977). G. L. DESlr~FA_~iS,Semicond. Sci. Technol. 6, C88 (1991). W. ROLLS and D. V. EDDOLS, Infrared Phys. 13, 143 (1972).

158

F . F . SIzov and A. ROGALSKI

24. E. O. GOBEL and K. PLOOG, Prog. Quant. Electron. 14, 289 (1991). 25. K. PLOOG and G. H. DOHLER,Adv. Phys. 32, 285 (1983). 26. G. BASTARD, Wave mechanics applied to semiconductor heterostructures. Les Editions de Physique. Paris (1988). 27. M. JAROS, Rep. Progr. Phys. 48, 1091 (1985); M. JAROS, Physics and Applications of Quantum Wells and Superlattices. Oxford University Press (1989). 28. K. PLOOG,In: Physics and Applications of Quantum Wells and Superlattices, E. E. MENDEZand K. YONKLITZING (eds) NATO ASI Series, Series Physics, Vol. 170, p. 43, Plenum Press, New York (1987). 29. G. H. DOHLER, CRC Crit. Rev. Solid St. Mater. Sci. 13, 87 (1987). 30. L. ESAKI, IEEE J. Quant. Electron. 22, 1611 (1986). 31. D. L. SMITH and C. MAILH1OT, Rev. Modern Phys. 62, 173 (1990). 32. C. MAILHIOT and D. L. SMITH, Solid St. Mater. Sci. 16, 131 (1990). 33. F. STERN, In: Physics and Applications of Quantum Wells and Superlattices, E. E. MENDEZand K. YONKL1TZING (eds) NATO ASI Series Physics, Vol. 170, p. 133, Plenum Press, New York (1987). 34. S. SCHMITT-RaNK, D. S. CHEMLA and D. A. MILLER, Adv. Phys. 38, 89 (1989). 35. D. S. CHEMLA, O. A. MILLER and P. W. SMITH, In: Semiconductors and Semimetals, R. WILLARDSON and A. C. BEER (eds) Vol. 24, p. 279, Academic Press, New York (1987). 36. G. C. OSBOURN, P. L. GOURLEY, I. J. FRITZ, R. M. BIEFELD, L. R. DAWSONand T. E. ZIPPERIAN, ibid. p. 459. 37. F. CAPASSO, Science 235, 172 (1987). 38. Physics of Quantum Electron Devices, F. CAPASSO (ed) Springer, Berlin (1990). 39. C. WEISBUCH, In: Semiconductors in Semimetals, R. K. WILLARDSON and A. C. BEER (eds) Vol. 24, p. 1, Academic Press, New York (1987). 40. L. V. KELDYSH, Physika Tverdogo Tela 4, 2265 (1962) (in Russian). 41. G. BASTARD, Phys. Rev. B24, 5693 (1981). 42. G. BASTARD, Phys. Rev. B25, 7584 (1982). 43. M. ALTAP,ELLI, U. EK~NBERGand A. FASOLINO, Phys. Rev. B32, 5138 (1985). 44. J. N. SCHULMANand T. C. McGILL, Phys. Rev. B19, 6341 (1979). 45. J. N. SCHULMAIqand Y. C. CHANG, Phys. Rev. B24, 4445 (1981). 46. J. N. SCrIULMANand Y. C. CHANG, Phys, Rev. 1331, 2056 (1985). 47. A. S. DAVlDOV, Quant. Mech. Moscow (1963) (in Russian). 48. S. FLUGGE, Pract. Quant. Mech. Springer, Berlin (1971). 49. For an extensive survey of MBE, see Proc. 5th Int. Conf. Molecular Beam Epitaxy, J. Cryst. Growth 111, Nos 1-4 (1991). 50. T. J. CI-mUNGand H. SANKUR,Solid St. Mater. Sci. 15, 63 (1988); H. SANKUR and J. T. CI-~UNG, Appl. Phys. A47, 271 (1988). 51. E. P. O'REILLY, Semicond. Sci. Technol. 4, 121 (1989). 52. R. L. ANDERSON, Solid St. Electron. 5, 341 (1962). 53. W. A. HARRISON, J. Vac. Sci. Technol. 14, 1016 (1977); W. A. HARRISON, J. Vac. Sci. Technol. 113, 1231 (1985). 54. J. TERSOFF, Phys. Rev. 1330, 4874 (1984); J. TERSOFF, Phys. Rev. B32, 6968 (1985). 55. H. KROr~mR, J. Vac. Sci. Technol. B2, 433 (1988); H. KROMER. In: Proceedings of the NATO Advanced Study Institute on Molecular Beam Epitaxy and Heterostructures, Erice, Sicily, 1983, L. L. CHANO and K. PLOOG(eds) Martinus Nijhoff, The Netherlands (1984). 56. G. MARGARITONDO, Phys. Rev. B31, 2526 (1985); G. MARGARITONDO, Solid St. Electron. 29, 123 (1986). 57. J. M. LANCER, C. DELERtrE, M. LANNOO and H. HEINRICrt, Phys. Rev. B38, 7723 (1988); J. M. LANGER and H. HEINRICH, Phys. Rev. Lett. 55, 1414 (1985). 58. W. POLLARD, J. Appl. Phys. 69, 3154 (1991). 59. J. MEr,~NDEZ and A. PINCZUK, IEEE J. Quant. Electron. 24, 1698 (1988). 60. C. G. VAN DEWALLEand R. M. MARTIN, Phys. Rev. B34, 5621 (1986); C. G. VAN DEWALLEand R. M. MARTIN, J. Vac. Sci. Technol. B3, 1256 (1985). 61. J. A. VAN VECHTEN. J. Vac. Sci. Technol. !i3, 1240 (1985). 62. R. C. MILLER, A. C. GOSSARDand D. A. KLEINMANN, Phys. Rev. B32, 5443 (1985). 63. K. YAMANAKA, T. FUKUNAGA, N. TSUKADA, K. L. I. KOBAYASHI and M. IshqI, AppI. Phys. Lett. 48, 840 (1986). 64. H. OKIMURA, S. M1SAWA, S. YOSHIDA and S. GONDA, Appl. Phys. Lett. 46, 377 (1985). 65. M. O. WATANABE, J. YOSmDA, M. MASHITA, T. NAKANISHI and A. HAJO, J. AppL Phys. 57, 5340 (1985). 66. E. A. KRAUT, R. W. GRANT, J. R. WALDROP and S. P. KOWALCZYK, Phys. Rev. B27, 1965 (1983). 67. S. P. KOWALCZYK, J. T. CHEUNG,E. A. KRAUT and R. W. GRANT, Phys. Rev. Lett. 56, 1605 (1986). 68. T. K. Ch'u, D. AGASSl and A. MARTIr,mZ, Appl. Phys. Lett. 50, 419 (1987). 69. A. LECrINER, M. Kr,rEIDINGER,K. LuBr,£ and H. TraM, In: GaAs and Related Compounds, Las Vegas, Nevada, 1986, Inst. Phys. Conf. Ser. No. 83 (IOP, Bristol, 1986), p. 267. 70. H. HEINRICH, C. PANI-IUBER,A. EISENBEISS,H. PREIER and Z. FLIT, Superlattices and Microstructures 5, 175 (1989). 71. W. A. HARRISON and J. TERSOrr, J. Vac. Sci. Technol. 114, 1068 (1986). 72. F. BECrISTEOTand R. Er~DERLEIN, Semiconductor Surfaces and Interfaces. Akademie, Berlin, 1988. 73. C. G. VAN DE WALLE and R. M. MARTIN, Phys. Rev. B35, 8154 (1987). 74. J. TERSOFF, Phys. Rev. Lett. 56, 2755 (1986).

