Kamakhya Prasad Ghatak

Simple theory of the optical absorption coefficient in nonparabolic semiconductors

A simple theory is developed of the optical absorption coefficient (OAC) in nonparabolic semiconductors on the basis of the three-band model of Kane, by considering the wave-vector (k) dependence of the optical matrix element. It has been found that the OAC is proportional to [(ℏω)2−Eg2]1/2 (ℏω and Eg are the energy of the incident radiation and the bandgap, respectively) instead of [(ℏω)−Eg]1/2, the conventional form. It has been demonstrated, by taking n-InAs, n-InSb, Hg1−xCdxTe, and In1−xGaxAs1−yP1−y lattice matched to InP as examples, that the OAC increases with increasing photon energy and the value of the same coefficient in the three band model of Kane is greater than that in parabolic energy bands in all the cases. The well-known result for wide gap materials having parabolic energy bands has also been obtained from our generalized formulation under certain limiting condition.

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

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.

Simple theory of the interband optical absorption in an external electric field for optoelectronic materials

We study theoretically the interband optical-absorption coefficient (OAC) of optoelectronic materials within the framework of the three-band model of Kane [J. Phys. Chem. Solids 12, 181 (1959)] in the presence of an external electric field for modified photon energy (ℏω1) below and above the band gap (Eg), respectively. The optical matrix element depends on the electron wave vector k and this practical aspect has been incorporated in the present analysis. It has been found, taking InAs, InSb, Hg1−xCdxTe, and In1−xGaxAsyP1−y lattice matched to InP as examples of optoelectronic compounds for numerical computations, that for modified photon energies below the band gap, the OAC exhibits an exponential fall off with the electric field and the photon energy, respectively. For the opposite inequality, the OAC oscillates with the modified photon energy without the consideration of the Wannier-Stark levels, which generally exist in a band due to the presence of an external electric field. In both cases, the OAC ex...

Thermoelectric power in carbon nanotubes and quantum wires of nonlinear optical, optoelectronic, and related materials under strong magnetic field: Simplified theory and relative comparison

We study thermoelectric power under strong magnetic field (TPM) in carbon nanotubes (CNTs) and quantum wires (QWs) of nonlinear optical, optoelectronic, and related materials. The corresponding results for QWs of III-V, ternary, and quaternary compounds form a special case of our generalized analysis. The TPM has also been investigated in QWs of II-VI, IV-VI, stressed materials, n-GaP, p-PtSb2, n-GaSb, and bismuth on the basis of the appropriate carrier dispersion laws in the respective cases. It has been found, taking QWs of n-CdGeAs2, n-Cd3As2, n-InAs, n-InSb, n-GaAs, n-Hg1?xCdxTe, n-In1?xGaxAsyP1?y lattice-matched to InP, p-CdS, n-PbTe, n-PbSnTe, n-Pb1?xSnxSe, stressed n-InSb, n-GaP, p-PtSb2, n-GaSb, and bismuth as examples, that the respective TPM in the QWs of the aforementioned materials exhibits increasing quantum steps with the decreasing electron statistics with different numerical values, and the nature of the variations are totally band-structure-dependent. In CNTs, the TPM exhibits periodic oscillations with decreasing amplitudes for increasing electron statistics, and its nature is radically different as compared with the corresponding TPM of QWs since they depend exclusively on the respective band structures emphasizing the different signatures of the two entirely different one-dimensional nanostructured systems in various cases. The well-known expression of the TPM for wide gap materials has been obtained as a special case under certain limiting conditions, and this compatibility is an indirect test for our generalized formalism. In addition, we have suggested the experimental methods of determining the Einstein relation for the diffusivity-mobility ratio and the carrier contribution to the elastic constants for materials having arbitrary dispersion laws.

