Fermi energy and band-tail parameters in heavily doped semiconductors

The density of states in heavily doped semiconductors is investigated by using the Green function method and the Feynman-path integral formulation applied to n -type semiconductor. It is suggested that in the present theory it takes an approximate form $\text{exp √}\text{(3}\text{2)}\text{(E}\text{σ)}$ for negative energies, and a parabolic form for positive energies. The Fermi energy and the band-tail parameters at low temperatures are calculated in the Thomas-Fermi approximation. An application to n-type GaAs is given; the present results are also compared to the theoretical results of Hwang and Brews at 77°K.     

Pseudogap and metal-insulator transitions in doped semiconductors

The electronic spectrum of a doped semiconductor described by the Anderson-Holstein impurity model and its conductivity derived from the Kubo linear response theory are calculated. Two characteristic temperatures depending on the doping level x are found in the phase diagram, T _PG and T _λ(x). The pseudogap that opens in the single-particle spectrum at low doping levels and temperatures closes at the lower one, T _PG. The pseudogap state of an insulator is attributed to spin fluctuations in a doped compound. At the higher characteristic temperature T _λ(x),, spin fluctuations vanish and the doped compound becomes a paramagnetic poor metal. Two distinct metal-insulator crossovers between semiconductor-like and metallic temperature dependence of resistivity are found. An insulator-to-poor-metal transition occurs at T ^*(x) ≈ T _λ(x). A poor-metal-to-insulator transition at a lower temperature is attributed to the temperature dependence of density of states in the pseudogap. It is shown that both transitions are observed in La_2?x Sr_xCUO₄.     

On the electron energy spectrum in heavily doped non-parabolic semiconductors

An attempt is made to present a simple theoretical analysis of the energy-wave vector dispersion relation of the conduction electrons in heavily doped non-parabolic semiconductors forming band tails. We observe that the complex energy spectrum in doped small-gap materials whose unperturbed conduction band is described by the three band model of Kane is due to the interaction of the impurity atoms in the tail with the spin-orbit splitting constant of the valence band (Δ), For band-gap (E_g)<Δ the imaginary part predominates which tails in to the conduction band. For the opposite inequality the real part comes in to play which tails in to the split-off band. In the absence of the band tailing effect, the imaginary part of the complex energy spectrum vanishes and the same is also true for doped two-band Kane-type and parabolic energy bands respectively. The present formulation helps us in investigating the Boltzmann transport equation dependent transport properties of degenerate semiconductors and are expected to agree better with experiments. The well-known results of unperturbed three and two band models of Kane together with wide-gap parabolic energy bands have been obtained as special cases of our generalized analysis under certain limiting conditions.     

Nonuniform state and hysteresis in resistivity of heavily doped ferromagnetic semiconductors

The low temperature anomaly in resistivity of heavily doped ferromagnetic semiconductors EuS can be explained by the first order phase transition from the uniform to a nonuniform state. At low temperatures the nonuniform state may realize as a metastable one.     

A performed model for band-gap narrowing of heavily doped semiconductors

The band-gap narrowing ΔE_g of n-type heavily doped crystals at an arbitrary temperature is investigated, basing on an extended Thomas-Fermi model given by Friedel and on our previous results.In highly degenerate semiconductors, the carrier-donor interaction contribution to ΔE_g is approximately proportional to the $\text{1}\text{6}$ power of electron concentration, in agreement with other theories.An exact expression for the inverse screening length is also obtained and compared with that given by Friedel.     

Anti-Stokes luminescence in heavily doped semiconductors as a mechanism of laser cooling

The anti-Stokes luminescence is a mechanism of the optical refrigeration in semiconductor light sources. The heavily doped semiconductors are considered as a material for the laser cooling. The limitation of this mechanism appears to be connected with a transition from the non-degenerate to degenerate occupation. This transition occurs at higher pumping rate (along with the transition to the optical gain and lasing) and at lower temperature. Thus, the limit for the laser cooling can be indicated. The minimal obtainable temperature is about 60–120 K depending on the doping level. The laser cooling of a semiconductor is impeded by the difficulty of extracting the spontaneous emission from a radiating body that is characterized by large angle of the total internal reflection.     

Localized ferrons and the Mott transition via the ferromagnetic phase in doped antiferromagnetic semiconductors

The states of single-and double-charge donors in an antiferromagnetic crystal are investigated taking into account the formation of magnetized regions (localized ferrons) around them. Double-charge donors should be in a state of the (1s)(2s) type, which is energetically favored over the (1s)² state. In doped antiferromagnetic semiconductors, the usual Mott transition is impossible because the single-charge donors in them are ferrons. Instead, the donor electrons are delocalized through the transition of the crystal to the single-electron state. It is unlikely that a ferromagnetic-antiferromagnetic (FM-AFM) mixed state will occur in this case. In the case of double-charge donors, transition to an FM-AFM mixed state should occur.     

Features of kinetic electron transitions in magnetic semiconductors

Peculiarities of kinetic electron transitions in magnetic semiconductors, emerging as a result of nonstationary self-heating by electric current, are described using spin-fluctuation theory. It is shown that, in the bistability region of FeSi, self-oscillations of temperature and current are excited, which correspond to transitions between the metal and semiconductor phases.     

