Cyclotron resonance and screening effects in GaAs-GaAlAs heterojunctions

Superlattices and Microstructures, VoL 2, N o 4, 1986

319

CYCLOTRON RESONANCE AND SCREENING EFFECTS IN GaAs-GaAIAs HETEROJUNCTIONS MoAo Hopkins, R.J. Nicholas, M.Ao Brurmmell, J.J. Harris + and C,To Foxon * Clarendon Laboratory, Parks Road, Oxford OXI 3PU, UoK. + Philips Research Laboratories,

Redhill, Surrey,

U.K.

(Received 18~ August 1986) Cyclotron resonance absorption has been studied in several high quality GaAs-GaAIAs heterojunctionso The dependence of the effective mass upon frequency, electron concentration and temperature has been measured and gives a nonparabolicity that is some 20% smaller than that measured in bulk GaAs. This is contrary to simple theory which predicts an enhanced polaron contribution in two-dimensional systems, and we attribute this difference to strong screening of the electron-phonon interaction. The presence of a small magnetic field component parallel to the interface introduces a coupling at energies corresponding to the electric subband separations. These couplings have been studied as a function of electron concentration and the results interpreted in terms of changes in the depletion charge in the GaAs layer~

Cyclotron resonance has proved to be a valuable technique for studying the electronic properties of two-dimensional systems, and the advent of extremely high quality GaAs-GaAIAs heterojunctions has allowed the band structure close to the band edge to be investigated in detail. Such measurements on bulk GaAs I-3 have been used to study the deviations from a parabolic conduction band due to interband coupling (nonparabolicity) and electron-optic phonon interactions (polaron coupling). This paper describes cyclotron resonance experiments on several high quality GaAs-GaAIAs heterojunctionso The dependence of the cyclotron mass upon transition energy, electron concentration and temperature have been measured, and we conclude that the total nonparabolicity in this system is reduced relative to bulk GaAs. This is attributed to changes in the polaron coupling caused by screening. The introduction of a component of magnetic field parallel to the heterojunction interface through slight tilting of the sample leads to a coupling between the electric subbands and the Landau levels. This allows the subband separations to be determined as a function of electron concentration, and interpreted in terms of the depletion charge in the GaAs. The samples studied were grown by MBE at Philips Research Laboratories Redhill ~. Nominally undoped GaAs, in fact slightly p-type, was grown on semi-insulating GaAs substrates, followed by spacer layers of undope~ Ga0.7AI0.3As with thicknesses between 0 and 800 A, and then a layer of n-Ga0.7Al0.3As. Cyclotron resonances were observed in the transmission of radiation from an optically pumped far infra-red laser, and the low-temperature linewidths were of order

0749-6036/86/040319+04 S02 00/0

0.02T. The effective mass was measured as a function of radiation energy over the range 4.9 - 29.4 meV and of electron concentration b e t w e e n 0 . 9 and 9ol x 101Icm- 2 . The c a r r i e r c o n c e n t r a t i o n s w e re d e t e r m i n e d from s i m u l t a n e o u s m e a s u r e m e n t s of t h e S h u b n i k o v - d e Haas o s c i l l a tions in the static conductivity. For a g i v e n s a m p l e , t h e e l e c t r o n c o n c e n t r a t i o n c o u l d be v a r i e d by a f a c t o r of a p p r o x i m a t e l y two u s i n g the p e r s i s t e n t p h o t o c o n d u e t i v i t y i n d u c e d by i l l u m i n a t i o n from a r e d LED, The s a m p l e s u b s t r a t e s w e re wedged t o a v o i d i n t e r f e r e n c e effects. At energies well below the LO phonon energy (37 meV), where resonant polaron coupling occurs, both nonparabolicity and polaron effects cause m* to increase approximately linearly with energy. Since both effects are weak, they may be considered separately and added together without introducing significant errors 5. The band nonparabolicity is treated using an expression derived from the three-band k.p theory of Palik et a16; 1 l 2K2 m---,-= m---~(l + --~--- ((L + I)5~c + z)) o g

(1)

where m Q is the band edge mass, E~ is the band gap, L is the quantum number of t~e initial Landau level and z is the kinetic energy due to motion perpendicular to the layers. This introduces the coefficient K 2 as a convenient measure of the low energy nonparabolicity. The original three-band theory 6 gave K 2 = -0.83 for GaAs, but recent studies considering five bands 7,8 suggest somewhat larger values between -1~I and -I~5o The kinetic energy z is a

© 1986 Academic Press Inc (London) Limited

320

Superlattices and Microstructures, Vol. 2, No. 4, 1986

function of the electron concentration, but is independent of perpendicular magnetic field. For the lowest subband, z may be estimated from the variational wavefunction proposed by Fang and Howard 9 for silicon inversion layers ~o(Z) = (b3/2) ~ z e -bz/2

z

= h2b2/8m *

I

I

mR.

