Gallium arsenide heterostructures

Gallium arsenide heterostructures

Chapter 2 GALLIUM ARSENIDE HETEROSTRUCTURES Eric Donkor Department of Electrical and Computer Engineering, University of Connecticut, Storrs, Connect...

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Chapter 2

GALLIUM ARSENIDE HETEROSTRUCTURES Eric Donkor Department of Electrical and Computer Engineering, University of Connecticut, Storrs, Connecticut, USA Contents 1. 2.

3.

4.

5.

6. 7.

Introduction 1.1. Growth of GaAs Heterostructures 1.2. Material Characterization Crystal Growth and Properties of GaAs 2.1. Crystal Growth 2.2. Impurities and Deep Levels 2.3. Crystal Structure and Lattice Properties 2.4. Electronic and Electrical Properties Growth and Material Properties of GaAs Heterostructures 3.1. Introduction 3.2. Critical Thickness of Strained-Layer Quantum Wells 3.3. Heterostructures of the Type III-V/GaAs 3.4. Heterostructures of the Type III^-IIIi_^-V/GaAs 3.5. Heterostructures of the Type III-V;,-Vi_^/GaAs 3.6. Heterostructures of the Type (III;,-IIIi_;,)^-IIIi_3, - V/GaAs 3.7. Heterostructures of the Type III^-IIIi_j,-V^-Vi_^/GaAs Physical Properties of GaAs-Based Quantum Well Structures and Superlattices 4.1. Introduction 4.2. Quantum Wells Energy Levels 4.3. Electrons and Holes in Superlattices GaAs Heterostructure Field Effect Transistors 5.1. Introduction 5.2. Energy Bands in Modulation-Doped Heterojunctions 5.3. Device Characteristics GaAs Heterostructure Bipolar Transistors 6.1. Introduction 6.2. HBT Modeling and Characteristics GaAs-Based Heterostructure Optoelectronic Devices 7.1. Introduction 7.2. GaAs-Based Heterostructure Lasers References

81 82 84 85 85 85 86 87 88 88 88 89 90 95 95 95 95 95 96 98 99 99 101 101 103 103 103 104 104 104 104

1. INTRODUCTION In 1970, Esaki and Tsu [5] predicted that such a structure has quantization of the electronic energy states, hole energy states, and density of states. One of the early experimental demonstrations of the quantum-mechanical characteristics of GaAs heterostructures was reported by Dingle et al. [6] and a year later by Chang et al. [7].

Gallium arsenide (GaAs) heterostructures are ultrathin heteroepitaxial layers of binary, tertiary, quaternary, or quinary III-V semiconductor alloys grown on GaAs substrates. The semiconductor heterostructure concept was first presented by Kroemer [1] in 1963 and rapidly developed in the 1970s [2-4].

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Handbook of Advanced Electronic and Photonic Materials and Devices, edited by H.S. Nalwa Volume 1: Semiconductors Copyright © 2001 by Academic Press All rights of reproduction in any form reserved. 81

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DONKOR

Heterostructures are commonly classified into single quantum The SEEDs operate on changes in the optical absorption induced wells (SQWs), double quantum wells (DQWs), multiple quan- by an electric field normal to the growth direction of the hettum wells (MQWs), and superlattices (SLs). A SQW is formed erostructure [19], according to the Franz-Keldysh effect [20, 21]. between smaller bandgap and wider bandgap materials. A DQW The quantization effect in quantum well structures causes the is formed if the smaller bandgap semiconductor is sandwiched resulting absorption spectrum to have large discrete steps. The between wider bandgap materials. If multiple quantum wells wavelengths of these absorption steps shift when the quantum (QWs) are stacked together, the structure formed is a MQW or well structure is placed under the influence of an electric field. SL. A SL is formed if the layers are so thin that carriers are able Furthermore, distinctive peaks exist in the absorption spectrum to tunnel from well to well. of quantum wells. These peaks also shift upon the apphcation of If the QW width is less than the de BrogHe wavelength of the an electric field. This peak shift is called the quantum confined carriers, which is about 100 A in GaAs, then the electrons and Stark effect, which is the basic phenomenon underlying the operholes can be spatially confined into two, one, or zero dimensions. ation of the more common heterostructure-based electrooptic A two-dimensional carrier confinement system is termed a quan- modulators. tum well structure, a one-dimensional carrier confinement system is called a quantum wire structure, and a zero-dimensional carrier confinement system is called a quantum dot structure. Carrier 1.1. Growth of GaAs Heterostructures confinement can be achieved either by an electrostatic potential 1.1.1. Metal-Organic Chemical Vapor Deposition Growth created by delta doping, by modulation doping, or by virtue of Metal-organic chemical vapor deposition (MOCVD) has evolved the band offset at the heterointerfaces. Evolution of GaAs heterostructure electronic devices began as a major technology [22-25] for the growth of GaAs hetin 1980 when Mimura et al. [8] succeeded in developing a high erostructures. The layers are grown by transporting different electron mobility transistor. Shortly thereafter, Delagebeaudeuf precursors or reactants in the vapor phase, under controlled et al. [9] and Solomon and Morkoc [10] published their ver- pressure, into a reactor (vertical, horizontal, or barrel) chamber sions named two-dimensional electron gas FETs and modulation- [26, 27] that holds the semi-insulating GaAs substrate. Alkyls of doped field effect transistor, respectively. Since then many new the group III metals and hydrides of the group V elements are heterostructure field effect transistors (HFETs) have evolved. typical precursors. Tables I and II list some common group III Some of the new devices are quite different in detail from the and group V precursors and their properties. conventional HFET. The motivation for improvement is mainly Three techniques have been introduced to improve the the need for high-current-drive field effect transistors (FETs) for MOCVD growth processes: plasma-enhanced (PE-MOCVD) digital electronics, high-current-high-breakdown-voltage power [28], atomic layer epitaxy (ALE) [29], and low-temperature FETs, and low-noise microwave and millimeter-wave FETs. (LT-MOCVD) [30] methods. In the PE-MOCVD growth, the The heterojunction bipolar transistors (HBTs) form another plasma induces precracking of the precursors into the various major class of heterostructure electronic devices that was first constituents, thereby facilitating the controlled incorporation of reported by Kroemer [11, 12]. The unique feature of HBT is the use of a wide bandgap emitter and a smaller bandgap base. Thus, a band offset is produced at the emitter-base heterointerface Table I. Properties of Common Group III Metals for the Epitaxial that favors electron injection into the base and retards hole injecGrowth of Some III-V Alloys on GaAs Substrate tion into the emitter. In addition, the base of the HBT is heavVapor pressure'' ily doped, resulting in minimization of the device parasitics and Melting Boiling increased current gain [13]. Consequently, the HBT has greater Precursor point (°C) point (°C) a b{Y.) ;?(torr)/r (°C) high-frequency response. 8.224 2134.83 2.2/0; 9/20 126 15 Gallium arsenide heterostructure-based optoelectronic TMAl 186(207) 10.784 3625 0.5/55 -52.5 devices can be laser sources, photodetectors, and modulators. TEAl 154 8.92 2575 2/25 Heterostructure lasers are more pervasive. They are classified as DMAIH 0.5/37 TIBAl 4.3 short wavelength (0.6-0.98-/xm), long wavelength (1.3-1.6-)Ltm), 8.501 1824 64.5/0; 66.0/0; 55.8 TMGa -15.8 and very long wavelength (2.0-30-/xm) lasers [14]. An alternative 178/20 classification scheme for heterostructure lasers is based on the TeGa 9.172 2532 143 3.4/20; 16/43 -82.5 nature of carrier confinement [15]. This leads to single quantum TIBGa 4.769 1718 0.078/18 well lasers, multiple (including double heterojunction) quantum TMGa—TMP 0.13/0; 1.71/20 56-57 well lasers, separate confinement quantum well lasers, which TMGa—TEP 0.008/0; 0.04/20 32-35 provide different confinement for carriers and photons, and TMGa—TMAs 1.3/0; 5.3/20 23-24 graded-index separate confinement quantum well lasers. 10.520 3014 0.3/0 135.8 TMIn 88 184 1.7/20 -32 Gallium arsenide heterostructure-based photodetectors [16, TEIn Sublimes at 50 Chap. 11; 17] transform electromagnetic radiation into electri- CpIn, (CsHjIn) (0.01 mm) cal signals. They offer high speed, high sensitivity, high quantum 0.85/17 EDMIn yield, and low intrinsic noise performances. Gallium arsenide het0.003/0; 0.03/20 TMIn—TMN 94-96 erostructure photodetectors that rely on interband transitions in 0.04/0; 0.22/20 TMIn—TMP 43-45 quantum well structures are often designed for the visible region, 0.0004/0; TMIn—TEP 33-36 whereas those that utilize intersubband transitions are designed 0.0003/20 to operate in the mid and far infrared region. 0.27/0; 1.2/20 TMIn—TMAs 28-29 The most common heterostructure-based electrooptic modulator is the self-electrooptic effect device (SEED) [18]. ' log(;?[torr]) = a- h/T.

83

GALLIUM ARSENIDE HETEROSTRUCTURES Table II. Properties of Common Group V Metals for the Epitaxial Growth of Some III-V Alloys on GaAs Substrate Vapor pressure*" Precursor P PH3 TMP TEP IBP TBP As ASH3 TMAs TEAS DMAs DEAs TBAs PhAsH2 TMSb TESb TMBi

Melting point (°C)

Boiling point (°C)

a

MK)

p{ton)IT

(°C)

1/260 -84 -88(-85) -20 4

38 127 78 54

7.7627 8.035 7.578 7.586

1518 2065 1648 1539

0.5/55 46.5/50 112/25 141/10 1/370

-87.3

-62.5 50 140

7.3936

1456

7.532 7.339 7.243 8.47 7.7068

1443 1680 1509 2410 1697

238/20 5/20 15.5/37 176/0 40/20 81/10 1.8/20

7.628

1816

-1

36.3 102 65

-87.6 -98 -107.7

80.6 160 110

4/25 27/20

' log(p[torr]) = a- b/T.

the different chemical elements in the alloy formation at lower temperatures. In ALE growth, the substrate is separately and alternatively exposed to the precursors containing the group III and group V elements. This alternation allows for better control of the growth process at the monolayer level. In LT-MOCVD growth, the growth rate of the layers is less dependent on temperature. Thus the growth rate can be held constant during the process. This enables layers to be grown with uniform thickness and composition, and interfaces have abrupt compositional changes. Key parameters that affect the MOCVD growth characteristics include the substrate orientation and preparation, flow rate of the precursors, growth temperature, pressure, and source material purity. The effect of substrate temperature during growth is different for different combinations of source material. Commercial MOCVD reactors are housed in a cabinet that provides for a continuous flow of air through the system by a negative exhaust. The major MOCVD subassembhes are (a) gas system, (b) temperature controller system, (c) electrical control system, (d) heating system, (e) purifier system, and (f) leak detection and safety system. The gas system includes metal-organic (and other gaseous) sources and mass flow controllers. Stainless steel tubes are used to transport sources to the reactor chamber. There is a separate temperature bath and controller for each of the metal-organic sources. Hydrogen, nitrogen, and helium are the most common carrier gases used in MOCVD growth processes. The carrier gases are highly purified to eliminate impurities. The most common impurities in a hydrogen carrier gas are oxygen and water vapor. Therefore, the MOCVD purification system usually includes an oxygen remover and a hydrogen purifier (palladium). The palladium is contained in a cell heated to about 400-425 °C . At this temperature, only hydrogen diffuses through the palladium tube and all other elements are blocked. The metal-organic sources are contained in stainless steel cylinders equipped with a temperature controlled bath. Commercial temperature control baths are capable of temperature control, using a thermocouple element, over a wide range from about

-20 to 100 °C at d=0.01% accuracy. Precisely controlling the temperature regulates the partial pressure of the source. Electronic mass flow controllers control the exact amount of carrier gas flowing through the bubblers and at the same time maintain a constant vapor pressure of the source. A heating system heats the substrate during growth. The heater can raise the temperature of the substrate to about 1000 °C. Heating can be achieved by radiofrequency (rf) induction heating, radiative heating, and resistance heating. Radiofrequency heating is common in large commercial systems. In this type of heating, the substrate susceptor is inductively coupled to the rf coil. In radiative heating, the heat energy from a resistance element is transformed into radiant energy. The susceptor absorbs the radiant energy and converts it back to heat energy. In the resistance heating method, current flows through an electrically conductive layer mounted to the susceptor to generate the required heat energy. Safety precautions include gas leak detectors for the carrier gas, the purifier, and toxic gases. Commercial MOCVD are computer controlled, and can be used to define the growth process and to monitor reactor conditions. 1,1.2. Molecular Beam Epitaxy Growth Figure 1 shows the basic components of a multichamber ultra high vacuum molecular beam epitaxy (MBE) system [31]. It consists of growth chamber, wafer loading and preparation chamber, and analytical chamber. The growth chamber, which usually has a 450-mm inner diameter, holds a removable source flange that provides support for effusion cells, their shutters, and their hquid nitrogen (LN2) shroud. The cells are oriented such that their beams converge on the substrate in the growth position. The beam sources are thermally isolated from each other by an LN2 cooled radial vane baffle, which prevents chemical crosscontamination. A second cryopanel surrounds the substrate such that the stainless steel bell jar is internally lined by this cryopanel

GROWTH CHAMBER

I ANALYTICAL I CHAMBER Transfer rod Electron analyser (AES,LEELS,ESCA)

Electron diffraction gon 10-50 keV

LN2 Effusion cells with shutters

WAFER LOADING AND PREPARATION CHAMBERS

Fig. 1. Schematic diagram of an MBE system showing the growth chamber, the wafer loading and preparation chambers, and the analytical chamber for surface analytical studies. Reproduced with permission from K. Ploog, "Springer Proceedings in Physics" (G. Lelay, J. Derrien, and N. Boccara, Eds.), Vol. 22, p. 10. ©1987 Springer-Verlag, New York.

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for the purpose of reducing contamination due to outgassing of the chamber walls. The sample preparation and loading chamber is connected to the growth chamber via large diameter channels and isolation valves. The analytical chamber allows for in situ and postgrowth surface analysis without exposing the sample to outside environments. The substrate surface must be prepared prior to epitaxial growth. Preparation of the surface entails preloading chemical treatment as well as in situ cleaning processes. The goal of the preloading chemical treatment is to provide either a clean chemical oxide layer of a few angstroms thick on the GaAs substrate surface or hydrogen passivation of the GaAs surface. An approach for GaAs surface preparation was described by Drummond et al. [32]. The first step is polishing of the substrate surface to mirror finish. One approach is to use pellon cloth saturated with Br—CH3OH. This is followed by wet chemical cleaning of the substrate in a 3 : 1 : 1 solution of H2SO4 : H2O2 : H2O for about 10 min to remove organic contamination. The wafers are then degreased, etched again in H2SO4: H2O2: H2O, and rinsed in deionized water. Next the substrate is loaded into the airlock high vacuum growth chamber. The pressure of the growth chamber is typically 10"^ torr. The growth chamber is equipped with Hquid nitrogen shrouds that surround the effusion cells and the substrate, and fine the walls of the chamber. The purpose of the shrouds around the effusion cells is to prevent excessive heating of the chamber, especially around the ovens, which can lead to contamination due to desorption of unwanted residues. The shrouds that surround the substrate and fine the walls condense residual gases and water vapor, especially those desorbed by the substrate heater, and remove any fluxes. An ionization gauge situated behind the substrate block, which is mounted in the growth chamber, monitors the As flux and a high-energy electron diffraction (HEED) system.

The shrouds arefilledwith liquid nitrogen well before growth is initiated and are kept on until the furnace temperatures are reduced after growth. Once the chamber has been chilled, the effusion cells are turned on and stabilized to the desired temperature with a dc current, controlled by a temperature controller (W-5%ReAV-26%Re) thermocouple. Likewise, the substrate surface is heated to about 630 °C. The HEED pattern is closely monitored to ensure that the native oxide layer is completely desorbed off the substrate at a precise temperature, say 580 °C. The substrate temperature is subsequently raised or lowered to the growth temperature. Once the desired growth temperature is reached, the shutters for the appropriate effusion cells are opened, followed by opening of the main shutter to initiate epitaxial growth. The initiation of the thin film is monitored by the HEED pattern. A commercial MBE facility is shown in Figure 2. The system is designed for the growth of GaAs-based heterostructure devices, optoelectronic devices, and integrated circuits. 1.2. Material Characterization The Hall effect is the most basic characterization technique for evaluating semiconductor heterostructures. It is used to determine the type and concentration of elements in a sample. It can also allow for determination of the electrical activation energy for donors and acceptors in GaAs and its alloys by analyzing ionized impurity scattering and its effect on carrier mobility. The measurement techniques are well estabUshed and widely reported in the literature [33]. Characterization of heterolayers based on techniques that givQ structural information include transmission electron microscopy, X-ray diffraction, scanning tunneling microscopy, and those that give information on the band structure. The latter comprise optical measurements such as photoluminescence excitation

Fig. 2. A commercial MBE system used for the growth and analysis of GaAs heterostructure materials and devices at the University of Connecticut.

GALLIUM ARSENIDE HETEROSTRUCTURES spectroscopy, absorption and reflectivity, and electrical measurements such as Hall and Shubnikov-de Haas measurements. Etching has been employed to characterize the structural and chemical inhomogeneities in semiconductors [34-36]. The structural and chemical defects are observed indirectly from their effects on the etching mechanism. Etching also has been used to study defects such as dislocations and staking faults [37]. The major drawback of this technique is that it resorts to destructive testing.

2. Crystal Growth and Properties of GaAs 2.1. Crystal Growth

85

reconstruct so that surface atoms care share bonds. This reconstruction results in a two-dimensional symmetry with periodicity differing from that of the underlying atoms of the GaAs crystal. The surface atoms may also relax, that is, change the bond angles, but not the number of nearest neighbors, to seek new equilibrium positions. The reconstructed GaAs surface has variety of structures. These are the (1 x l)_s_tructure of the (110) face, (2 x 2) structures of the (HI) and (ill) faces, and a series of structures [c(4 X 4), c(2 X 8), c(8 x 2), p(l x 6), p(4 x 6), etc.]. The letter ";?" indicates that the unit cell is primitive and "c" indicates that the unit cell has an additional scatter in the center. The GaAs surface structure has been studied using a variety of techniques such as reflection anisotropy spectroscopy (RAS) spectra for MBE- and MOCVD-grown (001) GaAs [51, 52]. The RAS method is based on the fact that a cubic material such as GaAs is optically isotropic in first-order reflectivity. Thus anisotropic reflectivity originates from the surface with different symmetries. A more common method for surface measurement is the low-energy electron diffraction (LEED) method. In LEED, electrons of well defined energy and direction diffract from the crystal surface. The low-energy electrons are scattered mainly by individual atoms on the surface and produce a pattern of spots on a fluorescent screen. The spots in the pattern correspond to the points in the two-dimensional reciprocal lattice.

