Dynamics of hot carrier cooling in photo-excited GaAs

t

809—813.

Solid State Communications, Vol.31,in pp. Pergamon Press Ltd. 1979. Printed Great Britain.

Dynamics of Hot Carrier Cooling in Photo—Excited GaAs by R. F. L.eheny, Jagdeep Shah, R. 1... Fork, C. V. Shank and A. Migus* Bell Telephone Laboratories, Incorporated Holadel, N.J. (Received 30 Nay 1979 by A. G. ~Chynoweth) Carrier relaxation following pulses,

excitation

with subpicosecond optical

determined from time resolved nearband gap transmission spec-

trum changes, is described for GaAs. For n < 5x1017cm3 the observed relaxation can be related to carrier—phonon interaction, but at higher densities the rate of relaxation is significantly slowed, possibly due to carrier screening.

For semiconductors where

carriers

are

gen—

the hot carriers to cool to the

lattice

tempera—

erated with photons having energy in excess of the band gap energy, relaxation of the carriers to the

ture since the rate of energy exchange with the lattice decreases rapidly at low carrier tempera-

band edge occurs as a result of carrier—carrier and carrier—lattice interactions.~~1) We have investigated the dynamics of these relaxation

tures.~3~Consistent with our previous results(2) we find for moderate excitation densities, n < 5 x 1O~ cm3, the initial cooling is due to

processes pulses.

LO phonon emission by the hot carriers; however, this polar optic scattering mechanism becomes less

in GaAs with subpicosecond optical Our previously reported investiga—

tions~2~, with the

sample maintained

at

80°K,

effective as carriers

cool.

Below

T

demonstrated that for the range of excitation 3 and den— for aities energy investigated excess of ~ (1016_1018 : 120 meV, cm carrier—carrier interactions scatter the carriers out of their

0 :50K the contribution of acoustic phonon scattering, has a weaker temperature dependence, becomes which reia— tively more significant. In addition, we find the initial cooling rate slows down for higher carrier

initial

densities,

states

in

less

than a picosecond.

For

this case a thermal distribution of carriers, with an effective carrier temperature T greater than the lattice equilibrium

temperature T

within

0, evolved following excitation and

one

picosecond

and

for n > ~O18,the carriers can no

longer be described by a thermal distribution for times as long as 10 picoseconds after excitation. These measurements provide the first direct cvi— dence for a change in the hot carrier energy loss

then cooled to the lattice temperature in ~ poec as a result of LO phonon emission by the hot carriers.

mechanism at high carrier densities.

papercooling we describe additional ments Inofthis carrier for the case of measure— the sample maintained at ~10°K. Lowering the sample tem-

The measurements were made1.5~thick on a sample of supported molecular beam grown GaAs and maintained with between layers of AlGaAs T 0 1O°K. The sample transmission was measured

perature

by

*

greatly

increases the time required for

probe

On leave from Laboratoire D’Optique Appliquee Ecole Polytechnique—ENSTA, Palaiseau, France with a grant from the European Space Agency. 809

pulses

using

the

filtered

810

DYNANICS OF HOT CARRIER COOLING IN PHOTO—EXCITED GaAs

Vol. 31, No. 11

0

(8000 < < 8200A) output of a broadband, subpi— cosecond continuum source excited by the output of an amplified 0.5 paso, ~

=

excitation was accomplished

6150A° laser. (U’‘ using

a

pump

Sample pulse 0

generated by stimulated Raman emission Q~:75OOA) from ethanol excited by the same amplified laser pulse. The relative time of arrival at the sample

1.0

GaAs 10. 10K

~ ~ 0.5 —

4

~

7900

of pump and probe pulse was adjusted by a variable

8100

8300

optical time delay. The probe and pump pulses were overlapped at the sample in a spot 1OO~i in

_______________________________________

dispersed by The diameter. a 1/U—meter transmitted spectrometer probe andbeam detected was with an optical multichannel. analyzer. sion spectrum for t < 0 where time is measured

~+1pwc 7900

810

~

Figure 1(a) shows the unperturbed sample tranamis— from the time the pump pulse arrives at the sample. Sensitivity to small changes in the transmission spectra is enhanced by electronically

_______________________________ 7900 8100 8300 0) 14

with takingthethe pump difference beam present between and spectra absent recorded as

illustrated

by

the

difference

spectra shown in

Figure 1(b). Screening of the free exciton and absorption induced by the shift of the band edge

~

r’+62p

14 14

~2: ~

7900

to lower energy as a result of the photo excited 5~is clearly evident in the trace for carriers~ t=1 psec, while at photon energies greater than the exciton energy there is a broad region of increased transmission.~2> With increasing time delay (Fig. lb) the transmission at these energies continues to evolve with the transmission increas— ing near the unperturbed band edge as the carriers

~

8100

r~+242ps.c —

7900

810 (b)

Fig. 1. (a)

Transmission spectrum of GaAs measured using the 0.5 psec continuum probe corrected for spectral variation of source and detector system.

