Recombination in GaSbAlSb multiple QWS under high excitation conditions

Superlattices

and Microstructures,

Vol.

10, No.

RECOMBINATION UNDER HIGH

3, 1991

361

IN GaSb/AISb EXCITATION

MULTIPLE CONDITIONS

QWS

G. Fuchs, S. HauBer, A. Hangleiter 4. Physikalisches Institut, Universitrit Stuttgart Pfaffenwaldring 57, D-7000 Stuttgart 80, F.R.Germany G. Griffiths, H. Kroemer, S. Subbanna ECE Department, University of California Santa Barbara, CA 93106, U.S.A (Received

13 August

1990)

We have studied the recombination dynamics in GaSb/AlSb MQW structures under high excitation conditions. Time-resolved measurements were performed using the up-conversion technique. The carrier dynamics in these structures is strongly influenced by the small energetic separation between the F-valley and the L-valleys even in the direct material with L, 2 40 A. At room-temperature we find that the Auger recombination with its coefficient C = 4. 10-2scmes-’ is the dominant recombination mechanism at high carrier densities. The Auger coefficient increase with temperature up to 400 K in contrast to theory.

1. Introduction GaSb/AlSb-MQWs show some important and unique effects of the band structure. As in the bulk material the split-off energy is nearly the same as the bandgap. This property should cause an enhanced CHSH-Auger process because of the small activation en-

C shows a monotonic

However, at higher excitation levels the indirect valleys have considerable influence on the recombination kinetics even in the direct material with L, effect is discussed in chapter 3.

> 40 A. This

In GaSb/AlSb QWs strain effects are present caused by the lattice mismatch of 0.65 % between GaSb and AlSb.

This gives rise to a modification

of the total va-

ergy [l, 21. In this process one conduction band electron (C) recombines with a heavy hole state (H) giving energy and momentum to an electron in the split-off band (S) which is lifted to the heavy hole band (H) (the name CHSH comes from the states involved in this process).

lence band structur. A detailed investigation of these effects can be found, for example, in [5, 9, lo]. These effects are taken into consideration as far as important for our evaluations.

As the bandgap is only slightly larger than the splitoff energy As and both show a different variation with temperature [3] there exists one temperature at which both energies are equal and the activation energy van-

Auger recombination

ishes (see chapter 5). At this point a resonant behaviour should occur. Optical gain measurements of Mozer et al. [4] indicate that this resonance takes place at about 100

In this paper we present time-resolved measurements of the recombination dynamics with special emphasis on which is the leading recombination

channel at high temperatures

and high carrier densities.

2. Samples and Experimental

Technique

K in the bulk material. However, the expected resonance in quantum well material at about 300 K for L, = 115 k has not been observed yet [5]. Another important property of this material system is the small energetic separation between the di-

The GaSb/AlSb-MQW samples investigated are MBE-grown (61 with well widths of 78 A and 115 A and barrier width of 120 8, grown on [lOO]-oriented GaAs substrate. The unintentional p-doping level is about 5. 1016cm-3.

rect F-valley and the indirect L-valleys of the conduction band. This causes a quantisation induced direct to indirect transition at well widths L, of about 40 A 16, 71.

We have used the up-conversion technique described by Shah [ll] in order to investigate the carrier dynamics in these structures. The time resolution is limited only

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0 1991 Academic Press Limited

362

Superlattices

and Microstructures,

Vol. 70, No. 3, 7997

by the excitation laser, which is a simultaneously modelocked and q-switched Nd:YAG laser with a pulse width of 100 psec. In order to obtain homogeneous excitation conditions we used a gating technique to select the signal from the 5 strongest pulses in the q-switch-mode-lock pulse train. To avoid stimulated emission in the timeresolved measurements, down to a diameter

3. PL Spectra High excitation

we have focused the laser spot

of about 20 pm.

and Recombination PL spectra

Dynamics

of GaSb/AlSb

MQWs

show some special features compared to GaInAs/InP QWs monitored under comparable excitation conditions [12]. Firstly, the width of the GaSb/AlSb spectra is clearly smaller than the InGaAs/InP spectra despite the fact that the effective conduction band masses are nearly equal in both materials. Secondly, in emission there is no contribution of higher subband transitions even in the generation phase of the excitation whereas these transition

are clearly

performed

resolved in absorption

conditions electrons are generonly a fast scattering process

causes an immediate population of the indirect valleys. Typical scattering times are estimated to be below 1 psec [13]. As a consequence, thermal equilibrium with one common quasi-fermi level for all electrons can be assumed on the time-scale

of this experiment.

In the case

of a degenerate conduction band and/or high temperatures most electrons are placed in the four equivalent indirect valleys because of their large density of states mass (mr. = 0.67m, [14]). In other words, we have an efficient pinning of the electron quasi-fermi level near the band edge of the L-minima. These qualitative arguments explain both the comparatively narrow high excitation spectra and the lack of higher subband transitions. In order to calculate the lineshape of the PL-spectra, the radiative recombination coefficient B and the modified recombination tions

rates, we have to evaluate

the equa-

ntot = nr +w

(1)

nr

=

hT T

nL

=

LTzD&ln j

10’6 cm-‘)

ntot (1 018

figure

1 - Relative

population

-’

nr/ntot of the direct min-

imum as a function of total carrier density ntot for L, = 78 A and various temperatures.

respective, of the indirect

L-valleys to the P-valley only separatet by about 90 meV [9] minus quantisation energies. Despite the fact that for our excitation ated in the I-minimum

3’1”‘V

10”

measurements

on the same samples [3].

