24T. Ando, Phys. Rev. B 13, 3468 (1976).2 5W. B. Chen, J. J. Chen, and E. Burstein, Surf. Sci., 58,

263 (1976).2 6 T. Ando, Solid State Commun. 21, 133 (1977).27R. G. Wheeler and H. S. Goldberg, IEEE Trans. Electron

Devices ED-22, 1001 (1975).28 M. von Ortenberg, K. Schwarzbeck, and G. Landwehr, in

Ref. 14b, p. 305.291(. Schwarzbeck, M. von Ortenberg, G. Landwehr, and R. R.

Galazka, in Ref. 20a, p. 435.30 P. Kacman and W. Zawadzli, Phys. Status Solidi B 47, 629

(1971).3iJ. Q. Ramage, R. A. Stradling, R. J. Tidey, and J. R.

Burke, in Ref. 14a, p. 531.

Submillimeter cyclotron resonance of electrons in accumulation layers onindium antimonide surfaces

Michael von Ortenberg and Ursula SteigenbergerUniversity of Wurzburg, D-8700 Wuirzburg, German Federal Republic

(Received 3 January 1977)

We report the submillimeter-laser-magnetotransmission of pure n-type InSb in a metal-insulator-semiconductor arrangement as a function of the applied gate voltage. From the recorded data we derive astrong dependence of the surface cylotron mass in accumulation layers on InSb on the electric field andhence on the surface density of electrons.

Indium antimonide is a narrow-gap semiconductor withstrongly nonparabolic energy bands. In the presence ofan external magnetic field the cyclotron mass dependsnot only on the magnetic field intensity, but also on thewave vector parallel to the magnetic field orientation. 1This wave vector can be changed considerably by a quan-tizing electric field perpendicular to the sample sur-face. Therefore, we observe a definite electric fielddependence of the cyclotron mass. The explicit varia-tion of the mass with the electric field intensity depends,of course, on the definite shape of the electrostatic sur-face potential. This potential, however, is affected bythe screening mechanism involved and is different forinversion and accumulation layers. After the study of thesurface cyclotron resonance of electrons in InSb inver-sion layers by Darr et al.2 the principal objective of thepresent experiments was to investigate the surfacecyclotron resonance in accumulation layers on n-typeInSb and to discuss the present results in comparisonwith those of the inversion layers.

In our experiments the quantizing electric field wasproduced in a metal-insulator-semiconductor (MIS) ar-rangement using a 6. 3-glm-thick Hostaphan layer as in-sulator. 2-5 The indium antimonide samples with anelectron concentration of some 1013 cm-3 were carefullylapped and subsequently etched in CP4A. To monitorthe dc surface properties during the experiment, thesample was provided with electrical contacts suitablefor the measurements of the field effect and the magneto-resistance. This monitoring of the dc surface propertiesduring the experiment proved to be of great importance,because the surface conditions were changing in timeeven at liquid-He temperatures depending on the sur-face preparation. In Fig. 1 we have plotted the low-temperature field-effect curve of an indium antimonidesample whose surface had been rinsed in pure propanol[CH3CH(OH)CH 3]. During the course of the experimentthe extremum of the field-effect curve, correspondingapproximately to the flat-band condition, was shifted.

This indicates a charge compensation by surface stateseven at He temperatures. Samples which were rinsed inammoniumhydroxyd [NH40H], however, exhibited stablesurface properties without any time-dependent compen-sation. In Fig. 2 we have plotted the field-effect curveof such a stable MIS arrangement for different intensi-ties of the external magnetic field as parameter. Thedifferent curves have a relative offset of 12. 5 kQ on theresistance axis. For positive applied gate voltage elec-trons are accumulated on the surface leading to a pro-nounced decrease in the sample resistance. For nega-tive gate voltage an inversion layer of holes is generated.The relative influence of the surface carriers on thesample conductivity increases with increasing magneticfield intensity because of the strong magnetic freeze-out in the bulk. 6 Whereas for accumulation pronouncedsurface quantum oscillations are visible, there is no in-dication of quantum effects for the surface hole in in-version. It should be noted that the variation of thequantum oscillations versus the magnetic field intensityis rather weak, so that for constant gate voltage onlyvery few magnetoquantum oscillations are recorded.[This experimental result for accumulation is in con-trast to the observation of three very pronounced seriesof magnetic quantum oscillations in inversion as recent-

a,Ua0)D

C

al-cC,

FIG. 1. Field-effect curve of anInSb sample rinsed inCH 3CH(OH)CH 3 before mountingin the MIS arrangement exhibits atime-dependent shift even at liquid-He temperatures.