(b)

high energy such as might occur if the carriers were to relax from their initial state solely by emission

without

8300

WAVELENGTH

relax into these states as a result of carrier— lattice interactions. At no time do we observe evidence for preferential occupation of states at

LO—phonon

~

Difference spectra for various time delays after excitation.

These

spectra are obtained by electronically

carrier—carrier

taking the difference between the

scattering. Rather the transmission spectrum corresponds at all times to a more uniform distri— bution characteristic of a thermal distribution of carriers. We estimate that the measured tranamis— sion spectrum at 1 psec iz approximately a thermal

spectra at time t and the spectra for t
distribution with carrier temperatura Tc > 150°K.

T a , according to c( d o (1—F e—F h ) where ~ 0 is the unperturbed absorption coefficient corresponding

We have also fitted the measured transmission spectra assuming the sample absorption coefficient

to band to band transitions and F e and Fh are the Fermi functions for electrons and holes resp.o—

~ varies with carrier density, n, and temperature,

tively.

The

details of this calculation, which

Vol. 31, No. 11

DYNAI4ICS OF HOT CARRIER COOLING IN PHOTO—EXCITED GaAs

takes account of band gap renormalization and which allows determination of both carrier density and temperature, have been discussed ousiy.’~~ Results of fitting three

150 fCc)

previ— spectra

measured at different excitation intensities, at a fixed time delay of 10 psec, are shown in Fig. 2. The temperature determined in this way, as a func—

81 I

‘ci

GaAs 10. 10K

‘~‘ ~1

14

~ 100

—

-

14

tion of time, is shown in Fig. 3. 14

I.. ‘S

1.5

(a)

I —~

50

‘S...

-

GaAs

-

‘S

T~.10K

10

~I

100

~ME (psec) I

I

I

7900

8100 WAVELENGTH

8300

ous time delays following pulsed excitation, the labeled points correspond to the

Fig. 2. Transmission spectra at 10 psec for three pump intensities 10, UI 0 and 15I~with IS 7 w/cm2. The dashed curves are 2x10 theoretical fits obtained as described in the text for (a) N=7x1016 ~ T 0=50K, 17cm3, Tc= 90K and Cc) N: (b) N=3x10 ixiOlScm3, T 0

=

Fig. 3. Measured hot carrier temperatures at van—

1UOK.

data of

Fig. 2.

The solid curve is car—

rier temperature an initial excess calculated energy ofassuming 120 meT. (Tc(0)

=

U65K) and the dashed curve mdi—

cates temperature expected if the the carrier —LO phononvariation scattering rate is decreased by a factor of 5.

12 cm3 For carrier densities thanan effective i0 carrier—carrier scattering greater provides mechanism for scattering the carriers out of their initial states to establish a Fermi distribution

energy range is so small that the processes involving acoustic phonocs (principally hole— acoustic phonon) become dominant.

with T 0 > I 0 . Carrier—lattice interactions, pro— vide the mechanism by which the thermalized carriers exchange energy with the lattice so as to

We have calculated the expected energy loss by the photo—excited carriers taking account of carrier—LO phonon and carrier—acoustic phonon

cool to the lattice temperature I. Considerable experimental and theoretical work has been done

scatter1ng~3~with the assumption that carrier— carrier scattering is sufficiently fast to main—

relating quasi—steady—state carrier temperatures to these processes.~6~The rate of energy loss by a hot carrier distribution in GaAs including polar

tam a nearly Fermi distribution of the carriers at all times. The calculated carrier temperature as a function of time, assuming an initial excess

optic (LO phonon), piezoelectric, and

energy of 120 meV, is shown by the solid

deformation

potential (acoustic phonon) scattering has been discussed by Ulbrich~~~ and by Gobel, et ~ Carriers with energy greater than Fii~are most effective for cooling via LO phonon emission, but for T~< 50°K the fraction of carriers in this

line

in

Fig. 3. This calculation yields a cooling rate that is independent of carrier density and is in good agreement with our results for n < 10~~ cal3. As predicted, carrier cooling is initially

rapid, achieving a temperature of

55°K

812

DYNA1IICS OF HOT CARRIER COOLING IN PHOTO—EXCITED GaAs

Vol. 31, No. 11

£n 10 psec, but subsequently slows down as the LO

where

phonon emission mechanism becomes less important.

