Hysteretic microwave cyclotron resonance of a laterally confined 2 DEG

Physica E 6 (2000) 182–186

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Hysteretic microwave cyclotron resonance of a laterally con ned 2 DEG B.M. Ashkinadze ∗ , V.I. Yudson 1 Solid State Institute, Technion- Israel Institute of Technology, Haifa 32000, Israel

Abstract A hysteretic cyclotron resonance (CR) is discovered in a laterally con ned high mobility two-dimensional electron gas (2DEG) in GaAs=AlGaAs heterostructures. The hysteresis and switching phenomena are observed in microwave radiation (36 GHz) transmission at temperature 1.8–25 K. It is found that the hysteresis is accompanied by long-lived, microwave-induced changes of the 2DEG density. These density changes is attributed to a modi cation of electron vertical transport processes in heterostructures under the microwave heating of the 2DEG. A phenomenological model based on the 2DEG density-dependent CR, describes reasonably the main experimental ndings. ? 2000 Elsevier Science B.V. All rights reserved. PACS: 73.20.Dx; 73.50.Fq; 73.50.Mx Keywords: Cyclotron resonance; Two-dimensional electron gas; Heterostructures

1. Introduction

radiation is described by

A cyclotron resonance (CR) is extensively used in study of high mobility 2D-electrons in modulation-doped GaAs–AlGaAs heterostructures [1–3]. For a laterally con ned 2DEG the CR is modi ed by a depolarization eect. This leads to the CR resonance frequency shift [4], and the resonance is considered as a dimensional magnetoplasma resonance (DMPR). The DMPR line shape for a linearly polarized mw

Pmwa (B) = C0 Pin

∗

Corresponding author. Fax: +972-4-823 51-07. E-mail address: [email protected] (B.M. Ashkinadze) 1 Permanent address: Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow r-n, 142092 Russia.

1 + (!L2 + !R2 )2m : 1 + (!L2 − !R2 )2m )2 + 4!R2 2m

(1)

Here Pmwa and Pin are absorbed and input mw powers, respectively, C is a factor which takes into account the waveguide and sample geometry, 0 is a DC conductivity, m is an electron momentum relaxation time, !R = ! − !p2 (n2D )=!; !p (n2D ) = [32 e2 n2D =(2am∗ )]1=2 is the plasmon frequency for the 2DEG con ned within the mesa of the diameter a (a is smaller than the mw wavelength),  is an averaged value for the dielectric constant of free space and GaAs [5]. At a given mw frequency ! = 2f, the DMPR occurs at the magnetic eld

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BR = BCR − 32 ecn2D =2!a which depends on a 2DEG density n2D , on a and diers from BCR taken from the standard CR condition: ! = !LCR = eBCR =(m∗ c). The CR experiments are usually performed at low temperatures and under low intensity far-infrared (FIR) or microwave (mw) irradiation that does not aect the 2DEG parameters. Increasing FIR=mw radiation intensity leads to electron heating that becomes more ecient at CR (DMPR). This gives rise to a resonant mw=FIR modulation of the photoluminescence (PL) (optically detected resonances — ODR) [6 –9], as well as to the resonant mw=FIR photoconductivity (PC) and photovoltage [11–14]. These eects, in particular the resonant electron heating of the laterally con ned 2DEG, are used to study the spectra of dynamic excitations of the 2DEG [12–14]. However, physical processes accompanying the electron heating as well as physical mechanisms underlying the PL and PC modulations under intense FIR=mw irradiation, are not well understood. We report the electron density decrease under the 2DEG heating by mw radiation, and as a result of this, an appearance of a hysteretic cyclotron resonance (CR) for the laterally con ned 2DEG. 2. Experiment A mw radiation (f = 36 GHz) transmission in a wide range of mw powers, Pin = 10−3 –5 mW, have been studied on high-quality modulation-doped GaAs=Al0:3 Ga0:7 As heterostructures (quantum wells and heterojunctions (HJ) grown by molecular beam epitaxy). The sample was inserted in 8-mm waveguide which was short-circuited at one end, and it was immersed in liquid He or in cold He gas so that the temperature can be varied in the range of T = 1:8 − 25 K. An external magnetic eld B is applied perpendicularly to the heterointerface, and it is slowly scanned back and forth in the range of 0 – 0.2 T. The experimental setup is shown in Fig. 1a. Here we discuss the results obtained on the HJ characterized by the dark 2DEG density n02D = 1:6 × 1011 cm−2 and a DC-measured mobility  of 2 106 cm2 =Vs. Electrons were supplied by a Si-doped layer separated from the interface by a 30 nm Al0:3 Ga0:7 As spacer. The lateral dimension of the