Infrared optoelectronics 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. lll. l l2. 113. 114. 115. 116. ll7. 118. 119. 120. 121. 122. 123. 124. 125.

159

Y. C. RUAN and W. Y. CLUNG, J. Appl. Phys. 64, 1271 (1988). S. MASSIDA, B. I. MIN and A. J. FREEMAN, Phys. Rev. 1135, 9871 (1987). K. K u ~ and R. M. M~a~TIN, Phys. Rev. B24, 3445 (1981). F. STERN, Phys. Rev. Lett. 33, 960 (1974). L. C, WEST and S. J. EGIASH, Appl, Phys. Lett. 46, 1156 (1985). K. W. Goos~N and S. A. LYON, Appl. Phys. Lett. 47, 1257 (1985). K. W. GOOSSENand S. A. LYON, J. Appl. Phys. 63, 5149 (1988). K. W. GOOS~N, S. A. LYON K. ALAVl, Appl. Phys. Lett. 53, 1027 (1988). G. HASNAIN, B. F. LEVINE, C. G. BETHEA, R. A. LOGAN, J. WALKER and R. J. MALIK, Appl. Phys. Lett. 54, 2515 (1989). R. P. G. K.~UNASIRX and K. L. WANG, J. Vac. Sci. Technol. B9, 2064 (1991). B. F. LEwNE, C. G. BETI-IEA,G. HASNA1N, J. WALKER and R. J. MALIK, Electron. Lett. 24, 747 (1988). A. D. WraCK, E. BATKE, D. HEITMAN and J. P. KOTTnAUS, Phys. Rev. B30, 4653 (1984). Y. C. C-"8AN~and R. B. JAMES, Phys. Rev. B39, 12672 (1989). C. L. YANG and D. S. PAN, J. Appl. Phys. 64, 1573 (1988). C. L. YANG, D. S. PAN and R. SO~tOANO. J. Appl. Phys. 65, 3253 (1989). E. R. BROWN and S. J. EGLASH, Phys. Rev. !141, 7559 (1990). D. L. SMITH, T. C. MCGILL and J. N. SCHULMAN,Appl. Phys. Lett. 43, 180 (1983). D. D. COON, R. KARUNASIRIand H. LIu, Appl. Phys. Lett. 47, 289 (1985). M. A. KINCH and A. YARIV, Appl. Phys. Lett. 55, 2093 (1989). G. C. OSnOURN, J. Vac. Sci. TechnoL A3, 826 (1985). B. F. LEVlNE, C. G. BETHEA, K. G. GLOGOVSKY,J. W. STAYTand R. E. LE1BENGUTH,Semicond. Sci. Technol. 6, CI14 (1991). L. J. KOZLOWSKI, G. M. WmLIAMS,G. J. SULLIVAN,G. W. FARLEY, R. J. ANDERSON, J. CI-mN, D. T. CHEUNG, W. E. TENNANT and R. E. DIWAINES, IEEE Trans. Electron. Devices 38, 1124 (1991). D. D. COON, R. P. G. KARUNASlRI and H. C. LIu, J. Appl. Phys. 60, 2636 (1985). M. K. BENEDICT, Proceed. SPIE 930, 87 (1988). B. F. LEVlNE, K. K. CHoI, C. G. BETHEA and J. MALIK, Appl. Phys. Lett. 50, 1092 (1987). R. R. CHOI, B. F. LEVINE, C. G. BETHEA, J. WALKER and R. J. MALIK, Appl. Phys. Lett. 50, 1814 (1987). B. F. LEVINE, K. K. CHOI, C. G. BETHEA, J. WALKER and R. J. MALIK, Appl. Phys. Lett. 51, 934 (1987). G. HASNA1N, B. F. LEVINE, C. G. BETHEA, R. R. ABBOTT and S. J. HSIEH, J. Appl. Phys. 67, 4361 (1990). J. C. SMITH, L. C. CHIU, S. MARGALIT, A. YARIV and A. Y. CHo, J. Vac. Sci. Technol. B1, 376 (1983). L. C. CHIU, J. S. SMITH, S. MARGALIT, A. YARIV and A. Y. CHO, Infrared Phys. 23, 93 (1983). A. YA. VUL, A. YA. SCHICK and Yu. V. SCHMARTSEV, J. Technic. Phys. 12, 257 (1986) (in Russian); A. YA. SCHICK, Physica Technica poluprovodnikov. 20, 1598 (1986) (in Russian, English translation: Soy. Phys. Semicond. 20 (1986)). E. ROSENCHER, E. MARTINET, E. BOCKENHOFF, PH. BOIS, S. DELAITRE and J. P. HIRTZ, Appl. Phys. Lett. 58, 2589 (1991). B. F. LEVINE, R. J. MALIK, J. WALKER, K. K. CHOI, C. G. BETHEA, D. A. KLEINMANand J. M. VANDENBERG, Appl. Phys. Left. 50, 273 (1987). A. HARWIT and J. S. HARRIS, Appl. Phys. Left. 50, 685 (1987). M. J. KANE, M. T. EMERY, N. APSLEY, C. R. WHITEHOUSE and D. LEE, Superlattices Microstruct. 5, 587 (1988). A. SEILMEIER,H.-J. HUBNER, M. WORNER,G. A. ABSTREITER,G. WEIMANNand W. SCLAPP,Solid St. Electron. 31, 767 (1988), H. SCHNEIDER, F. FUCHS, B. DISCHLER, J. D. RALSTON and P. KOIDL, Appl. Phys. Lett. 58, 2234 (1991). B. C. COVINGTON, C. C. LEE, B. H. HU, H. F. TAYLOR and D. C. STREIT, Appl. Phys. Lett. 54, 2145 (1989). P. VON ALLMEN, M. BERZ, K. REINHART and G. HARBEKE, Superlattices Microstruct. 5, 259 (1989). M. O. MANASRECH,F. SZMULOWlCZ,D. W. FISCHER, K. R. EVANSand C. E. STUTZ, Appl. Phys. Lett. 57, 1790 (1990). J. L. PAN, L. C. WEST, S. J. WALKER, R. J. MALIK and J. F. WALKER, Appl. Phys. Lett. 57, 366 (1990). B. F. LEVINE, A. Y. CHO, J. WALKER, R. J. MALIK, D. A. KLEINMAN and D. L. SIVCO, Appl. Phys. Lett. 52, 1481 (1988). H. ASAI and Yu. KAWAMURA, J. Appl. Phys. 68, 5890 (1990). H. ASAI and Y. KAWAMURA,Appl. Phys. Lett. 56, 1427 (1990). H. LOBENTANZER,W. KONIG,W. STOLZ,K. PLOOG, T. ELSAESSERand R. BAUERLE,Appl. Phys. Lett. 53, 571 (1988). X. Znou, P. K. BRATrACnAglA, G, HUGO, S. C. HONO and E. GULARI, Appl. Phys. Len 54, 855 (1989). F. MULLER, V. PETROVA-KOCH, M. ZACHAU, D. GRUTZMACHER, R. MEYER, H. JURGENSEN and P. BALK, Semicond. Sci. Technol. 3, 797 (1988). F. H. JULIEN, J.-M. LOURTIOZ, N. HERSCHKORN, D. DELACOURT, J. P. POCHOLLE, M. PAPUCHON, R. PLANEL and G. LE Roux, Appl. Phys. Left. 53, 116 (1988). B. F. LEVINE, C. G. BETHEA, K. K. CHOI, J. WALKER and R. J. MALIK, Appl. Phys. Lett. 53, 231 (1988). H. C. LIU and D. D. COON. Superlattices Microstruct. 3, 357 (1987). J. Y. ANDERSSON, L. LUNDQVlSTand Z. F. PASKA, Appl. Phys. Lett. 58, 2264 (1991).