Doping density striation effects in studies of the metal-nonmetal transition in heavily doped semiconductors

Significant oscillatory doping density inhomogeneities - striations - are reportedly a commonplace phenomenon in germanium and silicon crystals. Schottky barrier tunneling data on heavily doped and irradiation compensated silicon are presented which are consistent with the presence of such striations. The need for considering striations in studies of the metal-nonmetal transition is emphasized.     

The Mott transition in cold semiconductors

We discuss the Mott transition when a semiconductor is externally excited at low temperatures. We demonstrate that hysteresis is inevitable unless a phase separation occurs at higher temperatures or lower average excitation densities than necessary for the predicted ionization catastrophe. The critical temperature and pair density for hysteresis in Ge is of the order 6K and 3 · 10¹⁶ cm^-3, respectively, for a model involving dynamical screening.     

Indirect interactions between localized magnetic moments in doped semiconductors

The coupling between localized magnetic moments via conduction electrons is calculated taking into account the temperature and the mean free path of the electrons. For a fully degenerate electron gas and an infinite electronic mean free path the oscillatory RKKY interaction is obtained. On the limit of Boltzmann population and for infinite electronic mean free path the interaction can only be ferromagnetic. Taking into account the electronic mean free path the possibility of antiferromagnetism is restored. Furthermore the range of the interaction decreases. Several intermediate cases and possible applications are discussed.     

A fluctuation mechanism of electron transitions in magnetic semiconductors

The role of hybridization effects in a system of highly correlated electrons is studied. It is shown that a narrow band of heavy fermions is formed within the hybridization gap due to strong scattering of d-electrons by spin fluctuations. The heavy-fermion states undergo the Anderson localization with increase in the spin and charge-density fluctuations. The electron-phase transformations into La_0.65Ca_0.35MnO₃ are discussed on the basis of the proposed mechanism. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 3–7, November, 2006.     

Temperature dependence of the Debye screening length in heavily doped semiconductors having Gaussian band-tails

In the present work, a generalized expression is derived for the Debye screening length of the carriers in heavily doped semiconductors having Gaussian band-tails. The temperature dependence of the screening length is also computed for such semiconductors, taking n-type GaAs as an example.On leave of absence fromthe Department of Physics, B. N. College, University of Patna, India.     

Effect of temperature on the validity of the einstein relation in heavily doped semiconductors

An analytical expression of the modified form of the Einstein relation in heavily doped semiconductors in which Gaussian band tails are formed near the lower limit of heavy doping is derived for studying the temperature dependence of the diffusivity-mobility ratio of the carriers in such semiconductors. It is found that, with increasing temperature from relatively low values, the ratio first increases in a nonlinear manner and then decreases till, at high temperatures, it approaches its value corresponding to the non-degenerate condition resulting in a peak over a narrow range of temperatures.     

Magnetic quantization of the energy states in heavily doped semiconductors with nonparabolic energy bands

A formula for carrier concentration, and a relationship between mobility and diffusivity, have been presented for degenerate semiconductors with a nonparabolic energy band structure under the influence of a magnetic field. The relationships are general; they involve no approximation related to the comparative values of energy bandgap and spin orbit coupling. They should therefore, be applicable to both non-degenerate and degenerate semiconductors. They are quite suitable for the investigation of electrical transport in heavily doped semiconductors under the influence of a magnetic field. PACS 72.20.-I; 73.50.-h     

Mott transitions in multiorbital systems

Using the dynamical mean field theory it is shown that interorbital Coulomb interactions in nonisotropic multiorbital materials give rise to a single Mott transition. Nevertheless, narrow and wide subbands exhibit different excitation spectra in the metallic and insulating phases. The close analogy between "multigap" insulating behavior and multigap superconductivity is pointed out.     

On the nonlinearity of the P(V) characteristics of heavily doped semiconductors

The interrelation between the hydrostatic pressure P and the relative change of volume V in heavily doped semiconductors with a band structure containing several non-equivalent minima (A^IIIB^V type) is considered.It is shown that under the electron transition from a low central minimum into “heavy” subsidiary minima the P(V) dependence becomes superlinear.The possibility of the appearance in this case of a spontaneous deformation with a significant electron redistribution between the central and the subsidiary minima is treated.     

D-wave superconductivity in doped Mott insulators

The effect of proximity to a Mott insulating phase on the charge transport properties of a superconductor is determined. An action describing the low energy physics is formulated and different scenarios for the approach to the Mott phase are distinguished by different variation with doping of the parameters in the action. A crucial issue is found to be the doping dependence of the quasiparticle charge which is defined here and which controls the temperature and field dependence of the electromagnetic response functions. Presently available data on high-T_c superconductors are analyzed. The data, while neither complete nor entirely consistent, suggest that neither the quasiparticle velocity nor the quasiparticle charge vanish as the Mott phase is approached, in contradiction to the predictions of several widely studied theories of lightly doped Mott insulators. Implications of the results for the structure of vortices in high-T_c superconductors are determined.