Fig. 1. a. Experimental setup for measuring the mw transmission. b. The mw transmission versus B measured at low mw power (see text).

sample was reduced by fabricating mesa with the diameter a = 0:7 mm. The small sample size ensures the linearity of the mw absorption at low mw power. Fig. 1b presents the mw transmission (MWT) traces at lowest Pin . The traces are obtained under various experimental conditions aected the 2DEG at 2 K: (a) after cooling the sample in the dark, (b) under

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Fig. 2. MWT versus B as a function of Pin values, shown near the traces. The traces are shifted vertically for clarity. Continuos mw radiation: (a) TL = 2 K; (b) TL = 8 K. (c) Pulse-modulated mw radiation TL = 8 K, Pin = 100 W. Duty-cycle ratios, tp =Tp (10−3 s) are given near the curves. Four upper traces are obtained in dark, four bottom ones are measured under weak (10−7 W) He–Ne laser illumination. Arrows indicate the scanning direction of the magnetic eld.

He–Ne light illumination and (c) after the illumination is turned o. Each MWT trace exhibits the DMPR resonance at BR values that are lower than the resonant value BCR = 0:086 T expected for a free electron CR in GaAs at f = 36 GHz [15]. The DMPR shifts and the DMPR line width changes when the 2DEG density and the 2DEG mobility is modi ed either due to optical depletion under light illumination [10] or due to persistent photoconductivity. The MWT is strongly aected by increased Pin at 2 as well as 8 K (see Fig. 2a, b). One can see that the resonance line shifts to higher BR values as Pin increases. Above a certain threshold magnitude of Pin , a hysteresis occurs: there appears a dierence between the MWT traces obtained at increasing and at decreasing magnetic eld. At still higher Pin a sudden MWT switching is observed. Surprisingly, the CR hysteresis persists also under modulated mw irradiation (Fig. 2c). The microwave power is modulated by pulses. A pulse duration tp and a time-interval Tp between pulses are varied. We nd that the hysteresis loop depends only slightly on Tp as far as Tp ¡ 10−3 s and tp ¿ 10−5 s. Since the hysteresis exists even at small duty cycle ratios, tp =Tp , it means that the intense mw irradiation induces a long-lived

modi cation in the 2DEG state. This modi cation lasts after the mw pulse, and the 2DEG reaches its new steady-state after a certain number of mw pulses. The 2DEG changes recover with a characteristic time of 10−2 s at 1.8 K.

3. Discussion An intense mw eld heats up the 2DEG. Due to fast electron–electron scattering, this results in an increased 2DEG temperature Te . The electron heating experiments carried out in DC, FIR and mw electric eld [16,17], allow to estimate Te for a given mw power absorbed per electron. Measuring the total mw power absorbed by the mesa, we deduce that Te does not exceed 30 K in our experiments. In this regime the electron energy losses occur via an emission of low-energy acoustic phonons with the energies of skf (s is the sound velocity, kf is the 2DEG Fermi wave vector). At low temperature these phonons are ballistically propagated over whole sample [18]. To interpret the nonlinear and hysteretic CR we assume that an intense mw irradiation induces a long-lived reduction of the DEG density. This is

