Theoretical analysis of the gate capacitance inn-channel inversion layers on ternary chalcopyrite semiconductors in the presence of a quantizing magnetic field

An attempt is made to study theoretically, the dependence of the gate capacitance inn-channel inversion larges on ternary chalcopyrite semiconductors on a quantizing magnetic field, takingn-channel inversion layers on CdGeAs₂ as an example. It is found, on the basis of a newly derived electron energy spectrum of the above class of semiconductors, that the gate capacitance exhibits spiky oscillations with changing magnetic field and the oscillatory behaviour is in qualitative agreement with the experimental observation reported in the literature for the MOS structure of Hg_1–x Cd _x Te.     

Influence of magnetic quantization on the effective electron mass in Kane-type semiconductors

Summary We study the effective electron mass at the Fermi level in Kane-type semiconductors on the basis of fourth order in effective mass theory and taking into account the interactions of the conduction electrons, heavy holes, light holes and split-off holes, respectively. The results obtained are then compared to those derived on the basis of the well-known three-band Kane model. It is found, takingn-Hg_1−x Cd _x Te as an example, that the effective electron mass at the Fermi level in accordance with fourth-order model depends on the Fermi energy, magnetic quantum number and the electron spin respectively due to the influence of band nonparabolicity only. The dependence of effective mass on electron spin is due to spin-orbit splitting parameter of the valence band in three-band Kane model and the Fermi energy due to band nonparabolicity in two-band Kane model. The same mass exhibits an oscillatory magnetic-field dependence for all the band models as expected since the origin of oscillations in the effective mass in nonparabolic compounds is the same as that of the Shubnikov-de Hass oscillations. In addition, the corresponding results for parabolic energy bands have been obtained from the generalized expressions under certain limiting conditions.     

On the effective electron mass in ternary semiconductors in the presence of crossed electric and magnetic fields

The effective electron mass in ternary semiconductors under cross field configuration depends on the magnetic quantum number, besides the usual energy dependence of the same mass in non-parabolic bands. It is found, taking nHg_1−xCd_xTe as an example, that the index dependent masses are in agreement with the experimental observation.     

Influence of magnetic quantization on the effective mass in semiconductor superlattices

An attempt is made to study the effect of a quantizing magnetic field on the effective electron mass in a semiconductor superlattice at low temperatures. It is found on the basis of the tight-binding approximation, taking GaAs-Ga_1–x Al _x As an example, that the effective mass at the Fermi level depends on the magnetic quantum number due to the cosine dependence of the wave-vector in the superlattice direction. The mass also exhibits oscillatory features in the presence of magnetic quantization because of its dependence on Fermi energy which oscillates with changing magnetic field.     

On the Einstein Relation in Ternary Semiconductors in the Presence of Crossed Electric and Magnetic Fields

We investigate theoretically the Einstein relation for the diffusivity-mobility ratio of the electrons in ternary semiconductors at low temperatures in the presence of crossed electric and quantizing magnetic fields on the basis of threeband Kane model. It is found, taking n-Hg_1-xCd_xTe as an example, that DMR shows an oscillatory magnetic field dependence. Besides, the DMR increase both with increasing electron concentration and decreasing alloy composition respectively.     

Theoretical analysis of the oscillatory gate capacitance inn-channel inversion layers on ternary chalcopyrite semiconductors under magnetic quantization

An attempt is made to investigate theoretically the gate capacitance inn-channel inversion layers on ternary chalcopyrite semiconductors under both weak and strong electric field limits in the presence of a quantizing magnetic field, takingn-channel inversion layers on p-type Cd GaAs₂ as examples. It is found, on the basis of the newly derived 2D electron spectra in inversion layers on the above class of semiconductors, for both weak and strong electric field limits, that the gate capacitances oscillate with the quantizing magnetic field and the crystal field splitting parameter effectively enhances the oscillatory spikes. It has also been observed that the oscillatory behaviour is in qualitative agreement with experimental observation as reported elsewhere for MOS structure of Hg_1–xCd_xTe. In addition, the corresponding results for inversion layers on parabolic semi-conductors are also obtained from the expressions derived.     