160

F . F . SIZOV and A. ROGALSKI

126. S. G. GLrNAPALA, B. F. LEXqNE, L. P~IFmt and K. WEST, J. Appl. Phys. 69, 6517 (1991). 127. K. W. GOOSEs, S. A. LYON and K. ALAVl. Appl. Phys. Lett. 52, 1701 (1988). 128. V. V. OsWov, F. L. SEgZt~F.NKO and V. D. SCHADRIN. Physica Technicka Poluprovodnikov 23, 809 (1989) (in Russian, English transl; Soy. Phys. Semicond. 23, (1989)). 129. M. ZALUZ~', Solid St. Commun. 79, 1013 (1991); 82, 565 (1992). 130. T. EkS.~KSER, R. J. BAUERLE,W. KAISER, H. LOBENTANZER, W. STOLZ and K. PLOOG. Appl. Phys. Lett. 45, 256 (1989). 131, K. M. S. BANDANA,D. D. COON, O. BYtmGStn~G,Y. F. LIN and M. H. FRANCOMaE.Appl. Phys. Lett. 53, 1931 (1988). 132. J. W. Choe, O. BYNGStmG, K M. S. V. BANDARAand D. D. COON, Appl. Phys. Left. 56, 1679 (1990). 133, D. D. COON, K. M. S. V. BANDARA, O. BYUNGSUNG, J. W. C,OE, M. H. FRANCOMBE, Y. F. LIN and W. J. TAKEI, J. Vac. Sci. Technol. A9, 863 (1991). 134. D. J. NEWSON and A. KtmoaE, Semicond. Sci. Technol. 3, 786 (1988). 135, B. F. LEVlmL C. G. BETHEA, K. K. Crlol, J. WALKER and R. J. MALIK, J. Appl. Phys. 64, 1591 (1988). 136. B. K. JANOUSEK, M. J. DAUGHERTY, W. L. BLONd, M. L. ROSENnLUTH, M. J. O'LouoHLIN, H. KANTER, F. J. DE LUCOA and L. E. PERRY. J. Appl. Phys. 67, 7608 (1990). 137. D. Y. OBERLY, D, R. WAKE, M. V. KLEIN, T. HENDERSON and H. MORKOC, Solid St. Electron. 31, 413 (1988). 138. R. J. BAUERLE, T. ELSAESSER,W. KAISER, H. LOBENTANZER, W. STOLZ and K. PLOOG. Phys. Rev. B38, 4307 (1988). 139. A. SEILMEmR, H.-J. HUnteR, G. ABSTREITER, G. NEINMANN and W. SCHLAPP. Phys. Rev. Left. 59, 1345 (1987). 140. M. C. TATHAM, J. R. RYAN and C. T. FOXON, Solid St. Electron. 32, 1497 (1989). 141. F. A. RaDDOCH and B. K. ~DLEY, Physica 134B, 342 (1985). 142. B. K. RtOLEY, Phys. Rev. 1339, 5282 (1989). 143. J. K. JAIN and S. DAS SARMA, Phys. Rev. Left. 62, 2305 (1989). 144. D. J. NEWSON and A. KUROBE, Appl. Phys. Lett. 53, 2516 (1988). 145. S. V. KOZYREV and A. JA. SCHICK, Physica Technica Poluprovodnikov 19, 1667 (1965) (in Russian, English translation; Soy. Phys. Semicond. 19 0985). 146. C. G. BETttEA, B. F. LEVlNE, G. HASNAIN, J. WALKER and R. W. MALIK, J. Appl. Phys. 66, 963 (1989). 147. Z. IKomc, V. MILANOVIC and D. TJAPKIN. Appl. Phys. Lett. 54, 247 (1989). 148. A. JA. SCmCK. J. Technic. Physic. 15, NS, 40 (1989). 149. K. K. CHOl, B. F. LEVIrCE, C. G. BETHEA, J. WALKER and R. J. MALIK, Phys. Rev. Lett. 59, 2459 (1987). 150. K. K. CHOI, B. F. LEVINE, C. G. BETHEA, J. WALKER and R. J. MALIK, Appl. Phys. Lett. 52, 1979 (1988). 151. J. Y. ANDERSSON and G. LANDGREN. Inst. Phys. Conf. Set. 106, 731 (1990). 152. Z. E. PASKA, J. Y. ANDERSSON, L. LUNDQUISTand C. O. A. OLSSON, J. Cryst. Growth 107, 845 (1991). 153. D. D. COON, J. Vac. Sci. Technol. A8, 2950 (1990). 154. Y. J. Mll, R. P. G. KARUNASml, K. L. WANG, M. CHiN and P. F. YUH, Appl. Phys. Lett. 56, 1986 (1990). 155. D. AHN and S. L. CHUANG, Phys. Rev. 1335, 4149 (1987). 156. B. F. LEVI~, C. G. BETHEA, G. HASNAIN, V. O. SHEN, E. PEEVE, R. R. ABBOTTand S. J. HSmH, Appl. Phys. Left. 56, 851 (1990). 157. B. F. LEVINE, G. H. HASNAIN, C. G. BETHEA and NARESHCHAND, Appl. Phys. Left. 54, 2704 (1989). 158. M. ROSENBLLrrH, M. O'LOUGHLIN, W. BLOSS, F. DELuCCIA, H. KANTER, B. JANOUSEK, E. PERRY and M. DAUGHERTY, Proc. SPIE, N1283, 82 (1990). 159. W. BLOSS, M. O'LoUGHLIN and M. ROSENBLUTH, Proc. SPIE 1541 (1991). 160. E. PEEVE, F. BELTRAM,C. G. BETHEA, B. F. LEVINE,V. O. SHEN, S. J. HSmH and R. R. AnaoTr, J. Appl. Phys. 66, 5656 (1989). 161. C. G. BETHr.A, B. F. LEWNE, V. O. CHIN, R. R. AeBOTr and S. J. HSmH, IEEE Trans. Electron. Devices 38, 1118 (1991). 162. R. C. MILLER, D. A. KLE1NMANNand A. C. GOSSARD, Phys. Rev. B29 7085 (1984). 163. G. HASNAIN, B. F. LEVINE, D. L. SIVCO and A. Y. CHO, Appl. Phys. Lett. 56, 770 (1990). 164. U. K. I~DDY, J. CtmN, C. K. PENG and H. MARKOC, Appl. Phys. Lett. 48, 1799 0986). 165. B. F. LEVIte,, S. D. GUNAPALAand R. F. KOPF, Appl. Phys. Left. 58, 1551 (1991). 166. H. SCHNEIDER, F. FUCHS, B. DLSCHLER, J. D. RALSTON and P. KOIDL, Appl. Phys. Lett. 58, 2234 (1991). 167. S. D. G'UNAPALA,B. F. LEVINE, R. A. LOGAN, T. TANBUN-EK and D. A. HUMPHREY, Appl. Phys. Left. 57, 1802 (1990). 168. O. PdTTEg, R. A. HAMM, M. B. PANISn, J. M. VANDENBERG,D. GERSHONI, S. D. GUNAPALAand B. F. LEVINE, Appl. Phys. Lett. 59, 552 (1991). 169. S. D. GUNAPALA, B. F. LEVINE, D. RITTER, R. HAMM and M. B. PANISn, Proc. SPIE 1541, 11 (1991). 170. J. S. PARK, R. P. G. KARUNASlRI and K. L. WANG, Appl. Phys. Lett. 60, 103 (1992). 171. R. J. TURTON and M. JARos, Appl. Phys. Lett. 54, 1986 (1989). ,172. S. A. LYON, Surface Sci. 228, 508 (1990). 173. B. F. LEVINE, S. D. GUNAPALA and M. HGNG, Appl. Phys. Lett. 59, 1969 (1991). 174. A. KASTALSKY, T. DUFFIELD, S. J. ALL~N and J. HARBISON, Appl. Phys. Lett. 52, 1320 (1988).