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consistent with the observation of the DMPR shift to higher BR with increasing Pin (see Fig. 2) as well as with the observed the long-lived (of 10−2 s) modi cation of the 2DEG parameters. The only proper 2DEG parameter that can be characterized by such long relaxation times, is the 2DEG density determined by slow vertical electron transport (tunneling) processes. It should be noted that the long memory eect excludes any explanation based on the sample heating, since the transfer time of the ballistically propagated phonons into liquid He does not exceed 10−6 s. Therefore, the mw-induced 2DEG density decrease should be associated with the increase of the electron temperature and, perhaps, with a ux of the nonequilibrium acoustic phonons. We assume that the 2DEG heating modi es the rates of electron transport into and out of the 2DEG so that the 2DEG density reduces. At present we do not specify the mechanisms of mw-induced vertical electron transport and the role of the phonon wind. As a simple phenomenological model, we suppose that the rate of electron escape from the 2DEG increases linearly with the mw power absorbed per electron, Pmwa (B)=n2D , while the electron return rate −1 is unaected by mw radiation. Then, from the steady-state solution of the balance equation, we get n2D = n02D (1 − Pmwa =n02D ), where is a coecient of mw-induced nonlinearity. Thus, the resonant frequency !R in Eq. (1) depends on Pmwa , and Eq. (1) becomes a nonlinear equation which determines the nonlinear CR absorption in the steady-state regime. A numerical solution of Eq. (1) demonstrates the hysteretic phenomena (Fig. 3). For a circularly (electron CR-active) polarized mw eld, the conditions for the hysteresis were analytically found [19]. Comparison of the experimental results (Fig. 2) with the calculated curves shows that our model explains the main features of the nonlinear hysteretic CR found in the laterally con ned 2DEG systems The time-resolved mw experiments allow to measure the phenomenologically introduced time () of the electron transport from adjacent layers (spacer) into 2DEG. We have found that  varies from sample to sample and depends on the ambient temperature and light illumination. At illumination,  decreases, the hysteresis becomes sharper. At high illumination (when there is strong optical depletion), the hysteresis disappears.

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Fig. 3. Calculated mw absorption versus B for the nonlinear coef cient = 0:05;  = 1:4 × 106 cm2 =Vs; dimensionless input mw power are 5, 15, 50. The 2DEG density versus B is presented for input mw power of 15 and 50. The DMPR position BR is marked by an arrow.

The revealed 2DEG density decrease caused by the electron heating, is likely to be responsible for the optically or photoelectrically detected resonances observed in the heterostructures with the 2DEG [7–14]. The long relaxation time of the CR-induced photoconductivity [11], the resonant photo-electrical response due to the chemical potential shift of the bulk 2DEG states (or of the edge states) under CR heating [13], the strong saturation of the FIR intersubband absorption under high intense FIR [14], can be explained by fast transfer of the excited electrons to the spacer layer. It should be noted that vertical electron transport can be caused by the phonon wind resulting from the hot 2DEG [17]. This was revealed on high-quality heterojunctions by studying the modulation of the bulk free exciton PL by the spatially separated 2DEG heated at DMPR [17,20]. In conclusion, a novel hot-electron nonlinear phenomenon — the hysteretic cyclotron resonance under intense microwave irradiation — is observed for the 2DEG in laterally con ned GaAs=AlGaAs heterostructures. We assign the nonlinearity to 2DEG density changes caused by a modi cation of electron vertical transport processes under intense mw irradiation. A simple phenomenological model based on the 2DEG density-dependent CR, describes reasonably the experimental ndings. Further research is required for understanding the microscopic mechanisms of the revealed fast vertical electron transport.

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Acknowledgements We are grateful to L. Pfeier and V. Umansky for the sample growth and to E. Buchstab for the sample processing. We thank E. Cohen and Arza Ron for useful discussions. The research at Technion was done in the Barbara and Norman Seiden Center for Advanced Opto-electronics and was supported by US–Israel BSF grant. V.Y. acknowledges the hospitality at the Technion. References [1] G. Abstreiter, J. Kotthaus, J.F. Koch, G. Dorda, Phys. Rev. B 14 (1976) 2480. [2] M.J. Chou, D.C. Tsui, G. Weimann, Phys. Rev. B 37 (1988) 848. [3] J.P. Cheng, B.D. McCombe, Phys. Rev. B 44 (1991) 3070. [4] S.J. Allen, H.L. Stormer, J.C.M. Hwang, Phys. Rev. B 28 (1983) 4875.

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