GaAs heterojunction

394

Surface

Science 142 (1984) 394-399 North-Holland, Amsterdam

CYCLOTRON RESONANCE OF TWO-DIMENSIONAL AI,Ga,_,As/GaAs HETEROJUNCTION K. MURO, Depar~~nt MO, Jupan

S. MORI

ELECTRONS

IN

and S. NARITA

of Marrrial Physrcs. Facul~_vof Eng~neenng Scmm,

O.wku Unic1er.q.

T~gvrtuku. Osuko

and S. HIYAMIZU

and K. NANBU

Fujtsu

Ltd., One. Atsugr, Kumga:awu 24_1-Oll Japan

Received

Labomtorres

9 July 1983; accepted

for publication

8 September

1983

Peculiar behaviour of two-dimensional electron gas in the cyclotron resonance has been studied using a high mobility FET of AI,Ga, ,As/GaAs heteroJunction. The results are fairly well explained by the calculated results based on the theoretical model assuming the long-range scatterer scheme by Ando. However, we find remaining discrepancies between the experimental and the calculated results which have the possibility to be ascribed to some electron-electron correlation effects in the system.

1. Introduction Cyclotron resonance (CR) experiments [l] so far performed on Si-MOS inversion layers have revealed some specific properties of a two-dimensional (2D) electron system, especially in the quantum limit. These results have been discussed in a variety of theoretical models: the trapped electron model, the pinned charge density wave model and so on. However, the correspondence between the experimental and the theoretical results has not been made quite clear. On the other hand, we have extended the CR study to a new 2D system, the AI,Ga,_ ~As/GaAs heterojunction FET [2,3]. Though the characteristics of CR in the quantum limit resemble those in Si-MOS inversion layers in such aspects as the high energy shift of resonance peaks, and their temperature-dependence [3], there are some differences between the two systems. In the present work, detailed CR spectra of the 2D heterojunction electrons are measured over wide ranges of electron density, magnetic field and temperature, and the results are discussed in comparison with the calculation, according to the model presented by Ando [4]. 0039-6028/84/$03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

K. Mum et al. / Cyclotron resonance of 20 electrons

AhGal-xAs/

Gab

FET

MAGNETIC Fig. 1. CR spectra

observed

395

FIELD (Tesla)

at 118.8 and 170.6 pm.

The samples and the experimental setup used were almost the same as those described in previous reports [2,3]. However, in the first study [2] the too-highfrequency gate voltage modulation (- 1 kHz) brought some erroneous results, and in the second study [3] under static gate voltages, unfavourable baseline shift and additional structure appeared in the spectra. Therefore, in the present experiment, the gate voltage modulation technique with slow repetition rate (- 130 Hz) was adopted and the transmission signals after a sufficient delay time (3-4 ms) were picked up, in order to obtain good fidelity and improved S/N ratio.

2. Results and discussion Typical CR spectra for 118.8 and 170.6 pm laser lines observed at 4.2 K are shown in fig. 1 for various electron densities, n,, or filling factors, v (= n,/ 2~1’) where I= (CA/&)‘/’ (the cyclotron radius). The peak frequency shifts, w, - w,,, from the bulk CR frequency, w,, (which corresponds to the bulk mass, mb = O.O675m,, obtained experimentally at 118.8 pm with a high purity n-type GaAs sample), and the linewidths are shown against the filling factor, Y, in fig. 2. On the other hand, the Landau level width, r,, and CR width, r:, calculated theoretically by Ando and Uemura [5], and Prasad and Fujita [6], assuming a scattering potential with a gaussian form, V(r)

= V/n-d* exp( -r*/d’),

00

L. , . 1

1

2 Filling

Fig. 2. CR frequency

3

Factor

4

IJ

shift and linewidth

versus Y.

are shown in fig. 3 as a function of parameter (Y. Here, LY(= d/l) is the normalized range of scattering potential by the cyclotron radius 1. The theory about the CR lineshape presented by Ando [4] shows that CR under the long-range scattering potential (a 2 1) can be described as an inhomogeneously broadened system, and gives the CR linewidths with a similar cw-dependence to those by Prasad and Fujita, though the former does!not show the

Landau Level Width ;lk .,...k?... n=, ,, ...’ . ..‘. i.&:, ..” ..’ ,....’ .,,_ ..‘I ,... ,.. ‘tiz3 ,.” . ..”

OO

1

4 o(:d,l

Fig. 3. Theoretical

Landau

&, level width r, [4] and CR linewidth

rz [6] as a function

of 01.

