Superlattices and Microstructures, Vol. 1, No. 3, 1985 245

ELECTRON-HOLE PLASMA IN PULSE PHOTOEXCITED SINGLE QUANTUM WELLS

D. Fekete, S. Borenstain. A. Ron and E. Cohen

Solid State Institute, Technion, Haifa 32 000, Israel

and

R.D. Burnham

Xerox Palo Alto Research Center Palo Alto, Ca. 94304

U.S.A.

(Received 15th August 1984)

We report photoluminescence studies of MOCVD grown, GaAs-AI Ga As

single quantum wells which were intensly excited with a pulser ~9~

laser at T=2K. For a well width of d~40~, the spectra are interpreted

as due to the radiative recombination of a hot electron-hole plasma

confined to the well. The density of charge carriers and their

temperature depend upon the excitation intensity , and vary in the range of 1011-1013 cm~ 2 and I00-500K for an absorbed photon flux of

I01~-1016 photons-cm- per pulse, respectively. The observed spectral

features are identified as the el-hhl and e1-1hl transitions and hwo additional bands which are tentatively assigned to transitions involving virtual bound states of either the electron or the hole. The

electron-hole plasma spectra of the d~40~ sample are strongly

polarized perpendicular to the well quantization axis. For wider

wells (d-~80 and 150~ ) smaller photoexcited carrier densities were observed for the same absorbed photon flux. It is thus concluded

that the capture efficiency of the well is small.

I . Introduction

Intensly excited GaAs-AlxGa1_ x As quantum

wells(QW) emit a broad band whlcn is

distinctly different from the narrow lines observed under weak photoexcitation I-3 . Since

the light emitted perpendicular to the layer

is virtually unabsorbed, the band shape yields

a direct measure of the energy distribution of

the recombining particles. It has been argued

that the high excitation luminescence is due

to the radiatlve recombination of a hot

electron-hole plasma (EHP). The structure of the emission band has been correlated with the

various e-hh and e-lh transitions. However,

the*peaks observed in the high excitation spectra did not have the same energies as the

corresponding ones observed by cw excitation

spectroscopy. The discrepancy was explained

by either assuming that the bands observed in

the high excitation spectra were associated with forbidden transitions 2 or by invoking

conduction band non-parabolicity ~ . Time- resolved picosecond spectroscopy 4 indicate that electrons in the EHP thermalize at a much slower rate in the QW than they do'in bulk GaAs. In addition to these studies,

stimulated emzssion has been observed at several spectral ranges below the barrier

height of the cladding layer 1'5 . This is

taken as evidence for QW band filling under

intense photoexcitation.

In this paper we report on the results of high

excitation photoluminescence studies using a

pulsed dye laser pumped with a N 2 laser. The pulse duration (2 nsec) is much longer than

the expected EHP lifetime (The exciton lifetime is reported 6 to range from 0.35 - I

nsec). The spectra are thus observed under

steady state conditions and maximum excitation intensity of 1017 photons- cm -2 per pulse.The

spectral shape is calculated as a function of

e-h pair density and temperature, assuming k

conservation. Sub-band renormalization of ~he

QW EHP is observed, similar to the case of

bulk materials.

Most of the results reported here are for Qw

width of dN40~. Two interesting new features

are observed: I. e-h recombination involving

either electrons or holes in virtual bound 7

states (resonance states in the cladding

layer). 2. strong polarization of the emitted light which can qualitatively be

explained using the electronic wave functions.

2. Experiment

The samples grown in a

used in this study were all

MOCVD reactor. The

0749-6036/85/030245+05 $02.00/0 © 1 985 Academic Press Inc. (London) Limited

246 Superlattices and Microstructures, Vol. 1, No. 3, 1985

GaAs Qw ranged in width from 40-200~ an4 was cladded by A1 Ga As layers with x=0.35±0.05

xl- All layers were un~oped. In some samples the cladding layer was 600~ thick on each side of the QW while in others it was 0.5~thick. The samples were immersed in liquid helium and photoexcited with either a cw dye laser or a pulsed dye laser pumped with a N laser

2 In the latter case pumping was always into the cladding layer (E >1.9 eV). The pulse

• . e x c .

wldth was 2 nsec wlth a repetltlon rate of

200 Hz. The photon flux impinging on the sample ranged from 1014 to 101"photons.cm -2

per pulse. The luminescence was monitored with a double spectrometer and analyzed with either an electrometer or a boxcar with a

10 nsec gate. The results were identical in both methods. All spectra were taken at 2K.

Two excitation and detection configurations were used: a. The "perpendicular

configuration" in which the exciting beam impinges perpendicular to the QW layer

(along the z-axis) and very close to the cleaved edge. The emission is c o l l e c t e d

through this edge, perpendicular to the exciting beam (along the x-axis). It has the advantage that the polarization can be monitored both parallel and perpendicular

to the well quantization axis. On the other hand its drawback is the substantial absorption of the emitted light as it traverses a macroscopic path along the QW layer, b. The "backscattering confiquration" in which both excitation and emission are along the z-axis (We have actually monitored the fluorescence at,~30 ° off the layer normal). In this

configuration the emitted light is virtually unabsorbed by the well.