+

0.072 0"071

(3)

and nde p and nin v are the depletion and inversion charge densities respectively. The kinetic energy is then given by

l

(2)

where *2 b = (I2m e (nde p + (l]/32)ninv)/eEoh2)I/3

I

0070 ."

(4)

The expression (I) can be simplified in the low and high field limits. At fields above the fundamental field B F of the Shubnikov-de Haas oscillations, all the electrons lie in the lowest Landau level and hence L = 0. The cyclotron mass should therefore increase linearly with field. At low fields the average energy of the cyclotron transitions is close to the Fermi energy, and so the term (L + 1)~m c can be replaced by EF, giving a cyclotron mass independent of field. Polaron effects result from the interaction of electrons with the polar±sat±on field of the LO phonons, and are characterised by the Fr~hlich coupling constant ~, equal to 0.07 in GaAs. Away from the resonant region (mc/mLO < 0.5) the increase in m* with energy is almost linear, and hence it is very difficult to separate the effects of polaron coupling and band nonparabolicity. Polaron effects may be included in equation (I) by replacing K 2 with K2(tot) = K2(hnp) + K 2tpo , i,)" Various methods . . have been used ho solve t~e FrDhllch Hamlltonlan in both two and three dimensions I0-13, but all predict similar enhancements of the mass in the non-resonant region, with the coupling being stronger in the two-dimensional case by a factor of approximately three~ The work of Peeters and Devreese 12 gives the largest values, due to the inclusion of interactions with all higher levels, and the results may he approximated to K .~ I.D.O.l.) -0.4 and -1.0 for the three- and two-dimen~ional cases respectively in the region 0 < mc ~L0 < 0°5 Although polaron effects are stronger in ideal two-dimensional systems, the coupling will be reduced by the finite extent of the electron wavefunctions in the third dimension2, II,14 and may be further quenched by screening 2,14'15. Measurements on GaAs-GaAIAs heterojunctions 2,16' 17 have suggested that polaron effects are weaker than in bulk GaAs, but enhanced coupling has been observed in other two-dimensional systemsl8, 19 The frequency dependence of the c[clotron mass in sample G29, with n = 1.4 x 101~cm -2, is shown in Figure I. In the high field limit (hm c > EF, or mc > 40 cm-l), the expected linear increase in m* with energy is observed, and a fit to these results gives K2(tot) = 1.4 ± 0.I.

0'06~-

"

•

""

""

+.~

;

+

+ n = 1.4xI01~m~ • n=34xl@lcm-2-

0.06~ . . ~ /

0

I

50

I

I

100 150 Frequency, cm-1

I

200

Fisure I: The frequency dependence of the cyclotron mass in sample G29 at two different electron concentrations, measured as 1.5 K. The mass is approximately constant until the fundamental field is reached, after which it increases linearly with frequency. At the highest frequencies, a further increase due to resonant polaron effects is apparent. The solid line is a fit to the results with K 2 = -].4~

.

This is ~ 20% smaller than the value of -1.75 ± 0.05 measured in bulk GaAs3o Similar measurements on other samples gave the same result. At frequencies greater than ~ 150 cm -I the mass increases more rapidly with energy due to resonant polaron coupling 2,~7. Figure ] also shows the masses measured after illumination of the sample with a red LED, which increased the electron concentration to 3~4 x 1011cm -2. This increases the fundamental field BF, so that the high field limit is not reached until ~c = 95 cm -I. At lower frequencies the mass is approximately constant as expected~ in contrast to the measurements of Horst et al ~7 which showed an energy dependent mass well below B F. Figure 2 shows the electron concentration dependence of the cyclotron mass measured in the low field limit B < BF, where m* should be frequency independent. Several samples were used, and in each sample a range of electron concentrations was studied through the use of the persistent photoconductivity effect. This causes small deviations from the general trend, since the measurements of the subband separations described below show that the illumination

Superlattices and Microstructures, VoL 2, No. 4, 1986

321

0'074 0'0720

,%°

/

710

0-072

700 0.070 690

0068

006~

//

/ ~

/

I 0.066

I

J

i

020

I

% I

0

+ n= 0.9 x1011cm-2 " n=1"9x1011cm-2

2

1

4 EIecfron

I

6 Concentration

i

I

(811cm -21010)