K. Mum et al. / Cyclotron resonnnce

of 20 electrons

397

explicit form. In a long-range scatterer schemes ((Y 2 l), the CR linewidth I-T depends on the Landau quantum number, n, that is, on the filling factor v, and decreases with increasing magnetic field. By comparing the resonance field- and filling-factor-dependences of the CR linewidth (shown in fig. 2) with the theoretical ones, we derived the range of scattering potential to be 150-200 A. These long-range scattering potentials can be reasonably ascribed to the ionized donors in the Si-doped AlGaAs layer beyond the undoped AlGaAs interlayer with a thickness of 60 A, if we take into account the wavefunction thickness of the 2D electron, - 100 A, and the average distance of donors in the doped AlGaAs layer, - 108 A. The CR lineshape is numerically calculated according to equation (2.12) in ref. [4] for the dynamical conductivity u,,(w). The lineshapes of the partially occupied lowest Landau level calculated for cx= 2 are shown in fig. 4a, assuming that d - 200 A and I = 100 A, which corresponds to the spectra at 118.8 pm in fig. 1. Although the observed spectra are obtained against magnetic field, we can interpret the magnetic field axis as a frequency axis, but reversing the direction, because the CR linewidths is sufficiently narrow in the present experiments. The calculated spectra have a bell-shape due to the elliptic density of states in the self-consistent Born approximation [5], which is in contrast with the nearly Lorenzian lineshape of the observed spectra. However, the waning of the spectra from the high field (low frequency) side and the subsequent peak shift with decreasing filling factor in the experimental are deduced in the theoretical framework by Ando [4]. As seen in figs. 1 and 2, the waning of the CR spectra (peak shift to higher frequency) occurs even in the region v > 1, and this tendency becomes prominent with decreasing magnetic field. This effect is qualitatively understood by taking into account the incomplete spin splitting of the broadened Landau levels. Fig. 4b shows the calculated spectra for v < 2, where the spin splitting,

Complete

-n(uJ-wc,I

b)

a)

To

Fig. 4. CR lineshapes for different T=OK.(a)Ak2r,,,(b)A=r,/2.

Y, calculated

with the theory

by Ando

[4] assuming

a = 2 and

398

K. Mum et al. / Cyclotron i-esonancr of 2D electrons

AhGal-xAs/ GaAs FE 1 *820508-l L, =0.6

MAGNETIC

j

FIELD (Tesla)

Fig. 5. Temperature dependence of (a) CR lineshapes theoretical ones calculated for cr = 2. 3 > 2r,,.

for Y = 0.64 observed

at 118.8 pm and (b)

is equal to one half of the ground Landau level width, I;,. In the present experimental condition (cy = 1.5-2) the ground Landau level width r,, is estimated to be 7-9 cm- ’ and scarcely depends on the magnetic field, and therefore the present CR lineshape profiles with changing the filling factor are consistent with the enhanced effective g-value: - 5 (e.g. A = 14 cm-’ at 6 T) reported as an experimental result [7]. Figs. Sa and 5b show the observed temperature dependence of the CR spectra for 118.8 pm laser-incidence at v = 0.64 and the corresponding theoretical lineshape calculated assuming (Y= 2, respectively. The spreading out of the CR spectra to higher field from the spectra at 4.2 K with increasing temperature is considered to be caused by the thermal distribution with the inhomogeneous broadened Landau level in the above theoretical model. However, the experimental peak shift seems to be much larger than the theoretical expectation. In the above descriptions, we have examined the characteristics of the observed CR spectra, in the light of the theoretical model by Ando [4] under the long range scatterer scheme, and known that some aspects can be understood successfully. However, we find the following remaining discrepancies between the experimental and theoretical results: (1) observed CR lineshapes are rather Lorenzian in contrast with the bell-shape in the theory; (2) a part of the spectra at Y < 1 protrudes out to lower field from the full spectra at Y = 1, being inconsistent with the theory [4] and this tendency becomes prominent in high magnetic fields and at lower temperatures; (3) the temperature shift of the CR spectral peak at v < 1 is much larger than that expected from the thermal distribution in the lowest Landau level. The problem (1) may be improved to employ a more realistic density of states than the elliptic one in the theory, while points (2) and (3) seem to be

A,

K. Muro et al. / Cyclotron

resonance

of 20

electrons

399

difficult to be understood in the framework of the one electron theory, and can possibly be ascribed to some many body effects (the screening [8] or the correlation effects [9,10] in the 2D electron system) or other origins. Englert et al. [ll] have observed the oscillation of CR linewidth as a function of filling factor v and ascribed it to the screening effects [8]. In the present experiment, we have not observed such an oscillation, as seen in fig. 2, and the discrepancies (2) and (3) cannot be explained by introducing the screening effects as described by Das Sarma [8]. Though the observed discrepancies (2) and (3) seem to have the character associated with the pinned charge density wave model [lo], the whole feature of the present results cannot, as described previously [3], be explained by the model. In order to solve the above mentioned problems of the 2D electron system, more detailed CR experiments with high mobility samples in high magnetic fields are strongly requested.

References [l] B.A. Wilson, S.J. Allen, Jr. and D.C. Tsui, Phys. Rev. B24 (1981) 5887. [2] K. Muro, S. Narita, S. Hiyamizu, K. Nanbu and H. Hashimoto, Surface Sci. 113 (1982) 321. [3] S. Narita, K. Muro, S. Mori, S. Hiyamizu and K. Nanbu, in: Proc. Intern. Conf. on Application of High Magnetic Fields in Semiconductor Physics, Grenoble, 1982 [Lecture Notes in Physics 177 (1983) 1941. [4] T. Ando, J. Phys. Sot. Japan 38 (1975) 989. [S] T. Ando and Y. Uemura, J. Phys. Sot. Japan 36 (1974) 959. [6] M. Prasad and S. Fujita, Physica 91A (1978) 1. [7] Th. Englert, D.C. Tsui, A. Gossard and Ch. Uihlein, Surface Sci. 113 (1982) 295. [S] S. Das Sarma, Solid State Commun. 36 (1980) 357. [9] H. Fukuyama, P.M. Platzman and P.W. Anderson, Phys. Rev. B19 (1979) 5211. [lo] H. Fukuyama, and P.A. Lee, Phys. Rev. B18 (1978) 6245. [ll] Th. Englert, J.C. Maan, Ch. Uihelin, D.C. Tsui and A.C. Gossard, Physica 117/118 (1983) 631.