SolidState Electronics Vol. 32, No. 12, pp. 10571063, 1989
00381101/89 $3.00 + 0.00 Pergamon Press plc
Printed in Great Britain
Fen~osecond Bandedge Excitations in ModulationDoped Quantum Wells Wayne H. Knox AT&TBell Laboratories Holmdel, NJ07733 ABSTRACT Optical excitations near the bandedge of GaAs quantum wells have revealed interesting information about carrier scattering and renormalization. The extension of these studies to n~ulationdoped quantum wells is discussed. KEY WO~DS Semiconductors, renorm~lization.
quantum
wells,
femtosecond,
nonlinear
optics,
modulation
doping,
INTRODOCTION Direct excitation of nonthermal carrier distributions near the bandedge of GaAs bulk and quantum wells has been accomplished using techniques of femtoseccnd spectroscopy (Oudar et al., 1985 and Knox et al. 1985 and 1986). These initial experiments raised a number of interesting questions about the role of carriercarrier scattering, carrierphonon emission and absorption in the thermalization process, and also the role of bandgap renormalization, screening and excitonic effects. The extension of these studies to modulationdoped samples has provided interesting new information about the separate contributions of electrons and holes to the thermalization process, and the sensitivity of bandgap renormalization to the presence of a dense thermalized Fermi sea of electrons or holes (Knox et al. 1988). Several results are discussed here, including the dynamics of renormalization in ptype quantum wells, and intersubband excitations in ntype quantum wells.
INTRINSIC NTYPE
PTYPE
I
I
,I
o
I
Figure i. Nonthermal distributions of electrons and holes are created by optical excitation near the bandedge of doped quantum wells. Dense Fermi seas of electrons or holes initially thermalized to the lattice interact with injected carrier distributions in a com~)licated manner. 1057
1058
WAYNE H. KNOX
Figure 1 shows the scheme of the experiments. In the first case, nonthermal distributions of electrons and holes are excited between the n=l and n=2 quantum subbands. The mean energy of the distribution is 20 meV so that phonon emission can be avoided. At room temperature, phonon absorption is possible, b u t % c c u r ~ on a time scale of 300 fs in GaAsquantum wells (Knox et al. 1985). At low densities (2x10±u cm c) the nonthermal distribution thermalizes completely in about 200 fs (Knox et al. 1986). Optical excitation produces equal numbers of electrons and holes, of course, so that if we wish to learn something about the separate contributions of electrons and holes to the thermalization process, we must add some excess electrons or holes to break the symmetr~ Modulationdoping is a technique which allows the direct doping of quantum wells without addition of impurity scattering (Dingle et al. 1978). As Figure 1 shows, the case of excess electron doping is achieved by dopinq the b~rriers with silicon, and excess holes by doping with beryllium. The addition of 3.5x10 II cm c of electrons is found to greatly increase the thermalization rate. Thermalization times of less than 10 fs were observed (Knox et al. 1988). In the ptypecase, the excess holes do not appreciably speed upthe thermalizationprocessbecauseof their large mass which results in primarily elastic scattering of the electrons (Knox et al. 1988, Goodnick et al. 1987,1988). Addition of the dense sea of holes changes the gap renormalization considerably, and this effect is worth noting. PTYPE CASE Figure 2 shows the absorption spectrum of the ptype sample just before, at, and just after excitation near the bandedge with a 1 0 q ; s pu~se. The excitation density is about equal to the doping density for this case, about 3x10 ±x cm z. The nonthermal carrier distribution results in a spectral hole burning around the pump wavelength (albeit slightly shifted to lower energies). The bandgap is instantaneously re,ormalized, as shown by the downshifted edge. After a few hundred fs time delay, the distribution has completely thermalized and apparently the broadened and downshifted bandedge recovers completely. Of course, the states near the edge are phasespace filled by the low energy tail of the thermalized distribution, so some recovery is to he expected. The shape of the differential spectrum at~t=0 is complicated because it contains a contribution from the
I
I
PTYPE 2x1011 cm 2
~
0.1 OPTICAL
I
A t =  2 0 0 fs
At=0
DENSITY Z
O
At= +400 fs
O
09 ¢n <
Ao~ AT At=0
1.425
__J 1.450
1.475
ENERGY (eV)
1.500
1.525
•
Figure 2. Timeresolved absorption spectra for ptypecase. Positive lobe of differential spectrum is from holeburning, negative lobe is from renormalization.