He fi~nds a significant reduction in electron— phonon coupling when : u~,with the effects of

When the excitation

intensity is

increased

polar optic scattering limits the mobility.

screening increasing rapidly with decreasing

car—

beyond

n - io17 cm~we observe a slowing of the 17 we find carrier cooling. For n - 5 x10 (Fig. 2b) : 90°Kat 10 psec. When the excita—

rier temperature. In our measurements the onset of the decrease in carrier-phonon interaction appears to be more abrupt than these calculations

tion intensity is increased further the spectra at 10 psec (Fig. 2c) can no longer be fitted using

would predict and does not change with The dashed curve in Fig. 3 indicates the temperature

the assumed form for cC.

variation

A fit of the transmission

expected

for

the

case

where

the

data near the band edge yields a temperature I 1110°K, for this case, however the transmis— c sion at higher energy provides clear evidence for

electron — LO phonon scattering rate is reduced by a factor of five. In addition, while the decrease

a nonequilibrium distribution. It is significant to note that similar nonequilibrium distributions

screening of the electron—phonon interaction, this mechanism alone does not explain the nonthermal

of carriers at high excitation. densities have been (8) observed in photo—luminescence studies.

distribution evident in the data of Fig. 2c unless there is a similar reduction in effectiveness of carrier—carrier scattering. At present, no simple

These high

excitation

data

clearly

demon—

strate that the mechanism of carrier—phonon interaction responsible for rapid cooling of the carriers

at

lower

excitation

in

cooling

model

rate

appears

may

be attributed

to adequately

account

in part to

for these

observations.

intensity is less

In

conclusion,

we

have

investigated

the

effective at high carrier densities. This depar— tune occurs at a carrier density where the carrier

changes in transmission spectra of photo—excited GaAs using subpioosecond optical techniques to

plasmon energy (iia~r,) is approximately equal to ~ u,~. Raman scattering experimente’9~have demon— strated that at this density, the electron and phonon systems are strongly coupled with resultant screening of the polar optic modes. Screening may

show that in the excitation intensity range n 1016 — 1017 cal3 carriers relax into thermal distributions with I > T in a time < 1 psec and subsequently cool to the lattice temperature as a result of carrier—lattice interaction. At higher

effectively

energy

excitation densities this carrier lattice interac—

carriers and the lattice. calculated an increase in

tion cools the carriers less effectively, and for excitation densities > io18 cm the carriers can

reduce

exchange between the Ehrenreich~10~ has

the

efficiency

mobility as a result of screening

in

of

materials

no longer be described by a thermal distribution.

References [1] Jagdeep Shah, Solid State Electronics ji, U3 (1978). [2] C. V. Shank, H. L. Fork, R. F. Leheny and Rev. Letters .~iZ, 112 (1979).

Jagdeep

Shah,

Phys.

[3] E. 0. Goebel, 0. Hildebrand and K. M. Romanek, to be published in Proc. lUth International Conf. Phys. of Semiconductors, Edinburgh (1978). [U] E. P. Ippen and C. V. Shank in “Topics in Applied Physics” Vol. 18, ed. S. L. Shapiro, 83 (Springer—Verlag, New York, 1977). [5] Jagdeep Shah, R. F. Leheny, and W. 1577 (1977).

Wiegmam,

Phys.

Rev.

~

[6] See, for example, E. H. Conwell Solid—State Physics, Supplement 9 (Edited by F. Seitz, D. Turnbull, and H. Ebrenreich) Academic Press, New York (1967).

DYNANICS OF HOT CARRIER COOLING IN PHOTO—EXCITED GaAs

Vol. 31, No. 11

[7] R. G. Ulbrich, Phys. Rev. (8]

Jagdeep Shah, Phy. Rev.

[9] A. Mooradian and G. (1966).

B.

M

5719 (1973).

~J..Q3697

(197k).

Wright,

Phys.

[10] H. Ebrenreich, .1. Phys. Chem. Solids

~,

Rev.

Letters .i.~. 999

130 (1959).

813