Gate Voltage UG

Copyright 0 1977 by the Optical Society of America 928928 J. Opt. Soc. Am., Vol. 67, No. 7, July 1977

a

CC-)

Gate Voltage UG [V]

FIG. 2. Field-effect curve of an InSb sample rinsed inammoniumhydroxyd before mounting in the MIS arrangementdoes not depend on time and for the different parameters of ex-ternal magnetic fields exhibits quantum oscillation in accumula-tion for positive values of the gate voltage. In inversion, cor-responding to negative values of the gate voltage, no quantumeffects are observed.

0 1 2 3 4 5 6 7

Magnetic Field B [Teslal

FIG. 3. Spectra of the electric-field-induced change of thetransmission of 119 pam radiation through a MIS arrangementof InSb exhibit the broad surface cyclotron resonance of elec-trons in accumulation and the narrow absorption line of thebulk resonance in the substrate. This influence of the bulkresonance can be directly compared with the volume spectrumin the lower part. The parameters of the curves with arbitraryoffset indicate the gate voltage. For this set of surface spectrathe magnetic field was tilted by an angle b =450 relative to thesurface normal.

C:.

D n-InSb 23/0 12

0)

C)

Ec ja w800 V

a A 600 Vc

Y -1000 V

Qij

0 1 2 3 4 5 6 7Magnetic Field B [Tesla]

FIG. 4. For the corresponding spectra of the surface electroncyclotron resonance using 337 pm radiation, bulk and surfaceresonance overlap considerably. For this experimental datathe tilt angle of the surface normal relative to the external mag-netic field was c1 =30°. There is an arbitrary offset of the diff-erent curves.

ly observed by Ddrr et al. (private communication)even at very low magnetic-field intensities. ]

For the optical investigation we used only sampleswhich exhibited a well-developed field-effect curve. Toseparate the surface cyclotron resonance from the bulkresonances of the substrate, we had not only to apply asquare-wave modulation of the surface field, but alsoto vary the magnetic field orientation relative to the sur-face normal. For strong electric surface fields the ef-fective quantizing magnetic field intensity for the motionparallel to the surface is then reduced by the cosine ofthe tilt angle (. Under this experimental condition thesurface cyclotron resonance is therefore shifted to high-er magnetic field intensities relative to the bulk reso-nance. In Fig. 3 we have plotted in the upper part thesurface-cyclotron-resonance spectra of electrons in ac-cumulation as obtained by recording the electric field-induced change in the tranmission of 118 Am radiation.Actually there is a negative transmission change withpositive applied gate voltage. Because of the specialchoice of the phase of the reference signal we haveelectronically reversed this signal. The parametersindicate the gate voltage as measured relative to thethreshold voltage. For comparison, in the lower part theordinary spectrum of the bulk resonance is reproduced.This resonance has a strong influence on the surfacespectra because of the pronounced absorption of thetransmitted radiation in the substrate. The extrema ofthe surface cyclotron resonances are well defined forUg> 500 V and determine the surface cyclotron mass.In Fig. 4 we have plotted the corresponding data using337 ,um radiation of the HCN laser. For this laser linethe extremum of the surface cyclotron resonance is not

929 J. Opt. Soc. Am., Vol. 67, No. 7, July 1977 M. von Ortenberg and U. Steigenberger 929

LC-)

NS =5x101 2 cm2

6 d =01000cmC0U)

122s = 5x10 13cm '

d =0.1002 cm

Magnetic Field B [TeslaJ

FIG. 5. Simulated spectra of the electric-field-induced trans-mission change of an optical double layer system exhibit stronginterference effects.

so well separated from the bulk resonance. This datahas not been used to evaluate the surface cyclotronmass. For inversion no surface resonance was observedwith either wavelength. In the special choice of slightlycurved samples we were very anxious to suppress inter-ference effects as much as possible. 4' In our experi-mental data, however, near the bulk resonance devia-tions due to optical interference are stilipresent, as canbe seen from the pseudosplitting of the volume resonancein Figs. 3 and 4. How strongly surface-cyclotron-reso-nance spectra of InSb can be obscured by such effects isdemonstrated by a numerical simulation based on an op-

U)

/n-InSb 23/0 12

n 0L/ 4~\Sample =1luA

0 2

Magnetic Field B [Tesla

FMisio 6,changeise of anpia doule layrrangtemexhibith strong

mass.Forinvdersiono showh surface resontroneresonancevedwth e ithel wae lnce In the spe-efctidcial choisace ofhangh ftly

U4ic

in Fis. 3and 4 HowstMagnei ildy [Teslaceccoro]e

FIG.6 sphotoressa of can MIe arscranemen witsuh indctsiumantmonidraedoe not sho thmeria surflaccyltron raes onance but

the ifluece o thefiel-effet-inucedresitanc chneo h

device.