Fisure 2: The dependence of the cyclotron mass upon electron concentration at 4 K, measured in the low field limit where the mass is frequency independent. Several samples were studied, with the electron concentrations varied using the persistent photoconductivity. The solid line is a fit to the points with m~/m o = 0.0663, K 2 = -|.4.

reduces the depletion charge and hence z. The solid line is a fit to the results using ndep = 3 x I01°cm-2, which gives ~ / m o = 0.0663 _ 0.0002 and K 2 = -Io4 ± 0.]. It thus that K .zt~ot ... in the hetero• appears a junctions Is bout 20% smaller t~an the value measured in bulk GaAs 3, and we believe this to be a consequence of screening of the polaron contribution. Calculations for the zero field case 2,14,15 suggest that screening may reduce the polaron coupling by factors of order two or three. No theoretical studies of screening of the electron-optic phonon interaction in high fields have been reported, but the reduction in the coupling may be expected to be considerably greater because of the extreme degeneracy of the Landau levels in a high quality sample. This is supported by measurements of the temperature dependence of the cyclotron mass in our samples, described in detail elsewhere 20,21. The mass increases with temperature more rapidly than would be expected for a nonparabolicity given by ~2(tot) =.-1.4, and this is attributed to a ecrease in the screening as the temperature is raised and the Landau levels broaden. Observa-

015

,I

(TI

t j I

010

I

/~

f, BF 0

L

I ~ 50

/'/

I J 100 150 Frequency, cm 4

I --200

] 250

F i s u r e 3: The c y c l o t r o n mass and r e s o n a n c e l i n e width at !o5 K in sample G63 after tilting through 5 °, measured at two electron concentrations. The coupling to the subband separation E l - E 0 can be clearly seen, and a second coupling to E 2 - E0 is apparent at the lower electron concentration. The lines are guides to the eye°

tions of increased resonant polaron effects in GaAs-GaAIAs heterojunctions in high electric fields have been explained by a similar argument 22. It is interesting to note that the measured bulk and two-dimensional values of K2(tot) differ by -0.35, which is close te the calculated polaron contribution K2(_ol ) for bulk • P . GaAs. Thls suggests that the polaron contribution in the heterojunctions is very small at low temperatures. The cyclotron masses and resonance linewidths measured in sample G63, with n = 0.9 x ]011cm -2, after tilting the sample through 5 ° are shown in Figure 3o A discontinuity in the mass accompanied by a large increase in the

Superlattices and Microstructures, Vol. 2, No. 4, 1986

322

References

Table 1 The subband separations and depletion charges measured in samples G29 and G63.

I. 2.

Sample

G 63

3. n

EOI

E02

nde p

lO II cm -2

meV

meV

lO l l cm-2

0.9

13.3

2].I

1.9

13.8

0.20

1.4

15

0.42

3.4

17

0.275

0.38

4.

5. 6.

G 29

7. 8.

9. linewidth is seen at mc= II0 cm-I. This is attributed to coupling between the Landau levels and electric subbands when the cyclotron energy is equal to the separation of the two lowest subbands E l - E0, as first observed by Schlesinger et a123. Our measurements indicate that tilt angles of as little as 1° are sufficient to produce large increases in the resonance linewidth. Also shown are results obtained after the electron concentration had been increased to 1.9 x 1011cm -2 by illumination. The increased electron concentration has increased the subband separation slightly, but decreased the strength of the coupling. At the lower electron concentration a second coupling can be seen at ~ = 170 cm-I, and this is thought to arise from coupling involving the E 0 and E2 subbands. A maximum in the linewidth at the frequency corresponding to BF can also be seen for the lower electron concentration. This is consistent with the oscillatory linewidth observed by Englertet al. 24 and attributed to filling factor dependent screening24, 25 Numerical studies of the subband structure in GaAs-GaAIAs heterojunetions26, 27 indicate that the subband separations are primarily determined by the depletion charge in the GaAs layer at low electron concentrations~ Table I shows the subband separations measured in samples G29 and G63, together with the depletion charge densities deduced from the calculations of Stern and Das Sarma 27. It can be seen that the illumination reduces the depletion charge significantly° These results support the suggestions of other workers28, 29 that the creation of electron-hole pairs in the GaAs followed by trapping of the holes at acceptors contributes to the persistent photoconductivity. The data of Table ] implies that 10-15% of the additional carriers may be produced by this mechanism.

10. 11. 12. 13. 14. 15. 16.

17.

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