Energy relaxation of hot 2D carriers in strong magnetic fields due to optical and acoustic phonons

Superlattices

ENERGY

and Microstructures,

RELAXATION

OF HOT

2D CARRIERS AND

P.C.111. Christianen, Research

Institute

323

Vol. 9, No. 3, 7991

H.A.J.hl.

for Materials Toernooiveld.

IN STRONG

ACOUSTIC Reinen,

MAGNETIC

FIELDS

DUE TO OPTICAL

PHONONS

T.T. J.M.

Berendschot,

and High Field Magnet NL-6525 ED Nijmegen.

H. J.A.

Bluyssen

Laboratory, University The Netherlands.

of Nijmegen.

K. Ploog ?rIax-Planck-Inst,itut

fur Festkorperforschung,

(Received

Heisenbergstr.

12 August

The energy relaxation rate of hot carriers ture is studied for different, laser excitation c.w. photoluIninescence dominates the hot carrier For the lowest excitat,ion

1, 7000 Stuttgart

80. FRG.

1990)

in a GaAs/(Ga.Al)As powers in magnetic

quantum well strucfields up to 17 T using

spectroscopy. In the regime where LO-phonon scat,tering cooling a magnetic field reduces the energy relaxation rate. power used, an enhancement of t,he cooling with magnet,ic

held is fourld due to acoustic phonon scattering. These results are supported by model calculations. Furthermore the results are discussed with respect, to prcviouslv reported time resolved photolllIllinescerlce measurements on GaAs/( Ga,Al)As quantum well structures and bulk GaAs. The present c.w’. photoluminescence measurements provide a better quantitative understanding of the time resolved data and the comparison shows that the cooling of hot carriers in 3D and quasi application of a magnetic field is not fundamentally different.

2D under

the

Study of hot carrier energy relaxation rates in quasi OD carrier systems simulated by a GaAs/(Ga,Al)As quan-

photo-excitation tion with optical

tum well structure

the magnetic field on the energy relaxation rat,e is studied for different excitation int,msities, by det,ermination

been carried

(QWS)

out mainly

in strong

magnetic

by t,ime-energy

fields, has

resolved

photo-

luminescence (PL) spectroscopy.’ It was found that carrier cooling in bulk GaAs is reduced considerably

the in

strong magnetic fields.2 In GaAs/(Ga.Al)As QWS, however, an enhancement of the carrier cooling with magnetic field was observed after an initial reduction up to B =9 T.2,3 Although these time-energy resolved experiment,s provide valuable information on the carrier dynamics in these systems, a full comprehension of the

and the power loss due to the interacand acoustic phonons. The influence of

of 7’,,r from photoluminescence spectra. The measurements were performed on a MBE grown modulation doped QWS consist,ing of 10 GaAs layers of 9 mn widt,h. The details of the sample are discussed elsewhere.” A Kr ’ laser operating at 647.2 nm and 530 run and a HeNe laser were used to excit,e carriers optically. The sample was cooled down to a temperature of 4.2 K in a He bat,11 cryostat, which was mounted in OIW

results is difficult due to the variation in time of all the relevant paramet,ers like the carrier effective tempcrature (Tee) and densities n, and the Landau level (LL) linewidths. In this paper we describe t,he results of a st,udy on the energy rrlaxat,ion rate of quasi 2D carriers

of the hybrid

in magnct,ic fields up t,o 17 T using C.W. photolumnascence spectroscopy. Under these steady state conditions, hot carrier phenomena are gouverned by the balance between power input, int,o the carrier system due to

lines). Full luniinescence spectra were to obtain values for the carrier densities

0749-6036/91/030323+04$02.00/0

magnet

Magnet Laboratory Figure 1 shows

systems

(25 T) of the High Field

of the University of Nijmegen. the high energy tail of some spectra

for the 9 nm doped QWS on a logarit,hmic the resulting rffect.ive carrier temperatures

linewidths

Ii. which

of the experimental

scale with T,,r (dashed

also measured II, and the LL

are used in the theoretical data.

analysis

These values are deduced

0 1991 Academic

from

Press Limited

Superlattices and Microstructures.

324

9nm

QUANTUM

WELL

---

I

1

ADP

Vol. 9, No. 3, 7991

scattering

I

I

15 10 MAGNETIC FIELD (T)

/5

I

I

1.60

165 ENERGY

Figure 1 High energy spectra 011a logarithmic effective

carrier

the spectra

(eV) tail of some

scale witll temperature TeB,

usiug R model

photolllIniIlesc,en~e

the best line for tJle

for the luruinescrnc~r

radiation

I - J‘f(.,g,f,,,y,dE containiug the two diirlrnsional LL density of states functious !I~., and Feruli-Dirac distribution

functions

.fC,,. The analysis

detail in ref. 5. Figure :! shows of 2 kW/cm”.