Under weak cw excitation and in the backscattering configuration, all samples show the el-hhl transition as a broad ( 15 meV) or a double peaked emission (Figs. la and 2a ). Under more intense cw excitation the emission intensity shifts towards the high energy part of the band. In the perpendicular configuration only the low energy part of the emission band is observed (Figs. la and 2a).

All samples show intense emission from the cladding layers (above 1.85 eV) .

The intense pulse excltation spectra were obtained with the dye laser tuned deep into the cladding layer conduction band (around

2.1eV). The excitation intensity was in the range of 1014- 1017photons- cm- ~ per pulse. Assuming an absorption coefficient of~=105 cm -I and cladding layer width of I000~ the absorbed photon flux was 1013- 1016

ohotons-cm -2 per pulse. Figs. Ib, 2b and 3 show several examples.

The cw excitation spectra of the dr~40~ sample were obtained using a dye laser(operating with a LDS 698 dye) pumped by an Ar + laser. Fig. Ic shows excitation spectra of the emission

peaks). Spectra polarized either parallel or perpendicular to the well z-axis were taken in

"E

0we f 0ddng

2 \ xl

1.7 1.8 1.9

eV Fig. I: Spectroscopy of the d % 40~ sample at T=2K. a. cw emission spectrum excited at 1.887 eV. b. High excitation spectrum obtained in the perpendicular configuration. The pulse dye laser operated at 2.1 eV. c. cw excitation spectrum of the extrinsic exciton (top) and the intrinsic exciton (bottom).

the perpendicular configuration. The emisslon from the cladding layer was always polarized (20:1) perpendicular to the z-axis. The high intensity spectra of the d~40~ samples were also polarized ( 7:1) in the same direction. The wider well samples did not show any significant polarization.

3. Discussion

We first identify the transitions observed in the cw emission and excitation spectra. The d~40~ sample shows two emission peaks (Fig. !a). We attribute the low energy peak (centered at 1.664 eV) to the radiative recombination of extrinsic excitons and the high energy one (1.683 eV) to the intrinsic exciton (el-hhl band) The reasons for this assignment are: a. Under more intense cw

Superlattices and Microstructures, Vol. 1, No. 3, 1985 247

o

{ ® b

1.58 1.60 1.62 1.64 eV

Fig. 2: a. cw emission spectra of the d ~ 80~

sample obtained in the backscattering

configuration (I) and in the perpendicular

configuration (2). b. High excitation spectra for 1015and 1016photons cm-2per pulse.

1.66

CF 540 meV

el 142

23 hhl 44 ~hl

60 hr

Fig. 3: Schematic representation of the

sub bands of the d% 40~ sample, cr and vr

denote the virtual bound states of the

conduction and valence band, respectively .

excitation the emission intensity shifts to the higher energy peak, indicating saturation

of impurity centers, b. The excitation spectrum (Fig. Ic) has its lowest maximum at

1.693 eV and can thus be taken as the intrinsic exciton absorption band. c. Comparing the emission spectra obtained in

the perpendicular and backscattering

configurations, the former shows a high energy

cutoff at 1.674 eV. This can be taken as the

lowest intrinsic absorption edge.

The d~80~ sample shows a single emission band

under cw excitation (Fig. 2a). The spectrum

obtained in the perpendicular configuration

cuts off at 1.613 eV. A point by point

excitation spectrum (not shown) has its lowest

energy peak is at 1.616 eV. Thus , the cw

emission band in this sample consists of a low

energy extrinsic exciton which merges into a

higher lying intrinsic exciton band . Samples

with d>100~ had cw emission spectra similar

to the d-80~ . The observed band width in all samples is larger than that reported for MBE

grown QW's. Part of this width is probably

due to well width fluctuations However we cannot rule out macroscopic broadening.

Additional bands observed in either excitation

or emission spectra of the d-~40~ sample are of interest. The band centered at 1.725 eV in the

excitation spectum (Fig. Ic) is the e1-1hl transition . No more levels are expected for this well width. However, a band is observed

at 1.765 eV. Since the valence band discontinuity is about 60 meV (for the Qw

composition used here), the level giving rise

to this transition must be above the potential

barrier. We tentatively assign the band

centered at 1.765 eV to a transition between ~I

and a virtual bound state of the valence band

There are several emission bands in the spectral

range of 1.8-1.9 eV. They correspond to

transitions originating in the cladding layers.

The two lowest ones, centered at 1.825 and

1.859 eV(for the sample with d-~40~) , are

strongly excited by selectively pumping at the

lower edge of the cladding layer spectrum(around 1.87-1.9 eV) and only weakly so for higher

excitation energies. We tentatively attribute

these bands to transitions between the virtual bound state of the conduction band and the hhl

and lhl sub bands. The separation between them

(34 meV) is the same as that observed (in the excitation spectra) for the el-hhl and lhl

transitions. Fig. 3 is a schematic

representation of the various energy levels. The spectra obtained by intense pulse

excitation are analyzed in terms of the

radiative recombination of the EHP . The

density of e-h pairs, N, and the plasma

temperature are used as free parameters.