Infrared optoclcctronics

161

175. BYUNGSUNG O., J. W. CHOE, M. H. FRANCOMBE, K. M. S. V. BANDARA, D. D. COON, Y. F. LIN and W. J. TAKE[, Appl. Phys. Left. 57, 503 (1990). 176. K. K. CHOI, M. DUrrA, P. G. N E W M A N and M. L. SAUNDERS, Appl. Phys. Lett. 57, 1348 (1990). 177. K. K. CHOI, M. DUTTA, R. P. MOEKIRK, C. H. K U A N and G. J. IAFRATE, Appl. Phys. Left. 58, 1533 (1991). 178. K.K. CHOI, L. FOTIADIS, M. M. TAYSUNG-LARA,W. CHANG and G. J. IAFRAT~, Appl. Phys. Lett. 59, 3303 (1991). 179. R. MALIK, L. LUNARDI, B. LEVINE,C. BETHEA,F. BELTRAM,S. RALPH, L. HOPKINSand F. CAPASSO,Proc. SPIE 1285, 76 (1990). 180. BYu~suNo O., J. W. CHOE, M. H. FRANCOMBE, K. M. S. V. BANDARA, E. SORAR, D. D. COON, Y. F. LIN and W. J. TAKEI, J. Vae. Sci. Technol. B9, 1979 (1991). 181. J. M. LLOYD, Thermal Imaging Systems, Plenum Press, N e w York (1975). 182. A. F. MII.TON, F. R. BARONE and M, R. KRUER, Opt. Eng. 24, 855 (1985). 183. G. D. BOI~MAN and C. COSTANZO, Opt. Eng. 26, 981 0987). 184. F. D. SHEPHERD, Proc. SPIE 930, 2 (1988). 185. N. BLUZER, Proc. SPIE 930, 64 (1988). 186. B. F. LEVINE, Appl. Phys. Left. 56, 2354 0990). 187. F. W. ADAMS, K. F. CUFF, G. GAL, A. HARWIT and R. L. WmTh~Y, Proc. SPIE 1541, 24 (1991). 188. N. T. GORDON, Semicond. Sci. Technol. 6, CI06 (1991). 189. C. L. JONES, B. E. MATTHEWS, D. R. PURDY and N. E. METCALFE, Semicond. Sci. Technol. 6, CII0 (1991). 190. A. ROSE, Concepts in Photoconductivity Allied Problems, John Wiley, New York (1963). 191. B. F. LEVlNE, Proc. SPIE 1362, 163 (1990). 192. G. C. OSaOUgN, J. Appl. Phys. 53, 1586 (1982). 193. G. C. OSaOURN, Phys. Hey. B27, 6126 (1983). 194. F. C. FRANK and J. H. VAN DER MERVE, Proc. Roy. Soc., Lond. A198, 216 (1949). 195. F. C. FRANK, J. Appl. Phys. 34, 117 (1963). 196. J. H. VAN DER MERVE, J. Appl. Phys. 34, 123 (1963). 197. J. W. MA'rTHEWS, J. Vac. Sci. Technol. 12, 126 (1975). 198. J. W. MATrHEws and A. E. BLAKESLEE,J. Cryst. Growth 32, 265 (1976). 199. P. VOlSIN, C. DELANDE, M. Voos, L. L. CHANG, A. SEGMULLER,C.-A. CHANG and L. ESAKI, Phys. Hey. BSO, 2276 (1984). 200. G. PLATERO and M. ALTARELLI, Phys. Hey. B36, 6591 (1987). 201. C. MAILHIOT and D. L. SMITH, Phys. Hey. B36, 2942 (1987). 202. G. C. OSBOURN, J. Vac. Sci. Technol. 134, 1423 (1986). 203. S. S. BORISOVA,I. F. MICHAILOV,L. S. PALATNIK,A. YU. SIPATOV,A. I. FEDORENKOand L. P. SCHPAKOVSgA'~A, Kristallographia 34, 716 (1989) (in Russian). 204. S. R. KURTZ, G. C. OSBOURN, R. M. BIEFELD, L. R. DAWSON and H. J. STEIN, Appl. Phys. Lett. $2, 831 (1988). 205. G. C. OSnOURN, Semicond. Sci. Technol. 5, $5 (1990). 206. D. K. ARCH, G. WICKS, T. TONAUE and J. L. STAUDEHMANN,J. Appl. Phys. 58, 3933 0985). 207. D. L. SMITH and C. MAILH1OT, J. Appl. Phys. 62, 2545 (1987). 208. C. MAILmOT and D. L. SMITH, J. Vac. Sci. Technol. A7, 445 (1989). 209. S. R. KURTZ, G. C. OSBOURN, R. M. BIEFELD and S. R. LEE, Appl. Phys. Lett. 53, 216 0988). 210. D. H. CHow, R. H. MILES, J. R. SODERSTROM and T. C. McGILI., J. Vac. Sci. Teehnol. BH, 710 (1990). 211. G. C. OSBOURN, 1EEE J. Quant. Electron. 22, 1677 (1986). 212. R. C. HUGHES, Opt. Eng. 26, 249 (1987). 213. G. S. LEE, Y. LO, Y. F. LIN, M. BEDAIR and W. D. LAIDIG, Appl. Phys. Lett. 47, 1219 (1985). 214. U R. DAWSON, J. Vac. Sci. Technol. 34, 598 (1986). 215. L. R. DAWSON, J. Cryst. Growth 98, 220 (1989). 216. R. A. STRADLING, Proc. SPIE 1361, 630 (1990). 217. I. T. FERGUSON,A. G. NORMAN, B. A. JOYCE, T. Y. SEONG, G. R. BOOKER,R. H. THOMAS,C. C. PHILLIPSand R. A. STRADUNG. Appl. Phys. Left. 59, 3324 (1991). 218. R. M. BIEFELD, J. R. WENDT and S. R. KUgTZ, J. Cryst. Growth 107, 836 (1991). 219. S. R. KURTZ, L. R. DAWSON, R. M. BIEFELD and G. C. OSBOURN. Proc. SPIE 930, 101 (1988). 220. P. K. CHIArqG and S. M. BEDAIR, J. Electrochem. Soc. 131, 2422 (1984). 221. R. A. STRADUNG, Phys. Scr. T35, 237 (1991). 222. M. Y. YEN, R. PEOPLE, K. W. WECrrr and A, Y. CHO, Appl. Phys. Lett. 52, 489 (1988). 223. S. R. KURTZ, R. M. BtEFELD, L. R. DAWSON, I. J. FRITZ and T. E. ZIPPEPaAN, Appl. Phys. Lett. 53, 1961 (1988). 224. C. MAILHIOT and D. L. SmTH, J. Vac. Sci. Technol. EL5, 1268 (1987). 225. G. A. SAI-HALASZ, R. TSU and L. ESAKI, Appl. Phys. Lett. 30, 651 (1977). 226. L. L. CI~NG, N. J. KAWAI, G. A. SAI-HALASZ, R. LUDEKE and L. ESAKI, Appl. Phys. Lett. 35, 939 (1979). 227. J. C. MAAN, Y. GULDNER, J. P. VIEREN, P. VOISIN, M. VOOS, L. L. CHANG and L. ESAKI, Solid St. Commun. 39, 683 (1881). 228. D. H. CHow, R. H. MILES, C. W. NW.H and T. C. MCGILL, J. Cryst. Growth 111, 683 (1991).