On the gate capacitance of MOS structures of kane-type semiconductors under magnetic quantization

An attempt is made to formulate the gate capacitance of MOS structures of Kane-type semiconductors under magnetic quantization, without any approximations of weak or strong electric field limits, on the basis of the fourth-order effective mass theory and taking into account the interactions of the conduction, light-hole, heavy-hole, and split-off bands. It is found, taking n-channel Hg_1–x Cd _x Te as an example, that the gate capacitance exhibits spiky oscillations with changing magnetic field, which is in qualitative agreement with experimental observations, reported elsewhere, in MOS structures of the same semiconductor. The corresponding results for n-channel inversion layers on parabolic semiconductors are also obtained from the expressions derived.     

Theoretical study of the effective electron mass in ternary chalcopyrite semiconductors in the presence of crossed electric and magnetic fields

An attempt is made to investigate theoretically the effective electron mass in ternary chalcopyrite semiconductors at low temperatures on the basis of a newly derived dispersion relation of the conduction electrons under cross fields for the more generalized case which occurs from the consideration of the various types of anisotropies in the energy spectrum. It is found, taking degeneraten-CdGeAs₂ as an example, that the effective electron mass at the Fermi level along the direction of magnetic quantization depends on both the Fermi energy and the magnetic quantum number due to the combined influence of the crystal field splitting parameter and the anisotropic spin-orbit splitting parameter respectively, resulting in different effective masses at the Fermi level corresponding to different magnetic sub-bands. It is also observed that the same mass at the Fermi level in the direction normal to both magnetic and electric fields also varies both with Fermi energy and magnetic sub-band index, and the characteristic feature of cross-fields is to introduce the index-dependent oscillatory mass anisotropy. The theoretical results are in good agreement with the experimental observations as reported elsewhere.     

Concentration Dependence of Room Temperature Magnetic Ordering in Dilute Fe: Ge1 − x Te x Alloy

Hyperfine interaction techniques like Mossbauer spectroscopy are very sensitive tools to study the local probe interactions in dilute magnetic semiconductors. We report here a Mossbauer study on the concentration dependence in Fe_0.008Ge_{1 − x} Te _x for x = 0, 0.008, 0.016, 0.03 and 0.05. At room temperature magnetic interactions were observed for all concentrations of Te and the population of magnetic site was found to increase gradually with the Te concentration. A constant magnetic hyperfine field of 136 KOe was found. A quadrupole doublet due to the FeTe₂ compound phase was also seen.     

Peak in the magnetic-field dependence of diffusion-induced thermopower for n-Bi-Sb semiconducting alloys

A peak is detected on the dependence of the diffusion-induced thermopower on transverse magnetic field in degenerate semiconducting alloys n-Bi_1?x Sb_x (0.07≤x≤0.15) doped with tellurium donor impurity. The temperature gradient is directed along the bisector axis C ₁ of the monocrystalline sample and the magnetic field is along the triad axis C ₃. The electron spectrum of the Bi-Sb alloys under investigation consists of three equivalent ellipsoids with distinctly different effective masses along the axes of the ellipsoid (m _∥/m _⊥). A simple kinetic theory shows that the presence of the peak on the diffusion thermopower is a manifestation of this strong anisotropy in the electron spectrum and of the additive contribution of all three ellipsoids to electron transport. The nonmonotonic dependence of thermopower on the transverse magnetic field makes it possible to determine the electron relaxation time, while the temperature dependence of this relaxation time can be used to separate the relaxation time for electrons scattered from ionized impurities and from acoustic phonons.     

A simple analysis of the subband energies in quantum-confined non-parabolic semiconductors in the presence of a parallel magnetic field

Summary We study the subband energies in quantum wells and quantum wires in the presence of a parallel magnetic field in non-parabolic semiconductors, on the basis of a generalized dispersion relation considering all types of anisotropies of the energy-band parameters within the framework ofk·p formalism, by formulating the respective electron energy spectra. It is found, by takingn-Cd₃As₂ as an example, that the subband energies are greater for quantum wires and smaller for quantum wells, respectively. The magnetic field diminishes the above values and the corresponding well-known results for quantum-confined parabolic semiconductors have also been obtained from our generalized expressions under certain limiting conditions.     