QO*4-

E

0 1x105 2x105 3x105

Electric Surface Field [Vcm-ll

FIG. 7. Cyclotron mass of surface electrons in accumulationcompares rather well with the lowest electron-cyclotron massin inversion. The experimental data of Darr et al. areschematically represented by solid lines. The wavelength ofthe electromagnetic radiation is 118. 6 pm. For the derivationof the cyclotron mass the tilt angle i) has been considered byBetf = B cosqst

tical two-layer system. '7 These theoretical results forInSb are plotted in Fig. 5. As parameter we havechanged the substrate thickness only by a few gtm. Theresulting change in the spectra is considerable. Themagnetic-field-dependent carrier concentration of thesubstrate due to magnetic freeze-out involves additionalimplications which have not been included in our model.

In addition to the surface-transmission spectra wetried to detect the surface cyclotron resonance also inthe photoconducitivity. To avoid the disturbing effectsof the load current at square-wave modulation of the gatevoltage, we recorded the photoconductivity for differentstatistically applied values of the surface field as shownin Fig. 6. As a matter of fact we observe an effect ofthe gate voltage on the spectra. This change in the pho-toconductivity, however, is not due to the surface cyclo-tron resonance, but to a change of the effective resis-tance of the device with increasing gate voltage. Fromthe extrema of the surface cyclotron resonance in theelectric-field-induced transmission change, we derivethe surface cyclotron mass of electrons in accumulationas a function of the applied gate voltage. Generally it isnot possible to evaluate from gate volatge, geometry,and dielectric properties the effective charge of thesurface subbands, because of the unknown amount ofscreening due to surface states. To the surface cyclo-tron resonance contribute, however, only the chargecarriers in the surface subbands and not the deeplybound surface states. The screening due to surfacestates depends critically on the surface preparation andchanges from sample to sample. Nevertheless we triedat least to compare our results with those of Darr et al.in terms of the effective surface field below the surfacestates. In a first approximation we assumed this fieldto be the same for both experiments at the same giveneffective gate voltage. The cyclotron mass of the sur-face electron in accumulation derived from our experi-mental data compares rather well with the two lowervalues of the electron cyclotron mass in inversion asshown in Fig. 7. We cannot completely exclude in ourdata the possibility of any hidden splitting of the cyclo-tron resonance which could be obscured by accidentalinhomogeneous surface conditions. From the compari-

930 J. Opt. Soc. Am., Vol. 67. No. 7, July 1977

(0 =30 * X=118.6pmr /

=50O' 1

aa

-ul 1|

M. von Ortenberg and U. Steigenberger 930

son of our data with those of Darr et al. we conclude,however, that values corresponding to the highest of thethree mass values in inversion are not dominant in ac-cumulation. This indicates that within the quantizingrange the effective potential for accumulation and inver-sion on InSb surface do differ.

Besides the surface cyclotron resonance in accumula-tion, we tried to observe the-corresponding surface spinresonance. The observation of this resonance in inver-sion was reported by Darr et al. 8 Despite repeated ef-forts, we did not find any resonance in the magnetic fieldrange in question. The absence of the surface spin reso-nance in accumulation is not yet understood.

'E. 0. Kane, "Band Structure of Indium Antimonide, " J. Phys.Chem. Solids 1, 249-261 (1957).

2 A. Dgrr, J. P. Kotthaus, and J. F. Koch, "Surface Cyclotron

Resonance in InSb, " Solid State Commun. 17, 455-458 (1975).3M. von Ortenberg and R. Silbermann, "Cyclotron Resonance

of Electrons and Holes in Electric Subbands of Tellurium,"Solid State Commun. 17, 617-620 (1975).

4 M. von Ortenberg and R. Silbermann, "Surface CyclotronResonance of Accumulation and Inversion Layers in Tellur-ium, " Surf. Sci. 58, 202-206 (1976).