The MOCVD growth of GaAs results from the reaction between group III alkyls (e.g., TMGa, TEGa) and group V hydrides (e.g., ASH3, TEAs). The reaction takes place in a reactor chamber that contains a semiinsulating GaAs substrate placed on a heated carbon susceptor. Typically growth temperatures range between 575 and 700 °C, and depend on the precursors used. Highest purity material, using TMGa and ASH3, has been achieved [21, 22] in the temperature region from 600 to 650 °C. The chemical reactions that lead to the formation of GaAs from metal-organic precursors is a complex process that is not fully understood. The reactions break down into gas-phase reactions and surface reactions [38, 39]. The gas-phase reactions involve multiple 2.2. Impurities and Deep Levels pyrolytic decompositions of organometaUics and reactions with A number of elements are electrically active impurities in GaAs hydrogen radicals [40-42]. The surface reactions entail decompo- and produce shallow donor or acceptor levels [53]. Deep levsition, surface adsorption, and desorption. Volatile by-products els due to impurities or lattice defects [54] also exist. Table III are removed from the surface by adsorption, by colliding gas- gives a summary of some of the impurities, their activation enerphase radicals, and by bimolecular surface recombination. gies, and their diffusion in GaAs. The most common dopants One major problem with the group III sources is the uninten- for MBE-grown GaAs are Be for p type and Si, Ge, and Sn for tional doping of the layers with carbon [43-45], making the alloy n type. Beryllium acts as an acceptor in MBE-grown GaAs [55]. effectively p type [46]. However, GaAs grown from TEGa and Abrupt doping levels can be achieved due to the low diffussivASH3 turn out to have lower carbon contamination. The ratio of ity of Be in MBE-grown GaAs [56]. At substrate temperature group V to group III also affects the quality of the alloy growth. At low V : III values the GaAs is p type, having high carbon concentrations. The carbon concentration decreases with increasing Table III. Activation Energies of Impurities and Their Diffusion in GaAs V : III ratio, and at a critical ratio the GaAs material becomes Element Activation energy (meV) semi-insulating. The substrate orientation also affects the introduction of carbon. The (111) and (311) orientations show lesser Shallow donors 6.0% 5.89^ 5.845^, 5.87^^ S carbon incorporation, but (100) is the preferred substrate orienSe 6.0«,5.85%5.812^,5.789^ tation because it yields the best surface morphologies and cleaves Te 3.0« easily. Si 5.808%5.799^, 5.839^^ The MBE growth of GaAs occurs through the interaction of Sn 5.817^ Ga atoms and As2 (and/or AS4) molecules impinging on a GaAs Ge 5.908%5.949^, 5.888^ substrate [47, 48]. Most recent developments use gas sources Pb 5.773^ and are variously known as gas-source molecular beam epitaxy, C 5.937^ chemical beam epitaxy, or metal-organic molecular beam epitaxy (MOMBE). In this case the growth occurs between TMGa Shallow acceptors Zn 24%30.7'^ (or TEGa) and ASH3. The sticking coefficient of Ga atoms must Cd 21% 34.7^ approach unity, with condensation of AS2 via bonding with Ga Li 23^^ [49, 50] for growth to occur. The sticking coefficient of AS2 Ge 80% 40.4^ increases as the ratio of Ga flux to AS2flux((f>Ga/^As2) increases, Mg 12% 28.8^ Be 28^ reaching unity when AS2- This situation implies that stochiometric formation of GaAs can occur for (I>Q^ < 2(^^82 ^^d «S. M. Sze and J. C. Irvin, Solid State Electron. 11, 599 (1968). the excess As2 is lost by desorption. * C. M. Wolfe et al, Conf. Sen Inst. Phys. 33b, 120 (1977). The layer by layer growth of GaAs by MBE or MOCVD ' M. Ozeki et al, Conf. Ser. Inst. Phys. 45, 220 (1979). results in surface reconstruction, that is, a surface that is differ- ^ A. G. Milnes, Electron. Electron Phys. 61, 63 (1983). ent from the "native" surface of the material. The surface may ^ U. Kaufmann and J. Schneider, Electron. Electron Phys. 58, 81 (1982).

86

DONKOR TEMPERATURE C O 1100 KXX) 900 600

700

O.DDDU 1

600

1

1 11

GaAs

500

stoichiometric

5.5545

5.6540

6Q e x c e s s v y /^

5.6535

5.6530

5.6525

v^

A

07

0.8

Q9

1.0 U 1000/T (K'M

1,2

1.3

Fig. 3. Room temperature carrier concentration in MBE-grown GaAs as a function of effusion cell temperature for Si, Ge (n-type), Be, and Sn. The data were obtained from Hall effect and capacitance-voltage measurements at constant growth rate, substrate temperature, and AS4: Ga flux ratio. Reproduced with permission from K. Ploog, "Springer Proceedings in Physics" (G. Lelay, J. Derrien, and N. Boccara, Eds.), Vol. 22, p. 10. ©1987 Springer-Verlag, New York.

2.3. Crystal Structure and Lattice Properties The GaAs crystal structure has been studied and reported extensively [63]. It has a zincblende crystal structure with a lattice constant, aQ, that is temperature dependent as shown in Figure 4 [64]. The nearest-neighbor configurations are such that each Ga species is surrounded by four As species and vice versa, with a nearest-neighbor bond length of TQ = (V3flo/4) = 2.44793 A at 300 K, and a bond angle of 109.47°. Gallium arsenide cleaves most readily on {110} family planes, but can also cleave on {111} planes and between ( H I ) and (Oil). Of the eight planes in the

y .^ ^k% excess

Y

y/

20

30

40

50

60 'C 70

Fig. 4. Variation of lattice constant versus temperature for stoichiometric, Ga excess, and As excess MBE-grown GaAs. Reproduced with permission from O. Madelung, "Data in Science and Technology: Semiconductors," p. 104. ©1991. Springer-Verlag, New York.

Table IV Formulae for Acoustic and Mechanical Properties of GaAs Parameter Shear modulus Bulk modulus

exceeding 550 °C and at high doping levels above 5 x 10^^ cm~^, the surface morphology degrades [57] and the diffusion of Be is enhanced [58, 59], resulting in degradation of the doped epitaxy. On the other hand, lowering the substrate temperature to 500 °C lowers the diffusivity of Be and acceptor levels of 2 x 10^^ cm"^ can be achieved [60]. Silicon is the most commonly used n-type dopant in MBEgrown GaAs. It is incorporated on Ga sites under As-stabilized conditions and yields n-type material. Germanium is an amphoteric dopant and it can be used to prepare either p- or n-type films, depending on the growth condition [61, 62]. Germanium acts as an acceptor on As sites and as a donor on Ga sites. The site substitution depends critically on the As : Ga flux ratio and on substrate temperature. Figure 3 [31, p. 27] gives doping concentrations for Si, Be, Ge, and Sn in MBE-grown GaAs, as a function of temperature for a constant growth rate of 1 /xm/h [31].

3/^

^ /^

5.6520 . „ . _ 0 10

10'

^/ /

V

Young Modulus along [100] Poisson ratio along [100] Isotropic ratio

Formula

"'•-

Q i ~ Q2 2 Q i + 2Ci2

^" = y

3 (Q,+2C,2)(C„--Cn) Q i + Q2

p

c„ Q i + Q2

Q i — Q2 ' ~ 2C44

Cauchy ratio ^44

Born ratio

^

(Ci,+C,2)2 4 ^ 1 1 ( ^ 1 1 •" ^ 4 4 )

{111} family, four {111^} planes contain only Ga atoms and four {1115} contain only As atoms. These two planes have different chemical activity and behavior [65, 66]. The elastic properties of GaAs include compliance and second- and third-order moduli. The small-stress second-order moduli have only three independent components [67]. The shear modulus, bulk modulus. Young modulus, Poisson ratio, isotropy ratio, Cauchy ratio, and Born ratio are determined from the second-order moduli with the use of the formulae [63, p. 3] indicated in Table IV. The speed of nondispersive or (long-wavelength) bulk acoustic waves can be expressed in terms of the second-order moduli and the crystal density [63, p. 3], and is given for the high-symmetry [100], [110], and [111] directions as listed in Table V. The room temperature phonon dispersion curve reported by Waugh and Dolling [68] is represented graphically in Figure 5. The data are the wave vectors along the [100], [110], and [111] directions.

87

GALLIUM ARSENIDE HETEROSTRUCTURES Table V. Speed of Acoustic Waves in GaAs Wave Direction propagation or plane of Parameter direction particle motion [100] [100] [110] [110] [110] [111] [111]

[100] (100) plane [110] [001] [liO] [111] (111) plane

Wave speed (xlO^ cm/s) r = 300 K

r = 77 K

4.731 ± 0.005 3.345 ± 0.003 5.238 lb 0.008 3.345 ± 0.003 2.476 ± 0.005 5.397 ± 0.008 2.796 ± 0.006

4.784 ± 0.015 3.350 ± 0.005 5.289 ± 0.015 3.350 ± 0.005 2.479 ± 0.012 5.447 ± 0.015 2.799 ± 0.015

A F A X U.K REDUCED WAVE VECTOR

Fig. 6. Electronic band structure calculated by Chelikowsky and Cohen from a nonlocal empirical pseudopotential method. Reproduced with permission from J. R. Chelikowsky and M. L. Cohen, Phys. Rev. B 14, 555 (1976). © American Institute of Physics, New York.

used: 0

0.2 0.4 0.6 0.8 [qOOl

IJOI.0

0.8

0.6

0.A

0.Z

0 0 01 0.2 0.3 0 4 05

[Oqq]

— = -(—

tqqql

—]

(2.2)

REDUCED (DIMENSIONLESS) WAVE-VECTOR, q

Fig. 5. GaAs acoustic and optical branch phonon dispersion relation. The experimental points (•, A, o, A, D) were determined by Waugh and Dolling [68] by elastic neutron scattering, and the theoretical curves are represented by solid and dotted lines. The dashed lines near q ^ 0,v ^ 0 represent the initial slopes for the various speeds of sound. Reproduced with permission from O. Madelung, "Data in Science and Technology: Semiconductors," p. 104. ©1991. Springer-Verlag, New York.

2.4. Electronic and Electrical Properties

Determination of electronic effective mass at the high-symmetry points is derived from the k • p approach, which gives the expression [70]

m

r

^ ^ ^ [EQ

EQ-{-AQ\

-?[E(.rs,)-Eo

(2.3)

+ •

E(r 'c)-Eo\

where JTIQ is the free electron mass, P is the momentum matrix element connecting the p-like valence band with the s-like conduction band, and P' is the momentum matrix element connecting the s-like conduction band with the next higher lying bands. The effective density-of states hole mass, m^, at the valence band is given by the expression

Figure 6 shows the general features of the electron energy versus reduced wave vector for the valence band and a number of conduction bands for GaAs as calculated via a nonlocal empirical pseudopotential method by Chelikowsky and Cohen [69]. Gallium arsenide has a direct energy gap {Eg = Tg^ - Tg^) / ^^ \ 2/3 of 1.424 eV at 300 K. The spin-orbit interaction splits the r\^ (2.4) valence band into Tg and Tj, where the splitting energy difference is represented by AQ. Likewise the T{^ conduction band splits where the heavy-hole mass mhh = O.Slmo and O.SOmo at T = 0 into Fg and F7 with a splitting energy difference given by AQ. The and 300 K, respectively, and the light-hole mass mjh = 0.082mo spin-orbit interaction also splits the LKA^) valence band into and 0.0.076mo at T = 0 and 300 K, respectively, where JTIQ represents the electronic mass. The electronic effective masses m^ at the conduction band minThe effective electron mobility depends on scattering-limited ima a (=F, X, or L) based on density-of-states calculations is mechanisms, such as polar optical scattering, acoustic phonon given by scattering, piezoelectric scattering, intervalley scattering, impurity scattering, electron-electron scattering, and alloy scattering. 2/3_l/3 (2.1) At low fields, the electrons in GaAs occupy the lowest conduc= N'/'m1im, la tion band minima, Fg of the zone center. Using Mattiessen's where N is the number of equivalent minima, and m^^ and m/„ rule [71, 72] the total mobiUty is expressed as the sum of the are the transverse and longitudinal masses of the minima. For scattering rates of the dominant scattering process polar opticonductivity calculations, the conductivity effective mass m" is cal scattering /Xpo and impurity scattering fin. Expressions for

DONKOR the polar optical scattering-limited mobility and the impurity scattering-limited mobility were given by Ehrenreich [60, 73, 74] and Brooks-Herring [75], respectively, as l/2/,x2/^

x3/2

—'»"(3^)(^)(S) X MnG(z)[exp(z) - 1] ^ 2 7^3/2 r3/2

/x„ = 3.28 X 10''

b =

(2.5) /

^

_(,n,10,-j^)

1.29 X 10^4A:,m*r2

x-i

(2.) 3.2. Critical Thickness of Strained-Layer Quantum Wells

(2.7)

Wo"

ri = n +

{No-N^-n)

n + ^A

mainly as substrate materials [78-80]. Strain can affect the confinement of electronic states [81] by inducing large internal electric fields [82-84]. Furthermore, strain alters band structure and modifies transport and optical properties of the strained-layer heterostructure. Therefore, strained-layer structures offer a variety of material and physical properties that cannot be obtained with lattice-matched systems.

The lattice mismatch, / , between a substrate and an epitaxial layer is given by

(2.8) (2.9)

Here T is the temperature in kelvin, e is the electronic charge, and e* is the Callan effective charge (and e*/e = 0.20), M is the reduced mass of the cell that equals 5.92 x 10^^ kg, fl = 5.05 X 10"^^ m^ is the volume of the primitive cell, d is the polar phonon temperature, z = d/T, G(z) is a screening factor [60], n is the electron density, k^ is the static dielectric constant, and A^^ and N^^ (per cubic centimeter) are the donor and acceptor densities, respectively.

3. Growth and Material Properties of GaAs Heterostnictures 3.1. Introduction Epitaxial layers of GaAs-based heterostnictures are binary, tertiary, quaternary, or quinary alloys of III-V compounds. Binary systems are of the type III^-Vj.^, where III and V imply elements from group III and V, respectively. Ternary systems are of the type III^-IIIi_^-V and III-V^-Vi_^. Quaternary systems are of three main types and quinary systems are of two types. The three types for the quaternary system are III-(V^-Vi_^)^-Vi_^, III;^" IIIi_^-V^-Vi_^, and (III^-IIIi_^)^-IIIi_^-V, and for the quinary system, the two types are (III^-IIIi__^)^-IIIi_^-V^-Vi_^ and III^^IIIi_^-(V^-Vi_p^-Vi_„ where 0 < x < 1, 0 < y < 1, and 0 < z < 1. Heterostnictures may be lattice-matched or latticemismatched based on the relative lattice constant of the constituent alloys. In lattice-matched structures, the lattice constants of constituent alloys are practically equal. As a result, interface defects are eliminated and a device grade crystalline structure is formed. The difference in lattice constant of a lattice-mismatched structure is accommodated by a combination of coherent strain and misfit dislocations at the heterointerfaces. Misfit dislocations are defects that severely degrade material properties, especially if the epilayers have thickness in excess of 1000 A. However, there exists a critical layer thickness below which the energy of the lattice mismatch at a heterointerface is totally accommodated by strain. The mismatch layers can be strain-reUeved (i.e., elastic or coherent strained) [76, 77]. Coherent-strained (or pseudomorphic) structures have negligible misfit defects and are, therefore, used as active media for electrical and optical device apphcations. Strain-relieved layers produce defects to accommodate stress relief. They are electrically and optically inactive, and serve

-•^sub

/=

•*epi

(3.1)

where c^sub ^^^ ^epi ^^e the lattice parameters for the substrate and epilayer, respectively. The lattice mismatch is generally accommodated by a combination of in-plane coherent strain Sn and misfit dislocation 5: / = en + 5. Under appropriate growth conditions the lattice mismatch is compensated for by distortion of the lattice of the epilayer without formation of misfit dislocations or clusters. That is, the strain of the epilayer film equals the mismatch, f = Sn. This growth mode continues only up to a critical film thickness, h^, which is a function of the lattice mismatch and the growth temperature. Two models for determining the critical thickness are owing to Matthews and Blakeslee [85] and People and Bean [86], respectively. In the Matthews and Blakeslee model, the critical strain is given by

e„: 2/i(l + i/)cosAL

277
Here /x^ and ^f are the shear moduli of the substrate and the epitaxial film, respectively, v is the Poisson ratio, b is Burger's vector, A is the angle between the slip direction and the direction in the film plane (which is perpendicular to the line of intersection of the slip plane and the interface), and h is the thickness of the epitaxial layer. The angle of inclination between Burger's vector and the dislocation line [87] is B^b ^^^ P is the core energy parameter, which is )3 = 1 for metals and )8 = 4 for semiconductors [88]. Setting / = e^ gives the critical thickness as

K=

ta-vcos^e^O 477/(l + ^)COSA fJLf

u
(3.3)

For a MQW consisting of n pairs of wells (thickness h^ and strain s^) and barriers (thickness hf, and strain e^), the critical thickness can be expressed in terms of an effective strain e* and total thickness h* as h: =

Ml-^cos^Odb) 87re*(l + i')cosA ^w'^w

K, + h

m)]

(3.4)

h* = (h^ + h,)n

(3.5)

Figure 7 is a composite graph of wavelength versus lattice constant, and energy bandgap versus lattice constant for III-V compounds [89]. The figure suggests a vast number of binary, ternary, quaternary, and quinary alloys that can be grown on GaAs. However, the criteria for choosing any compound is dictated by the desired energy band and band offset. Compounds that

GALLIUM ARSENIDE HETEROSTRUCTURES

GaP

r ^ - ^

2.0 ' 1.6 GaAs"

\

f***^

^N

-AlSb

0.002

/.AS

lAIAs \

\ \

1

••

-^

:

-InP

^

0.620

V"^-^.^^^ inpyv

"\

^ \

\

N<

GaSb

/GaP

- n/>'^ 1 5.5

/>-^

L_ii..j 5.6

57

1

. 1

5.8

'5.9 InP

1.033

\

JlcaSb

"^

1.550

cu

Z

0.001

i

!>

U


«

1

\ H 3.100 ^—^lnSb\

^V,

AlSb !^^^v^^^ GaSb 1 . 1 1 1

'»^^"""*'*-*—.—

6.0 ' 6,1 InAs

«

1

c

>

>iAs

/ X ^' A l A s

is

CO

< c/) S 1

.^GaAs

-InAs X lnSbX>AIP

0.775

\

1 1 1

0.8

0

AlSb 1 1 1 1

^aAs

1.2

0.4

89

6^2

1

1

6^3

6^4

0.000

1 "6.5 InSb

Lattice Parameter (A)

Fig. 7. Lattice parameters, band gaps, and emission wavelengths of binary III-V compounds. Reproduced with permission from A. Zunger and S. Mahajan, "Handbook on Semiconductors" (S. Mahajan, Ed.), Vol. 3b, p. 1403. ©1992 North-Holland, Amsterdam.

form lattice mismatches of less than 2% with GaAs can form either lattice-matched or strained-layer coherent epitaxy films. Although attempts have been made to grow epitaxial layers with lattice mismatches between 2 and 7% with GaAs, the quality of such materials degrades due to the high density of misfit dislocations.

