Multivalley Semiconductors Research Articles

Electronic structure of disordered systems with multi-orbitals

The electronic structure of disordered systems in which unperturbed dispersion consists of a number of equivalent bands is investigated. By analysing the nature of the eigenstates including localisation for two- and four-orbital systems with various degrees of disorder and magnitudes of mixing, it is shown that the interband mixing is essential in characterising an eigenstate, which exhibits an interplay of disorder and band admixing specific to completely overlapping bands. Implications for multi-valley semiconductors and d-band systems are discussed.

Effects of uniaxial stress and magnetic field of D - center in germanium and silicon

By means of long-wavelength photoconductivity and very low temperature techniques, some properties of isolated D - centers in Ge and Si have been investigated. The characteristics natures of D - states in multi-valley semiconductors have revealed themselves especially under uniaxial stress and in a strong magnetic field, and difference of the electron and spin structures due to the difference of doped impurities has been clarified.

Optical absorption by electron plasma in multivalley polar semiconductors with impurities

A systematic analysis of the high-frequency free-carrier absorption due to ionised-impurity-mediated processes is given for a highly polar doped degenerate semiconductor taking into account the plasma-phonon coupling and the anisotropy of the multivalley conduction band. In the approximation of isotropic valleys, the bump in the absorption due to higher-frequency plasmon-phonon excitations is shown to dominate strongly (by an order of magnitude for PbSe with n approximately=1018 cm-3) the single-particle absorption calculated taking into account the dynamic screening. The absorption due to polariton excitations is found to be negligible. The absorption due to the long-wavelength plasmon-phonon excitations is then investigated in the case of an anisotropic multivalley conduction band. For PbSe and PbTe with n approximately=1018 cm-3 the plasma anisotropy lowers the absorption by about 5 and 50% respectively, as compared with the isotropic approximation. A comparison with previous theories and the reflectivity data for n-PbSe is given. A possibility for a sharp dip in the reflectivity coefficient at the plasmon-phonon mode frequency is indicated.

Polarizabilities of shallow donors in multivalley semiconductors

With the use of the multivalley effective-mass equation with an envelope function containing a sum of many exponentials and the Hass\'e variational approach, an expression for the polarizabilities of shallow donors in a multivalley semiconductor is obtained. The polarizabilities of isolated P, As, and Sb donors in Si are computed with a two-exponential envelope function and are compared with the polarizability values of isolated P and Sb in Si deduced from recent piezocapacitance measurements.

Optical Orientation and Polarized Luminescence in Silicon

AbstractThe polarization properties of the recombinative photoluminescence of free electrons excited to the conduction band of a cubic multivalley semiconductor by linearly and circularly polarized light are studied theoretically. The electron transitions from the valence band and impurities to the valleys of the conduction band are considered. The phonon‐assisted and phononless indirect transitions are taken into account. Unlike the case of semiconductors with direct interband transitions polarized light is emitted not only by hot electrons but also by cold ones, and by excitons.

Uniaxial Stress and Magnetic Field Effects on Far-Infrared Photoconductivity of D- Centers in P, As and Li Doped Si Crystals

Some properties of D - centers which are characteristic of multi-valley semiconductors have been investigated by means of far-infrared photoconductivity. They have revealed themselves particularly in the differences of the uniaxial stress and magnetic field effects on the D - centers between Si(P), [or Si(As)] and Si(Li). The experimental results have been compared with the theories.

Theory of multiexciton complexes bound to donors in multivalley semiconductors

We report a theory for bound multiexciton complexes (BMEC) associated with donors in multivalley semiconductors. The energy separations between the low-lying electronic states and the ground state are calculated in the Hartree-Fock approximation. By incorporating the effect of the anisotropic, multivalley band structures with interparticle interactions, we obtain energy separations in good agreement with the available experimental data. This agreement between theory and experiment suggests that the assignment of electrons and holes to single-particle states is a good description of the BMEC in multivalley semiconductors.

Clustering in the approach to the metal-insulator transition

Abstract A phenomenological model of donor clusters is found to describe the optical and magnetic properties well at donor densities below the Mott density. The effects of clustering on the single-particle density of states is discussed. Microscopic calculations lead to the conclusion that in multi-valley semiconductors large clusters are sufficiently electronegative to attract an electron from isolated donors or donor pairs and as a result, there is no Mott-Hubbard gap due to correlation. The insulating property is ascribed to Anderson localization at the Fermi level.

The dispersion relation for magneto-plasma waves in multivalley semiconductors

The dispersion relation for plasma waves, propagation at an arbitrary angle to an external magnetic field, has been calculated on the basis of the Vlasov equation. The energy bands are assumed to be multivalley, non-parabolic and non-spherical. The case of strong degeneracy of the electron gas has been analysed.

Donor binding energies in multivalley semiconductors

The equation for the binding energy of donor impurity states in multi-valley semiconductors, with full inclusion of the Umklapp contributions to intervalley potential matrix elements and of the mass anisotropy is solved variationally for a point-charge impurity pseudopotential. The results are in very good agreement with experiment for Si:P, and Ge:As. The crucial role of Umklapp intervalley scattering contributions to the binding of the ground state is discussed.

