An attempt is made to study the effective electron mass in strained layer superlattices of non-parabolic semiconductors with graded structures under sirong magnetic quantization and to compare the same with the bulk specimens of the constituent materials, by formulating the appropriate magneto-dispersion laws. It is found, taking InAs/GaSb superlattice as an example, that the effective electron mass oscillates with the inverse quantizing magnetic field due to the Shubnikov-de Hass effect. The dependence of the effective mass on the magnetic quantum number in addition to Fermi energy is an intrinsic property of such semiconductor heterostructures. The stress makes the mass quantum number dependent in bulk specimens and even in the presence of broadening, the effective masses in superlattices exhibit significant oscillations with enhanced numerical values from that of the constituent semiconductors. Besides the effective electron masses also increase in an oscillatory way with increasing electron c...

On the effective electron mass in strained layer superlattices of non-parabolic semiconductors under strong magnetic quantization

We study the effective electron mass at the Fermi-level on the basis of a newly formulated electron energy spectrum for heavily doped non-parabolic III–V semiconductors forming band-tails, taking n-InSb as an example. The investigation on the mass includes both the presence and absence of band-tailing states, in parabolic and non-parabolic energy band structures, respectively. The effective mass exists in the forbidden region, which is impossible without band-tailing effects. The analyses have been carried out for the Fermi-energy and other entities, like screening length and impurity screening potential, respectively. The values of the effective mass with band-tailing states are found much less as compared with in the absence of band-tails. The well-known results for unperturbed two-band model of Kane have also been obtained from our generalized analysis under certain limiting conditions.

https://iopscience.iop.org/article/10.1238/Physica.Regular.068a00368/pdf

A simple theoretical analysis of the effective electron mass in heavily doped III-V semiconductors in the presence of band-tails

We present a simple theoretical analysis of the effective electron mass (EEM) at the Fermi level for III–V, ternary and quaternary materials, on the basis of a newly formulated electron energy spectra in the presence of light waves whose unperturbed energy band structures are defined by the three-band model of Kane The solution of the Boltzmann transport equation on the basis of this newly formulated electron dispersion law will introduce new physical ideas and experimental findings under different external conditions It has been observed that the unperturbed isotropic energy spectrum in the presence of light changes into an anisotropic dispersion relation with the energy-dependent mass anisotropy In the presence of light, the conduction band moves vertically upward and the band gap increases with the intensity and colours of light It has been found, taking n-InAs, n-InSb, n-Hg1−xCdxTe and n-In1−xGaxAsyP1−y lattice matched to InP as examples, that the EEM increases with increasing electron concentration, intensity and wavelength in various manners The strong dependence of the effective momentum mass (EMM) at the Fermi level on both the light intensity and wavelength reflects the direct signature of the light waves which is in contrast with the corresponding bulk specimens of the said materials in the absence of photo-excitation The rate of change is totally band-structure-dependent and is influenced by the presence of the different energy band constants The well known result for the EEM at the Fermi level for degenerate wide gap materials in the absence of light waves has been obtained as a special case of the present analysis under certain limiting conditions, and this compatibility is the indirect test of our generalized formalism

http://iopscience.iop.org/article/10.1088/0031-8949/75/6/012/pdf

A simple theoretical analysis of the effective electron mass in III-V, ternary and quaternary materials in the presence of light waves

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/Ga1−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.

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

An attempt is made to study the Einstein relation for the diffusivity‐mobility ratio of the electrons in degenerate n‐type small‐gap semiconductors under strong magnetic field on the basis of three‐band Kane model without any approximations of band parameters and incorporating the electron spin and broadening of Landau levels, respectively. It is found, taking n‐Hg1−xCdxTe as an example, that the Einstein relation exhibits an oscillatory magnetic field dependence due to Shubnikov–de Haas effect and decreases with increasing alloy composition. Besides the same ratio increases with increasing electron concentration and is in close agreement with the suggested experimental method of determining the Einstein relation in degenerate semiconductors having arbitrary dispersion laws. In addition, the corresponding well‐known results of parabolic semiconductors both in the presence and absence of magnetic field have been obtained from the generalized expressions under certain limiting conditions.

On the diffusivity‐mobility ratio in small‐gap semiconductors in the presence of a strong magnetic field: Theory and suggestion for experimental determination

On the Thermoelectric Power in Superlattices of III–V Semiconductors under Magnetic Quantization

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-Hg1−xCdxTe 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.

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

Analyse de la variation de la masse effective en fonction du nombre quantique magnetique pour les semiconducteurs paraboliques et non paraboliques. Presentation d'un exemple pour le superreseau Ga In PSb/GaAs

On the Effective Electron Mass in Superlattices of III–V Semiconductors in the Presence of a Quantizing Magnetic Field

Analyse du rapport diffusivite-mobilite des electrons, en fonction du dopage et du champ magnetique, en champ magnetique quantifiant et champ electrique croise. Presentation d'un exemple sur GaAs

Influence of Quantizing Magnetic and Crossed Oscillatory Electric Fields on the Einstein Relation in Wide-Gap Semiconductors

An attempt is made to study effective electron mass in quantum well wires of ternary chalcopyrite semiconductors by formulating a new 1D dispersion relation, within the framework of thek·p formalism considering the anisotropies in the band parameters. It is found, taking quantum well wires ofn-CdGeAs2 as an example, that the effective Fermi level mass depends on the subband index due to the combined influence of crystal-field splitting parameter and the anisotropic spinorbit splitting parameters, respectively. The masses increase with increasing carrier degeneracy and decreasing film thickness, respectively. In addition, the well-known results for the corresponding parabolic energy bands have been derived as special cases of the generalized formulations.

A. Ghoshal

Papers

On the Thermoelectric Power in Superlattices of III–V Semiconductors under Magnetic Quantization

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

On the Effective Electron Mass in Superlattices of III–V Semiconductors in the Presence of a Quantizing Magnetic Field

Influence of Quantizing Magnetic and Crossed Oscillatory Electric Fields on the Einstein Relation in Wide-Gap Semiconductors

On the effective electron mass in quantum well wires of ternary chalcopyrite semiconductors