1 2 3 4 5 6 Li^er Thi ckness [fim]

7

Fig. 8. Layer thickness dependence of the biaxial compressive strain for heteroepitaxial InP on GaAs substrates. Results show X-ray diffraction, PL measurements, and the theoretical model. Reproduced with permission from D. J. Olego, Y. Okuno, T. Kawano, and M. Tamura, /. Appl. Phys. 71, 4492 (1992). © American Institute of Physics, New York.

A(1w419«V)

T-IOK P=1W.CDI^

3

(d (0

c

0)

3.3. 33.1.

Heterostructures of the Type III-V/GaAs

8

InP/GoAs Lattice-Mismatched System

C

Heteroepitaxial InP has been successfully grown on (001) surfaces [90-92], as well as (111) surfaces [93] of GaAs-oriented substrate. Typical MOCVD growth uses TMIn and PH3 (diluted in hydrogen) as source materials [94]. Growth temperature falls within 570-680° C. In one such growth [95], the V : III ratio was 80, with flow rates of 8.8 x 10"^ and 7.0 x lO""^ mol/min for TMIn and PH3, respectively. Growth at both low pressure [92] and atmospheric pressure [93] has been demonstrated. The InP/GaAs heterostructure has a lattice mismatch that gives rise to strain along the growth axis, e^^, and a biaxial strain in the interfacial plane, Sn, a ±GaAs ~ a InP

Q^ II GaAs ~ Q^InP

<^InP ^11 =

«InP

2Q,

(3.6)

where Cn = 10.2 x lO^^ dyne/cm^, and C12 = 5.76 x lO^^ dyne/ cm^ are the elastic stiffness constants of InP. The strains perpendicular and parallel to the interface measured at room temperature are 2.7 x 10"^ and -2.4 x 10-^ respectively [90], depending on the layer thickness [92]. The lattice-mismatch strain e^^ lies between 3.7 and 4%, and the compressive in-plane strain depends on layer thickness as shown in Figure 8 [92]. A second source of strain in InP/GaAs heterostructure is the linear thermal expansion mismatch between InP and GaAs that also leads to compression [96, 97]. Typical photoluminescence (PL) spectra for InP epitaxial layers on GaAs substrates is shown in Figure 9 [90]. The emission at wavelength A < 880 nm (for T = 24 K) corresponds to near band-edge radiative recombination originating from excitons. For

8 CO

0)

c

*E o

Z

sz CL

InP/GaAs (111)B,

8400

8800

9200

9600

Wavelength (A) Fig. 9. Comparative PL spectra at low temperature for homoepitaxial InP and heteroepitaxial InP/GaAs(001), InP/GaAs(lllA), and InP/GaAs(lllB). Reproduced with permission from M. B. Derbali, J. Meddeb, H. Maaret, D. Buttard, P Abraham, and Y. Monteil, /. Appl. Phys. 84, 503 (1998). © American Institute of Physics, New York.

A > 880 nm, the PL bands involve transition to impurity or defect states [92]. As the temperature increases, the transitions associated with the light hole (Ih) increase. As the layer thickness decreases (below 2 fim), the band-edge emission broadens and shifts toward the red end of the spectrum due to band-edge recombination at low temperatures [92]. The PL intensity has been found to increase with the flow rate of the reactants during growth [95]. The mobility and carrier concentration of InP grown on GaAs both depend on the flow rate. The carrier concentration

90

DONKOR

rapidly decreases with increasedflowrate and the electron mobility increases with increased flow rate [95]. 3.3.2. GaSb/GoAs Lattice-Mismatched System The lattice mismatch of about 7% between GaSb and GaAs makes it difficult to grow high quahty materials. Graham et al. [98] proposed a solution that entailed incorporating a lowtemperature-grown GaSb buffer layer. The high-temperature (about 600 °C) growth of GaAs from the common precursors TMGa and TMSb hampers bandgap engineering, which requires material growth at lower temperatures. Also using TMSb as a source for Sb causes carbon contamination due to methyl radicals [99]. Sources for Sb that have been utilized for low-temperature MOCVD growth include terbutyldimethylantimony (TBDMSb) [100], triisopropylantimony (TIPSb) [101], and tridimethylaminoantimony (TDMASb) [102]. A V : III ratio of nearly unity offers optimum low-temperature growth. Gallium antimonide on GaAs has also been grown by metal-organic molecular beam epitaxy using TEGa, TDMAAs, and TDMASb as sources [103]. Low-temperature PL measurements by Shin et al. [102] indicate a dominant peak at between 775 and 778 meV that is beheved to arise from native defects that are a combination of Ga vacancy and Ga antisites [104]. Near band-edge transitions occur at about 810 meV and are attributed to excitons bound to neutral acceptors. 3.4. Heterostnictures of the Type III^-IIIi_^-V/GaAs 3.4.1. Al^Gai_^As/GaAs Systems Triethyl (e.g., TEGa, TEAl) and trimethyl alkyls (e.g., TMGa, TMAl) of group III elements and AsHg (sometimes replaced by organoarsenic materials) are the main precursors used in the MOCVD growth of lattice-matched Al^^Gaj.^As/GaAs heteroepitaxy. The trimethyl sources are most often used due to their higher vapor pressure and greater stability. A disadvantage in using TMAl as a source for growing Al^Ga^.^^As layers is the high level of oxygen and carbon contamination it introduces. This is because the pyrolysis of TMAl produces CH3 radicals, which are the source of the carbon. The carbon is introduced into the epilayer by reacting with the aluminum to form aluminum carbide. Oxygen contamination also occurs due to the strong bond that can be formed with aluminum. In MOCVD growth, the oxygen contamination may come from traces of oxygen and water vapor in arsine, in the carrier gas, and in alkoxides in the metal-organic sources. Triethyl sources show relatively low carbon contamination in Al^Gai_^As/GaAs grown at low pressures, since they pyrolyze without producing CH3 radicals. However, they are less stable and have low vapor pressure at room temperature, which is a disadvantage in MOCVD growth. The use of DMAIH as an Al precursor has been shown to yield Al^Gai_;pAs layers with lower carbon contamination than layers grown with TMAl [105]. The main problem with the group V sources is their toxicity andflammability.For example, ASH3 has a toxicity threshold level of 0.05 ppm. Consequently, organometalhc group V and other molecules are now replacing arsine as sources for As. Such materials include trimethylarsenic (TMAs) [106], triethylarsenic (TEAs) [107], terbutylarsine (TBAs) [108, 109], isobutylarsine

(IBAs) [110, 111], dimethylarsine (DMAsH) [112], diethylarsine (DEAsH) [113], and phenylarsine (PhAsH2). Growth of high quahty Al^Gaj.^As is affected by many factors including growth temperature, substrate orientation [114-117] and introduction of unintentional impurities, especially carbon and oxygen. Oxygen is incorporated into Al;,Gai_^As as an impurity by virtue of the strong bond formed with aluminum. The oxygen incorporation leads to compensation of shallow donors [118-123], causing low electron mobility [124] and making Al^Gaj.^As layers highly resistive [125]. In MBE growth, the sources of oxygen contamination may arise from carbon monoxide, carbon dioxide, oxygen, and water vapor molecules adsorbed on the reactor chamber walls or as oxides in effusion cells. Concentration levels of oxygen contamination can range between 10^^ and 10^^ cm"^ in both MBE and MOCVD growth [126-131]. The growth temperature of the Al;j.Gai_^As strongly influences the incorporation of oxygen impurities: lower oxygen content occurs at higher growth temperatures [132, 133]. The incorporation of unintentional impurities is also affected by substrate orientation [134]. Surface orientation also has been shown to affect electronic and optical [135] properties of AlGaAs/GaAs systems. Typical species used for n-type doping in Al^Gai_^As/GaAs are Si, S, Se, Te, Ge, and Sn. However, Si is by far the most preferred dopant [136]. Some of its advantages are high electrical activation, low diffusivity, and room temperature implantation. Generally, implanted Si atoms preferentially occupy Ga sublattices in Al^^-Gai.^As/GaAs, thereby acting as donors. However, Si may also occupy As sites, where it acts as an acceptor. The relative occupancy of Ga and As sites depends on the concentration of the Al;^Gai_;^As (or GaAs), the annealing temperature, and the concentration of As vacancies [137]. The p-type dopants in AlGaAs/GaAs include Be, Mg, Zn, and Cd. Cadmium is the heaviest p-type dopant and as a result may cause severe damage during implantation. It also requires a high annealing temperature to achieve activation [138]. Zinc gives the highest hole concentration, with high and rapid diffusivity [139]. High dose implantation of Zn often requires anneahng for complete activation [140]. Compared to Zn and Cd, p-type doping by ion implantation with Mg causes less damage. Annealing after implantation achieves higher electrical activation [141]. Beryllium causes the least damage; nonetheless, its toxicity has prevented wide use. Comparisons of the electrical activation as a function of annealing temperature and implanted dose are shown in Figure 10a and b, respectively, for Be, Zn, and Cd species [136]. Another source of unintentional impurities is DX centers. A DX center behaves as a donor and can bind an electron in either a shallow extended donor state or a deep localized donor state. The deep state is located either close to the edge of the conduction band or is degenerate with it [142]. Unlike oxygen defects, the DX defects are affected less by growth conditions. Rather, their concentrations depend on the shallow dopants, which do not change with the growth temperature. Various methods have been employed for unintentional impurity removal including gettering, use of purified hydrogen as the carrier gas, molecular sieving, and liquid metal bubblers. Wet etching in AlGaAs/GaAs systems poses a major challenge because an etching solution that can selectively etch AlGaAs and stop at GaAs is not readily available. Limited success for selective etching for AlGaAs/GaAs systems has been reported using a ferric-ferrocyanide solution [143]. Wet etchants

GALLIUM ARSENIDE HETEROSTRUCTURES (a)



AlGaAs

B«.40k*V

91 GaAs

AlGaAs Ec

fT

o **ai.iook«v o"*Cd,iook»v

Ec2

AEc

39ANNEALS

Ed

E z

10

13

o

i

1X10

o z

3X10

IZ UJ

(0

o

^12

> ^

E o

1000

o cc

111

QJ

cr

krIEh: q^

k~

y.

CO

DC

< o

O

LU X

>11 700

-l750

800

-l850

900

J 950

O

L. 1000

X

1050

Fig. 11. The electronic energy band states of an AlGaAs/GaAs/AlGaAs double QW, showing electronic subbands of the conduction band (£cij^c2)> heavy-hole subbands (^^hu^hi)? ^^^ light-hole subbands ( M I ? -^12)-

ANNEAUNG TEMPERATURE ( ^ )

(b)

10'V

100% '^'^T-ix/AXirvM

^ /

X

• Be, 40keV ozn, lOOkeV a Cd, 100 keV 10'^h r 900*^. 3s /'f
50% ACTIVATION

10''

12

10

Z... A_

10^.12

J... ,13

10'

1

10^-*

1

10^>15

1

10^'

ION D O S E (cm-2)

Fig. 10. (a) Hole density in GaAs samples implanted with Be, Zn, and Cd after annealing at various temperatures for 3 s. The implanted doses are 3 x lO^^ ^nd 1 x 10^^ c m ' ^ (b) Hole density in GaAs samples implanted with Be, Zn, and Cd as function of implated dose. The samples were annealed at 950 °C for 3 s. Reproduced with permission from J. D. de Souza and D. K. Sadana, "Handbook on Semiconductors" (S. Mahajan, Ed.), Vol. 3b, Chap. 27. ©1992 North-Holland, Amsterdam.

for AlGaAs/GaAs systems contain diluted mixtures of acids and hydrogen peroxide. Typical acids are phosphoric acid [144, 145], nitric acid, sulfuric acid [65, 146-148], hydrochloric acid [149], and citric acid [150]. The hydrogen peroxide is added to dissolve oxidized by-products created by acidic reactions. The alkalinebased ammonium peroxide-water mixture etchant offers controlled etch rate and has been used for AlGaAs/GaAs [151]. Another alkaline-based etchant that has proved successful for AlGaAs/GaAs processing is sodium hydroxide-peroxide-water [152]. For selective etching of AlGaAs in a Al^Gai_^As/GaAs material system, HF-based solutions are used for x > 0.4 and KI/I2 with low pH values are used for x < 0.4. A dry etching process commonly used for Al^Gai_^As/GaAs material systems is reactive ion etching. Etchants are chlorine mixtures diluted with

arsenic, helium, or oxygen. The process occurs at low pressure between 5 and 100 mtorr [153]. Early studies by Esaki et al. [5] and Kazarinov et al. [154] revealed quantum mechanical behavior of the electronic and transport properties. The electronic energy band states of an AlGaAs/GaAs/AlGaAs quantum well is illustrated in Figure 11. The key features of the energy band structure are confinement of the carriers to discrete energy subbands in both the conduction and valence bands, and discontinuity in the conduction and valence bands. Lifting the degeneracy in the valence band creates light- and heavy-hole energy levels. A photoluminescence excitation spectrum reveals detailed features of the energy band structure. An illustration of this is shown in Figure 12 [155]. The figure shows heavy (E^^, £2^, E^^, E^^) and light {E^^, E^i, ^31, ^41) transitions, as well as excitonic {E^^, E^, EQ, E^^) transitions. The periodic alternation of thin film layers with different energy gaps in superlattices produces a periodic potential of the same form as the Kronig-Penney potential. As a result, minibands are formed within the conduction band. The widths of the minibands are a function of the well and barrier thickness and of the size of the confining potential. Computed minibands [156] for a symmetric superlattice with a barrier height of 0.4 eV are shown in Figure 13. The density of states of noncommunicating QW is discrete. In contrast, due to the miniband formation, the superlattice density of states becomes less discrete. Exciton formation occurs particularly at low temperature and arises from the interaction of the photoexcited electrons and holes with energies given by

^f =

jxe*

(3.7)

where n (= 1, 2, 3, 4 , . . . ) is the principal quantum number, /x is the electron-hole reduced effective mass, s is the background dielectric constant, and h is Planck's constant. The light and heavy excitons arise from lifting of the valence band degeneracy at /: = 0. At elevated temperatures, an exciton, X, is ionized into the constituent electron, e, and hole, h, (X ;:^ e + h), according

92

DONKOR ature. Interface defects contribute to the width of the excitonic line [158]. AppHcation of a magnetic field to the QW results in the appearance of Landau levels in the energy band spectrum. Consider a QW in which the layers are grown in the z direction. If the magnetic field is appHed along the growth direction, then degeneracy in the energies along the x and y directions is lifted in addition to lifting of the degeneracy along the z direction due to carrier confinement [159].

tn H

§

^ <

pPUMP

>-


UJ An

»UJ

1

Ezh

A l\

^

UJ

E,i

UJ

z

\ ^^

^311

^^3 / N 1 / \

'

mev

£41. .

Ef4

1

^31

1

'" E.eJ/ ^ V-s.,W<',

IL

° I o

/ l/

^

Jtir^^

V^fl^^ffh*

X

3.4.2. Ga^Ini_^P/GaAs, Al^Iiii_^P/GaAs, and Al^Gai_^P/GaAs

16

- 9 m«v

mev

1

1

Lattice-matched Ga^^In^.^F/GaAs systems have been grown by MOCVD in the range 0.48 < x < 0.50. The first such growth 156 1.62 164 was reported in 1981 by Yoshino et al. [160], who used TEGa, ENERGY (eV» TEIn, ASH3, and PH3 as precursors. The growth temperature was between 600 and 675 °C, at a reactor pressure of 40 torr. Hino Fig. 12. Photoluminescence excitation spectrum from a GaAs/AlGaAs and Suzuki [161] utilized similar reactants at a reactor pressure MOW structure containing heavy holes {E^^^E^^^.E^^^^E^^, Hght holes (£11, £21»^31J ^41)J and excitons {E^^,E^, E^, E^^). Reproduced with per- of 70 torr and growth temperature of 640 °C. Razeghi et al. [162] mission from B. D. McCombe and A. Petron, "Handbook on Semicon- utilized TEGa, TMGa, AsHg PH3, and AsHg as precursors. Their ductors" (M. Balkanski Ed.), Vol. 2, Chp. 6. © North-Holland, Amster- optimum growth parameters are as indicated in Table VI. In addition, Ga^In^.^^P/GaAs has been grown using the trimethyl dam. precursors TMIn, TMGa, AsHg, and PH3 at atmospheric pressure [163]. Molecular beam epitaxy growth of GaAs/GalnP was achieved to the mass action law [157] with gas sources by Blood et al. [164]. Hafich et al. [165] have grown GaAs/GalnP on (lOO)-oriented semi-insulating GaAs substrates. First they degreased the substrate and etched it in (3.8) 77^2 N^ H2SO4: H2O2, followed by the formation of an oxide layer by resting the substrate in deionized water. The oxide was removed where N^yN^^, and A^x ^^e the electron, hole, and exciton densi- in vacuum under an AS2 flux produced by thermal decomposities. Ex is the binding energy of the exciton, and T is the temper- tion of ASH3 in a low-pressure cracking oven at 900 °C. Epitaxial growth was carried out at a substrate temperature of 500 °C using P2 and As2 molecular beams produced by thermal decomposition of the gaseous hydrides PH3 and ASH3 in a low-pressure cracking 0.45| oven at 900 °C. Rao et al. [166] reported growth of GaAs/InGaP epilayers on GaAs substrates. The substrates were cleaned in organic solvents, etched in NH4OH : H2O2 : H2O = 2 : 1 : 20 at room temperature for 2 min, and rinsed for 10 min in deionized water to form native oxide. The oxide was desorbed by heating at a substrate temperature of 600 °C in the presence of an AS2 flux for 7 min. The GaAs layers were grown at 605 °C at a growth rate of 0.35 jjum/h. The arsenic to gallium flux ratio was approximately 3 : 1 . The growth of the InGaP layer used a heated P2 source obtained from the decomposition of GaP. The Ga^Iuj.^P J 152

_J 154

1

L_ 160

L. 158

1—

1

ALLOWED BANDS FOR SUPERLATTICE

20

Table VI. Optimum Growth Parameters for Ga^In^.^P/GaAs

30

40

50

60

70

80

90

100

WELL OR BARRIER WIDTH a IN A

Fig. 13. Allowed energy bands, E^, E2, £3, E^ (hatched), calculated as a function of well or barrier (L^ = L^ = «) in a superlattice with a barrier potential V = 0.4 V. Reproduced with permission from L. Esaki, "Recent Topics in Semiconductor Physics" (H. Kamimura and Y. Toyozawa, Eds.). ©1983 World Scientific, Singapore.

