PHYSICAL REVIE%' B VOLUME 41, NUMBER 3 15 JANUARY 1990-II Giant diamagnetic effect in InAs electron inversion layers measured by Zener tunneling U. Kunze Institut fiir Technische Physik, Universitiit Erlangen-IV urnberg, D-8520 Erlangen, Federal Republic of Germany and Hochmagnetfeldanlage der Technischen Universitiit Braunschweig, D 5300 -Braunschweig, Federal Republic of Germany (Received 26 July 1989; revised manuscript received 20 November 1989) Electron inversion layers on degenerate p-type InAs substrate are studied by means of Zener tunneling through the depletion layer. Two occupied subbands manifest themselves by current maxima occurring at forward biases which correspond to their minimum energies relative to the Fermi level. At magnetic 6elds 2.5 & 8 & 6.2 T applied parallel to the surface, in the reverse-bias range the second-derivative characteristic shows new oscillations arising from diamagnetically shifted higher subbands. In contrast to the occupied subbands, the diamagnetic eFect of higher subbands exceeds by a factor of 10 what is expected from the strength of the depletion field. Subband-valence-band mixing and a particular form of the surface potential well are discussed as possible reasons. The phenomenon of a diamagnetic rise of the subband minima in quasi-two-dimensional electron systems has been widely used to study the subband structure and, in particular, to get information concerning the form of the potential well in terms of the spatial extent of the elec- tronic wave functions. Corresponding experiments have been performed by means of optical absorption, ' trans- port, 3 and tunneling. 9' Among these methods, only tunneling provides a direct measure of the diamagnetic shift of higher, empty subbands. So far, tunneling spectroscopy of the subband structure has been performed by tunneling through the oxide bar- rier of a metal-oxide-semiconductor (MOS) structure, 9' the Schottky barrier of a metal-semiconductor con- f act i i, l 2 or a heteroj unction semiconductor barrier i 3 — i s Only recently, interband tunneling between a degenerate p-type lnAs electrode and an electron inversion layer has been observed in special MOS surface contacts. ' For the first time these junctions offer the possibility of studying the empty higher subbands in InAs electron inversion lay- ers in addition to the occupied levels. We may expect the spatial extent of the excited subband's wave functions to be mainly determined by the high depletion field that is present in electron layers on degenerately doped p-type InAs, while the spread of the ground-state wave function is mainly controlled by the electric surface field as in the work of Tsui on accumulation layers on degenerate n-type InAs. The samples used in the present experiments are MOS tunnel junctions (Fig. 1) prepared on lnAs(100) wafers by the same procedure as described previously. ' The bulk hole concentration at T 77 K amounts to 2. 3x10' cm, which corresponds to an energy range of empty states in the valence band of 3. 3 meV at T 0. Metal dots of 50-pm diameter are separated from the InAs surface by a thermally grown oxide with a thickness of a few monolayers. Because of the presence of the oxide barrier, the low work function of the Yb electrode induces a high surface-electron density as indicated in the inset of Fig. l. The small oxide thickness also provides a low-resistive tunneling contact of the top metal to the inversion chan- nel. Most of the applied voltage drops across the de- pletion layer and thus the current-voltage (I-V) charac- teristic is mainly determined by the Zener tunnel junction. The I-V curve measured from a junction at T 4.2 K (Fig. 1) exhibits two current peaks at biases V 42 and 226 mV. The nearly symmetric structure of the peaks, which are imposed on a smooth background, arises from the two-dimensional character of the subbands. ' As shown recently by studies under quantizing magnetic fields, ' the current peak arising from the nth occupied 0. 5 t ~oxlde Yb p - type lnAs 0. 3— 0. 2— n=1 0. 1— C Os - 0. 1 CJ -0. 2— oxide - InAs -0. 5 ' -200 f f I -100 0 100 bias voltage (mV) 200 FIG. l. Current-voltage characteristic of an Yb-oxide-InAs tunnel junction at T 4.2 K, whose energy-band diagram is shown in the inset (not to scale). The current peaks correspond to bottoms of occupied subbands E as indicated. The bias sign refers to that of the InAs electrode. 1990 The American Physical Society