The reason for this is the proximity

o-

D&, In (1 + ew)

(2) >

.

(3)

ntot,nr and nL are the total electron concentration, the concentration in the P-valley and in the L-valleys,

Dlo are the steplike densities of states,

the quantisation separation

energies of the subbands

energy.

Given a certain

Eci,j)

and EEL the

mot, the quasi-fermi

level can be calculated by a numerical inversion of eqns. (l)-(3) together with the populations nr and no. Fig. 1 shows the ratio nr/nt,* for a sample with L, = 78 8, as a function of ntot for various temperatures. At T = 150 K and low density about 75% of the carriers are in the direct minimum whereas for higher temperatures and densities

this fraction

drops below 20%.

This effect modifies the recombination dynamics of a high density electron-hole plasma which is governed by the rate equation

ri = G -

R.CHSH - R+mt - Rczt,

Here G stands for the generation

rate.

(4)

The Auger rate

is &HSH = Co”s~ nr p1 where p is the hole concentration and C cask the Auger coefficient. The modification compared to the usually used expression Cn3 (15, 121 comes from the fact that the CHSH process involves one I-electron and two heavy hole states. In the degenerate limit the order of the reaction is reduced from third to nearly second order because nr is nearly constant in this cape. The second expression in eqn. (4) is the spontaneous recombination rate R-t = B(n, 7’) nr p. With increasing carrier density it’s order is reduced from second- to nearly first-order kinetics. In order to keep the number of parameters small we have calculated the spontaneous rate as a function of temperature and carrier density according to the model given in (81. The last term in eqn. (4), R&r = An stands for some extrinsic recombination via impurity levels and interface recom-

Superlattices and Microstructures, Vol. 10, No. 3, 199 7

363

1.50-

GaSb/AISb-MQW

GaSb/AISb-MQW

&=7,8

nm

1.25c ( 10sn cm%-‘ _.----.* ( l@ .-I )

l.OO-

075

6

2obo

lob0 Time

)

c)--- . . . . . -.--...____o___ .__.. ..__o________.. -0 -

3600

360

250

260

140

(psec)

T(K)

figure2 - Luminescence decay curve for a sample with L, = 115 A at a temperature of 375 K . The superexponential decay at its beginning is caused by the Auger recombination. The inset shows a result our line-shape analysis.

from

00

bination. So there are only two unknown parameters, A and C, which can be determined easily by a fit to our decay-curves. 4. Results

0.75- * 0.50 -

The super-exponential decay at its beginning is caused by the Auger process allowing us to determine it with high precision. The determination of C and A is done by a numerical integration of eqn. (4) and a least-square fit to our decay curves. Because of the nonlinear nature of the Auger recombination we have to know the excess carrier density in our samples at any time of the recombination process. For this the effect of bandfilling is used which influences the width and the total lineshape of the transient PL spectra. So a fit of the PL-spectra to our line-shape model [8] allows for the determination of the excess carrier density. In order to ensure well defined conditions we have taken PL-spectra monitored 500 psec after excitation or later because the thermalisation of the plasma has been almost completed [17] and we can assume equality between bath and plasma temperature within an accuracy of 5 %. A transient PLspectrum at a carrier density of 2.5 . 101scm-3 together with the fit is shown in the inset of fig. 2. The recombination coefficients A and C obtained by this method are shown in fig. 3 as a function of temperature for well widths of 78 A and 115 A. In both cases the extrinsic recombination coefficient A slightly decreases with increasing temperature. However, the nature of

y7 ._.c" * *-. ...t-.

0.25 o-

r

100

Fig. 2 shows a typical luminescence decay curve for a sample with L, = 115 8, at a temperature of 375 K.

O"\_

I

150

I

200

~.,.._.~.~i~"~ i

I

250

I

300

I

350

I

400

T(K) figure

3 - Temperature

dependence of the recombina-

tion coefficients for well widths of 78 A and 115 A. The Auger coefficient increases monotonously with temperature.

this process cannot be specified from our experiment. The Auger coefficient shows a monothonic increase with increasing temperature in both cases. For L, = 115 A and T = 300 K we find C = (4 f 1) . 10-sscm6s-1. We find no significant well width dependence of the Auger coefficient.