Growth parameter

GaAs

GalnP

Pressure (torr) Temperature (°C) Total H2flowrate (1/min) ASH3flowrate (cm^/min) H2 through TEGa bubbler atO°C(cmVmin) H2 through TMIn bubbler at 18°C(cmVmin) PH3flowrate (cmVmin) Growth rate (A/min)

76 510 3 30

76 510 3

120

120



200 300 200

100



GALLIUM ARSENIDE HETEROSTRUCTURES

93

HCi 112,000

16.000

12.000

H3PO4

Fig. 14. Etch rates of InGaP (in angstroms per minute) at 25 °C in H3PO4/HCI/H2O solutions. Reproduced with permission from S. J. Pearton, "Handbook of Compound Semiconductors" (P. H. HoUoway and G. E. McGuire, Eds.), Chap. 8. ©1995 Noyes, Park Ridge, NJ.

layer was nucleated at a substrate temperature of 505 °C at a growth rate of 0.7 /Ain/h. The growth of Al^Ini_^P and Al^Ga^.^,.? by MBE and MOCVD is similar to Ga^^Ini,^? and was described by Abernathy [167] and Hobson [168]. Species for n-type doping in MOCVD-grown Gain? include Si (SiH4) and (Se) H2Se [169-171]. Silicon turns out to occupy the column III sublattice, whereas Se preferentially occupies the column V sublattice. Doping concentrations as high as 10"^^ cm~^ have been achieved with both Si and Se doping. However, the concentration levels reduce with increasing temperature. Molecular beam expitaxy-grown GalnP n-type layers have been doped with Sn [164] to achieve doping concentrations as low as 10"^^ cm~^. In MOCVD-grown InGaP, p-type doping has been obtained with Zn (DMZn), Te (DeTe), and Mg [172], and is incorporated in preference to P. Additionally, p-type doping has been obtained with Be in MBE-grown InGaP. A solution containing HCI with or without an oxidizing agent can be used for wet chemical etching of InGaP [173, 174]. Figure 14 shows the etch rates of InGaP in HCI/H3PO4/H2O mixtures as a function of the relative ratio of the etchants [151]. The etch rates increase with increasing HCI concentration, but the fastest rate is achieved with the addition of dilute H3PO4 solution. In general, the etch rate of InGaP varies between 1 and 1.2 /im/min in a pure solution of HCI at room temperature [175]. A comparison of dry etching by reactive ion etching and electron cyclotron resonance has been reported. The crystalline structure of GalnP may be ordered such that sheets of pure Ga, In, and P atoms alternate on the planes of the basic unit cell without intermixing of the Ga and In atoms on the same lattice plane as shown in Figure 15. Transmission electron diffraction (TED), transmission electron microscopy. X-ray diffraction, and variations in energy bandgap all have been used to study ordering. However, these methods can lead to significantly different conditions for ordering. For example, widely different optimal conditions have been reported for ordering in Ga^Ini_^P by Kondow et al. [176], Suzuki et al. [172], and

Fig. 15. Ordering of In, Ga, and P atoms in InGaP structure. The structure shows alternate sheets of pure In, Ga, and P atoms on the planes of the unit cell without intermixing of the species.

Gomyo et al. [177]. Such discrepancies can be attributed to the dependence of image patterns on film thickness, beam profile, and substrate quality. Growth temperature, growth rate, V : III ratio, substrate quality, substrate orientation, and dopants are some of the parameters that influence ordering of atoms in epitaxial layers. The effect of growth temperature on atomic ordering in Ga^Ini_^P was studied by Gomyo et al. [177], Morita et al. [178], Kurtz et al. [179], and Okuda et al. [180]. These studies indicate that, for a fixed V : III ratio and substrate orientation, ordering is maximal in the temperature range 650 < T < 680 °C. Liu et al. [181] used TED to study the effect of temperature on Ga^In^.^P epitaxial layers grown by MOCVD on (100) GaAs substrate. Their results are illustrated in Figure 16. Likewise, Figure 17 is a TED pattern by Cao et al. [182] that illustrates the effect of growth rate on atomic ordering in Ga^IUj.^P layers. The pattern depicts diffused intensity spikes at higher growth rate that imply a greater degree of disordering. Substrate orientation also greatly influences the long range ordering. For instance. Gag 51% 5 P grown on (001) has long range ordering, but growth on (111)^ and (110) shows disordering [183, 184]. The bandgap of Gaj,Ini_^P lattice-matched to GaAs have been shown to differ by as much as 100 meV [185]. The bandgap varies from 1.90 eV for layers grown at temperatures of greater than 700 °C to 1.85 eV for layers grown at 650 °C. A similar variation of between 0.03 and 0.39 eV has been observed in the conduction band discontinuity [186, 187]. There is, however, less variation in the bandgap discontinuity [165, 166, 188-193] between 0.43 and 0.48 eV.

3.4.3. InjpGai_^As/GaAs and Iiij^Al^.^As/GaAs High quaUty In^.^Ga^As/GaAs pseudomorphic QWs and SLs have been grown on GaAs substrate by both MBE and MOCVD processes. Conventional solid source MBE growth of Ini_^Ga^As/GaAs structures utilizes elemental In, Ga, and As2 (or AS4). lni_ fia^As/Gsu\s has been grown on (001)-oriented substrates, misoriented (001) GaAs substrate toward (110) [194],

94

DONKOR

(a)

(b)

Fig. 17. Transmission electron diffraction patterns that illustrate the effect of growth temperature on the ordering in InGaP layers. The electron beam was incident along the [110] direction. The layers were grown by MOCVD at growth rates G^ of (a) 4.1, (b) 6.3 (c) 8.3, (d) 12, and (e) 12 jjLin/h. Reproduced with permission from D. S. Cao, E. H. Reihlen, G. S. Chen, A. W. Kimball, and G. B. Stringfellow, /. Cryst. Growth 109, 279 (1991). © North-Holland, Amsterdam. (c)

the partial pressures of TMIn and TMGa in the reactor as 1 Fig. 16. Transmission electron diffraction pattern of (a) an ordered GalnP epitaxial layer, (b) a semiordered GalnP epitaxial layer, and (c) a disordered GalnP epitaxial layer. Reproduced with permission from W. Liu, E. Beam, III, T. Kim, and A. Khatibzadeh, "Current Trends in Heterojunction Bipolar Transistors" (M. F. Chang, Ed.), pp. 241-301. ©1996 World Scientific, Singapore.

(lll)-oriented substrate [195], and (311)-oriented substrate [196]. The difficulty in MBE growth of Inj.^Ga^As/Ga^As is attributed to the fact Ini.^Ga^As and GaAs alloys have different optimal growth temperatures (about 540 °C for Inl_;^.GaJ:As with x > 0.7 and 580-600 °C for GaAs). One approach is to grow most of the GaAs at 580 °C and the Ini_^Ga^As at 540 °C, and to ramp down the substrate temperature from 580 to 540 °C during the last 350 A of the GaAs preceding the Ini_j^Ga^As growth [197]. After growth, the substrate temperature is quickly ramped back to 580 °C so that all but the first 50 A of the next GaAs is grown under optimal conditions. Typical MOCVD growth of In^Gai_;,As/GaAs uses AsHg, TMGa, and TMIn for sources and SiH4 and DEZn for dopants at a growth temperature of 650 °C and a reactor pressure of 20 hPa. The growth rate used by Hasenohr et al. [198] for Inj.^^Ga^^As was 3.2 fjLmJh and varied between 2.5 and 2.8 fim/h for GaAs. The vapor pressure ratio V : III in the reactor was 84 for In^^Ga^.^^As and varied between 108 and 118 for GaAs. Hasenohr et al. determined the dependence of the In : Ga ratio on the ratio between

(3.9)

: 0.029 + 0.636 PTMGa

Here Xj^ is the indium composition, ;?TMin/^TMGa> ^re the partial vapor pressures of In and Ga, respectively. The strain in the lattice-mismatched In^.^Ga^As/GaAs heterostructure can be accommodated between the GaAs substrate and the In^.^^Ga^As epitaxial layer through the use of an Ini_^Ga;,.As buffer layer matched to the in-plane lattice constant of the strained-layer system. Alternatively, the strain can be totally confined to the Ini_;^.Ga^As layer through the use of a GaAs buffer with an in-plane lattice constant that matches the GaAs substrate. Proteitti et al. [199] found that the strain is accommodated by bond stretching and bond bending, with the lattice expanding in the growth directions. The molar fraction x, may be expressed in terms of the elastic strain as X = ^GaAs ~ <^InAs

h-l^+Q^)—] ^'-''^

Here C^ and C12 are the elastic stiffness constants of the epilayer material, and aca^s ^^^ <^inAs ^re the lattice constants for GaAs and InAs, respectively. The strain relaxation processes of the epitaxial mismatched layers give rise to surface fluctuations [200, 201]. Two known types of surface fluctuations are island formation [202, 203] and striations [204]. The dependence of the energy gap of In^^Ga^.^^As on the Xj^ composition is [205] Eg = 0.475(1 - x^^f + 0.6337(1 - jCi„) + 0.4105

(3.11)

The energies of the conduction and valence band extrema of the Ga^Ini_^As show a linear relationship for the valence band

GALLIUM ARSENIDE HETEROSTRUCTURES energy and a quadratic function for the conduction band energy. Photoluminescence excitation data appear to indicate that Hght holes are confined in the GaAs layer, while the heavy holes are confined in the In^Ga^.^^As layer. This analysis is confirmed by a number of theoretical reports [206-209]. Electron Raman scattering experiments indicate a dependence of the band offset on transition energy [210]. 3.5. Heterostructures of the Type III-y,-Vi_^/GaAs 3.5.1. GaAsi_^P^/GaAs and GaAsi_^Sb^/GaAs

95

(Al;,-Gai_j,)o.5lno.5P increases with increasing mole fraction of dopant, but decreases with increasing V : III ratio. Diluted SiH4 is a common source for n doping. Incidentally, increased concentrations of SiH4 have been known to reduce the Al content of the alloy [226]. (Al^-Gai_;,)o.5lno.5P grown on (001) exhibits a CuPt-type crystal ordering of the group III atoms on the column III sublattice. However, thermal annealing can convert an ordered (Al^-Gai_;^)o.5lno.5P alloy into a disordered structure [227]. Disordering can also occur due to diffusion of heavy atomic species such as Zn and Mg. The room temperature energy gap [228] and electron effective mass [229] as functions of composition x are, respectively, given by

The MOCVD growth of GaAsi_;,Sb^/GaAs has been reported under atmospheric pressure [211, 212]. The most common precursors are TMGa, TMSb, and ASH3. Iwamura et al. [213] used (3.14) : 1.9 + 0.6A: TEGa, TBAs, and TMSb as precursors at low pressure on (001) semi-insulating GaAs. The partial pressure of the TEGa was 0.5 : 0.042 + 0.0328JC (3.15) rriQ Pa, the V : III ratio was between 1 and 7, and the growth temperature was between 475 and 550 °C. Egger et al. [214] have grown both GaAsi_;^P;,/GaAs and GaAs^.^Sb^/GaAs. The sub- 3.7. Heterostructures of the strate temperature for the GaAsi_^P^/GaAs growth was 650 °C lype ni,-rai_,-V,-V,_/GaAs and for the GaAsj.^^Sb^/GaAs was 525 °C. Sources used for the growth of the GaAs substrate were TBAs and TEGa. The The most important heterostructure in this family is ternary alloys GaAsj.^^P^^ and GaAs^.^j-Sb^^ were grown by the Ga;^Ini_^As^Pi_^/GaAs. It has been grown by both addition of PH3 and TMSb, respectively. The reactor chamber MOCVD [230] and MBE [231]. Zhang et al. [232] have grown was 50 mbar in the case of GaAsi_^P^/GaAs and 100 mbar for lattice-matched Ga^In^.^As^Pj.^ on GaAs for the entire comGaAsi_;^Sb^/GaAs. The structures were grown on (100) GaAs position range 0 < y < 1 using gas source MBE process. Their substrate oriented by 2° toward (110). Compositional mixing also sources were In and Ga molecular beams produced from Knudhas been reported for GaAsi_^P;,,/GaAs [215-217]. These results sen effusion cells and AS2 and P2 molecular beams produced indicate that compositional mixing on the anion sublattice has by thermal decomposition of AsHg and PH3 in a high-pressure a nonlinear dependence on the incident flux ratio. Cunningham cracker cell at 950 °C. The growth temperature was 583 °C. et al. [218] fitted a quadratic relation for the anion incorpora- For MOCVD growth, Ishibashi et al. [233] used TMGa, TMIn, tion of relaxed GaAsi_^Pj^ layers. The GaAsi_^Sb^ has a wide TMAl, ASH3, and PH3 as precursors and (001) GaAs substrate. miscibility gap, which can induce phase separation. This can The growth temperature was 750 °C, under low pressure of lead to compositional mixing if the growth process is away from 76 torr with a V : III ratio of 350. The p-type dopant was Zn thermal equilibrium. At a low growth temperature of 420 °C, using DEZn as a source. The activation of the Zn acceptors GaAsi_;pSb;^ can be grown over the entire range 0 < JC < 1. At a depended strongly on postanneahng cooling. The most comhigher growth temperature, the As content in the alloy increases, mon n-type dopant is from Si (silane). The energy gap of the and the MOCVD-grown GaAsi_^Sb^ material is unintentionally Ga;^.Ini_^As^Pi_^/GaAs system is given by [234] p-type doped. Energy gaps given by Capizzi et al. for GaAs^.^P^^ E, = 1.35 + 0.668JC - 1.068v + 0.758x2 + 0.07/ [219] and by Nahory et al. [220] for GaAsi_^Sb^ are , , (3.16) -0.069;c3; - 0322x^y + 0.03xy^ ^GaAsP = 1-42 + 1.172A: + 0.186^2 0 < A: < 1 (3.12) The energy gap of Ga^^In^.^As^Pi.^/GaAs can be tailored to cor^GaAsSb = 1.42 - 1.9;c + 1.2^2 0 < ;t < 1 (3.13) respond to the wavelength region between 0.6 < A < 1.1 /mm [235, 236]. 3.6. Heterostructures of the Type (III,-IIIi_J^-IIIi_^V/GaAs (Alj^-Gai_^)o.5lno5P lattice-matched to GaAs is the most com- 4. Physical Properties of GaAs-Based Quantum Well Structures and Superlattices mon heterostructure of this family system and its growth by MOCVD for the entire range 0 < x < 1 is well established [221-223]. The alloy is typical grown on (OOl)-oriented GaAs substrate at low pressure. Nozaki et al. [224] used source materials TMIn, TMGa, TMAl, and PH3, and a V : III ratio of 400. Growth occurred at a wide temperature range between 570 and 700 °C. Qingxuan et al. [225] demonstrated growth at atmospheric pressure and a V : III ratio between 50 and 200. The GaAs substrate was misoriented by 2-3° toward (110). Growth rates between 1 and 4 jxra were reported. The most common n- and p-type dopants are Si and Zn, respectively. The carrier concentration of Si-doped

4.1. Introduction Consider a heterostructure formed from alternating layers of semiconductors A and B, where the constituents A and B may be elemental or n-ary compound alloys. Let the energy gap of A be larger than the energy gap of B (Egj^ > Eg^). Three basic band alignments can arise from a heterostructure formed from different types of A and B: (1) type I or straddling alignment, (2) type II or staggered alignment, and (3) type III or broken gap alignment. These different configurations are depicted in Figure 18. Figure 18a illustrates

96

DONKOR

a type I (straddling) configuration formed at the hetrointerface of Ino.53Gao.47As (E^^ = 0.75 eV) and Ino.52Gao.48As (Egj^ = 1.44 eV). The structure has conduction and valence band offsets of opposite sign (A^^ = 0.47 eV and AE^ = -0.22 eV, respectively). In the type I configuration, the electrons and holes are both confined within the same layer. A type II (staggered) configuration is formed between AlSb (Egj^ = 1.58 eV) and InAs (Eg^ = 0.36 eV) as shown in Figure 18b. In contrast to type I, we notice here that the valence band of the smaller bandgap material lies below that of the larger bandgap material, so that the band offsets have the same sign (A^^ = 1.35 eV and AE„ = 0.13 eV). Ino.53Gao.47As

Ino.52Alo.48As

AEc EgB=0.75eV

i

jA=1.44eV

;AEV

AEc=0.47eV, AEv=0.22eV a) Type-I or straddling

InAs

AlSb i

i

k

AEc^ f EgA=1.58eV

i i

EgB=0.36eV AEv AEc=1.35eV,AEv=-0.13eV b) Type-II or staggered

EgA=0.73 eV

AEc 1f T

t EgB=0.36eV

In the type III (broken gap) configuration shown in Figure 18c, the magnitude of the offset is so large between InAs and GaSb that the forbidden gap no longer overlaps. However, the band offsets have the same sign (AE, = 0.88 eV and AE^ = 0.51 eV). In the type III configuration, the electrons and holes are confined to different layers. 4.2. Quantum Wells Energy Levels Figure 11 shows a type I QW structure composed of AlGaAs/GaAs/AlGaAs. The figure shows discrete energy levels due to the confinement of electrons in the conduction band and holes in the valence bands. The figure shows the conduction (Eci>^c2)? light-hole (Eii,Eii), and heavy-hole (E^i,E^2) subbands. The size of the confining barriers or band-edge offsets AE^ and AE^, determining the effectiveness of the wells to confine the carriers. There are a number of techniques that have been successfully utilized to calculate the QW energy levels. They most common are (a) the tight-binding approximation [237, 238], (b) the effective-mass or pseudopotential method [239, 240], and (c) the envelope-function approximation [241, 242]. In the tight-binding approximation, one begins with a series of energies, which are characteristics of the sp^ bonds linking one atom to its neighbors. The heterostructure wave function is then built atom after atom. In the pseudopotential method, staking of the constituents is considered as a perturbation over a zero-order situation, which corresponds to the bulk of one of the constituents. The method is analogous to deep level calculation in bulk semiconductor materials. The tight-binding approximation and the pseudopotential method are essentially microscopic methods. These two techniques give accurate calculations of heterostructure energy levels and are able to reproduce the whole dispersion relation. These two calculations often require intensive computer computation and do not easily provide tractable information about the dispersion relation. The envelope-function approximation is restricted to calculating the dispersion relation only at high-symmetry points in the Brillouin zone of the host material. Its advantages include simplicity and closed-form analytically tractable solutions. The key tenets of the envelope-function approximation are described and used to determine the wave functions and subbands for QW, MQW, and SL structures.