162

F . F . SIZOV and A. ROGALSKI

229. D. H. CHow, R. H. MILES, N. J. SCHULMAN,D. A. COLLINS and T. C. McGILL, Semicond. Sci. Technol. 6, C47 (1991). 230. R. FASI~, J. T. ZBOROWSKI, T. D. GOLDING, H. D. Sma, P. C. CHow, K. MATSUICm, B. C. COVINGTON, A. Cm, J. ZHENG and H. F. SCHAAKE, J. Cryst. Growth 111, 677 (1991). 23 I. I. SELA, I. H. CAMPaELL, B. K. LAURICH, D. L. SMITH, L. A. SAMOSKA,C. R. BOLOGNESI,A. C. GOSSARDand H. KROEMER, J. Appl. Phys. 70, 5608 (1991). 232. R. H. MILES, D. H. CHow and W. J. HAMILTON, J. Appl. Phys. 71, 211 (1992). 233. I. H. CAMPBELL,I. SELA)B. K. LAURiCH, D. L. SMITH, C. R. BOLOG~r.Sl, L. A. SAMOSKA,A. C. ~ A R D and H. KROEMER, Appl. Phys. Left. 59, 846 (1991). 234. S. R. KURTZ, L. R. DAWSON, TH. E. ZiPPERIAN and S. R. LEE, Appl. Phys. Left. 52, 1581 (1988). 235. S. R. KURTZ, L. R. DAWSON, R. M. BIEFELD, I. J. FRITZ and TH. E. ZIPPERIAN, IEEE Electron. Device Lett. 10, 150 (1989). 236. J. N. SCHULMANand T. C. McGILL, J. Vac. Sci. Technol. 16, 1513 (1979). 237. J. Vac. Sci. Technol. 21(1) (1982); A1(3) (1983); A3(1) (1984); A4(4) (1986); A5(5) (1987); A6(4) (1988); A7(2) (1989); A8(2) (1990) and 139(3) (1991). 238. J. Cryst. Growth 59 (1982); 72 (1985); 86 (1986) and 101 (1988). 239. J. P. FAURIE, IEEE J. Quant. Electron. 22, 1656 (1986). 240. J. L. STAUDENMANN,R. D. KNOX and R. D. HORNING, J. Cryst. Growth. 86, 436 (1988). 241. K. K. MAHAVADI,J. BLEUSE,S. SIVANANTHAMand J. P. FAURIE, Appl. Phys. Left. 56, 2077 (1990). 242. J. P. FAURm, X. CI-r~, S. SIVANANTHAM,J. RENO and P. S. WIJEWARNASURIJA)J. Vac. Sci. Technol. 135, 700 (1987). 243. X. CHU, S. SIVANANTHAMand J. P. FAURm. Superlattices Microstruct. 4, 173 (1988). 244. N. F. JOHNSON, P. J. HuI and H. EHRENR£ICH, Phys. Rev. Left. 61, 1993 (1988). 245. K. C. Woo, S. RAFOL and J. P. FAURIE, J. Vac. Sci. Technok AS, 3093 (1987), 246. Y. C. CHANG, J. N. SCHULMAN, G. BASTARD, Y. GULDNER and M. Voos, Phys. Rev. B31, 2557 (1985). 247. N. A. CADE, J. Phys. C: Solid State Phys. 18, 5135 0985). 248. Y. R. LIN-LIU and L. J. SHAM, Phys. Rev. B32, 5561 (1985). 249. A. W. BEAWISand M. JAROS, Phys. Rev. IM1, 7903 (1990). 250. A. W. BEAWIS, M. JAROS, A. ZORYK and I. MORRISON, Semicond. Sci. Technol. 5, 1051 (1990). 251. M. JAROS, A. ZORYK and D. NINNO, Phys. Rev. B35, 8277 (1987). 252. G. BASTARD, Phys. Rev. Lett. 60, 2561 (1988). 253. C. L. C'ESAR, N. N. ISLAM, R. D. FELDMAN, R. F. AUSTIN, O. S. CHEMLA, L. C. WEST and A. E. DIGIOVANNI, Appl. Phys. Lett. 56, 283 (1990). 254. T. C. McGILL, G. Y. Wu and S. R. HETZLER, J. Vac. Sci. Technol. A4, 2091 (1986). 