Femtosecond band~dge excitations
1059
direct phasospace filling ("spectral hole burning" means phasespace filling due to a nonthermal distribution in the case of a continuum); and a contribution from the renormalization. We note that the sianal due to " " is as larue as the direct ~ ~ siunal. Renormalization is not a small effect, and this topic needs further experimental and theoretical study. The general shape of the differential signal due to renormalization can be easily seen. Figure 3 shows one approach. The linear absorption spectrum is reproduced as is the pump distribution, and the t=0 differential signal. The dotted curve is obtained by subtracting the initial absorption spectrum from the absorption spectrum which is rigidly shifted down by a few meV in energy. This is essentially the largesignal version of the derivative of the linear absorption
PTYPE .630 2"5x1011cm2 ~
/
"
[ 1.425
I 1.450
""1 I 1.475 1.500 ENERGY(eV)
I
1.525
Figure 3. Linear absorption spectrum of ptype quantum wells, and the differential spectrum at t=0 compared with the pump pulse spectrum. The dotted curve is obtained by downshifting the linear absorption a few meV and subtracting.
spectrum. The general shape matches reasonably well the negative tail of the differential signal, although it iS clear that the actual femtosecond data indicates more than a simple rigid shift of the absorption spectrum in energy. In fact, a broadening is also indicated from the femtosecond data. The dynamics of the two portions of the differential signal are indicated in Figure 4. The upper signal (a) represents the differential absorption dynamics around the excitation wavelength, i.e. integrated over a 100 fs bandwidth around 1.49 eV. This yields the holeburning dynamics, and reflects the carrier population at the injection energy. The lower signal (b) represents the differential signal integrated at the low energy side of the b ~ e d g e , or integrated over a 100 fs bandwidth at about 1.46 eV. This shows primarily the edge renormalization response, but contains a subsequent phase space filling due to the scattering of carriers down to the bandedge. The holeburning signal rises and then falls as the carriers scatter out of their inital states with about a 60 fs time constant. The edge signal, however, reslxmds instantaneously. The measured FWFR of 150 fs is the same as the measured system crosscorrelation response which is obtained by replacing the sample with a thin LiIO 3 crystal (Knox, 1987). Therefore, the large bandedge broadening is instantaneous on the time scale of i00 fs. Renormalization is fast. In addition, a nonthermal distribution of carriers can instantaneously renormalize the gap; it is not necessary to wait until the carriers thermalize in order to obtain renormalization. Very clearly, the theoretical issues need to be sorted out. NTYPE CASE As mentioned previously, the addition of 3.5xi0II cm 2 causes the carriers to thermalize so rapidly that the nonthermal distribution cannot be observed with i00 fs optical pulses. This case is shown
1060
WAYNE H. KNOX
~9
(a) Hole
burning
signal
¢J
~9
0
O
0
.1
I
,
~
Time Delay
(fs)
<
Figure ~. Dynamics of absorption change (a) at the injection energy, and (b) at the bandedge, integrated over a 100 fs bandwidth. The renormalization is instantaneous. in Figure 5. In this case, the excitation at 20 meV above the bandedge allows the carriers sufficient phase space for scattering that they can rapidly (less than 10 fs is the conjecture) cover all energy space from 0 to 50 meV or so. In addition, the small negative lobe on the differential signals at low energies represents the bandgap renormalization in the ntype case, which is not as spectacular as the ptype case. An interesting comparison is made if the excess energy is reduced to zero in the case of the ntype quantum wells. Then, the carriers cannot scatter to lower energy states because they are filled, and they cannot scatter to higher energy states because of energy conservation. Therefore, the continuum resonance (Livescu et al 1988), which is normally a sharp exciton line in undoped quantum wells, bleaches when excited and remains so for almost a picosecond.This long time is obtained because the only mechanism for thermalization is absorption of phonons at room temperature, and carriercarrier scattering within a restricted energy space given by the excitation bandwidth. Figure 6 shows this case. The differential signal at t=0 is shown when exciting at the continuum resonance. The ii electronhole state is bleached, and we note a small 22 renormalization which is exactly the same as that observed in previous low density
nTYPE
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~
.