J ii

J^

f

^ '

4.2.1. Conduction Bands in Quantum Wells

The energy levels of electrons in the conduction band can be calculated using the envelope-function approximation along with the c) Type-Ill or broken gap Kane model to describe the electronic states of the host A and B Fig. 18. (a) Type I (straddling) configuration formed at the het- materials. The approximation assumes (1) an interface potential rointerface of Ino53Gao47As (Eg^ = 0.75 eV) and Ino52Gao.48As that is strongly localized at the interfaces between the A and B (Egj^ = 1.44 eV). The structure has conduction and valence band off- materials, (2) that the interface potential does not mix the bandsets of opposite sign (A£^ = 0.47 eV and A£„ = -0.22 eV, respec- edge wave functions but only shifts them, and (3) perfect lattice match between the A and B materials, which also crystallizes with tively), (b) Type II (staggered) configuration formed between AlSb the same crystallographic structure. (Egj^ = 1.58 eV) and InAs (Eg^ = 0.36 eV), where the valence band of The generalized electronic wave function thus consists of two the smaller bandgap material lies below that of the larger bandgap matecomponents: the fast varying Bloch function, w^kJ ^^^ the slowly rial, so that the band offsets have the same sign (A^^ = 1.35 eV and varying envelope function, x- The two components are normalAE^ = 0.13 eV). (c) Type III (broken gap) configuration between InAs ized such that and GaSb. The magnitude of the offset is so large that the forbidden gap no longer overlaps. However, the band offsets have the same sign ixlx) Jsfx*xdS = l {u\u) = ^K,cf -^unit.^ cell u*udV = l(4A) (AE, = 0.88 eV and A£„ = 0.51 eV). AEc=0.88eV,AEv=-0.51eV

97

GALLIUM ARSENIDE HETEROSTRUCTURES where S is the sample area and V^^ is the volume of a single unit cell. Inside each layer the wave function is expanded on the periodic parts of the Bloch functions. This gives the electronic wave functions for the edges of the A and B layers, respectively,

The constants A and B can be determined by matching x and (l/mi)(dx/dz) across each well-barrier interface. For the solution to Eq. (4.9) these conditions yield (4.12a)

^ c o s ( ^ ) = ^ (4.2) n

^b

(4.3)

'A = Eexp[i(k±T)]Mf^Ar„

where the growth direction is assumed to be in the z direction and kj^ is the transverse electron wave vector. The periodic parts of the Bloch functions are also assumed to be the same in each kind of layer that constitutes the QW; therefore, M 4 = "nitThe summation index, n, runs over as many edges as might be included in the analysis. Since the conduction band is nondegenerate, the envelope wave function satisfies Schrodinger's equation {H, + V)x„=E^Xn

(4.4)

V 2 /

nif,

Divide (4.12b) by (4.12a) to get

^tan(M) = ^

H. = -,r^V^ 2w*.

= - ^ { k l + kl+ kl) '2ml

(4.5)

Here the index i = w,b stands for the well and barrier regions, respectively. The Schrodinger equation then becomes /

h^kl Wk^

h^ d^

h^kl K-ki\

6)

That is,

{

m^ m^

_ J0 11^

if z corresponds to the well layer if 2 corresponds to the barrier layer

(4.7)

if z corresponds to the well layer if z corresponds to the barrier layer

where V^ is the conduction band offset. The solution to Eq. (4.6) with (4.7) and (4.8) is given as ATeven = A COS{k,Z)\z\

<

-

= 5exp[-)8,(^z-|^j|z|>^

(4.9)

= ^exp[-^,(z-|)]|\z\ > A'odd = ^sin(A:,z)

\z\ <

-

= ^exp[-^,(z-§)] = ^exp[/3,(z-|)]

\z\ > 2"

(4.10)

|z|>

where 2mu Pi = -f(K-E,) h'

-K
2m„ ki = -fE, h'

(4.11)

(4.13)

Similarly, Eq. (4.10) gives

J^eotfM)=_^ m^

\

2 J

m^

(4.14)

The number of states bound by the well at A:^ = A: = 0 is given by

m-r]

AT = 1 + Int where the Hamiltonian operator for the conduction band is

(4.12b)

(4.15)

4,2,2. Valence Bands in Quantum Wells The simphcity of the conduction band structure in QWs relies on the fact that the conduction bands are nondegenerate and the interaction with other energy bands is weak. As a result of this weak interaction, the perturbation method can be used to describe the dynamics of the conduction band in terms of an effective mass approximation, which signifies the weak interactions of the conduction band. If the bands were degenerate, weak interactions could no longer be assumed and, therefore, the effective mass approximation would have to be modified. One such modification is owing to Luttinger and Kohn [243, 244]. Their approach is to modify the effective mass approximation to the one electron Schrodinger equation for each degenerate band by incorporating additional terms to account for coupling between the degenerate bands as well as spin degeneracy. Depending on the effective couphng between the degenerate bands and spin at the band edge, there can be either two, four, six, or eight coupled differential equations obtained from the modified effective-mass approximation of the Schrodinger equation. Four sets of coupled effective mass equations result if coupling is between only two bands, say the heavy hole (HH) and light hole (LH). Six coupled effective mass equations result for three band couphng between the HH, LH, and spin-orbit (SO) bands. Eight sets of equations result if there is coupling between the three valence bands (HH, LH, SO) and the conduction band. A four band model that leads to eight effective mass equations has been analyzed [245-247]. However, interaction between the HH and LH bands is by far the strongest and, to a good approximation, the other interactions may be neglected. Only when we consider energy levels deep into the valence band (energies comparable to the spin-orbit sphtting energy A) do we need to include the SO band in the interactions. The four coupled effective-mass equations that arise from interactions between the HH and LH bands can be greatly simplified using a modified k • p representation of the energy bands [248-250]. The approach is to define a new set of Bloch functions for the HH and LH (
DONKOR H H a n d L H (M^h? "hh» "ih? "ih) equations. T h e new set of Bloch functions is given by [249]
--=(aMhh-a''«hh)

(4.16)

^hh

=

-^(a«hh-a'"hh)

(4.17)


-=(^M,h-)8*Mhh)

(4.18)

^Ih

-^(/3M,h-r"hh)

(4.19)

=

a =

p=

"./STT

36I\'

T!''^ 7=2'"^

1

(4.20) (4.21)

A-4+2)J

where 6 = tan ^(ky/k^). T h e Hamiltonian for t h e new basis set can b e written in matrix form as

H =

^u

^12

^13

0

^12

^22

0

^13

HI,

0

^22

-/:^l

0

^13

-^12

^11

(4.22)

The matrix in Eq. (4.22) can be block-diagonalized as if^ 0

H' =

0 if^

(4.23)

where the upper and lower blocks are given by H"=\

R

P+ Q R*

P-Q

P-Q R*

R P+Q

(4.24a)

(4.24b) (4.24c)

R=\T\-i\S\ p =

R

-V3

=

P±(Q^-^R*R)^/^

(4.26)

w h e r e t h e positive sign is for t h e heavy holes and t h e negative sign is for t h e light holes; that is,

E = A(kl-^kl)±[B^(kl-\-kl)^ +C\klk] + k]kl + k]kl)Y (4.27) A = n?-yJ2m

B =

h^y2lm

-«-©)

(4.28)

4.3. Electrons and Holes in Superlattices In principle, t h e energy of electrons and holes in superlattices can b e calculated in t h e same way as for q u a n t u m wells, with t h e use of appropriate boundary conditions. T h e periodicity of t h e superlattice, with period equal t o t h e s u m of t h e widths of a well and a barrier, imposes t h e same boundary conditions on t h e electron wave function as a periodic potential of a one-dimensional crystal. A s a result, it should b e possible to express t h e envelope wave function, xi^)^ for ^^ electron in t h e conduction b a n d in t h e form of Bloch waves propagating along t h e direction of growth of t h e SL. Let us now consider a system that consists of a large n u m b e r of alternating layers A and B, with t h e layers so narrow that t h e wave functions in t h e adjacent wells begin to overlap as indicated in Figure 19. T h e solid Hne in each well indicates t h e position of t h e lowest confined state, E^, obtained in t h e M Q W limit. Because of t h e finite overlap, an electron in such a system is free to travel from o n e well to another.

(4.24e)

+ kl)

{y2 +

E-V

(4.24d)

Il(kl^k]^kl)

Q=yM-2kl^k]

where fl a n d rj a r e to b e chosen. T h e eigenvalues for t h e Hamiltonian, H', are

y3){k^-iky)

V3

(4.24f) Eo

S = sfl-y^k.ik^

(4.24g)

- iky)

where 71,725 73 ^^^ the Luttinger parameters. The unitary transformation, U, which forms a block-diagonaHzation of the Hamiltonian, H, into H' = UHU* is given by ^=:exp(-/n) 0 0 —-Qxp(in) V2 ^ ^ V2 0 -j= exp(-/T7) - — cxp(i7]) 0 U = 0 1 ^:zexp(-/a) . V2

— exp(-/i7) 0

— exp(/i7) 0

0 1 — exp(/a) V2 (4.25)

d

»'<

d

—W

->k. 7i/d

(a)

(b)

Fig. 19. (a) Superlattice structure made up of a large number of alternating layers of different bandgap materials with the layers so narrow that the wave functions in the adjacent wells begin to overlap. The solid line in each well indicates the position of the lowest confined state, EQ, obtained in the MQW limit. Because of the finite overlap, an electron in such a system is free to travel from one well to another, (b) Variation of electron energy as a function of wave vector expressed in units of the reciprocal of the well (or barrier) thickness.

GALLIUM ARSENIDE HETEROSTRUCTURES

99

4.3.L Kronig-Penney (Tight-Binding) Model for Superlattice Electronic States

The transcendental equations (4.36) and (4.37) are usually solved numerically.

A simplified calculation of the electronic energy states of the superlattice can be made by assuming a one-dimensional KronigPenney model. The envelope wave functions in the well and the barrier are

5. GaAs Heterostructure Field Effect Transistors

X^{z) = A exp[//:^z] + B Qxp[-ik^z]

0
(4.29)

5.1. Introduction

In a conventional metal-semiconductor FET, the active channel Xb(z) = CQxp[ikijZ] + Dexp[-/A:^z] a < z ^ for digital integrated circuits, (2) a high-current-high-breakdownvoltage device for power FETs, and (3) low-noise microwave and When £; < F, we substitute ik2 = K, where K^ = (2m(V-E)/h?), millimeter-wave FETs. There are two basic variants of the HFET. and Eq. (4.36) becomes One is a device whose structure is optimized to achieve the best channel confinement. This type of HFET requires an adjustment cos(A:^) = cos(k^a) cosh(Kb) of the layer thickness and composition. The second variant is (4.37) an HFET in which doping is distributed to allow the charge to — sin(k^a) sinh( E
4^]

100

DONKOR

Heterostructure FETs

Conventional HFET

[MODFET I

Insulated iGate HFET

|5-M0DFET ] |SL-MODFET] [MISFET

Inverted HFET

] [SISFET

| |SQW-HEMT "^ JI-HEMT

| [l^-HEMT

|

Fig. 20. Family tree of heterostructure field effect transistors. layer, a delta-doped layer, or a superlattice, by doping the conduction layer itself, or by the creation of an inversion layer with no doping. Figure 20 shows a family tree of current heterostructure FETs. They are classified into conventional, insulated gate, and inverted structures based on whether or not the channel is doped and on the arrangement of the gate relative to the channel. In the conventional structure, the gate is placed on top of the doped wide-gap material. There are three distinct types: normal (N-) MODFET, delta-doped (6-) MODFET, and superlattice (SL-) MODFET The insulated structure is similar to the conventional structure except that the epitaxial layer that forms an interface with the channel material is undoped. These devices have evolved into two forms: one where the gate consists of a metal gate and one where the gate is a semiconductor. The inverted HFET structure is significantly different from the conventional HFET in that the Schottky gate is applied to the small-gap material of the heterointerface. In this case, the small-gap material has to be grown on the wide-gap material, which means that the sequence of layers has to be inverted. There are two main variations: one where the doping lies below the channel and another where the gate is placed on an undoped epitaxial layer under which lies the channel layer and then the donor layer. When a normal and an inverted HFET are placed close together, a single quantum well (SQW-) HFET is formed. Figure 21 shows the energy band diagram of normal, insulated gate, and inverted HFETs. Conventional HFETs are designed with lattice-matched heterostructure systems with carriers confined to a single or double quantum well, of which the GaAs/Al^Gai_^As HFET is the prototype. Figure 22 is a cross-sectional view of a GaAs/Alj^Gai_j^As single quantum well HFET. It shows the various GaAs and AlGaAs layers. Due to the higher bandgap of AlGaAs compared with the adjacent GaAs region, free electrons diffuse from the AlGaAs into the GaAs and form a two-dimensional electron gas (2DEG) at the heterojunction. A potential barrier confines the free electrons in the GaAs layer to a very thin sheet. The transport properties of this 2DEG are considerably superior to those of free electrons in, say, GaAs MESFETs, where the channel region must be doped to obtain the charge carriers. Due to the absence of ionized donors in the channel of a HFET, electrons that form the 2DEG suffer little Coulomb scattering and enjoy high mobility. Other saHent features of the HFET active layer are the thin (50 A) "spacer" layer of undoped AlGaAs between the

AlGaAs Gate I AlGaAs

Gate JAlGaAsI GaAs

|

| GaAs

n+

n

i

Fermi level (b)

(a)

GaAs GaAs |AlGaAs| AlGaAs

Gate |AlGaAs|

| AlGaAs

n+

Gate

Fermi level

(c)

(d)

Fig. 21. Energy band diagram of (a) a normal AlGaAs/GaAs single quantum well HFET, (b) a normal single quantum HFET with an undoped spacer layer, (c) an insulated gate HFET, and (d) an inverted HFET Source MMMM^M N^-GaAs

Drain

\

Gate Hig

/

N^-GaAs

N^- AlGaAs N - AlGaAs soacer

1

1 - : ^ 2 D E G

N" -GaAs

GaAs substrate

Fig. 22. Cross-sectional view and energy band diagram of a conventional modulation-doped HFET. doped AlGaAs and the undoped GaAs. The spacer layer further separates the 2DEG from the ionized donors at the interface, increasing electron mobility at the cost of total charge transferred to the interface. The heavily doped GaAs "cap" layer simply facilitates formation of ohmic contacts to the device. An undoped

GALLIUM ARSENIDE HETEROSTRUCTURES AlGaAs spacer layer is inserted between the GaAs and the doped AlGaAs to reduce ion scattering. 5.2. E n e i ^ Bands in Modulation-Doped Heterojunctions The energy band diagram of the modulation-doped heterojunction is shown in Figure 23. The difference in electron affinities translates into a discontinuity in the conduction band at the heterojunction. Electrons diffuse from AlGaAs to GaAs, causing a dipole layer to form with ionized donors on one side and electrons on the other. Equilibrium is estabhshed when the potential difference equals AE^- Charge transfer across the heterointerface requires only that a discontinuity of greater than 2 kT appear in the conduction band, not a difference in bandgaps. Electrons in the 2DEG are confined to a potential well at the heterojunction that is often approximated as a triangular well. Electron energies are quantized perpendicular to the heterointerface. Motion in the other two directions is unconstrained. A simplified explanation for the formation of the energy band structure is to consider the impurities of the doped (AlGaAs) region to be isolated with binding energy Ei,. At very low temperatures, Eij > k^T, and the carriers remain frozen onto the impurity sites. When Ei, = k^T, carrier detrapping takes place. To establish thermal equilibrium, the electrons escape, either by diffusion or quantum mechanical tunneling, into the small bandgap (GaAs) material. The electrons quickly lose energy by emitting phonons in a time scale on the order of 1 pS. The reverse process, that is, recapture of the electrons by the ionized impurities, is prevented by the built-in potential. However the residual impurities affect the charge transfer. Band bending takes place due to the formation of a dipole between the ionized impurities and the electrons. An improvement on the conventional HFET is obtained by grading the epilayers that form the heterointerface. The goal is to Doped Ali.xGaxAs

Undoped Ali.xGaxAs

Undoped GaAs

qV2o

101

lower the effective interfacial resistance between the Al;,Gai_j,As at the A/^+—GaAs/A/^+—Al^Gaj.^As [252]. The x value is also chosen so as to eliminate band-edge discontinuity of the N^— Al;,Gai_;,As and the undoped Al^^Gaj.^^As that forms the heterojunction with the active undoped GaAs that confines the 2DEG. Another modification of the conventional HFET incorporates multiple heterojunction layer density [253]. The goal here is to increase the 2DEG sheet density. This allows for increased device current and improved power performance. The disadvantage is lower frequency and speed performance [254] compared to a single quantum well HFET. Doped impurities and DX centers in heavily doped AlGaAs layer of HFETs degrade device performance. One method to resolve this problem is to incorporate superlattice donor layers in place of the doped AlGaAs layers [255, 256]. A pseudomorphic HFET (PHEFT) can also improve upon the basic HFET performance by replacing the GaAs active region with a different material, such as InGaAs, that has relatively low DX centers and higher mobihty [257, 258]. PHFETs have been designed for low-noise amplification [259], high-frequency operations, and high-power operations [260]. Pereiaslavets et al. [261] designed a narrow channel Ga^Ini_^P/In^Gai_3.As/GaAs PHFET for high-frequency and high-power apphcations. They observed that the 2DEG populated the energy level, which in turn lead to enhanced carrier mobihty. The f^ of the device was found to be 100 GHz and the f^^ found to be 180 GHz. Similar highfrequency and high-power operations have been reported [262] for (Alo.7Gao.3)o.5lno.5P/Ino.i5Gao.85As/GaAs PHFETs. To minimize the DX centers, Se instead of Si was used as an n-dopant for the (Alo.7Gao.3)o.5lno.5P. The maximum current density and transconductance were measured to be I^s = 326 mA/mm and ^mmax = ^^8 mS/mm, respectively, and the intrinsic transconductance was measured as gi = 620 mS/mm at gate vohage FGS = 0.7V.

Heterostructure insulated-gate field effect transistors form another class of HFET. There are two main subclasses: the semiconductor-insulator-semiconductor FET (SISFET) [263,264] and the metal-insulator-semiconductor FET [265-266]. The SISFET has a semiconductor gate and a heterojunction barrier instead of a metal gate and a Schottky barrier in the conventional HFET. The SISFET energy band structure is akin to the Si MOSFET It exhibits good thermal stabihty, its threshold voltage is near zero, and it is less dependent on material characteristics [267]. The transconductance versus gate voltage shows a distinctive sharp turn on at low temperatures near its knee region and has a higher slope in the linear region than conventional HFETs.

5.3. Device Characteristics 5.3.1. Sheet Carrier Density di

Fig. 23. The energy band diagram of a modulation-doped heterojunction. The difference in electron affinities translates into a discontinuity in the conduction band at the heterojunction. Electrons diffuse from AlGaAs to GaAs, causing a 2DEG confined by a potential well at the heterojunction, which is often approximated as a triangular well.