Formation of bound magnetic polarons in Cd1−x MnxTe crystals. Contribution of the average exchange field and thermodynamic fluctuations of the magnetization to the binding energy

It is shown that the temperature dependence of the binding energy of exciton-impurity complexes in the semimagnetic semiconductors Cd_1−x Mn_xTe (x≈0.05) is described well in the donor-electron model with an effective characteristic magnetic-polaron energy. The contributions of the average exchange field and of thermodynamic fluctuations of the magnetization to the binding energy and their variation with temperature with and without a weak magnetic field (H⩽3.5 kOe) are determined. How doping with scandium, vanadium, and cobalt effects the appearance of the magnetic-polaron in the experimental crystals was studied. Fiz. Tverd. Tela (St. Petersburg) 39, 527–535 (March 1997)     

Fir magnetospectroscopy on (CuIn)1?xMn2xTe2

The paramagnetic resonance of Mn²⁺ in the diluted magnetic semiconductor (CuIn)_1–xMn_2xTe₂ was observed in a pulsed magnetic field up to 15 T at temperatures ranging from 4.2 K to 45 K. The temperature dependence of the line width of the paramagnetic resonance in (CuIn)_1–xMn_2xTe₂ resembles the behaviour of other diluted magnetic semiconductors. A Dzyaloshinski-Moriya exchange constant of approximately 0.62 K was derived. This value fits well with the values reported for II–VI based diluted magnetic semiconductors [1], if we consider the larger degree hybridization of the 3d electrons with the band electrons in chalcopyrite semiconductors.     

Thermoelectric power in superlattices of nonparabolic semiconductors with graded interfaces under magnetic quantization

Summary We study the thermoelectric power of the electrons under magnetic quantization in III–V, II–VI, PbTe/PbSnTe and strained layer superlattices with graded interfaces and compare the same with the corresponding bulk specimens of the constituent materials by formulating the respective expressions incorporating the broadening. It is found, by taking GaAs/Ga_1−x Al _x As, CdS/CdTe, PbTe/PbSnTe and InAs/GaSb superlattices with graded interfaces as examples, that the thermoelectric power exhibits oscillatory dependence with the inverse quantizing magnetic field due to Shubnikov-de Hass effect and increases with decreasing electron concentration in an oscillatory manner in all the aforementioned cases. The thermopower in graded superlattices is greater than that of constituent bulk materials together with the fact that the oscillations in superlattices show up much more significantly as compared to the respective constituent materials. In addition, the well-known expressions for bulk specimens of wide-gap semiconductors have also been obtained as special cases from our generalized expressions under certain limiting conditions.     

2D-Electron Heating in Electric and Magnetic Crossed Fields

2D-electron heating in a potential well of a single n-(AlAs) _x (GaAs)_1–x /i-GaAs (x = 0.28) heterojunction is studied for the cases of a classical (weak) magnetic field B and constant and pulsed electric fields at fixed temperatures 77 and 4.2 K. It is shown that the heating of two-dimensional electrons is similar to that of the bulk ones. The magnetic field cools electrons, and this is manifested in the shifts of the characteristic critical electric fields E _{c 1} and E _{c 2} and in the regions of nonlinearity of voltage-current characteristics. The dependence of the effective electron temperature on the electric field T _e(E)_B is determined.     

Influence of alloy composition on the dependence of the diffusivity-mobility ratio in ternary semiconductors on a quantizing magnetic field

An expression is derived for the diffusivity-mobility ratio in degenerate narrow-gap ternary semiconductors in the presence of a quantizing magnetic field. With the help of this expression, the diffusivity-mobility ratio is shown, taking n-Hg_1–xCd_xTe as an example, to have an oscillatory dependence on a quantizing magnetic field. The influence of alloy composition on such dependence is also investigated.     