~
o.15
"~0 /v"~' ~'~~~""~~ 33 '.
~
, 1.425 1.4 ENERGY (eV)
/2
 66 '~' 165 .~" 25 231
Figure 5. Dynamics of ntype sample excited about 20 meV above edge. No nonthermal distribution is observed. The small kink below the edge indicates that renormalization is also fast for the ntype sample.
Fcmtosecond band¢dg¢ excitations
1061
excitations in undoped quantum wells {Knox 1986). Interestingly, there is no differential signal at the spectral feature corresponding to the n=l electron n=3 hole state (Livescu et al 1988). This makes no sense. After a 1 ps time delay, the ii continuum resonance partially recovers, and it grows a thermal tail as it approaches a 300 K thermalized distribution. It is important to note that the weak 22 renormalization does not change as the n=l subkmnd distribution function changes, a l s o t h e same a s
1.0

11 f Aot(t=0) t~
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z
i ~
Aoz(t=l ps)
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o
/ .i
",~
13 22
P>
UJ I 1.425
I 1.450
I 1.475
I 1.500
I 1.525
ENERGY(eV) Figure 6. Ntype sample differential absorption spectra when excited at continuum resonance at t=O and after 1 pa delay. in undoped quantum wells (Knox 1986). Figure 7 shows the differential signal with (a) Ii continuum resonant excitation and ~) excitation at 13 end 22 simultaneously. ~nis shows that the
13 resonance is in fact active in a nonlinear optics sense when directly excited, but excitation of the 11 resonance directly does not cause any direct change in the 13 absorption line. In the case of the 13 and 22 excitations, information on the intersubband scattering dynamics is available, although it is significantly complicated by two factors. Firstly, the conditions shown in Figure 7b leads to not only direct excitation of 13 and 22 resonances, but also a simultaneous excitation of the n=li continuum, and it would be difficult to sort out the separate contributions from the different subbands in this way. Secondly, and perhaps more interestingly, the optical signals reveal the sum of the electron and hole occupation functions, so we obtain information
0.6 22 z O
22
3 / ~ 11
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1
n 0.3
a)
o
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0.6 /
0.3
I
22
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o~(t=0)
J _L 0 "" ~:~:~,'~'  1.475  1.525 1.425 1.475
ENERGY(eV)
1.525
ENERGY(eV)
Figure 7. Excitation of different continuum resonances in ntype quantum wells. (a) at the ii transition, and (b) at the 13 and 22 resonances simultaneously.
1062
WAYNE H. KNOX
about the electron and hole relaxations through their sum. Figure 8 shows the differential signal obtained at long time delays after excitation at 13 and 22 simultaneously as in Figure 7b. We find a thermalized (Boltzmannlike) distribution in the ii subband, as we expect, but in addition, we find that the 13 and 22 lines remain bleached for a long time. The electron states should have completely relaxed in a long time delay of 17 ps, due to phonon assisted intersubband scattering, however the holes are apparently trapped, since the n=l to n=2 hole energy difference (and also the 13 energy) is less than a phonon energy. This study should he extended to many different well widths and temperatures to obtain further information about hole intersubband scattering. Experiments wherein electron levels are directly excited with infrared pulses (Seilmeier et al. 1987) reveal information about electron subband scattering only, therefore a comparison between these results can reveal information about the hole subband relaxations.
