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IN OF IN CONDENSATE GERMANIUM OSCILLATIONS THE CURRENT AN ELECTRON-HOLE QUANTUM V. F. Gantmakher and V. N. Zverev Academy Sciences of Institute of Solid State Physics, USSR subnirted 3 July 1973 Pis. Red. 18, No. 3, 180 - 183 (5 August 1973) ZhETF Using laser radiation to produce a high photocarrier density in gernaniurn, we succeeded in observing quantum oscillations of the photocurrent as a functi.on of the magnetic field. The presence of such oscillations confirms the existence of a two-phase system, nanely an electron-hole condensate with exciton "vapor" [1]. The oscillations are apparently due to the heavy holes. Their period in terms of the reciprocal field determines the carrier density N in the condensate and the Fermi energies Es and E5 of the electrons and holes. The experiment was perforned in the following rnanner. Ttre germanium samples (p-type, total content of electrically-active impurities about 10r'cm-', [100] axis normal to the surface of plates measuring 4x4x0.3 mm) were etched in CP-4A. Two strips of an indium-ga1lium alloy were then deposited on each sample in such a way that a band of pure germanium surface, with approximate width 1 mrn,remained between these electrodes. Sample I (see Fig. 1), which was freely placed in mount 2 in the center of a superconducting solenoid, was imnersed directly in superfluid,helium (T = 1.5oK). The bean 4 from an He-Ne laser (I = 6328 A, approximate power 10 nW) was focused with a short-focus (t = 7 mm) cylindrical lens 3 into a strip approximately 20 p wide that crossed the gap between the electrodes 6. A constant voltage V was applied to the sanple, and the current I was measured as a function of the field H. Usually I ranged from 0.05 - 0.1 to I - 2 UA. To compensate at least partially for the monotonic course of the I(H) curve and to increase the gain thereby, a signal i = oH from a Hall pickup, also placed inside the solenoid, was applied to the The proporx-y recorder in series with the measuredsignal. tionality coefficient o was regulated by the current through the pickup.
Fig. l

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The insert of the diagram shows clearly the periodicity of the minina as a function of the reciprocal field; devi.ations for the periodi.city appear only for the first nunbers. This indicates that the oscillations are connected with the Landau quantization of the photocarrier spectrum. Such a quantization of the excitation spectrum in the condensate was already observed by spectroscopic nethods both i-n germanium [2] and in silicon [3]. As is clear from_the description of the experiment, the electron-hole pairs were produced in the surface layer of a very snall part of the sample, the greater part of the latter serving only as a radiator to transfer the heat to the helium. Observation oi quantumoscillations of the current under these conditions, especially the fact that the period of the oscillations is independent of the intensity of the light, is convincing proof of the presence of a two-phase svstem of excitations. Indeed, were there no interphase boundary, the carrj-er density w;uld decrease away from the axis of the illuminated strip towards the interior and along tire surface. Then the period of the oscillations, if observed at all, would be determined by thJ maxirnum value of the concentration near the axis of the strip, and could therefore be varried by varying the pump. Owing to the presence of the two-phase system, only the depth of the strip octupied by the condensate changes with changing pump, while the Fermi energy of the carrieri, which is determined by the thermodynamic relations, remains constant o't"" ttr" entire volume of the condensate. The minimumpossible stqip thickness de is deternined by the depth of concentration of the light, and also by the diffusion of the;lectrons and of tire trorei during the time of their cooling. From the mj.nimum value of the illumination, at which the oscillations were observed, we obtai-n the estimate do - I - 2 p. (Wenote for comparison that estimates of the radius of the electron-ho1e drops give values from 2 to g y t4]).' Generally speaking, one can inagine two mechanismsthrough which the Landau quantization causes oscillations of the current: the Shubnikov{e Haas effect (oscillations of the bulk conductivity), and phenomena occurring in the region near the contacts, .g., oscillations of the probabi-lity of tunneling through the Schottky barrier. The contact phJnomenashould be quite conplicated in our case, since we have on one side of the boundary t*o d"g"nerate groups of carriers with different Fermi quasilevels. By producing contacts known to be non-ohmic wit! the aid of a conducting adhesive based on colloidal silver, we also observed oscillations in fields 20 - 4s kOe, but we have seen also intermediate minima in addition to the nini,mum noted 106