255. J. R. MEYER, F. J. BARTOLI, C. A. HOFFMAN and L. R. RAM-MOHAN, Phys. Rev. Lett. 64, 1963 (1990). 256. J. R. MEYER, F. J. BARTOLI, C. A. HOFFMAN and J. N. SCHULMAN,Phys. Rev. B38, 12457 (1988). 257. J. R. MEYER, C. A. HOFFMAN, F. J. BARTOLI and J. N. SCHULMAN. J. Vac. Sci. Technol. A7, 404 0989). 258. J. R. MEYER, R. J. WAGNER, F. J. BARTOLI, C. A. HOFFMAN, M. DOBROWOLSKA, T. Woyrowcz, J. K. FURDYNA and L. R. RAM-MOHAN, Phys. Rev. 1342, 9050 (1990). 259. C. A. HOFFMAN, J. R. MEYER, F. J. BARTOLI, J. W. HAN, J. W. COOK, J. F. SCHETZINAand J. N. SCHULMAN, Phys. Rev. 1339, 5208 (1989). 260. N. F. JOHNSON, P. M. Hut and H. EHRENREICH, Phys. Rev. Left. 61, 1993 0988). 261. J. GULDNER, G. BASTARD,J. P. VIEREN, M. VooS, J. P. FAURIE and A. M. MILLION, Phys. Rev. Lett. 51, 907 (1983). 262. Y. GULDNER, G. BASTARD, J. P. VIEREN, M. VOOS, J. P. FAURIE and A. M. MILLION, Surface Sci. 142, 593 (1984). 263. J. P. BAUKUS, A. T. HUNTER, O. J. MARSH, C. E. JON~S, G. Y. Wu, S. R. HETZLER, T. C. McGILL and J. P. FAURIE, J. Vac. Sci. Technol. A4, 2110 (1986). 264. J. M. BERRO1R, Y. GULDNER, J. P. VIEREN,M. VOOS and J. P. FAURIE, Phys. Rev. 1334, 891 (1986). 265. J. M. BERRO1R, Y. GULDNER and M. Voos, IEEE J. Quant. Electron. 22, 1793 (1986). 266. J. N. SCHULMAN, O. K. WU, E. A. PATTEN, J. W. HAN, Y. LANSARI, L. S. KIM and J. F. SCHETZINA, Appl. Phys. Lett. 53, 2420 0988). 267. J. M. PEREZ, R. J. WAGNER, J. R. MEYER, J. W. HAN, J. W. COOK and J. F. SH~TZINA, Phys. Rev. Left. 61, 2261 (1988). 268. C. L. CESAR, M. N. ISLAM, R. D. FELDMAN, R. SP1TZER, R. F. AUSTIN, A. E. DIGIOVANN1, J. SHAH and J. ORENSTEIN, Appl. Phys. Lett. 54, 745 (1989). 269. M. DOBROWOLSKA, T. WOJTOWlCZ, J. K. FURDYNA, J. R. MEYER, R. D. FELDMAN, R. F. AUSTIN and L R. RAM-MOHAN, Appl. Phys. Lett. 57, 1781 (1990). 270. T. M. Duc, C. Hsu and J. P. FAURIE, Phys. Rev. Left. 58, 1127 (1987). 271. J. P. FAURIE, C. HSU and T. M. Duc, J. Vac. Sci. Technol. AS, 3075 (1987). 272. Y. LANSARI,J. W. HAN, S. HWANG, L. S. KIM, J. W. COOK, J. F. SCHETZINA,J. N. SCHULMANand N. OTSUKA, J. Vac. Sci. Technol. B7, 241 (1989). 273. R. SPORKEN, S. SlVANANTHAN,J. P. FAURm, D. H. EHLERS, J. FRAXEDAS,L. LEY, J. J. PW,EAUXand R. CAUDANO, J. Vac. Sci. Technol. A7, 427 (1989). 274. Z, YANG, Z. Yu, Y. LANSARI, J. W. COOK and J. F. SCVlETZlNA.J. Vac. Sci. Technol. 139, 1805 (1991). 275. C. R. BECKER, Y. S. Wu, A. WAAG, M. M. KRAUS and G. LANDWEHR, Semicond. Sci. Technol. 6, C76 (1991). 276. J. TERSOFF. Phys. Rev. IMO, 10615 (1989).