Magnetoplasma resonance in a GaAs/AlGaAs quantum well in a strong parallel magnetic field

The dispersion of magnetoplasma excitations in two-dimensional electron systems in a strong parallel magnetic field has been studied. A considerable increase in the electron cyclotron mass with an increase in the parallel component of magnetic field has been detected. It has been found that the cyclotron mass increment is a quadratic function of the magnetic field parallel to the interface. It has been shown that the mass anisotropy of 2D electrons induced by the parallel magnetic field reaches nearly 2.5 in B _‖ = 7 T. The energy of space quantization of the electron in the quantum well has been estimated from the magnetic field dependence of the anisotropy.     

Magneto-optics of strongly correlated two-dimensional electrons in single heterojunctions

Investigations of two-dimensional (2D) electron systems in semiconductors subjected to a strong perpendicular magnetic field with the use of photoluminescence are reviewed. The foundation of the optical spectroscopy method using the radiative recombination of 2D electrons with photoexcited holes bound to acceptors in a δ-doped monolayer in GaAs/Al _x Ga_1-x As single heterojunctions is presented. Optical spectroscopy studies of the energy spectra of 2D electrons imposed on transverse magnetic fields in the regimes of the integer and fractional quantum Hall effects are discussed. The relationship between the mean energy of the 2D electron gas and the first moment of their radiative recombination is analysed. It is shown that the magnetic field dependence of the first moment provides a method to measure the cyclotron, enhanced spin and quasiparticle energy gaps at the same time. Therefore it is shown how magneto-optics ‘see’ the ground state of interacting 2D electrons in the extreme quantum limit and how an optical ‘tool’ is efficient for the determination of Coulomb gaps of incompressible Fermi fluids in the fractional quantum Hall effect. Finally optical observations and studies of the Wigner crystallization of 2D electrons are presented. The corresponding liquid-solid phase diagram is discussed.     

Transport properties of electrons in energy band tails

Transport properties of electrons in energy band tails of disordered semiconductors are studied experimentally using a material system in which (i) the width and shape of the band-tail are approximately known and (ii) the Fermi energy is controllable. The material is heavily-doped, closely-compensated, crystalline n-GaAs whose compensation ratio can be made arbitrarily close to unity by the use of two techniques that are described in detail. This control of the Fermi level through compensation permits the measurement of the transport properties of electrons at various energies in the band-tail.

Using band tails having a width of ～50 meV, measurements have been made of the temperature dependence of the d.c. conductivity and Hall coefficient, the frequency dependence of the a.c. conductivity and the electric field dependence of the d.c. conductivity (the last two at low temperatures).

The evidence demonstrates the progressively greater localization of states deeper in the tails. No sign is found of a sharp mobility edge. There is a number of close similarities to the properties of amorphous semiconductors but some significant differences. The frequency dependence of the a.c. conductivity at low temperatures is essentially identical with that of amorphous semiconductors in accord with the general interpretation that conductivity at low temperatures takes place by electron hopping among localized states near the Fermi energy. The detailed temperature dependence of the d.c. conductivity at low temperatures is log σ=σ ₀ exp [?(T ₀/T)^1/2], thus disagreeing with a theoretical expectation that the exponent for low temperature hopping conduction should be 1/4. At low temperatures, the electric field dependence of the conductivity shows a variation as σ～exp (bF/T) over a considerable range extending down to field strengths close to 1 V/cm. This closely resembles recent observations on amorphous semiconductors but the range of field strengths here is lower by several orders of magnitude.     

Galvanomagnetic properties of Hg1−x MnxTe1−y Sey semimagnetic semiconductors

The galvanomagnetic properties of single crystals of the semimagnetic semiconductors Hg_1−x Mn_xTe_1−y Se_y with 0.01<y<0.1 and x=0.05 and 0.14 in the temperature range 4.2–300 K are investigated. The features of the temperature dependence of the Hall coefficient R _H and the complicated behavior of R _H in a magnetic field are attributed quantitatively to the existence of three groups of current carriers, viz., electrons and two types of holes, for which the temperature dependences of the densities and mobilities are obtained. A transition from p-type to n-type conductivity is observed as the Se content is increased, and the negative magnetoresistance simultaneously gives way to positive magnetoresistance. Zh. éksp. Teor. Fiz. 112, 1809–1815 (November 1997)