GaAlAs heterostructures

Physica 134B (1985) 323-326 North-Holland,Amsterdam

323

HOT ELECTRONLANDAULEVEL LIFETIME IN GaAs/GaAIAs HETEROSTRUCTURES M. HELMand E. GDRNIK I n s t i t u t fur Experimentalphysik, Universit~t Innsbruck, A-6020 Innsbruck, Austria A. BLACK, G.R. ALLAN, C.R. PIDGEONand K. MITCHELL Physics Department, Heriot-Watt University, Edinburgh, U.K. G. WEIMANN Forschungsinstitut der Deutschen Bundespost beim Fernmeldetechnischen Zentralamt, D-6100 Darmstadt, Germany We report the f i r s t measurement of inter-Landau level lifetimes in GaAs/GaAIAs-heterostructures. Saturation cyclotron resonance has been measured using a high intensity o p t i c a l l y pumped far infrared laser. The results are analyzed on the basis of a three level model. The obtained l i f e times vary from 0.18 to 1.2 ns for samples with different carrier concentration. I. INTRODUCTION In the recent past high

heterostructures. This technique is a direct power f a r infrared

spectroscopy has been used to determine the l i f e -

method for probing the inter-LL lifetime. The absorption process is described on the basis of

times of impurity and Landau states in semi-

a three level model. By comparison with the ex-

conductors I-3. Up to now these investigations

perimental data the lifetime is deduced and

have been r e s t r i c t e d to bulk m a t e r i a l . Another

found to vary from 0.18 ns to 1.2 ns for samples

method to determine energy r e l a x a t i o n times was

with different carrier concentrations indicating

employed by Bauer and Kahlert 4 f o r degenerate

the influence of an electron-electron scattering

bulk material and recently by Sakaki et al 5 f o r

process also in the 2D situation. A direct com-

GaAs/GaAIAs-heterostructures: The energy relaxa-

parison with theoretical calculations is d i f f i -

t i o n time in a magnetic f i e l d was deduced from

c u l t , since most of the calculations concerning

the strength of the Shubnikov-de Haas (SdH) os-

energy relaxation in 2D-systems do not include a magnetic f i e l d 6-8.

c i l l a t i o n s as a function of the e l e c t r i c f i e l d . I t was found by Gornik et a l . I and Allan et a l . 3 that in bulk material e l e c t r o n - e l e c t r o n scattering plays a dominant role fo r the i n t e r -

2. EXPERIMENTAL The samples were grown by molecular beam

Landau level (LL) l i f e t i m e . A connection between

epitaxy, t h e i r mobilities vary between 105 and

electron density in the excited level and l i f e -

106 cm2/Vs, t h e i r carrier concentrations between

time was established. The aim of the present paper is to find out

1.2 and 3.1011 cm-2. A high power quasi cw optically pumped FIR laser was used in the pulsed

whether a s i m i l a r mechanism controls the relaxa-

mode. The pulse duration (0.3 ms) was adjusted

t i o n in 2D-layers as present in heterolayers,

to be much longer than the'expected relaxation

We have performed cyclotron resonance (CR) ab-

time, ensuring steady-state conditions during

sorption saturation measurements on GaAs/GaAIAs-

optical excitation. In the present work only the

0378-4363/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

M. Heinz et al. / Hot electron Landau level lifetime in GaAs/GaA1As heterostmctures

324

118.8 Nm methanol l i n e was used, because i t yielded the highest i n t e n s i t i e s . Moreover, at

df o I Po . . . . A + fi(I dt hw o

Po - fo ) - -

(I)

the corresponding energy of 10.43 meV the nonp a r a b o l i c i t y and polaron

e f f e c t are large

enough to enable saturation. The FIR i n t e n s i t y

df I PO

dt

I =

~

~ PO (Ao- AI) + [ f 2 ( I - f 1 ) - f 1 ( 1 - ~ ) ] - -

(2)

in the sample was determined by a calibrated p y r o e l e c t r i c detector taking into account the losses of the l i g h t pipe and the r e f l e c t i o n at

df 2 I 0o P o - - = - - A I - f 2 (I - f l ) - dt h~

(3)

the substrate surface. Due to the l i g h t pipe optics the sample was subjected to unpolarized