Influence of quantum confinement on the carrier contribution to the elastic constants in quantum confined heavily doped non-linear optical and optoelectronic materials: simplified theory and the suggestion for experimental determination

In this paper we study the carrier contribution to elastic constants in quantum confined heavily doped non-linear optical compounds on the basis of a newly formulated electron dispersion law taking into account the anisotropies of the effective electron masses and spin orbit splitting constants together with the proper inclusion of the crystal field splitting in the Hamiltonian within the framework of k.p formalism. All the results of heavily doped three, and two models of Kane for heavily doped III-V materials form special cases of our generalized analysis. It has been found, taking different heavily doped quantum confined materials that, the carrier contribution to the elastic constants increases with increase in electron statistics and decrease in film thickness in ladder like manners for all types of quantum confinements with different numerical values which are totally dependent on the energy band constants. The said contribution is greatest in quantum dots and least in quantum wells together with the fact the heavy doping enhances the said contributions for all types of quantum confined materials. We have suggested an experimental method of determining the carrier contribution to the elastic constants in nanostructured materials having arbitrary band structures.

Influence of light on the debye screening length in III-V, ternary, and quaternary materials

We study the electron energy spectrum and the Debye screening length (DSL) for III–V, ternary, and quaternary materials 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 in the presence of external photoexcitation. 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 DSL decreases with the increase in electron concentration, intensity, and wavelength, respectively in various manners. The strong dependence of the DSL on both light intensity and wavelength reflects the direct signature of light waves which is in contrast as compared with the corresponding bulk specimens of the said materials in the absence of external photoexcitation. The rate of change is totally band structure dependent and is significa...

The carrier contribution to the elastic constants in small-gap materials

We present a simple theoretical analysis of the carrier contribution to the second and third order elastic constants in nonparabolic materials on the basis of an electron dispersion law by taking into account various anisotropies of the energy band structure within the framework of k⋅p formalism. It is found that the carrier contributions to the elastic constants in n-Cd3As2, InSb, InAs, GaAs, Hg1−xCdxTe, and lattice matched In1−xGaxAsyP1−y increase with the increase of carrier degeneracy in different manners which, depend on the material parameters and band structure. A relationship between the said contributions and the thermoelectric power has been derived for materials obeying arbitrary dispersion laws in the presence of a classically large magnetic field. Our analysis is based on the derivation of a more generalized band structure of the materials which agrees well with the relationship suggested. It is also observed that the second and third order elastic constants increase with the decrease of allo...

Effective electron mass in low-dimensional semiconductors

Part I: Influence of Light Waves on the Effective Electron Mass (EEM) in Optoelectronic Semiconductors.- Part II: Influence of Quantum Confinement on the EEM in Non-Parabolic Semiconductors.- Part III: The EEM in Quantum Confined Superlattices of Non- Parabolic Semiconductors.- Part IV: Influence of Intense Electric Field on the EEM in Optoelectronic Semiconductors.

The Einstein relation in quantum wires of III-V, ternary, and quaternary materials in the presence of light waves: Simplified theory, relative comparison, and suggestion for experimental determination

We study the Einstein relation for the diffusivity to mobility ratio (DMR) in quantum wires (QWs) of III-V, ternary, and quaternary materials in the presence of light waves, whose unperturbed energy band structures are defined by the three band model of Kane. It has been found, taking n-InAs, n-InSb, n-Hg1?xCdxTe, n-In1?xGaxAsyP1?y lattice matched to InP as examples, that the respective DMRs exhibit decreasing quantum step dependence with the increasing film thickness, decreasing electron statistics, increasing light intensity and wavelength, with different numerical values. The nature of the variations is totally band structure dependent and is influenced by the presence of the different energy band constants. The strong dependence of the DMR on both the light intensity and the wavelength reflects the direct signature of the light waves which is in contrast as compared to the corresponding QWs of the said materials in the absence of photoexcitation. The classical equation of the DMR in the absence of any field has been obtained as a special case of the present analysis under certain limiting conditions and this is the indirect test of the generalized formalism. We have suggested an experimental method of determining the DMR in QWs of degenerate materials having arbitrary dispersion laws and our results find six applications in the field of quantum effect devices.

On the carrier contribution to the elastic constants in ultrathin films of IV-VI compounds in the presence of a parallel magnetic field

We study the carrier contribution to the elastic constants in ultrathin films of IV-VI compounds in the presence of a parallel magnetic field on the basis of a new 2D carrier dispersion law. It is found, taking ultrathin films of PbS, PbSe and PbTe as examples, that the carrier contribution to the second and third order elastic constants increases with decreasing film thickness in various oscillatory manners. The magnetic field and the ultrathin structure enhance the numerical values of the same contribution. We have suggested an experimental method of determining the said contribution in ultrathin materials having arbitrary dispersion laws.