5M. von Ortenberg, S, Merz, and A. Schlachetzki, "Magneto-Spectroscopy of Electrons in Accumulation Layers on Gallium-arsenide Surfaces, " in Proceedings of the Thirteenth Inter-national Conference on the Physics of Semiconductors, Rome,1976, edited by F. G. Fumi (Marves, Rome, 1976), p. 766.

6 M. von Ortenberg, "On the Problem of Magnetic Freeze-Outin Indiumantimonide," J. Phys. Chem. Solids 34, 397-411(1973).

7M. von Ortenberg "Substrate Effects on the Cyclotron Reso-nance in Surface Layers of Silicon, " Solid State Commun. 17,1335-1338 (1975).

8A. Darr, J. P. Kotthaus, and T. Ando, "Electron Spin Reso-nance in an Inversion Layer on InSb, " in Ref. 5.

Far-infrared study of excitons, electron-hole drops, and impuritysystems in germanium

E. Otsuka, T. Ohyama, H. Nakata, and Y. Okada*Department of Physics, College of General Education, Osaka University, Toyonaka, Osaka 560, Japan

(Received 3 November 1976)

Decay kinetics of exciton and electron-hole drop systems in a highly photoexcited germanium crystal areinvestigated by observing time-resolved far-infrared laser magnetoabsorption. Magnetospectroscopy of indium-doped material is also studied over 48-220 tm.

I. INTRODUCTION

Excitons, electron-hole drops (EHD), and impurity sys-tems in germanium are accessible for far-infrared la-ser investigation in the sense of magneto-optical ab-sorption. The coexisting system of excitons and EHD,in which excitons are considered to have evaporatedfrom the surface of EHD, offers an example of dynami-cal spectroscopy, since both excitons and EHD areshort-lived and their quantity changes depending on themanner of photoexcitation. Absorption arising fromtransitions between the discrete levels of the excitonsand that arising from magnetoplasma resonance of EHDare readily distinguishable through changing laser wave-length, sample temperature, power of photoexcitation,and delay-time of observation after the light pulse.Time resolution of these two kinds of absorption leadsto a unique analysis of the decay kinetics of the coexist-ing system. The far-infrared absorption inherent in theimpurity system in a crystal, on the other hand, issteadily observable, since the lifetime of an impurityis infinite. The magneto-optical transition of the shal-low impurity states in germanium has been investigatedonly recently. 1-3 Especially poor is the information onp-type materials. Owing to the degeneracy at the topof the valence bands, a rigorous treatment of the ac-ceptor eigenstates is rather difficult. Nevertheless,with appropriate theoretical simplifications, magneto-spectroscopy measurements are carried out for indium-doped germanium by using various laser wavelengths.

931 J. Opt. Soc. Am., Vol. 67, No. 7, July 1977

II. COEXISTING SYSTEM OF EXCITONS AND EHD

A pure germanium crystal is illuminated either by axenon flash lamp (width -1 uIs) or by a Q-switched YAGlaser (width 200 ns) at liquid-helium temperatures.The block diagram for carrying out time-resolved mag-netoabsorption measurements is shown in Fig. 1. Thefar-infrared laser is operated at pulses (20-30 Hz) insynchronized combination with the photoexcitation lightpulses (10-15 Hz), with the necessary delay after ex-citation. Signal detection is made by an n-InSb Putleydetector making use of a persistent current solenoid.The two-channel boxcar system has been useful foreliminating laser fluctuations. Typical traces of mag-neto-absorption are shown in Fig. 2 for the wavelengthof 84.3 ,um (D20 laser) at various delay times. Out ofmany excitonic transitions arising from the deep-lyingdiscrete levels, the lowest field (is - 2p-)-type transi-tion is sharply defined and most readily accessible.The line shows up at 50 kOe for 84.3 um and we takeit as the monitoring signal for the exciton system. Ab-sorption due to EHD appears as a broad backgroundnear the magnetic field of 50 kOe. The EHD absorptionin our experimental condition can be interpreted byMie's scattering theory. 4 The lowest-order absorptionis given by Q = Im{1/(i + 2)}, where ' is the relative di-electric function inside EHD. This quantity has somepoles for longer wavelength, say 337 ,um, but has nonefor such wavelengths as 84 or 119 gm in the neighbor-hood of 50 kOe. Hence the EHD absorption appears as

Copyright © 1977 by the Optical Society of America 931