with I the e f f e c t i v e laser i n t e n s i t y in the

r a d i a t i o n . Therefore the e f f e c t i v e i n t e n s i t y in

sample, Po = e B / ~ the electron concentration

the sample was one h a l f of the t o t a l i n t e n s i t y

per LL, and z the r e l a x a t i o n time. T is chosen

in the sample as the geometry was rather a Fara-

to be the same for both the n = I and the n = 2

day geometry. An n-type InSb photoconductive

LL since the experimental information is not

detector was used, situated below the sample in

enough to d i s t i n g u i s h a separate TI and T2"

the l i q u i d He-bath. The electron concentration

An is the a b s o r p t i v i t y of a 2D electron gas

was determined from SdH-measurements.

given by

3. THEORETICALMODEL

4 ~ Re ~(n)/EoC A _~ n ( ~ + i + Re a(n)/coC)2

Saturation of cyclotron resonance t r a n s i t i o n s is not possible in a e q u i d i s t a n t Landau ladder. However, i f a s u f f i c i e n t amount of nonparabolic i t y and polaron c o n t r i b u t i o n to the e f f e c t i v e

with

(Im o ~ Re assumed) (4)

Rea(n)/co c = r

)2

C'hmc(fn- fn+1) (n + I )

mass is present, the level s h i f t s can be larger

'~En+1- en + hm

+

F2

than the l i n e w i d t h of the i n d i v i d u a l t r a n s i t i o n s . In t h i s case saturation can be achieved. Recent

the real part of the dynamical c o n d u c t i v i t y .

experiments 9 have shown that the influence of

C is a dimensionless constant determined from

the L0-phonon (h~,~ 36 meV) on the energy levels

the value of the l o w - i n t e n s i t y absorption. The

in GaAs/GaAIAs-heterostructures is n e g l i g i b l e

in the numerator of Eq. (4) is due to the

below 25 meV, but becomes strong above t h i s

experimental set-up since the laser beam passes

value. In the present s i t u a t i o n the photon ener-

the GaAs substrate p r i o r to the 2D system. The

gy is h~ = 10.43 meV, which means that the LL

usual expansion of An f o r Reo(n)/EoC ~ I

is

n = O, I and 2 undergo small polaron s h i f t s ,

not employed, because the changes in trans-

whereas the n = 3 LL is shifted considerably.

mission reach 65% in the CR-active p o l a r i z a -

Thus for a not too broad absorption line the

t i o n . In steady state, Eq. ( I ) - (3) are solved

analysis has to include up to three levels. I f

numerically together with the condition

the absorption linewidth is smaller than the

fo + f l + f2 = ~

nonparaboli c i t y (? < (hmc)2/mg), only two levels need to be considered. The rate equations can, therefore, be written as:

(5)

where ~ is the number of (spin degenerate) filled

LL, ~ =~nsh/eB. For a comparison with

the experiment the normalized transmission change I - T / T ( o = O )

is calculated, with

325

M. Helm et al. / Hot electron Landau level lifetime in GaAs/GaAIAs heterostructures

4vT

with the best f i t from Eq. ( I ) - ( 5 )

T _~ ( / E + I + Reo(°)/Co c + Reo(1)/~oC)Z

(6)

for sample

1360.

4. RESULTSAND DISCUSSION Typical experimental traces are shown in Fig. I for sample 1433 (n^ = 1.2.1011cm -2) and sample 1360 (n s = 3 . 1011~m-2).

0.6

,

0.4

0.2

i 10

i 1OO

= 1OOO

i

INTENSITY (mW/cm 2)

3.3

7!