Two analytical approaches for describing the charge distribution across the heterojunction are the self-consistent method [268] and the variational method [241, Chap. 5]. At temperatures of 300 K and below, only the lowest two quantized energy subbands are significantly populated and need to be included in modeling the device characteristics. Under these conditions, the sheet

102

DONKOR

carrier density of the 2DEG is given by

»-(/¥F

^Ep^{T)

+ 8\+Nl{d, + MA

field. The I-V models for the Hnear and saturation regions are respectively of the form (5.1)

^^ ^

wtxe2 (VG-VTH)'-(VG-VTo-Vd)' 2(d + M) L, + VJF,

-NM + ^d)

(5 5>,

1/2

where ^Q is as defined in Figure 23, 62 is the permittivity of the doped layer, A^^ is the ionized donor density in the doped layer, di is the thickness of the undoped spacer layer, and 5 is a correction factor required due to the use of the depletion approximation in the doped layer. For a donor binding energy of 15 meV, 5 is 25 meV at 300 K and 50 meV at 77 K. The position of the Fermi level measured from the bottom of the potential well at the heterointerface is a function of the sheet carrier density. Lee et al. [269] reported a graphical relationship as well as analytical expressions for 300 K, 77 K and 4 K. The linear approximations are valid for values of n^, between 5.0 and 15 x 10^^ cm"^ and can be expressed as OeV, r = 300K Ep = ^EPQ(T) + qan, AEpQ = I 0.025 eV, r < 7 7 K (5.2) the constant a = 0.125 x 10"^^ V/m^ and e is the electronic charge. Control of the sheet carrier in HFETs is achieved through a Schottky gate. Accounting for the gate voltage, the sheet carrier density expression Eq. (5.1) can be modified as e? Vn

e

^TH

d-\-^d AK + AEp

(5.3)

/3F,^(l + i8i?,F;)

(5.6)

Here F ; = VG - V^, V,, = F,L^, p = S2ixW/{d + ^d\ L, is the gate length, W is the gate width, and R^ is the source series resistance. A comparison between the preceding models and experimental results shows good agreement [272]. The ac model attempts to determine nonlinear elements such as gate capacitance and other parasitic capacitances found in the equivalent circuit [273] of the HFET as shown in Figure 24, as well as the frequency response of HFETs. The parasitic capacitances are determined from the derivative of the sheet carrier density with respect to the bias voltages. The relation between the maximum frequency, f^^, and the cutoff frequency, /^, in terms of parasitics has been widely reported and takes the form

'•"-'•/{hfX^-"'-^) IS

^(l + 5C„, /.=

27rC

+ ^ ) ( l + ^.i^.)^)

(5.7) (5.8)

Here g^ is the transconductance, and the other parameters are given in Figure 24 and are as defined in the hterature [274]. The dc characteristics turn out to depend on the device strucwhere d = d^-\- d^, d^ is the thickness of the doped AlGaAs beneath the Schottky gate, <^^ is the Schottky barrier height, Vp ture and the material systems used to design the HFET. SQW is the pinch-off voltage, and 62 is the dielectric permittivity of the conventional AlGaAs/GaAs HFETs with gate lengths on the order of 1 /xm are capable of delivering drain saturation current AlGaAs layer. of about 10 mA and transconductance values of about 200-300 mS/mm at room temperature [275]. As the gate length shrinks 5,3,2. Alternating Current and below 1 /x,m, the dc characteristics generally improve [273]. Direct Current Characteristics Improvement in device characteristics is also observed at low Current-voltage (I-V), transconductance-voltage, and capaci- temperatures [267]. The growth of pseudomorphic HFETs has tance-voltage are the three most common dc characteristics. opened up new approaches to achieving enhancement in device characteristics. Dickmann et al. [262] achieved transconductance A simplified analytical model for these characteristics is derived of 368 mS/mm and a drain saturation current of 326 mA/mm in from the charge control method [269]. The main difference between various analytical models is due to the choice of the functional relationship between the drift velocity and the appHed electric field. The import of this relationship is to account for the velocity overshoot and other nonequilibrium effects, while still providing a tractable or closed-form functional relationship [270, 271]. A multiregion model, whereby the linear and saturation regions are analyzed separately and then integrated into a unified model is often employed to obtain analytical closed-form expressions for the I-V characteristics. The linear region also corresponds to low applied electric field, such that the velocity of carriers in the channel is directly proportional to the appHed Fig. 24. Equivalent circuit of an HFET. Reproduced with permission field, whereas the saturation region is taken as corresponding to from M. B. Das, IEEE Trans. Electron Devices ED-32,11 (1985). © IEEE, the saturation (or constant) velocity of the carriers with appUed New York. VTH =

t-Vp-

(5.4)

103

GALLIUM ARSENIDE HETEROSTRUCTURES a 0.35-/xm (Alo.7Gao.3)o.5lno.5P/Ino.i5Gao.85As/GaAs pseudomorphic HFET. Likewise, Pereiaslavets et al. [261] reported drain saturation current of 800 mA/mm and transconductance of 600 mS/mm for a narrow channel(50-80-A) GalnP/InGaAs/GaAs pseudomorphic HFET. The ac characteristics show a similar trend of improvement in short-channel devices and in pseudomorphic structures that incorporate devices with high mobility and high-velocity overshoot effects.

6. GaAs Heterostructure Bipolar Transistors 6.1. Introduction Figure 25 depicts a cross section of an npn AlGaAs/GaAs single heterojunction bipolar transistor. The structure consists of a lightly (N~-) doped wide bandgap Alj,Gai_^As emitter, a heavily (P+-) doped GaAs base, and an N~-doped GaAs collector. A double heterostructure bipolar transistor is formed by replacing the GaAs collector with another wide bandgap material such as AlGaAs. The performance enhancement that an HBT offers compared to a homojunction bipolar transistor can be deduced from the current gain figure of merit, which is given by [276]

^~.'--^^'^{^)

(6.1)

Here N^ and P^ are the emitter and the base doping levels, and Vnb and Vpg are the mean speeds of electrons at the emitter end of the base and holes at the base end of the emitter, respectively. Also the energy gap difference is Ae^ = eiVp — VJ, where Vp and V^ are the potential barriers of holes and electrons. The energy gap difference of HBTs is several kTs. As a result, very high i^max > 1000 can be achieved [276, 277]. Improvement in high-frequency performance can be realized in an HBT because the base can be highly doped to reduce base resistance without deteriorating the current gain. However, the process of heavily doping the base can be impeded due to the increasing diffusion coefficient of the base acceptors at higher concentrations. Furthermore, the p dopant may fall short of the emitter-base interface and diffuse into the emitter. Thus the choice of dopant species become very important. Carbon appears to be a promising acceptor in MBE, MOMBE, and MOCVD

emitter metal Insulator Implantation damage

base metal

growth. Carbon diffuses less in comparison with Be or Zn, allowing for high-temperature processing and high doping concentrations. The discontinuity in the energy bands may be abrupt or graded, and the advantages and disadvantages of each have been discussed in the Hterature [276]. Lattice-matched Gao.52Ino.48P/GaAs HBT [186, 188, 278] has evolved as an alternative to the more conventional AlGaAs/GaAs HBT Some of its attractive features include near ideal currentvoltage characteristics, high current gain [279, 280], and constant current gain for a wide range of temperatures [281]. Etching solutions for GalnP do not attack GaAs [282] making selective etching possible for material processing. Also, GalnP is less susceptible to oxidation, whereas AlGaAs is readily oxidized due to the acute reactivity of Al. In addition, DX centers are relatively less concentrated compared with AlGaAs. 6.2. HBT Modeling and Characteristics The procedure for modeling HBTs was developed from a modification of the basic theory of homojunction BJTs to account for variation in semiconductor composition. In the simplest approximation, carrier fluxes are taken to be linear functions of the apphed external biases, which leads to the drift-diffusion theory. In the drift-diffusion approximation, the electron current density, /„, and the hole current density, Jp, are expressed as the sum of two terms: a drift term due to the electrical field (-grad V) and a diffusion term due to the inhomogeneous carrier densities. For the HBT, these terms are given by

f-dVdV_ dx J = pefi

IdE, \ ^ /dn q dx )^'''\TX-%^)

^_^)_eDj^-^^) P[dx + q dx J P\dx

liilliliiiii^^ K$;§;^

N" -GaAs collector

t-JXX^iS

,^ ^. ^'-'^

N, dx )

(6.3) ^ ^

Here /x„, /x^, D„, and Dp are, respectively, the mobihty and diffusion coefficients for electrons and holes, and e is the electronic charge. In general these parameters are dependent on the electric field. In addition, E^, N^ and E^, N^ are, respectively, the energy and effective density of states in the conduction and valence bands. The terms that involve the derivatives of the conduction and valence bands act as quasielectric fields that act on the electrons and holes, respectively. Similarly the derivatives of the densities of states act like diffusion terms for electrons and holes. The Poisson equation has to be solved simultaneously with the drift-diffusion equation to obtain the behavior of carrier transport in the HBT If we assume that the conduction and valence band bending are the same, then the Poisson equation can be written simply as div (fieff grad (V)) = e(n-p-\-

collector metal

n dNr\

N; - N^)

(6.4)

where e^g is the effective permittivity, and N~ and N^ are the ionized acceptors and donors, respectively. The solution to the coupled equations (6.1)-(6.4) can be given by [283]

N^-GaAs sub collector

Semi insulating GaAs Substrate

, dF„ Jn = en^„ — dFp

Fig. 25. Cross-sectional view of an AlGaAs/GaAs single quantum well HBT

(6.5) (6.6)

where F^ and Fp are the quasi-Fermi levels for the conduction and valence bands, respectively. Numerical techniques such as

104

DONKOR

the Monte Carlo method offer an alternative approach to solving the governing equations for the HBT. The Monte Carlo method is more appropriate if generation-recombination processes are to be accounted for [284]. Refinements of the basic drift-diffusion model are the themionic-difusion model and thermionic-field model [285, Chap. 3]. Liou [285, Chap. 7] compared the accuracy of the different models against measured data for emitter-base voltage versus collector current and found the thermionic-field diffusion model to be a better approximation. The dc modeling of HBT entails determination of the emitter current density (Z^), collector current density (7^), base current density (JQ), transconductance (g^) and current gain factor (j8). These terminal currents can be obtained from the electron and hole current densities using the Ebers-MoU approach. The ac model determines device parasitics [286]. The unity power gain frequency, f^^, and the unity current gain frequency, /^, also determine high frequency and switching performance of the HBT. 7. GaAs-Based Heterostructure Optoelectronic Devices 7.1. Introduction The most common GaAs-based heterostructure optoelectronic devices are lasers, photodetectors, and modulators. Heterostructure lasers span short wavelength (0.6-0.98-/Am), long wavelength (1.3-1.6-/xm), and very long wavelength (2.0-30-/im) regimes of the electromagnetic spectrum [14]. Gallium arsenide heterostructure-based photodetectors [16, 17] offer high speed, high sensitivity, high quantum yield, and low intrinsic noise. Some photodetectors rely on interband transitions and are designed for the visible region. Others utilize intersubband transitions and are designed to operate in the mid and far infrared. The most common heterostructure-based modulator is the self-electrooptic effect device, which operates on changes in the optical absorption induced by an electric field normal to the growth direction of the heterostructure, according to the Franz-Keldysh effect [20, 21]. The quantization effect in quantum well structures causes the resulting absorption spectrum to have large discrete steps. The wavelengths of these absorption steps shift when the quantum well structure is placed under the influence of an electric field. Furthermore, distinctive peaks exist in the absorption spectrum of quantum wells. These peaks also shift upon the application of an electric field; this is called the quantum confined Stark effect, which is the basic phenomenon underlying the operation of the more common heterostructure-based electrooptic modulators. We limit our discussion to a few exemplary devices, because a more comprehensive treatment is beyond the scope of this chapter. Earlier treatment of heterostructure optoelectronics devices and the underlying process can be found in books such as "Semiconductor Optoelectronics" [287] and "Heterojunctions and Semiconductor Superlattices" [288]. More recent treatments are found in "Quantum Well Lasers" [15 and refs. therein] "Electronic States and Optical Transitions in Semiconductor Heterostructures" [16], and "Optoelectronic Properties of Semiconductors and Superlattices" [289]. 7.2. GaAs-Based Heterostructure Lasers Gallium arsenide-based heterostructure visible emitting lasers have been designed with Ga^Ini_^P/(Alo.5Gao.5)o.52lno.48P/GaAs

and Ga^Ini_^P/GaAs strained quantum wells that cover the 0.61 [290] to 0.7-/jLm wavelengths [291-293] and utilize compressive and tensile strain, respectively. Design of such wavelengths takes into account the changes in the emission wavelength due to the effects of crystal structure ordering and operating temperature. The Al^Gaj.^As/GaAs [294-296] laser emits in the 0.65-0.88-/i,m wavelength range that corresponds to the Al molar fraction x < 0.4. For an Al fraction X > 4, the Alj^Gai_^As no longer has a direct bandgap. Lasers designed with In^Gai_^As/(Gao.5Aso.5)o.52lno.48P/OaAs and In^^Ga^.^As/GaAs, cover the 0.9-1. l-/xm near infrared emission wavelengths [297] and are used as pumps for erbiumdoped fiber amplifiers [298]. Heterostructure lasers based on Ga^Ini_j^As^Pi_^ can cover the 13-1.7-fim wavelength range.

REFERENCES 1. H. Kroemer, Proc. IEEE 51, 1782 (1963). 2 B. L. Sharma and R. K. Purohit, "Semiconductor Heterojuctions." Pergamon, Oxford, 1974. 3. A. G. Milnes and D. L. Feucht, "Heterojunction and Metal Semiconductor Junctions." Academic Press, New York, 1972. 4. H. Kressel and J. K. Butler, "Semiconductor Lasers and Heterojuction LEDs." Academic Press, New York, 1977. 5. L. Esaki and R. Tsu, IBM J. Res. Dev. 14, 61 (1970). 6. L. L. Chang, L. Esaki, and R. Tsu, AppL Phys. Lett 24, 495 (1974). 7. R. Tsu and L. Esaki, ^pp/. Phys. Lett. 22, 562 (1973). 8. T Mimura, S. Hiyamizi, T Fujii, and K. Nanbu, Jpn. J. AppL Phys. 19, L225 (1980). 9. D. Delagebeaudeuf, P. Delescluse, P. Etienne, M. Laviron, J. Chaplart, and N. T. Linh, Electron. Lett. 16, 667 (1980). 10. P. M. Solomon and H. Morkoc, IEEE Trans. Electron. Devices 31, 1015 (1984). 11. H. Kroemer, Proc. IRE 45, 1535 (1957). 12. H. Kroemer, Proc. IEEE 70, 13 (1982). 13. J. I. Song, K. B. Chough, C. J. Palmstrom, B. P Van der Gaag, and W. P. Hong, "IEEE Device Research Conference," 1994, paper IVB-5. 14. W. T Tsang, in "Semiconductors and Semimetals" (R. Dingle, Ed.), Vol. 24, Chap. 7. Academic Press, New York, 1987. 15. P S. Zory, Ed., "Quantum Well Lasers." Academic Press, New York, 1993. 16. E T. Vasko and A. V. Kuznetsov, "Electronic States and Optical Transitions" in Semiconductor Heterostructures," Springer-Verlag, New York, 1999. 17. V I. Korol'kov, in "Semiconductor Optoelectronics," (M. A. Herman, Ed.), Chap. 14. Wiley, New York, 1978. 18. D. A. B. Miller, D. S. Chemla, T. C. Damen, T. H. Wood, C. A. Burrus, A. C. Gossard, and W. Wiegmann, IEEE J. Quantum Electron. 21, 1462 (1985). 19. S. Schmitt-Rink, D. S. Chemla, and D. A. B. Miller, ^^v. Phys. 38, 89 (1989). 20. W Franz, Z. Naturforsch 13a, 484 (1958). 2L L. V Keldysh, Sov. Phys. lETP 7, 788 (1958). 22. H. M. Manasevit,^;?^/. Phys. Lett. 12, 156 (1968). 23. H. M. Manasevit, /. Cryst. Growth 55, 1 (1981). 24. G. B. Stringfellow, in "Semiconductors and Semimetals" (R. K. Willardson and A. K. Beer, Eds.), Vol. 22, pp. 209-259. Academic Press, New York, 1985. 25. G. B. Stringfellow, "Organometallic Vapor-Phase Epitaxy: Theory and Practice." Academic Press, New York, 1989. 26. T F Kuech, Mater Sci. Rep. 2(1), 1 (1987). 27. P M. Frijlink, /. Cryst. Growth 93, 292 (1988). 28. M. Behet, A. Brauers, and P Balk, /. Cryst. Growth 107, 209 (1991).