nTYPE 3.5x1011 cm 2 22
0.6 [._
f
13
a
o.9_. z
11
o_
0.3
nO II1 <
0
J, 1.425
0.14
f O
0.07 0.017
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1.475
1.500
1.525
A
./
/\
At=17
Ds
0.0036 I
I
1.425
1.450
1.475 1.500
1.525
ENERGY(eV)
Figure 8. Long time dependence of intersubband excitations. (upper) shows the absorption spectrum of ntype quantum wells at 300 K, and the excitation pulse spectrum. (lower) shows the differential spectrum at t=17 ps time delay. A thermal tail in the n=l continuum is obtained as expected, but the 13 and 22 lines remain bleached for long times. This is due to hole trapping in the wells. DISCUSSION The extension of femtosecond studies of nonlinear optical response of semiconductors quantum wells has provided a new experimental degree of freedom for us to test our understanding of manybody effects in 2d dense systems. From a theoretical point of view, Monte Carlo techniques have been applied to studies of femtosecond carrier thermalization (Goodnick at al. 1987, 1988 and Bailey et al. 1987), but several major problems arise when we wish to relate theory and experiment. In optical experiments, we measure differential transmission signals. In theory, distributions are calculated. There is no direct comparison which can be made between these quanities. The Pauli
Femtosecond bandedge excitations
1063
exclusion principal gives a starting point, of course, but a complete model of the bandedge dynamics including excitonic and manybody interactions in the case of dense electron and hole systems is required. A second major problem arises with this approach. Renormalization must be added to theories of bandedge dynamics. In some cases, the signals due to renormalization can be as large as those due to phasespace filling, as has been shown here. Nttmerical tec~iques certainly have some attractive features in that many interactions can he included and separately turned on and off. This is very good for understanding which interactions are the most important. Manybody theory for such a complicated system may be possible, but it looks as though some kind of a breakthrough would be required in order to obtain a realistic description of the present experiments, including 2dimensional effects, n or ptype doping with a real valence band structure and excitonic effects and acorrect description of the renormalization due to an arbitrary distribution function in the presence^of a thermalized background of carriers. AC~NU~%~GZR~E The author would like to thank a number of collaborators who have contributed to this work: D.S. Chemla, G. Livescu, J.E. Henry. J. Cunningham, A.C.Gossard, S.M. Goodnick. REFERENCES
Bailey, D.W., Artaki, M., Stanton, C. and Hess, K., (1987) J. Auol. phys. 62, 4639. Dingle, R., Stormer, H., A.C. Gossard and Wiegmann, W., (1978) ADD1. Phys. Lett. 33, 665. Goodnick, S.M. and Lugli, P. (1987) ADD1. Phys. Left. 51, 585. Knox, W.H., Fork, R.L., Downer, M.C., Miller, D2%.B., Chemla, D.S., Shank, C.V., Gossard, A.C. and Wiegmann, W., (1985) Phys. Rev. Lett. 54, 1306. Knox, W.H., Hirlimann, C., Miller, D.A.B., Chemla, D.S. and Shank, C.V. (1986) Phvs. Rev. Lett. 56 , 1191. Knox, W.H. (1987) J. Out. Soc. of Am. B4, 1771. Knox, W.H., Chemla, D.S., Livescu, Cunningham, J.E. and Henry, J.E. (1988) Phys. Rev. Lett. 61, 1290. Livescu, G., Miller, D.A.B., Chemla, D.S., Ramaswamy, M., Chang, T.Y., Sauer, N., Gossard, A.C. and English, J.H., (1988) IEEE J. Ouant. El~tron. 24, 1677. Oudar, J.L., Hulin, D., Migus, A., Antonetti, A. and Alexandre, F. (1985), phys. Rev. Latt. 55. 2074. Seilmeier, A., Dubner, H.J., Abstreiter, G., Weimann, G. and Schlapp, W., (1987) Phys. Rev. Lett. 59, 1345.