5. Discussion The CHSH-Auger process in GaSb/AlSb is the most basic test case for’calculations of Auger processes in MQWs because all states -one electron, two heavy holes and one electron in the split off band- are close to the P-point where the band structure is comparatively well known. However, the temperature dependence of the Auger recombination we have found is in striking con-

364

Superlattlces

trat to cadculations by Haug (11. As the bandgap E, drops more rapidly than the split-off gap A, there is one temperaturr, depending on well width, at which both energies are the equal [3]. At this temperature the activation

energy

of the CHSH-Auger

process

becomes

zero

giving rise to a resonance in the Auger coefficient [l]. This resonance should occur at about 400K for L, = 78 8( and at about 300 K for L, = 115 8. However, our measurements show a monotonic increase of the Auger coefficient, even in the case of L, = 115;1 where this resonance should be within the range accessible in our experiment. The predicted resonance is smeared out and/or shifted to higher energies. One possible cause for this may be the complex its modification

due to strain

valence

band

effects

ing effects causing nonparabolicities relations [18]. A complete treatment nation in GaSb/AISb MQWs should these effects. Recently

measurements

of Auger

structure

with

[lo] and band

mix-

in the dispersion of Auger recombitake into account recombination

in

the bulk material were reported by Snow et al. [16]. They observed an Auger coefficient of C= 3.10-28cm6s-’ at T = 275 K. Their value agrees well with our MQWApparvalues obtained at comparable temperatures. ently

there

is no reduction

of the Auger

coefficient

in

the quantum well material in contrast to the material system GaInAs/lnP [12]. There exists one other determination of Auger recombination in GaSb/AlSb-MQWs [19] giving values which are far too large because neglect of the influence of the L-valleys.

of their

(l] A.Hallg:,

J. Phys.

(‘: Solid

State

Phys.

17.

till)1

.J. Phys.

C: Solid

State

Phys.

20,

1293

(1987) [3] U.(:ebulla,

presented

time-resolved

on

the recombination dynamics in GaSb/AlSb-MQW structures under high temperature and high excitation conditions. At 300K we find C= 4 lo-**cm%for a well width of 115 I%, so the CHSH-Auger process is the dominant recombination order of magnitude

channel under these conditions. of the Auger coefficient agrees

The with

theoretical calculations whereas the temperature dependence does not show the expected resonance. We find a monotonic increase of Auger recombination in the temperature range 1OOK 400K. A well width dependence is not observed. Acknowledgement - We would like to thank Prof. M.H. Pilkuhn and Dr. E. Zielinski for fruitful disThe financial support by the Deutsche cussions. contract number Forschungsgemeinschaft under Pi 71/24 is gratefully appreciated.

G. I’raenkle,

A.Forchel.

[5] H.Schweizer, E.Zielinski, S.HauBer, R.Stuber. M.H.Pilkuhn, G.Griffiths, H.Kroemer, S.Subbanna, IEEE J. of Quantum Electron. QE-23, 977 (1987) [6] G.Griffiths, K.Mohammed, SSubbanna, H.Kroemer, J.Merz, Appl. Phys. Lett. 43, 1059 (1983) [7] A.Forchel, U.Cebulla, G.Traenkle, G.Griffiths, S.Subbanna, H.Kroemer, Surf. Sci. 174, 143 (1986) [8] E.Zielinski, H.Schweizer, S.HauSer, R.Stuber, M.H.Pilkuhn, G.Weimann, IEEE J. Quantum [9] LJ.Cebulla,

Electron. QE-23, 969 (1987) G.Traenkle, U.Ziem, A.Forchel

G.Griffiths, H.Kroemer, S.Subbanna, Phys. Rev. B, 37, 6278 (1988) [lo] P.Voisin, C.Delalande, M.Voos, A.Segmuller, C.A.Chang, L.Esaki, Phy. Rev. B, 30, 2276 (1984) [ll]

J.Shah,

[13] S.Zollner, [14] U.Cebulla, measurements

1;.Ziem,

G.Griffiths, S.Subbanna, H.Kroemer, Superlattices and Microstructures, Vol.3, No.1 (1987) [4] A.Mozer, K.M.Romanek, O.Hildebrand, W.Schmid, M.H.Pilkuhn, IEEE J. of Quantum Electron. QE-19 913 (1983)

IEEE

(1988) (121 S.Ha&r,

6. Conclusion

Vol. 70, No. 3. 799 I

(1984) [2] A.Haug,

W.T.Tsang,

We have

and Mlcrostructures,

J. Quantum G.Fuchs,

Appl.

Phys.

S.Gopalan, diploma

Electron.

A.Hangleiter, Lett.

L.L.Chang

QE-24,

K.Streubel,

56, 913 (1990)

M.Cardona, to be published thesis, University of Stuttgart

(1985) [15] B.Sermage, D.S.Chemla, D.Sivco, A.Y.Cho, IEEE J. Quantum Electron. QE-22, 774 (1986) [16] P.A.Snow, P.Maly, D.J.Westland, J.F.Ryan, State Electron. 32 1485 (1989) [17] P.A.Snow, D.J.Westland, H.Munekata L.L.Chang, Superlattices and Microstructures, [18] M.Altarelli, J.Luminescence [19] E.Zielinski, H.Schweizer, H.Kroemer, S.Subbanna, Superlattices

276

and Microstructures

J.F.Ryan,

Solid T.Kerr,

5, 595 (1989) 30, 472 (1985) R.Stuber, G.Griffiths, 4, 473 (1988)