lig. Z. Dependenceof the photocurrent on the nagnetic field. The vertical scale pertains to curves 2 and S (curves I and 4 were recorded wi.th double the nagnification). V = I voLt. Variation of the value of the compensatingsignal nakes it possible to reveal more distinctly the extrema i-n different sections. Curves l, 2: q = 3.5x10-3 Uf/k0e, curve 3: q, = 9x10-3 pA/kOe, curve 4: 0 = 4.5x10-2 uA/kOe.

Figure 2 shows typical curves obtained with one of the three investigated samples. Six distinct ninima on these curves are marked by arrows. The accuracy with which the positions of the minima were established is apparently t 5%. The positions of the minima remained constant, with the same accuracy, from sample to sample, did not depend on the sign and rnagnitude of V in the range from 0.3 to 3 V, and remained practically the same when the illumination intensity was decreased by at least a factor of 30. With further decrease of the intensity, the amplitude of the oscillations decreased and vanished, while their period remained the same. The oscillations vanished also when the bean was defocused into a strip wider than 0.5 mm.


in Fig,2, and the contacts used by us the sample to room the oscillations in

The ohnic character of the indium-gal1ium entire picture was less distinct. and the complete reproducibility of the curves after repeated heating of temperatures and using different samples give grounds, in our opinion, that Fig. 2 are due precisely to the Shubnikov-deHaas effect.

There are few experimental facts concerning the parameters of the excitation spectrum and specthe condensate. It is clear, however, that this spectrum should be close to the initial trum of the electrons and holes in germaniun. It cannot be deterrnined beforehand whether the observedperi.od P = 1.3'10-s Oe-l ii due to electrons or heavy holes. For both variants, it is possible to deternine first t[e Fermi energy E = fie/Pmcc of the carriers causing"ghe oscillations (ms is the cyclotron mass at H ll [100]), and then thei-r concentration N = v(2mE)'t'/31t'6' (v is the number of valleys and m is the mass determining the density of states) and the Ferni energy of the carriers of opposite sign. If the oscillations were due to electrons, the values obtained would not agree with the spectroscopic data [4, 5]. 0n the other hand, the assumption that the oscillations are determined by holes (m = 0.347m0, rc = 0.28n0) leads to values that agree splendidly with [4, 5]: N = l.?5.1017cm-,. E. = 2 meY, E, = 3,2 rneV.

It is understandable here why no oscillations due to electrons are observed, since their period i.s too large to be recorded by such a crude method. It is known that for the heavy holes in germaniun the magnetic levels corresponding to The experimental accuracy, however, is insuffismall quantun nunbers are not equidistant [6]. cient as yet to investigate this circumstance. We are grateful to V. B. Tinofeev who stimulated our interest in this research, for numerous fruitful discussion, to A. F. Dite and V. G. Lysenko for valuable advice, and to G. V. Merzlyakov for technical help.

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L. V. Keldysh, Trudy IX Mezhdynarodnoi konfer. po fizike polyprovodnikov (Proceedings of the Ninth International Conference on SemiconductorPhysics), Nauka, Leningrad, 1969, p.1384. V. S. Bagaev, T. I. Galkina, N. A. Penin, V. B. Stopachinskii, and M. N. Churaeva, ZhETF Pis. Red. t6, r20 (L972) [JETPLett. 16, 83 (L972)]. Pis. Red. 18, A. F. Dite, V. G. Lysenko, V. D. Likhnytin, and V. B. Timofeev, ZhETF 114 (1973) [JETPLett. 18, 65 (1973)]. Ya. Pokrovskii, Phys. Stat.. So1. (a) 11, 385 (1.972). C. Benoit atla Guillaume, M. Voos, and F. Salvan, Phys. Rev. 85, 3079 (L972). J. Halpern and B. Lax, J. Phys. Chem.So1. 26,9f1 (1965).