Assuming an effective plasma temperature means

that the EHP is treated in a quasiequilibrium state. The Fermi energy for the holes is

givenm by solving the following equation for

~F (T) : h E F - E i (I)

N={ gi kBTln(1+exp { ~ } )"

248 Superlattices and Microstructures, Vol. 1, No. 3, 1985

- - exp --- CQI

= j , _

E b , , ~ , . \ A

S

I / ' ' " , . . . . .~ . . . . . L

C ~ xl

1.6 1.7 1.8 1.9 eV

F ig . 4: Exper imenta l and c a l c u l a t e d h igh e x c i t a t i o n spec t ra o f the d~40~ sample. -2 a. Excitation intensity 1 015photons cm per pulse. N=9x1011cm I and T=450K. b. 1016

2xi012 and 450K. c. 10 7 5x1012an d T=I00K.

g.=m*/@h 2 is the density of states in the 1 1 m* i-th sub-band is the effective mass for

either the heav~ or light hole. The index i is

used to denote both the sub-band (with E being its threshold) and the type of hole I.

For the electrons all bands have the same g.

Then, the spectral shape of the EHP emission

is given by:

I(~m)=AZ I S f (E.(k)) f (-E (-k))- ij E -E c 1 -- v 3 --

l 3

m'm* 6(E (k)-E (-k)-J%~) dEdE . (2) i 3 i -- 3 -- i ]

The indices i and j refer to electron and hole sub-bands, respectively. The factor A contains

all constants, including the dipole matrix element which is assumed to be independent of k, the two dimensional wave vector. We assume

~hat k is conserved in the EHP radiative recombination.

Fig. 4 shows EHP spectra obtained for the

d~40~ sample under excitation in[ensities of 10 ~5, 1016and 1017photons.cm - per pulse.

The data are fitted by using only the el-hhl and lhl transitions and excluding the

transitions involving the virtual bound

states. The intensity of these latter

transitions indicate that states involved do

not fully thermalize with the rest of the Qw states. The spectrum 9hown in Fig. 4a is

fitted with N=9xl 011 cm-, T=450 ± 50K. The

lowest energy peak is assumed to contain a contribution from excitons from crystalline

regions which are weakly excited . In fig. 4b the data is fitted with N=2.3x1012 cm -2

and T in the same range. Fig. 4c shows the spectrum obtained under most intense excitation. It is fitted with N= 5.5xi012 -2 cm and T=I00K. The temperature cannot be

estimated in this case because the QW states are completely filled.

Several points should be noted: a. The e-h

pair density is much smaller than the density

of absorbed photons (by the cladding layers).

This means that the particle capture by the Qw

is inefficient, b. The EHP spectrum is red

shifted (by % 10 meV) with respect to the

intrinsic exciton transitions and broadens towards lower energies as the excitation

intensities. These might be due to many body

interactions in the plasma, c. The high

effective plasma temperatures indicate slow thermalization in the Qw.

Finally we comment about the possible origin

of the observed polarization of the EHP

emission in the d 40~ sample. The electron

and hole wavefunctions for the n=1 states have

the form: 9(r, z)= Bexp{ i~'~ } .cos(~ zn/d).

The matrix eTement of the z-component of the

dipole operator vanishes for a An=0 transition while the x or y components , which operate on

the exponential part of the wavefunction do

not. This argument is independent of the well

width and thus it is not clear why no

polarization is observed for wider wells.

Acknowledgement: This work was supported by

the Fund for Basic Research administered by

the Israel Academy of Sciences and Humanities.

References

I. N. Holonyak, R.M. Kolbas, R.D. Dupuis and P.D. Dapkus, IEEE QE-16, 170(1980).

2. R.C. Miller, D.A. Kleinman, O. Munteanu

and W.T. Tsang, Appl. Phys. Lett. 39, 1(1981).

3. Z.Y. Xu, V.G. Krelsmanis and C.L. Tang,

Appl. Phys. Lett. 43, 415 (1983). 4. Z.Y. Xu and C.L. Tany, Appl. Phys. Lett.

44, 692 (1984). 5. M.D. C amras, N. Holonyak, M.A. Nixon,

R.D. Burnham, W. Streifer, D.R. Scifres,

T.L. Paoli and C. Lindstrom, Appl. Phys. Lett. 42, 761 (19831.

Superlattices and Microstructures, Vol. 1, No. 3, 1985 249

6. E.O. Goebel, H. Jung, J. Kuhl and K.Ploog, Phys. Rev. Lett. 51, 1588 (1983).

7. G. Bastard, U.O. Ziemelis, C. Delalande and M. Voos, Solid State Comm. 49, 671 (1984).

8. R.C. Miller, A.C. Gessard, W.T. Tsang

9.

and O. Munteanu, Phys. Rev. B25 , 3871 (1982).

C. Weisbuch, R. Dingle, A.C. Gossard and W. Wiegmann, Solid State Comm. 38, 709 (1981).