Infrared optoelectronics

163

277. C. G. VAN DE WALLE and R. M. MARTIN, Phys. ReG. B37, 4081 (1988). 278. P. M. HuI, H. EHRENREICH and N. E. JOnNEON, J. Vac. Sci. Teclmol. A7, 424 (1989). 279. R. J. WAGNER, J. M. PEgEZ, J. R. MEYER, J. W. HAN, J. W. COOK and J. F. Scr~rzINA, J. Vac. Sci. Technol. AT, 411 (1989). 280. M. Voos, J. MANAgSES,J. M. BERROIR, Y. GULDNER, J. P. VIEREN, X. CHU and J. P. FAtram, Surface Sci. 228, 37 (1990). 281. J. R. MEYER, C. A. HOFFMAN and R. J. BARTOLI, Semicond. Sci. Technol. 5, $90 (1990). 282. J. P. FAURm, A. MILLION and J. PIAGUET, Appl. Phys. Lett. 41, 713 (1982). 283. J. T. CnEUNG, G. NIIZAWA, J. MOYLE, N. P. ONG, B. M. PAINE and T. VP,~LANG, J. Vac. Sci. TechnoL A4, 2086 (1986). 284. L. C i t r o n , R. G. MANI, J. R. ANDERSON and J. T. CHFJ.rNG. Solid. St. Commun. 75, 341 (1990). 285. T. H. MYEgS, R. W. YANKA, K. A. HARRIS, A. R. REISINGER,J. HAN, S. HWANG, Z. YANG, N. C. GILES, J. W. COOK, J. F. SCHETZINA, R. W. GREEN and S. McDEVITT, J. Vac. Sci. Technol. A7, 300 (1989). 286. D. J. LEOPOLD, J. G BROERMAN, D. J. PETERMANand M. L. WROGE, Appl. Phys. Lett. 52, 969 (1988). 287. E. A. PATTEN, K. KOSAI, T. N. CASSELMAN, J. N. SCHULMAN, Y. CH. CHANG and J. L. STAUDENMAmq, J. Vac. Sci. Technol. A5, 3102 (1987). 288. N. F. JOHNSON and H. EHRENREICH, Surface Sci. 228, 197 (1990). 289. S. R. HETZLER, J. P. BAUKUS, A. T. HUNTER, J. P. FAURIE, P. P. CHOW and T. C. MCGILL, AppL Phys. Lett. 47, 260 (1985). 290. J. RENO, I. K. Sou, J. P. FAURIE, J. M. BERROIR, Y. GULDNER and J. P. VIEREN, Appl. Phys. Lett. 49, 106 (1986). 291. D. K. ARCH, J. P. FAURIE, J. L. STAUDENMANN,M. HmBS-BRENNERand P. CHOW. J. Vac. Sci. Technol. A4, 2101 (1986). 292. J. P. MEYER, D. J. ARNOLD, C. A. HOFFMAN, F. J. BARTOLIand L. R. RAM-MOHAM.J. Vac. Sci. Technol. 119, 1818 (1991). 293. N. P. ONG, J. K. MOYLE, J. B ~ and J. T. CHEUNG. J. Vac. Sci. Technol. A5, 3079 0987). 294. Z. YANG, Z. Yu, Y. LANSARL J. W. COOK, and J. F. SCnETZINA. J. Vac. Sci. Technol. 119, 1805 (1991). 295. E. R. YOUNGDALE,C. A. HOFFMAN,J. R. MEYER, F. J. BARTOLI,X. CHU, J. P. FAURIE,J. W. HAN, J. W. COOK and J. F. SCHETZINA, J. Vac. Sci. Technol. A7, 365 (1989). 296. M. W. GOODWIN, M. A. KINCH and R. J. KOESTLER. J. Vac. Sci. Technol. A6, 2685 (1988). 297. P. A. CLIFTON, J. T. MULLINS, P. O. BROWN, N. LOVERGINE,A. BRINKMAN and J. WOODS, J. Cryst. Growth 99, 468 (1990). 298. M. Voos, J. MANASSES,Y. GULDNER, J. M. BERROIR,J. P. VIERRENand J. P. FAURIE, Superlattices Microstruct. 10, 311 (1991). 299. J. MANASSES,J. M. BERROIR,Y. GULDNER, J. P. VIERENand J. P. FAURIE, Semicond. Sci. Technol. 6, C80 (1991). 300. K. A. HARRIS, S. HWANG, Y. LANSARI, R. P. BURUS, J. W. COOK and J. F. SCHETZINA, J. Vac. Sci. Technol. BS, 699 (1987). 301. M. DOBROWOLSKA, Z. YANG, H. LUG, J. K. FURDYNA, K. A. HARRIS, J. W. CX)OK and J. F. SCHETZlNA, J. Vac. Sci. Technol. AS, 3089 (1987). 302. H. KRENN, K. KALTENEGGER,T. DIETL, J. 8PALEK and G. BAUER, Phys. Rev. B39, 10918 (1989). 303. K. PLOOG and G. H. DOHLER, Adv. Phys. 32, 285 (1983). 304. G. H. DOHLER, IEEE J. Quant. Electron. 22, 1682 (1986). 305. G. H. DOHLER, Optic. Quant. Electron. 22, 121 (1990). 306. J. MASERJIAN, F. J. GRUNTHANERand C. T. ELLIOT, Infrared Phys. 30, 27 (1990). 307. C. C. PHILLIPS,Appl. Phys. Lett. 56, 151 (1990). 308. K. C. HAAS and D. J. KIRILL, J. Appl. Phys. 68, 1923 (1990). 309. W. JANTSCH, K. LISCHKA, A. EISENBEIS, P. PICHLER, H. CLEMENSand G. BAUER, Appl. Phys. Lett. 50, 1654 (1987). 310. C. C. HOOGE, C. C. PHILLIPS, R. H. THOMAS, S. D. PARKER, R. L. WILLIAMSand R. DROOPAD, Semicond. Sci. Technol. 5, $319 (1990). 311. P. PICHLER,H. CLEMENS,H. KRENN,J. OSWALD and G. BAUER, Superlattices Microstruct. 3, 225 (1987). 312. W. JANTSC8, G. BAUER, P. PICHLER and H. CLEMENS, Appl. Phys. Left. 47, 738 (1985). 313. M. ZALUZNY, Acta Phys. Polonica A75, 19 (1989). 314. J. V. GUMENJUK-SICHEVSKAYAand F. F. SlZOV, Ukrainian Fiz. Zhurn. 34, 1811 (1989) (in Russian). 315. D. L. PARrm, In: Semiconductors and Semimetals, T. P. PEARSALL(ed.) Vo1. 33, p. 311, Academic Press, New York (1991). 316. J. W. TOMM, K. H. HERRMANN and A. E. YUNOVICH, Phys. Stat. Solid A122, 11 (1990). 317. F. F. StaGy, Acta Phys. Polonica. A79, 83 (1991). 318. H. KINOSHITA and H. FUJ1YASU,J. Appl. Phys. 51, 5845 (1980). 319. K. MURASE, S. SmMOMURA, S. TAKAOKA, A. ISmDA and H. FUJIYASU, Superlattices Microstruct. 1, 177 (1985). 320. S. SmMOMURA,Y. URAKAWA,S. TAKAOKA,K. MURASE,A. ISHIDAand H. FUJIYASU.Superlattices Microstruct. 7, 5 (1990). 321. M. KRIECHMAN, K. E. AMBROSH, E. J. TAMOR, H. CLEMENSand G. BAUER, Phys. Rev. !!30, 3394 (1984). 322. P. PICHLER, E. J. FANTNER, G. BAUER and H. CLEMENS. Superlattices Microstruct. 1, I (1985). 323. M. KRmCHBAUM, P. KOCEVAR, H. PASHER and G. BAUER. IEEE J. Quant. Electron. 24, 1727 (1988). 324. M. KRIECHnAUM, H. PASrmR, P. ROTHLEIN, G. BAUER and H. CLEMENS, Superlattices Microstruct. 5, 93 (1989).