GALLIUM A R S E N I D E H E T E R O S T R U C T U R E S 29. P. D. Dapkus, B. Y. Maa, Q. Chen, W. G. Jeon, and S. P. Den Baars, /. Cryst. Growth 107, 73 (1991). 30. J. P. Hirtz, M. Razeghi, M. Bonnet, and J. P. Duchemin, in "GalnAsP Alloy Semiconductors" (T P Pearsall, Ed.). Wiley, New York, 1982. 31. K. Ploog, in "Springer Proceedings in Physics" (G. LeLay, J. Derrien, and N. Boccara, Eds.), Vol. 22, p. 10. Springer-Verlag, New York, 1987. 32. T J. Drummond, H. Morkoc, and A. Y. Cho, /. Cryst. Growth 56, 449 (1982). 33. G. E. Stillman, S. S. Bose, M. H. Kim, B. Lee, and T. S. Low, in "Handbook on Semiconductors" (S. Mahajan, Ed.), Vol. 3a, Chap. 10. North-Holland, Amsterdam, 1992. 34. S. Amelinckx, in "Supplement to Solid State Physics" (F. Seitz and D. Turnbull, Eds.), Vol. 6, p. 15. Academic Press, New York, 1964. 35. K. Sangwal, "Etching of Crystals," North-Holland, Amsterdam, 1987. 36. P H. L. Notten, J. E. A. M. vanden Meerakker, and J. J. Kelly, "Etching of II-V Semiconductors: An Electrochemical Approach." Elsevier, Oxford, 1991. 37. J. L. Weyher, in "Handbook on Semiconductors" (S. Mahajan, Ed.), Vol. 3a, Chap. 11. North-Holland, New York, 1994. 38. K. E Jensen, /. Cryst. Growth 107, 1 (1991). 39. M. Razeghi, in "Handbook on Semiconductors" (S. Mahajan, Ed.), Vol. 3a. North-Holland, New York, 1994. 40. G. A. Hebner, K. P Kileen, and R. M. Biefeld, /. Cryst. Growth 98, 293 (1989). 41. D. K. Gaskill V. Kolubeyev, N. Bottka, R. S. Sillmon, and J. E. Butler, / Cryst. Growth 93, 1 (1988). 42. C. A. Larsen, N. I. Buchan, and G. B. Stringfellow, Appl. Phys. Lett. 52, 480 (1988). 43. T. E Kuech, E. Veuhoff, T. S. Kuan, V. Deline, and R. Potemski, /. Cryst. Growth 77, 257 (1986). 44. N. Kobayashi and T Makimoto, Jpn. J. Appl. Phys. 24, L824 (1985). 45. P Rai-Chaudhury,/. Electrochem. Soc. 116, 1745 (1969). 46. T. E Kuech, M. A. Tischler, P J. Wang, G Scilla, R. Potemski, and E Cardone, Appl. Phys. Lett. 53, 1317 (1988). 47. A. Y. Cho and J. R. Arthur, in "Progress in Solid State Chemistry" ( G Somojai and J. McCaldin, Eds.), Vol. 10, Chap. 3, pp. 157-191. Pergamon, New York, 1975. 48. L. L. Chang and R. Ludeke, in "Epitaxial Growth" (J. W. Matthews, Ed.), Part A, Chap. 2, pp. 37-72. Academic Press, New York, 1975. 49. J. R. Arthur, Surf. Sci. 43, 449 (1974). 50. C. T. Foxon and B. A. Joyce, Surf. Sci. 64, 293 (1977). 51. D. K. Biegelsen, R. D. Bringans, J. E. Northrup, and L. E. Swartz, Phys. Rev. B 41, 5701 (1990). 52. I. Kamiya, D. E. Aspnes, H. Tanaka, L. F Florez, M. A. Koza, R. Bhat, and J. P. Harbison, in "Semiconductor Growth, Surfaces and Interfaces" ( G J. Davies and R. H. Williams, Eds.), Chap. 1. Chapman and Hall, New York, 1994. 53. A. G Milnes, in "Advances in Electronics and Electron Physics" (P W Hawkes, Ed.), pp. 64-161. Academic Press, New York, 1983. 54. G. M. Martin and S. Makram-Ebeid, in "Deep Centers in Semiconductors," 2nd ed. (S. T. Pantelides, Ed.), Chap. 6. Gordon and Breach, Philadelphia, 1992. 55. M. Ilegems, /. Appl. Phys. 48, 1278 (1977). 56. K. Ploog, A. Fischer, and H. Kunzel, /. Electrochem. Soc. 128, 400 (1981). 57. N. Duhamel, P Henoc, F Alexandre, and E. V. K. KdiO, Appl. Phys. Lett. 39, 49 (1981). 58. D. L. Miller and P M. Asbeck, /. Appl. Phys. 57, 1816 (1985). 59. Y. C. Pao, T. Hierl, and T. Cooper, /. Appl. Phys. 60, 201 (1986). 60. J. L. Lievin and F Alexandre, Electron. Lett. 21, 413 (1985). 6L A. Y. Cho and I. Hayashi, /. Appl. Phys. 42, 4422 (1971). 62. C. E. C. Wood, J. Woodcook, and J. J. Harris, Inst. Phys. Conf Sen 45, 28 (1979).

105

63. J. S. Blakemore, "Gallium Arsenide," Vol. 1, Chap. 1. American Institute of Physics, New York, 1987. 64. O. Madelung, "Data in Science and Technology: Semiconductors," p. 104. Springer-Verlag, New York, 1991. 65. S. Ida and K. Ito, /. Electrochem. Soc. 118, 768 (1971). 66. W. Kern, RCA Rev. 39, 278 (1978). 67. J. de Launay, in "SoHd State Physics" (F Seitz and D. Turnbull, Eds.), Vol. 2, p. 219. Academic Press, New York, 1956. 68. Data in science and technology: Semiconductor Group IV Elements and III-V compounds, Ed, O. Mandelung, pp. 104, SpringerVerlag, New York, 1991. 69. J. R. Chelikowsky and M. L. Cohen, Phys. Rev. B 14, 555 (1976). 70. C. Hermann and C. Weisbuch, Phys. Rev. B 15, 823 (1977). 71. D. L. Rode, in "Semiconductors and Semimetals" (R. K. Willardson and A. C. Beer, Eds.), pp. 1-89. Academic Press, New York, 1975. 72. J. H. Marsh, P. A. Houston, and P. N. Robson, "Gallium Arsenide and Related Compounds," Institute of Physics, Bristol, 1981. 73. H. Ehrenreich, /. Phys. Chem. Solids 8, 130 (1959). 74. A. Fortini, D. Diguet, and J. Lugand,/. Appl. Phys. 41, 3121 (1970). 75. J. R. Hayes, A. R. Adams, and P. D. Greene, in "Low-Field Carrier Mobility in GalnAsP" (T P Pearsall, Ed.), Chap. 8. Wiley, New York, 1982. 76. F C. Frank and J. H. van der Merwe, Proc. R. Soc. London, Sen A 198, 216 (1949). 77 J. H. van der Merwe, Crit. Rev. Solid State Mater Sci. 7, 209 (1978). 78. Y. H. Lo, Appl. Phys. Lett. 59, 2311 (1996). 79. C. Carter-Coman, R. Bicknell-Tassius, A. S. Brown, and N. M. Jokevst, Appl. Phys. Lett. 70, 1754 (1997). 80. L. B. Freund and W. D. Nix, Appl. Phys. Lett. 69, 173 (1996). 81. D. L. Smith and C. Mailhiot, Rev. Mod. Phys. 62, 173 (1990). 82. K. B. Launch, K. Elcess, C. G Fonstad, J. G Beery, C. Mailhiot, and D. L. Smith, Phys. Rev. Lett. 62, 649 (1989). 83. B. S. Yoo, B. D. McCombe, and W Schaff, Phys. Rev. B 44, 13,152 (1991). 84. U. D. Venkateswaran, T Burnett, L. J. Cui, M. Li, B. Weinstein, H. M. Kim, C. R. Wie, K. Elcess, C. G Fostand, and C. Mailhiot, Phys. Rev. B 42, 3100 (1990). 85. J. W Matthews and A. E. Blakeslee, /. Cryst. Growth 27,118 (1974). 86. R. People and J. C. Boan, Appl. Phys. Lett. 47, 322 (1985). 87 W A. Jesser and D. Kuhlmann-Wilsdorf, Phys. Status Solidi 19, 95 (1967). 88. J. P Hirth and J. Lothe, "Theory of Dislocation." Wiley, New York, 1982. 89. A. Zunger and S. Mahajan, in "Handbook on Semiconductors" (S. Mahajan, Ed.), Vol. 3b, p. 1403. North-Holland, New York, 1992. 90. M. B. Derbali, J. Meddeb, H. Maaref, D. Buttard, P Abraham, and Y. Monteil, /. Appl. Phys. 84, 503 (1998). 91. T. Kimura, T. Kimura, E. Ishimura, F Uesugi, M. Tsugami, K. Mizuguchi, and T. Murotani, /. Cryst. Growth 107, 827 (1991). 92. D. J. Olego, Y. Okuno, T. Kawano, and M. Tamura, /. Appl. Phys. 71, 4492 (1992). 93. S. J. J. Teng, J. M. Ballingal, and F J. Rosenbaum, ^p/?/. Phys. Lett. 48, 1217 (1986). 94. M. K. Lee, D. S. Wuu, and H. H. Tung, /. Appl. Phys. 62, 3209 (1987). 95. A. Yoshikawa, T Sugino, A. Nakamura, G Kano, and I. Teramoto, /. Cryst. Growth 93, 532 (1988). 96. J. W Matthews, Ed., "Epitaxial Growth," Part B, p. 560. Academic Press, New York, 1975. 97. R. Hull and J. C. Bean, in "Semiconductors and Semimetals" (T Pearsall, Ed.), Vol. 33, p. 1. Academic Press, San Diego, 1991. 98. R. M. Graham, A. C. Jones, N. J. Mason, S. Rushworth, L. Smith, and P J. Walker, /. Cryst. Growth 145, 363 (1994). 99. T F Keuch and E. Veuhoff, /. Cryst. Growth 68, 148 (1984). 100. C. H. Chen, C. T Chiu, L. C. Su, K. T Huang, J. Shin, and G B. Stringfellow, /. Electron. Mater 22, 87 (1993).

106

DONKOR

101. C. H. Chen, Z. M. Fang, G. B. Stringfellow, and R. W. Gedridge, Jr., /. Appl Phys. 69, 7605 (1991). 102. J. Shin, A. Verma, G. B. Stringfellow, and R. W. Gedridge, Jr., /. Cryst. Growth 151, 1 (1995). 103. H. Asahi, X. F. Liu, K. Inoue, D. Marx, K. Asami, K. Miki, and S. Gonda, /. Cryst. Growth 145, 668 (1994). 104. M. Ichimura, K. Higuchi, Y. Hattori, and T. Wada, /. Appl Phys. 68, 6153 (1990). 105. M. Razeghi, in "Handbook on Semiconductors" (S. Mahajan, Ed,), Vol. 3b, Chap. 3. North-Holland, Amsterdam, 1994. 106. L. M. Fraas, P. S. McLeod, R. E. Weiss, L. D. Partian, and J. Cape, /. Appl. Phys. 62, 299 (1987). 107. M. Razeghi, M. Defour, F. Omnes, M. Dobers, J. P. Vieren, and Y. GMldntx, Appl Phys. Lett. 55, 457 (1989). 108. A. Brauers, M. Weyers, and R Balk, Chemtronics 4, 8 (1989). 109. G. Haacke, S. R Watkins, and H. Burnhard, Appl Phys. Lett. 54, 2009 (1989). 110. C. H. Chen, C. A. Larsen, and G. B. Stringfellow,^/?/?/. Phys. Lett. 50, 218 (1987). 111. R. H. Lum, J. K. Kingert, and M. G. Lamon, Appl Phys. Lett. 50, 284 (1987). 111 C. H. Chen, E. H. Reihlen, and G. B. Stringfellow, /. Cryst. Growth 96, 497 (1989). 113. R. Bath, M. A. Koza, and B. J. Skromme,^/?/?/. Phys. Lett. 14,1386 (1987). 114. T. Fukunaga, T. Takamori, and H. Nakashima, /. Cryst. Growth 81, 85 (1987). 115. W. I. Wang, Surf. Set 174, 31 (1986). 116. S. Subbanna, H. Kroemer, and J. L. Merz, /. Appl Phys. 59, 488 (1986). 117. A. Y. Cho, /. Appl Phys. 41, 2780 (1970). 118. R. H. WaUis, M. A. D. Forte-Poisson, M. Bonnet, G. Beuchet, and J. R Duchemin, Inst. Phys. Conf. Sen 56, 73 (1981). 119. H. Terao and H. Sunakawa, /. Cryst. Growth 68, 157 (1984). 120. M. Hata, N. Fukuhara, Y. Zempo, M. Isemura, T. Yako, and T. Maeda, /. Cryst. Growth 93, 543 (1988). 121. M. S. Goorsky, T. F Kuech, F Cardone, R M. Mooney, G. J. Scilla, and R. M. Potemski, ^/?/7/. Phys. Lett. 58, 1979 (1991). 122. C. R. Abernathy, A. S. Jordan, S. J. Pearton, W. S. Hobson, D. A. Bohling, and G. T. Muhr, Appl Phys. Lett. 56, 2654 (1990). 123. H. C. Casey, Jr., A. Y. Cho, D. V. Lang, E. H. NicoUian, and R W. Foy, /. Appl Phys. 50, 3484 (1979). 124. H. Morkoc, A. Y. Cho, and C. Radice, /. Appl Phys. 51, 4882 (1980). 125. J. P. Andre, C. Schiller, A. Mitonneau, A. Bnere, and J. Y. Aupied, Inst. Phys. Conf. Sen 65, 117 (1983). 126. C. T. Foxon, J. B. Clegg, K. Woodbridge, D. Hilton, R Dawson, and R Blood, /. Vac. Sd. Technol, B 3, 703 (1985). 727. K. Akimoto, M. Kamada, K. Taira, M. Arai, and N. Watanabe, /. Appl Phys. 59, 2833 (1986). 128. C. Amano, K. Ando, and M. Yamaguchi, /. Appl Phys. 63, 2853 (1988). 129. M. Meuris, W Vandervorst, and G. Borghs, /. Vac. ScL Technol, A 7, 1663 (1989). 130. T. Achtnich, G. Burri, and M. Ilegems, /. Vac. Scl Technol, A 7, 2532 (1989). 13L D. W. Kisker, J. N. Miller, and G. B. Stringfellow, /. Appl Phys. Lett. 40, 614 (1982). 132. R D. Kirchner, J. M. Woodall, J. L. Freeouf, and G. D. ?Qttit, Appl Phys. Lett. 38, 427 (1981). 133. K. A. Prior, G. J. Davies, and R. Heckingbottom, /. Cryst. Growth 66, 55 (1984). 134. K. Tamamura, J. Ogawa, K. Akimoto, Y. Mori, and C. Kojima, Appl Phys. Lett. 50, 1149 (1987). 135. T. Hayakawa, M. Kondo, T. Suyama, K. Takahashi, S. Yamamoto, and T. Hijikata, ^p/?/. Phys. Lett. 52, 339 (1988).

136. J. P. de Souza and D. K. Sadana in "Handbook on Semiconductors" (S. Mahajan, Ed.), Vol. 3b, Chap. 27. North-Holland, Amsterdam, 1994. 137. S. K. Tiku and W M. Duncan,/. Electrochem. Soc. 123, 2237 (1985). 138. R. Zolch, H. Ryssel, H. Kranz, H. Reichel, and L Ruge, in "Ion Implantation in Semiconductors" (F. Chernow, J. A. Borders, and D. K. Brice, Eds.), p. 595. Plenum, New York, 1976. 139. D. E. Davies and R J. McNally, IEEE Electron Device Lett. EDL-4, 356 (1983). 140. K. Tabatabaie-Alavi and I. W Smith, IEEE Trans. Electron Devices 37, 96 (1990). 141. R. T Blunt, R. Szweda, M. S. M. Lamb, and A. G. CuUis, Electron. Lett. 20, 444 (1984). 142. M. Skowronski, in "Handbook on Semiconductors" (S. Mahajan, Ed.), Vol. 3b, Chap. 18. North-Holland, Amsterdam, 1994. 143. Y. Mori and N. Watanabe, /. Electrochem. Soc. 125, 1510 (1978). 144. J. L. Merz and R. A. Logan, /. Appl Phys. 47, 3503 (1976). 145. R K. Chatterjee and G. B. Larrabee, IEEE Trans. VLSI Syst. 1, 7 (1993). 146. S. K. Ghandhi, "VLSI Fabrication Principles, Silicon and Gallium Arsenide," pp. 475-532. Wiley Interscience, New York, 1983. 147 S. Adachi and K. Oe, /. Electrochem. Soc. 130, 2427 (1983). 148. D. N. MacFadyen, /. Electrochem. Soc. 130, 1934 (1983). 149. D. W Shaw, /. Electrochem. Soc. 128, 874 (1981). 75a M. Otsubo, T. Oda, H. Kurmale, and H. Miki, /. Electrochem. Soc. 123, 576 (1976). 757. S. J. Pearton, in "Handbook of Compound Semiconductors" (P. H. HoUoway and G. E. McGuire, Eds.), Chap. 8. Noyes Park Ridge, NJ, 1995. 752. D. W Shaw,/. Electrochem. Soc. 113, 958 (1966). 755. C. M. MeUiar-Smith and C. J. Mogab, in "Thin Film Processes" (J. L. Vossen and W Kerns, Eds.), p. 497. Academic Press, New York, 1978. 154. R. F Kazarinov and R. A. Suris, Sov Phys. Semicond. 7, 347 (1973). 755. B. D. McCombe and A. Petron in "Handbook on Semiconductors," Vol. 2, (M. Balkanski, Ed.), Chap. 6, North-Holland, 1994. 756. C. Weisbuch, "Semiconductor and Semimetals," Vol. 24 (R. Dingle, Ed.), Chap. 1, Academic, New York. 757. D. S. Chelma, D. A. B. Miller, R W. Smith, A. C. Gossard, and W Wiegmann, IEEE J. Quantum Electron. QE-20, 265 (1984). 158. C. Weisbuch, R. C. Miller, R. Dingle, A. C. Gossard, and W Wiegmann, Solid State Commun. 37, 219 (1981). 759. J. C. Mann, in "Physics and Applications of Quantum Wells and Superlattices" (E. E. Mendez and K. von Klitzing, Eds.), p. 347. Plenum, New York, 1987. 160. J. Yoshino, T. Iwamoto, and H. Kukimoto, / Cryst. Growth 55, 74 (1981). 767. I. Hino and T. Suzuki, / Cryst. Growth 68, 483 (1984). 762. M. Razeghi, M. Defour, and F. Omnes, Appl Phys. Lett. 55, 457 (1989). 765. C. C. Hsu, R. M. Cohen, and G. B. Stringfellow, / Cryst. Growth 62, 648 (1983). 76^. R Blood, J. S. Roberts, and J. R Stagg, / Appl Phys. 53, 3145 (1982). 765. M. J. Hafich, J. H. Quigley, R. E. Owens, G. Y. Robinson, and D. L. Oimkdi, Appl Phys. Lett. 54, 2686 (1989). 766. M. A. Rao, E. J. Caine, H. Kroemer, S. I. Long, and D. I. Babic, / Appl Phy 61, 643 (1986). 767 C. R. Arbernathy, / Vac. ScL Technol, A 11, 869 (1993). 168. W S. Hobson, "Proceedings of the Seminar on Wide Bandgap Semiconductor and Devices." Electrochemical Society Proceedings Vol. 95-21, pp. 26-42, Electrochemical Society, Pennington, NJ, 1995. 769. T. Iwamoto, K. Mori, M. Mizuta, and H. Kukimoto, / Cryst. Growth 68, 483 (1984). 170. J. Penndorf, G. Kuhn, H. Neumann, and A. Miiller, Krist. Tech. 15, 169 (1980).