Properties of biexcitons in multi-valley semiconductors

This paper considers the effects on the symmetries and binding energies of biexcitons of 1) the short-range interaction (Coulomb and exchange), 2) a multi-valley conduction band and 3) the mass anisotropy of the valleys. It demonstrates that the ground state of the biexciton in a multi-valley semiconductor should be a spin triplet with an antisymmetric valley function and that poly-excitons Xx,x>2, should be stable in a material like Si.

Scattering of Electrons in Heavily Doped Semiconductors

An analysis is made for systematic change of the low temperature resistivity versus temperature curves with the change of donor concentration found in heavily Sb-doped germanium. The observed results are consistently accounted for in terms of the assumption that the donor electrons are degenerate in a rigid band with the same structure as the pure crystal, and of a specific assumption for the energy dependence of the coulomb scattering which deviates distinctly from the usual one at low energies where the electron wavelength is greater than the average impurity distance. The assumptions are shown to be consistent with observed temperature dependence of the Hall effect. The resistivity vs temperature curves for single valley, including the case induced by applying uniaxial stress, and other multivalley semiconductors are interpreted on the same basis.

The Effective Mass Equation for the Multi-Valley Semiconductors

The validity of the multivalley effective mass equation which has been conventionally used by many authors is examined. It is shown that the equation will not describe the intervalley mixing properly. An alternative equation which replaces the conventional equation is derived and discussed. Essential features of the new equation are: the lack of the intervalley mixing via kinetic energy, and the modification of impurity potential by the product of the periodic parts of the Bloch functions at the conduction band minima. Importance of the effect of anisotropy of the effective mass is discussed.

Valley selection by linear optical pumping in PbTe

Due to the anisotropy of optical matrix elements, selective population of valleys is possible in multivalley semiconductors under linearly polarized light excitation. We observe this effect by measuring the linear polarization ratio of recombination light of a PbTe sample at low temperature.

Mott transition in multivalley semiconductors

We show that the original ideas of Mott when properly extended to the multivalley case to include the effects of intervalley mixing, can still lead to the correct estimate of the critical density at which semiconductor-metal transition should occur in a doped semiconductor. Our treatment does take into account the exact numerical solution for the critical screening of a screened Coulomb potential as pointed out by Martino et al. and the multivalley extension of the Mott model by Krieger and Nightingale. We show that the critical density ${n}_{c}$ is given by the formula ${n}_{c}^{\frac{1}{3}}{N}^{\frac{2}{3}}(\frac{{E}_{c}}{{E}_{g}})(\frac{{e}^{2}}{2K{E}_{g}})=M$. The value of the constant $M$ from the experimental data on Si and Ge appears to be 0.47 \ifmmode\pm\else\textpm\fi{} 0.03. We discuss the possibility of obtaining this value for $M$ by an appropriate theory.

Current–voltage characteristics of tunnelling Schottky barriers

Tunnelling current contributions to the current from the various valleys in a multi-valley semiconductor have been studied in a Schottky barrier. The effect of doping densities and temperature on currents–voltage characteristics for a Schottky diode with a multivalley semiconductor has been evaluated. It has been found that satellite valleys, specially with low effective mass, contribute significantly to the current.

Knight Shift in Multivalley Semiconductors. I. Theory of Contact, Orbital, and Dipolar Shift and Relativistic Effects

A theory of the Knight shift in degenerate multivalley semiconductors is presented which takes into account the spin-orbit interaction and the relativistic effects on the hyperfine coupling. This theory treats rigorously the spinor character of the wave function and the nontensorial nature of the $g$ matrix. We give a formula for the shift created by an arbitrary ellipsoidal valley. This formula involves a simple linear combination of $g$ factors and matrix elements of the hyperfine field. In most cases (except that of a spherical valley) the Knight shift is not proportional to the Pauli paramagnetic susceptibility.

Theory of electrical resistance of multivalley semiconductors with screw dislocations

The diffusion theory of electrical resistance in multivalley semiconductors of Si-type with screw dislocations is developed. Intervalley electron transitions are taken into account. The effect of the inhomogeneous dislocation distribution on the electrical resistance of the crystal is considered.

The diffusion of electrons in semiconductors in high electric fields

A theory is presented for the diffusion coefficients of electrons in a single valley or multivalley semiconductor in a high electric field. The valleys may be isotropic or anisotropic and the coefficients describe diffusion transverse and longitudinal to the field. Generalized Einstein relations are found for a single valley semiconductor and for transverse diffusion in a semiconductor with two types of isotropic valleys. The general method is applied to gallium arsenide and silicon.

Frequency shift of the plasma reflectivity minimum due to uniaxial stress in n-type silicon

The pronounced influence of 〈100〉 compressive stress on the frequency of the reflectivity minimum associated with free carrier dispersion has been measured for radiation polarized perpendicular or parallel to stress. Interpretation of the results in terms of the electron transfer model suggests that the phenomenon might be used to determine effective mass anisotropies in multivalley semiconductors.