T,B wrsus

T,f increases

is tlescril~etl

B for an rxcitatim from

60 K at B=7

in morr l~nvcr T up to

80 K at B=ll T. then decreases to 40 K at B=17 T. while ate 15 T a shoulder is ol~erved. The incrrasd cooling for B > 11 T, result,ing in a lower Tee. VW attrilmte to acoustic deformation potential (ADP) scattering. In order to support this ass&ion. wc have calc~ latetl Tef=T&( B) from the equilihrimn c,oIldit,ion < dE/dt >i,,=< dE/dt >phonC,,,6. Here < tlE/dt >i,, is the average power input, per carrier into the ‘LD gas 1)~ laser plloto-rx~it,atioll. which was kept constant for all values of B. < dE/dt >p~,ono,,s is thcl average energy rrlaxation rate per carrier due to carrier-phonon interactions. which depends on 71,. Tea. Ti and B.” Since it is difficult to determine < tlE/tlt >i,, directly from the laser rxcitation power. its value was calculated from the rquililb rium condition and the expressions for < tlE/tlt >,,honl,n5 as given in ref. 6. for one value of B = B,, (10 T in Fig. 2) and with the experimentally detrrnbrd vallics of T,ff% II,. Ti at B = BO. For all other values of B this < dE/clt >i,, was assumed to be condant and TFB was

Superlattices

and Microstructures,

Vol. 9, No. 3, 1991

325 to the

variation

time resolved tra in ref. partially

scajter

k!i

of the

carrier

3 show roughly

Landau

density

However,

one full and two

level at field values

to t,he occupat,ion corresponding

in the

t,he PL sperabove

9 T.

observed in our c.w. to Fig. 2. Therefore

our measurements and theoretical analysis confirm the conclusions by Hollering et al. that the enhancement of the carrier cooling for B >9 T is due to ADP scatter-

150 -

k!!

ing which dominates the cooling in this field range and thrse c,arrier densities (- 1 x 10z3 m “). i.e. observed LL occupation.

P $ F

2 and ref. filled

which is similar PL measurements

ing

z

s

in time

PL measurements.

loo-

However crease

B ii

that

becomes

Our

calculat,ions

scattering

50I

I

0

5

I

10 FIELD

MAGNETIC

with

of T,B with

increasing

excitation

B changes

even stronger show

dominates

at higher

that the

power

in this carrier

rxcit,ation regime

1

haviour

(T)

from

Figure 3 T,B WTSIISB for two excitation powers: ?? =IO kl;t’/cm’ and ? = ?20 kW/cm2. The dashed curve is a JIlOdd c-akulation for LO phonon scattering with experimental values for n, and Fi and Bs=ll T. The oscillations are due to HEAfPR.

of T,a with time

where

resolved

LO phonon

B resembles

which This

an can-

br-

the results

GaAs’,

on bulk

was found

phoi~011

although

very much

PL measurements scattering

powers.

LO

cooling.

de-

increase.

additional reduction on thr cooling is found not be ascribed to LO phonon interactions.

15

the

into a monotonic

to dominate

the

energy relaxation up to the highest magnetic fields used. and where a monotonic reduction of the carrier cooling with increasing magnetic field was found. Therefore we conclude

from

the present

measurements

and the time

resolved PL data that in t,he regime where LO phonon scatt,ering dominat,es the carrier cooling, a magnetic field a previous

publication.8

ers, i.e. 20 kW/cm’,

For even higher T,s increases

excitation

more drastically

B. The dashed curve in Fig. 3 shows the the energy relaxation rate due t,o LO-phonon < dE/dt

>~o

using

the model

pow-

mentioned

with

results for scattering

above.

Rea-

sonable agreement is obtained showing that LO-phonon scattering dominates t,he cooling. However t,hc monotonic increase of T,f wit,11 B is not explained by the model, indicating an addit,ional reduction of t,he carrier c,ooling due to the magnetic field. Time-energy resolved PL measurements on GaAs/( Ga.Al)As Q\$:S in st,rong magnet,ic fields showed a reduction of t,he carrier cooling up to B -9 T, follonctl

by an enhancement

due to LO-phonon

up to 20 T. The

interact,ions

spect to the zero field cooling formation of quasi OD carrier Landau levels. and a resulting

comparison

the

relaxation.

For lower

carrier

densi-

lower LL occupation where acoustic phonon dominates the carrier cooling, an increase of

carrier

cooling

rate

with

magnetic

field

is found.

Finally it should be not,ed that a transition from LO.phonon scattering to ADP scattering dominating the hot. carrier cooling should be observed both in bulk and lower dimensional structures. The magnetic held value at which this transition will occur depends on the excit,ation

condit,ions.

Acknowledgement - Part of this work was supported by FOM with financial support of NWO.

re-

rates, was assigned to the states, i.e. well separated enhancrment~ of nonequi-

of LL occupation

the energy

ties. i.e. scattering

reduction

up to B rz9 T with

librium phonon effects.’ The enhancement observed for B >9 T in these QLVS was assigned to an increased hole-phonon c,oupling &‘) and an increase of ADP scat t,cring with B.’ The measurements in Fig. 2 show a similar variation of the carrier cooling, and consequently T,f-, with B. Also the Landau level occupation observed in the experiments of Fig. 2 are comparable to those 01). scrvcd in the t,ime resolved exprrimrnts on the Q1VS. A direct

reduces

is difficult

due

References:

1. J. Shah:

IEEE

J. of Quantum

Electron.

Q_E22,

1728 (1986) Hollering, T.T.J.M. Berendschot, H.J.A. 2. R.W.J. Bluyssen, H.A.J.M. Reinen, P. Wyder and F. Roozeboom: Phys. Rev. B38, 13323 (1988) and J.M. 3. J.F. Ryan. R.A. Taylor, A.J. Turberfield Warlock: Surf. Sci. 170, 511 (1986) 4. K. Leo, W.W. Riihle, H.J. Queisser and K. Ploog: Appl. Phys. &, 35 (1988) Berendschot: Ph.D. 5. T.T.J.hI.

thesis Nijmegen

1989

326

Superlattices

and Microstructures,

Vol. 9, No. 3, 799 7