GALLIUM A R S E N I D E H E T E R O S T R U C T U R E S 171. Akiku Gomyo, Hitoshi Hotta, Isao Hino, Seiji Kawata, Kenichi Kobayashi and Tohru Suzuki, Jpn. J. Appl Phys. 28, L1330 (1989). 172. Tohru Suzuki, Akiku Gomyo, Isao Hino, Kenichi Kobayashi, Seiji Kawata, and Sumio lijima, Jpn. J. Appl. Phys. 27, L1549 (1988). 173. J. R. Flemish, and K. A. Jones,/. Electrochem. Soc. 140, 844 (1993). 174. J. R. Lothian, J. M. Kuo, W. S. Hobson, E. Ren, and S. J. Pearton, /. Vac. Sci. Technol, B 11, 606 (1992). 175. J. R. Lothian, J. M. Kuo, F. Ren, and S. J. Pearton, /. Electron. Mater. 21, 441 (1992). 176. M. Kondow, H. Kakibayashi, S. Minagawa, Y. Inoue, T. Nishino, and Y. Hamakawa, ^/?p/. Phys. Lett. 53, 2053 (1988). 177. A. Gomyo, T. Suzuki, and S. lijima, Phys. Rev. Lett. 60, 2645 (1988). 178. E. Morita, M. Ikeda, O. Kumagai, and K. Kaneko, y4/?p/. Phys. Lett. 53, 2164 (1988). 179. S. R. Kurtz, J. M. Olson, and A. Kibbler,^/?/?/. Phys. Lett. 54, 718 (1989). 180. H. Okuda, C. Anayama, T. Tanahashi, and K. Nakajima, ^/?p/. Phys. Lett. 55, 2190 (1989). 181. W. Liu, E. Beam, III, T. Kim, and A. Khatibzadeh, in "Current Trends in Heterojunction Bipolar Transistors" (M. F. Chang, Ed.), pp. 241-301. World Scientific, Singapore, 1996. 182. D. S. Cao, E. H. Reihlen, G S. Chen, A. W. Kimball, and G B. Stringfellow, /. Cryst. Growth 109, 279 (1991). 183. O. Ueda, Y. Nakata, and T V\x]\\,Appl. Phys. Lett. 58, 705 (1991). 184. T S. Kuan, T F. Kuech, W. I. Wang, and E. L. Wilkie, Phys. Rev. Lett. 54, 201 (1985). 185. G B. Stringfellow, /. Electron. Mater 1, 437 (1972). 186. T. Kobayashi, F. Nakamura, K. Taira, and H. Kawai, /. Appl. Phys. 65, 4898 (1989). 187. K. Kodama, M. Hoshino, K. Kitahara, M. Takikawa, and M. Ozeki, Jpn. J Appl. Phys. 25, L127 (1986). 188. M. J. Mondry and H. Kroemer, IEEE Electron Device Lett. 6, 175 (1985). 189. M. O. Watanabe, and Y. Ohhdi, Appl. Phys. Lett. 50, 906 (1987). 190. D. Biswas, N. Debbar, P. Bhattacharya, M. Razeghi, M. Defour, and F Omnes, Appl. Phys. Lett. 56, 833 (1990). 191. S. D. Gunapala, B. F Levine, R. A. Logan, T. Tanbun-Ek, and D. A. Humphrey, ^pp/. Phys. Lett. 57, 1802 (1990). 192. M. Razeghi, F. Omnes, M. Defour, P Maurel, J. Hu, E. Wolk, and D. Pavlidis, Semicond. Technol 5, 278 (1990). 193. J. Chen, J. R. Sites, I. L. Spain, M. J. Hafich, and F Y. Robinson, Appl. Phys. Lett. 58, 744 (1991). 194. D. C. Reynolds and K. R. Evans, in "Semiconductor Interfaces and Microstructure" (Z. C. Feng, Ed.), pp. 168-198. World Scientific, Singapore, 1992. 195. J. L. Sanchez-Rojas, A. Sacedon, A. Sanz-Hervas, E. Calleja, E. Munoz, and E. J. Abril, Solid State Electron. 40, 591 (1996). 196. F. E. G Guimaraes, P. P. Gonzalez-Borrero, D. Lubyshev, and P Basmaji, Solid State Electron. 40, 659 (1996). 197. P B. Kirby, J. A. Constable, and R. S. Smith, Phys. Rev B 40, 3013 (1989). 198. S. Hasenohr, M. Kucera, J. Novak, M. Bujdak, P Elias, and R. Kiidela, Solid State Electron. 42, 263 (1998). 199. M. G. Proteitti, S. Turchini, J. Garcia, G. Lambel, F Martelli, and T Prosperi, Solid State Electron. 40, 653 (1996). 200. K. H. Chang, R. Gibala, D. J. Srolovitz, P K. Bhattacharya, and J. F Mansfield, /. Appl. Phys. 67, 4093 (1990). 201. T Nishioka, Y. Itoh, A. Yamamoto, and M. Yamaguchi, ^/?/?/. Phys. Lett. 51, 1928 (1987). 202. C. W. Synder, B. G Orr, D. Kessler, and L. M. Sander, Phys. Rev Lett. 66, 3032 (1991). 203. G. L. Price, Phys. Rev Lett. 66, 469 (1991). 204. L. K. Howard, P Kidd, and R. H. Dixon, /. Cryst. Growth 125, 281 (1992). 205. O. Madelung, and M. Schulz, Eds., "Landolt-Bornstein, New Series Group III, Vol. 22a. Springer-Verlag, Berlin, 1992. 206. J. Y. Marzin, M. N. Charasse, and B. Sermage, Phys. Rev. B 31, 8298 (1985).

107

207. G. Ji, U. K. Reddy, D. Huang, T S. Henderson, and H. Morkoc, /. Appl. Phys. 62, 3366 (1987). 208. D. J. Arent, K. Deneffe, C. Van Hoof, J. De Boeck, and C. Borghs, / Appl. Phys. 66, 1739 (1989). 209. Y. Zou, P Grodzinski, E. P Menu, W. G. Jeong, P D. Dapkus, J. J. Alwan, and J. J. Coleman, Appl. Phys. Lett. 58, 601 (1991). 210. J. P Reithmaier, R. Hoger, H. Riechert, A. Herbele, G. Abstreiter, and G Wienmann, y4pp/. Phys. Lett. 56, 536 (1990). 211. M. J. Cherng, R. M. Cohen, and G B. Stringfellow, /. Electron. Mater 13, 799 (1984). 212. Y. Iwamura, T. Takeuchi, and N. Watanabe, /. Cryst. Growth 145, 82 (1994). 213. C. B. Cooper, III, R. R. Saxena, and M. J. Ludowise, /. Electron. Mater 11, 1001 (1982). 214. U. Egger, M. Schultz, P Werner, O. Breitensen, T. Y. Tan, and U. Gosele, /. Appl. Phys. 81, 6056 (1997). 215. J. E. Cunningham, M. B. Santos, K. W. Goosen, T H. Chiu, M. D. Williams, and W Jan, /. Cryst. Growth 136, 282 (1994). 216. C. T Foxon, B. A. Joyce, and M. T Norris, /. Cryst. Growth 49,132 (1981). 217 B. W Liang, and C. W Tu, /. Appl. Phys. 74, 255 (1993). 218. J. E. Cunningham, K. W Goosen, M. B. Santos, M. D. WiUiams, and W. Un,Appl. Phys. Lett. 64, 2418 (1994). 219. M. Capizzi, S. Modeti, F Martelli, and A. Frova, Solid State Commun. 39, 333 (1981). 220. R. L. Nahory, M. A. Pollack, J. C. DeWinter, and K. M. WiUiams, /. Appl. Phys. 48, 513 (1997). 221. J. Hashimoto, T. Katsuyama, J. Shinkai, I. Yoshida, and H. Hayashi, Electron. Lett. 28, 1329 (1992). 222. G B. Stringfellow, /. Cryst. Growth 53, 42 (1981). 223. K. Kobayashi, S. Kawata, A. Gomyo, I. Hino, and T. Suzuki, Electron. Lett. 1, 1084 (1985). 224. C. Nozaki, Y. Ohba, H. Sugawara, S. Yasuami, and T. Nakansi, /. Cryst. Growth 93, 406 (1988). 225. Y. Qingxuan, P. Raiwu, and L. Cuiyun, /. Cryst. Growth 148, 13 (1995). 226. M. Suzuki, M. Ishikawa, K. Itaya, Y. Nishikawa, G. Hatakoshi, Y. Kokubun, J. Nishizawa, and Y. Oyama, /. Cryst. Growth 108, 728 (1991). 227. P Gavrilovic, F P Dabkowski, K. Meehan, J. E. Williams, W Stutius, K. C. Hsieh, N. Holonyak, Jr., M. A Shahid, and S. Mahajan, /. Cryst. Growth 93, 426 (1988). 228. H. Asahi, Y. Kawamura, and H. Nagai, /. Appl. Phys. 53, 4928 (1982). 229. D. Olego, T Y. Chang, E. Silberg, E. A. Caridi, and A. Pinczuk, Appl. Phys. Lett. 41, 476 (1982). 230. S. H. Groves, J. N. Walpole, and L. J. Missaggia, Appl. Phys. Lett. 61, 255 (1992). 231. G. Zhang, A. Ovtchinnikov, J. Nappi, H. Asonen, and M. Pessa, IEEE J Quantum Electron. 29, 1943 (1993). 232. G Zhang, M. Pessa, K. Hjelt, H. CoUan, and T. Tuomi, /. Cryst. Growth 150, 607 (1995). 233. A. Ishibashi, M. Mannoh, and K. Ohnaka, /. Cryst. Growth 145, 414 (1994). 234. E. Kuphal, /. Cryst. Growth 67, 441 (1984). 235. D. Z. Garbuzov, N. Yu. Antonishkis, A. D. Bondarev, A. B. Gulakov, S. N. Zhigulin, N. I. Katsavets, A. V. Kochergin, and E. V. Rafailov, IEEE J Quantum Electron. 27, 1531 (1991). 236. G. Zhang, J. Nappi, H. Asonen, and M. Pessa, IEEE Photon. Technol. Lett. 6, 1 (1994). 237 J. N. Schulman and Y. C. Chang, Phys. Rev B 31, 2056 (1985). 238. S. Wang, "Fundamentals of Semiconductor Theory and Device Physics." Prentice-Hall, Englewood Cliffs, NJ, 1989. 239. M. Jaros and K. B. Wong, /. Phys. C 17 L765 (1984). 240. M. Jaros, K. B. Wong, and M. A. Gell, Phys. Rev B 31,1205 (1985). 241. G Bastard, "Wave Mechanics Applied to Semiconductor Heterostructures." Wiley, New York, 1988.

108 241 243. 244. 245. 246. 247.

248. 249. 250. 251. 252. 253. 254. 255. 256. 257.

258.

259. 260.

261.

262. 263. 264. 265. 266.

267 268. 269. 270. 271. 272.

DONKOR M. Altarelli, Phys. Rev. B 32, 5138 (1985). J. M. Luttinger, and W. Kohn, Phys. Rev. 97, 869, 1955. J. M. Luttinger, Phys. Rev 102, 1030 (1956). R. Eppenga, M. F. H. Schuurmans, and S. Colak, Phys. Rev B 36, 1554 (1987). S. Colak, R. Eppenga, and M. E H. Schuurmans, IEEE J. Quantum Electron. 23, 960 (1987). G. Bastard, C. Delalande, Y. Guldner, and P. Vosin, in "Advances in Electronics and Electron Physics" (P. Hawkes, Ed.), Vol. 72, pp. 1-170. Academic Press, New York, 1988. D. A. Broido and L. J. Sham, Phys. Rev. B 31, 888 (1985). S. L. Chuang, Phys. Rev B 40, 10,379 (1989). D. Ahn and S. L. Chuang, IEEE J. Quantum Electron. 26,13 (1990). R. Dingle, H. L. Stormer, A. C. Gossard, and W. Wiegman, Appl. Phys. Lett. 33, 665 (1978). M. Feuer, IEEE Trans. Electron Devices ED-31, 7 (1985). P Saunier and J. W. Lee. IEEE Electron Device Lett. EDL-7, 503 (1986). E. Sovero, A. K. Gupta, J. A. Higgins, and W. A. Hill, IEEE Trans. Electron Devices ED-33, 1434 (1986). T. Baba, T. Mizutani, and M. Ogawa, /. Appl. Phys. 59, 526 (1986). C. W. Tu, W. L. Jones, R. F Kopf, L. D. Urbanek, and S.-S. Pei, IEEE Electron Device Lett. EDL-7, 552 (1986). H. Morkoc, and H. Unlu, in "Semiconductors and Semimetals" (R. Dingle, Ed.), Vol. 24, Chap. 2. Academic Press, New York, 1987. A. A. Ketterson, M. Moloney, W. T. Masselink, J. Klem, R. Fischer, W. Koop, and H. Morkoc, IEEE Electron Device Lett. EDL-6, 628 (1985). Y. Itoh, Y. Horie, K. Nakahara, N. Yoshida, T. Katoh, and T. Takagi, IEEE Microwave Guided Wave Lett. 5, 48 (1995). Y. L. Lai, E. Y. Chang, C. Y. Chang, T. K. Chen, T. H. Lui, S. P Wang, T. H. Chen, and C. T. Lee, IEEE Electron Device Lett. 17, 229 (1996). B. Pereiaslavets, G. H. Martin, L. F. Eastmann, R. W. Yanka, J. M. Ballingall, J. Braunstein, K. H. Bachem, and B. K. Ridley, IEEE Trans. Electron Devices 44, 1341 (1997). J. Dickmann, M. Berg, A. Geyer, H. Daembkes, F. Scholz, and M. Moser, IEEE Trans. Electron Devices 42, 2 (1995). P M. Solomon, C. M. Knoeder, and S. L. Wright, IEEE Electron Device Lett. EDL-5, 379 (1984). M. K. Matsumoto, M. Ogura, T. Wada, N. Hashizume, and Y. Hayashi, Electron. Lett. 20, 462 (1984). R. R. Daniels, R. MacTaggart, J. K. Abrokwah, O. N. Tufte, M. Shur, J. Back, and P Tenkins, lEDM Tech. Dig. 448 (1986). H. Baratte, D. C. LaTulipe, C. M. Knoedler, T N. Jackson, D. J. Frank, P M. Solomon, and S. L. Wright, lEDM Tech. Dig. 444 (1986). R. A. Kiehl, P M. Solomons, and D. J. Frank, IBM I. Res. Dev 34, 506 (1990). T. J. Drummond, W. T. Masselink, and H. Morkoc, IEEE Proc. 74, 773 (1986). K. Lee, M. S. Shur, T. J. Drummond, and H. Morkoc, IEEE. Trans. Electron Devices ED-30, 207 (1983). H. Hida, T. Itoh, and K. Ohata, IEEE Trans. Electron Devices ED-33, 1580 (1986). K. Yokoyama and H. Sakaki, IEEE Electron Device Lett. 8, 73 (1987). M. H. Weiler, and Y. Ayasli, in "Microwave and Millimeter-wave Heterostructure Transistors and Their Application" (F Ali, L Bahl, and A. Gupta, Eds.), pp. 133-140. Artech, Norwood, MA, 1989.

273. L. F Lester, P M. Smith, P Ho, P C. Chao, R. C. Tiberio, K. H. Duh, and E. D. Wolf, in "Microwave and Millimeter Wave Heterostructure Transistors and Their Applications" (F Ali, L Bahl, and A. Gupta, Eds.), pp. 254-257. Artech, Norwood, MA, 1989. 274. M. B. Das, IEEE Trans. Electron. Devices ED-32, 11 (1985). 275. A. K. Gupta, J. A. Higgins, and C. P. Lee, in "Microwave and Millimeter-Wave Heterostructure Transistors and Their Applications" (F Ali, L Bahl, and A. Gupta, Eds.), p. 55. Artech House, Norwood, MA, 1989. 276. H. Kroemer, in "Microwave and Millimeter-Wave Heterostructure Transistors and Their Applications" (F Ali, L Bahl, and A. Gupta, Eds.), p. 78. Artech House, Norwood, MA, 1989. 277. M. Konagai, K. Katsukawa, and K. Takahashi, /. Appl. Phys. 48, 4389 (1977). 278. C. R. Abernathy, F Ren, P W Wisk, S. J. Pearton, and R. Esagui, Appl. Phys. Lett. 61, 1092 (1992). 279. W Liu, E. Beam, T Henderson, and S. K. Fan, IEEE Electron Device Lett. 14, 301 (1993). 280. W Liu, and S. K. Fan, IEEE Electron Device Lett. 13, 510 (1992). 281. W Liu, S. K. Fan, T. Henderson, and D. Davito, IEEE Trans. Electron Devices 40, 1351 (1993). 282. J. R. Lothian, J. M. Kuo, F Ren, and S. J. Pearton, /. Electron Mater 21, 441 (1992). 283. D. Ankri, R. Azoulay, E. Caquot, J. Dangla, C. Dubon, and J. F Palmier, in "Microwave and Millimeter-Wave Heterostructure Transistors and Their Applications" (F Ali, L Bahl, and A. Gupta, Eds.), p. 179. Artech House, Norwood, MA, 1989. 284. K. Tomizawa, "Numerical Simulation of Submicron Semiconductor Devices," Chap. 4. Artech House, Norwood, MA, 1993. 285. J. J. Liou, "Advanced Semiconductor Device Physics and Modeling," Chap. 3. Artech House, Norwood, MA, 1994. 286. M. B. Das, in "Microwave and Millimeter-Wave Heterostructure Transistors and Their Applications" (F Ali, L Bahl, and A. Gupta, Eds.), p. 227-237. Artech House, Norwood, MA, 1989. 287. M. A. Herman, Ed., "Semiconductor Optoelectronics." Wiley, New York, 1978. 288. G. Allan, G. Bastard, and N. Boccara, Eds., "Heterojunctions and Semiconductor Superlattices." Springer-Verlag, New York, 1986. 289. M. O. Manasrehm, Ed. "Optoelectronic Properties of Semiconductors and Superlattices," Vols. 1-4, Gordon and Breach, New York, 1997. 290. Y. Ueno, H. Fujii, H. Sawano, K. Kobahashi, K. Hara, A. Gomyo, and K. Endo, IEEE I. Quantum Electron. 29, 1851 (1993). 297. D. P Bour, D. W Treat, K. J. Beernink, B. S. Krusor, R. S. Geels, and D. F Welch, IEEE Photon. Technol. Lett. 6, 128 (1994). 292. H. Hamada, K. Tominaga, M. Shono, S. Honda, K. Yodoshi, and T Yamaguchi, Electron. Lett. 28, 1834 (1992). 293. P. M. Snowton and P. Blood, in "Optoelectronic Properties of Semiconductors and Superlattices" (M. O. Manasreh, Ed.), Vol. 4, Chap. 9. Gordon and Breach, New York, 1997. 294. S. D. Hersee, B. deCremoux, and J. P. Duchemin, Appl. Phys. Lett. 44, 476 (1984). 295. R. D. Dupuis, P D. Dapkus, R. Chin, N. Holonyak, Jr., and S. W Kirchoefer,^pp/. Phys. Lett. 34, 265 (1979). 296. T Hayakawa, T Suyama, K. Takahashi, M. Kondo, S. Yamamoto, and T Hijikata, ^p/?/. Phys. Lett. 49, 636 (1986). 297. S. W Park, in "Optoelectronic Properties of Semiconductors and Superlattices" (M. O. Manasreh, Ed.), Vol. 4, Chap. 2. Gordon and Breach, New York, 1997. 298. T J. Whitley, M. J. Creaner, R. C. Steele, M. C. Brain, and C. A. Millar, IEEE Photon. Technol. Lett. 1, 425 (1989).