Yasutada Uemura

Theory of Quantum Transport in a Two-Dimensional Electron System under Magnetic Fields. I. Characteristics of Level Broadening and Transport under Strong Fields

Characteristics of level broadening and transverse conductivity of a two-dimensional electron system under extremely strong fields have been theoretically investigated in the simplest approximation without the difficulty of divergence, i e. in the so-called damping theoretical one. Those of various cases of short- and long-ranged scatterers have been obtained. To see the dependence on the range explicitly, numerical calculation has been performed for the system with scatterers with the Gaussian potential. Especially in case of short-ranged ones the peak value of the transverse conductivity has been shown to be \((N+1/2)e^{2}/\pi^{2}\hbar\) which depends only on the natural constants and the Landau level index. It has been argued from general point of view that this fact is approximately true without reference to kinds of approximations. Such characteristic of the conductivity was confirmed experimentally, but there still remain some problems as to the absolute value of the level width.

Theory of Oscillatory g Factor in an MOS Inversion Layer under Strong Magnetic Fields

The oscillatory enhancement of the g factor caused by the exchange interaction among electrons is calculated. The degree of the spin splitting of each Landau level observed in Schubnikov-de Haas oscillation is shown to be explained by the theory of the level broadening of Landau levels if such enhancement is taken into account. The g factor is also calculated under tilted magnetic fields, and the theoretical one is in excellent agreement with the experiment by Fang and Stiles, and with the similar one performed recently by Kobayashi and Komatsubara. It is proposed that the valley splitting is enhanced by just the same mechanism and that such enhancement is a possible reason why it is observed experimentally in low-lying Landau levels.

Theory of Hall Effect in a Two-Dimensional Electron System

Hall conductivity σ XY is studied in various approximations. Characteristics of σ XY are obtained for the case of both short- and long-ranged scatterers in the self-consistent Born approximation, which is the simplest one free form the difficulty of divergence. In case of short-ranged scatterers, a relation is shown to hold between σ XY and σ XX within this approximation, if one uses a relaxation time under magnetic fields. Under strong magnetic fields, effects of higher Born scattering become important in low-lying Landau levels. They depend on the sign of scatterers and strongly on their concentrations. Effects of simultaneous scattering from many scatterers are calculated to the lowest order.

Theory of Valley Splitting in an N-Channel (100) Inversion Layer of Si. : I. Formulation by Extended Zone Effective Mass Theory

The theories based upon the multi-valley effective mass equation proposed by Twose are criticized and it is concluded that they can not explain the observed valley splittings. In order to treat valley splittings correctly, a formulation based upon the extended zone scheme is presented with the main interest in the valley splitting in an n -channel (100) inversion layer of Si.

Theory of Electronic Properties in N-Channel Inversion Layers on Narrow-Gap Semiconductors I. Subband Structure of InSb

The subband structure of n -channel inversion layers on InSb its calculated self-consistently in the Hartree approximation. A new method of the effective-mass approach for the nonparabolic band is presented. The splitting, of the spin states caused by the surface potential is calculated to be small and the resonance effect with the hole state in the bulk is found to be very small. The calculated effective masses of the occupied subbands at the Fermi level agree quite well with those measured by Daerr et al. for a wide range of the carrier concentration.

Theory of Valley Splitting in an N-Channel (100) Inversion Layer of Si II. Electric Break Through

The extended zone effective mass equation as proposed in the preceding paper is applied to the vally splitting in an n -channel (100) inversion layer of Si, and the valley splitting is explained theoretically for the first time. The splitting turns out to be about Δ E =0.15×( N inv +32/11 N depl ) meV for the carrier concentrations N inv and N depl of the inversion and depletion layers which are in 10 12 cm -2 unit. The mechanism of the splitting is the electric break through, and two kinds of break through play a role in this system. The estimated splitting is too small to be observed, and it is suggested that the splitting will be greatly enhanced by many-body effects under a high magnetic field. However the appearance of the characteristic cusps in the measured line shapes of the Schubnikov-de Haas oscillation confirms that the theory gives the correct magnitude of the valley splitting without the enhancement by many-body effects.

Subband Structures of N-Channel Inversion Layers on III–V Compounds –A Possibility of the Gate Controlled Gunn Effect–

Multi-subband structures of n-channel inversion layers on the surface of p-type III–V compounds are calculated by a variational method. Nonparabolicity is taken into account in the bulk dispersion relation of the \(\varGamma\)-valley. When the surface electron density is low, electrons occupy only the subbands in the \(\varGamma\)-valley, while when it exceeds certain critical value, most electrons occupy the ground subband in the second minimum valleys. From this behavior, the working condition of the Gunn effect in the system can be changed by applying the gate voltage in the MOS structure. The critical surface electron density depends on the charge density in the depletion layer and the surface orientation, but in case of GaAs, it is about 7×10 12 cm -2 for typical operating conditions.

Valley splitting in an n-channel (100) inversion layer on p-type silicon

Abstract The extended zone effective mass theory is proposed and is applied to the investigation of the valley splitting in an n-channel (100)Si inversion layer. The splitting is due to a tunnelling effect in k -space, and is given approximately as ΔE ≈ 0.15 ( N inv + g −1 N depl ) meV ( N inv and N depl in units of 10 12 cm −2 g = 11 32 ). When the strain exists, or when k x and k y are both non-zero, the splitting is a little larger than this value. The enhancements of the Zeeman splittings and the valley splittings caused by the many body effects under strong magnetic fields are taken into account. The theory predicts the structure and line shape of the transverse magnetoconductivity oscillations, and the results show a very good agreement with the experiment including the cusps at the peak of the Landau levels in the indices N ⩾ 3.

Theory of Impurity Bands in Magnetic Fields. I. Magnetic Susceptibility

By using the Green function method for the random lattice, the susceptibility of the impurity band in weak magnetic fields is investigated in a simplified model in which the impurity potential is attractive and of short range and the electron-electron correlation can be negligible. Simple analytical expressions for the susceptibility are obtained and are computed numerically as a function of the concentration of impurities c . When c / c 0 ( c 0 is the critical concentration at which the impurity band touches the conduction band) is very small so that the impurity band width is smaller than the binding energy of the impurity potential, the orbital susceptibility in the impurity band region is simply of the type of the atomic diamagnetism, while it is of the type of the ordinary Landau diamagnetism in the conduction band region. The result for the case c / c 0 ≫1 explains the observed discrepancy from the existing Landau theory.

Scattering Mechanism and Low Temperature Mobility of MOS Inversion Layers

For the interpretation of observed low temperature mobility in n-channel inversion layers of Si MOS, two scattering mechanisms are discussed theoretically. The one is the scattering due to interface roughness and a simplified model is investigated. The other is the scattering by the charged centers. The former can explain the carrier concentration dependence of the mobility in high carrier concentration region. The latter is introduced for the interpretation of the mobility at low carrier concentration with some considerations of the charge distribution.