FIGURE 2 Intensity dependence of the relative transmission change for a laser l i n e of 118.8 pm for sample 1360. The solid line represents the

best f i t from Eq. ( I ) - (5). An onset of saturation is observed with a reZERO

ZE.O' g~

61

MAGNETIC

FIELD (kG)

MAGNETIC

& FIELD (kG)

FIGURE I Cyclotron resonance absorption for two different

GaAs/GaAIAs-heterostructures at 118.8 pm for several laser intensities. (a) sample 1433 (b) sample 1360 The transmission zero corresponds to CR-active polarization. Two features can be clearly seen: In both samples saturation has been achieved, but more easily in the low concentration sample. Furthermore, a s h i f t of several hundred Gauss is observed only in Fig. Ib, indicating a transfer of electrons

duction of I - T / T o up to 30 %. A further increase in intensity was limited by the experimental system. Table I gives the resulting lifetimes for a l l samples investigated: TABLE I sample

ns(1011cm-2)

z(ns)

1360 1355 1234 1395 1433

3.0 3.0 2.0 1.5 1.2

0.18 0.25 0.65 0.55 1.20

to the n = 2 LL, which also makes the saturation more d i f f i c u l t . This clearly shows the requirement of including this level into the analysis as described before. In Fig. la the linewidth is so small that there is no overlap between the two transitions and accordingly no s h i f t . In Fig. 2 the intensity dependence of the relative transmission change is plotted together

The lifetimes were all obtained under conditions, where the n = 0 LL is just f i l l e d or p a r t i a l l y filled. Within the experimental error the lifetime increases with decreasing carrier concentration. In an e a r l i e r paper Sakaki et al.5 reported somewhat larger T-values, but the same depen-

326

M. Helm et a L / H o t electron Landau level hlf~'time itl GaA s/GaA 1As hcterostructure,s

dence on c a r r i e r concentration. This was ex-

times in GaAs/GaAIAs-heterostructures. We have

plained by a concentration dependent acoustic

found clear evidence for an electron concentra-

phonon rate. His experiment, however, was per-

t i o n dependent l i f e t i m e ranging from 0.18 ns to

formed in the weak heating regime (T < 30 K) and

1.2 ns. This suggests that electron-electron

with small magnetic f i e l d s (B < 3T).

scattering is playing a dominant role in the

In the

present work a considerable part of electrons

energy loss mechanism. A detailed description

is excited to higher LL, corresponding to i n t e r -

of the process needs more experimental and

subband temperatures well above 100K.

t h e o r e t i c a l work.

In addi-

t i o n , for a LL separation of 10 meV the acoustic phonon emission is most l i k e l y not the dominant r e l a x a t i o n process. The influence of an elec-

ACKNOWLEDGEMENTS This work was p a r t l y supported by the Jubi-

t r o n - e l e c t r o n scattering process s i m i l a r to that

]~umsfonds der ~sterreichischen Nationalbank,

found in bulk material 1'3 seems to be evident

the European Research Office of the US-Army,

for the observed density dependence. To examine

London, and by the Science and Engineering Re-

t h i s process in d e t a i l the excited level c a r r i e r

search Council (SERC) of the United Kingdom.

concentration has to be determined. Up to now

The collaboration between the Heriot Watt Uni-

there are not enough data available reaching out

v e r s i t y , Edinburgh, and the U n i v e r s i t y of Inns-

in the strong saturation regime to make a mean-

bruck was made possible by the B r i t i s h Council.

ingful evaluation about the density dependence. We found that the obtained l i f e t i m e s depend strongly on the analysis of the data. The f a c t o r

(1-fi)

in Eq. ( I ) -

(3) gives rise to a much

slower decrease in the saturation curve (Fig. 2) and to an e a r l i e r threshold for s a t u r a t i o n , esp e c i a l l y in the case of a f i l l e d

LL. Neglecting

t h i s factor would r e s u l t in a longer l i f e t i m e up to a factor of f i v e . From t h i s we conclude that a r e l i a b l e evaluation needs more data and data to higher power l e v e l s , where t h i s f a c t o r plays a less important role. A large uncertainty is found in the evaluation for the low density samples 1395 and 1433 caused by experimental problems: The magnitude of the

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low-power absorption was not well reproducible

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according to the unstable experimental condi-

8. E. Vass, t h i s volume.

t i o n s . This seems to come from the f l a t inversion channel in these samples. Similar effects have been observed with DC f i e l d s I0. I t was, therefore, d i f f i c u l t

to determine the constant

C in Eq. (4) accurately. In summary, we have used FIR saturation spectroscopy to determine inter-Landau level l i f e -

9. M. Horst, U. Merkt, W. Zawadzki, J.C. Maan, and K. Ploog, Solid State Commun. 53 (1985) 403. 10. W. Seidenbusch, private communication.