164

F . F . SIZOV and A. ROGALSKI

325. F. F. Slzov, V. V. TETYORKIN,J. V. GUMENJUK-SICHEVSKAYAand M. V. APATSKAYA.Superlattices Microstruct. 9, 483 (1991). 326. M. V. VALEIKO,I. I. ZASAVITSKII,A. V. MATVEENKOand B. N. MATSONASHVlLI,Zh. Eksper. Teor. Fiz, 43, 140 (1986) (in Russian). 327. M. V. VALEIKO,I. I. ZASAVITSKII,A. V. MATVEENKO, B. N. MATSONASHVILIand D. A. SAKSEEV,Fig. Tekhn. Poluprov. 21, 57 (1987) (in Russian). 328. M. V. VALEIKO, I. I. ZASAVITSKII,A. V. MATVEENKOand B. N. MATSONASHVILI,Superlattices Microstruct. 9, 195 (1991). 329. K. SmNomemA, Y. N1smv~A, H. EBE, A. ISHmA and H. FunYASU, Appl. Phys. Lett. 47, 1184 (1985). 330. A. ISmDA, M. AO~ and H. FunYASU, £ Appl. Phys. 58, 797 (1985). 331. A. ISHID^, H. FUJIYASU, H. EBE and K. SmNo~a~A, £ Appl. Phys. 59, 3023 (1986). 332. M. A. TAMOR, H. HOLLOWAY, L. C. DAvis, R. J. BAmO and R. E. CHASE, Superlattices Microstruct. 4, 493 (1988). 333. A. ISHIDA, M. AOKI and H. FUJIYASU, .]. Appl. Phys. 58, 1901 (1985). 334. S. T^KAOKA, T. OKUMURA, K. MURASE, A. ISmDA and H. FUJIYASUSolid Sl. Commun. 58, 637 (1986). 335. A. Is810^, S. MATStrURA and H. FUJIYASU, Superlattices Microstruct. 2, 575 (1986). 336. A. ISmDA, S. MATSUURA, M. MIZUNO and H. FuJIYASU, Appl. Phys. Lett. 51, 478 (1987). 337. T. N^KAMURA, A. ISmDA and H. FUJIYASU, Thin Solid Films 161, 149 (1988). 338. D. L. PARXaN, Superlattices Microstruct. 1, 131 (1985). 339. L. S. KIM, H. D. DREW, R. E. DOEZEMA, J. P. HEREMANS and D. L. PARTIN, Phys. Rev. B35, 3521 (1987). 340. D. L. PARTIN, IEEE J. Quant. Electron. 24, 1716 (1988). 341. T. TAKAJI, H. TAKAOKA, Y. KURIYAMAand K. MATSUBARA. Thin Solid Films 126, 149 (1985). 342. L. S. PALATNIK and A. I. FEDORENKO, J. Cryst. Growth. 52, 917 (1981). 343. O. A. MIRONOV, S. V. CmSTYAKOV, I. YU. SKRYLIOV,V. V. ZORCHENKO, B. A. SAWTSKILA. YU. SIPATOVand A. I. FEDORENKO. Zh. Eksper. Teor. Fiz. 50, 300 (1989) (in Russian). 344. F. F. SIzOV, V. V. TETYORKIN and S. N. DAWDENKO. Dokl. Ukranian Acad. Sci. N6, 68 (1992) (in Russian). 345. I. V. KOLESNIKOV,A. N. KOVALEV,A. Yu. SIPATOV,V. I. PARAMONOV,A. I. FEDORENKOand A. E. YUNOVICH. Fiz. Technol. Poluprov. 23, 960 (1989) (in Russian). 346. I. V. KOLESNIKOV,V. A. LITVINOV,A. Yu. SIPATOV,A. I. FEDORENKOand A. E. YUNOVICH, Zh. Eksper. Teor. Fiz. 94, 239 (1988) (in Russian). 347. I. V. KOLESNIKOVand A. Yu. SWATOV, Fiz. Tekhn. Poluprov. 23, 954 (1989) (in Russian). 348. K. H. BACHEM, P. NORTON and H. PREmR, Springer SeT. Solid St. Sci. 53, 147 (1984). 349. A. P. SHOTOV and Yu. G. SELIVANOV.Semicond. Sci. Technol. 5, $27 (1990). 350. D. L. PARTIN, R. F. MAJKOWSK1and D. E. SWETS. J. Vac. Sci. Technol. B3, 576 (1985). 351. R. ROSMA, A. KATZIR, P. NORTON, K. H. BACHEM and H. M. PREIER. IEEE J. Quant. Electron. 23, 94 (1987). 352. J. N. WALPOLE, A. R. CALAWA, T. C. HARMAN and S. H. GROVES. Appl. Phys. Lett. 28, 552 (1976).