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.     

On the gate capacitance of mos structures in N-Channel inversion layers on ternary chalcopyrite semiconductors

An attempt is made to investigate the gate capacitance of MOS structures in n-channel inversion layers on ternary chalcopyrite semiconductors at low temperatures, taking n-channel inversion layers on CdGeAs₂ as examples, under both the weak and strong electric field limits, respectively. We have formulated the gate capacitance on the basis of newly derived 2D electron energy spectra for both the limits by considering the various anisotropies of the band parameters within the framework ofk·p formalism. It has been observed that, the gate capacitance increases with increasing surface electric field in an oscillatory manner and the theoretical results are in good agreement with the experimental observations as reported elsewhere. In addition, the corresponding well-known results for n-channel inversion layers on isotropic parabolic semiconductors are also obtained from the generalized expressions derived under certain limiting conditions.     

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.     

On the oscillatory nature of the Debye screening length in degenerate semiconductors under magnetic quantization

The nature of the magnetic field dependence of the Debye screening length in degenerate semiconductors is shown to be oscillatory under the influence of magnetic quantization.     

Heat of formation of ternary chalcopyrite semiconductors

Heat of formation of I-III-VI₂ and II-IV-V₂ groups of ternary chalcopyrite semiconductors has been calculated using plasma oscillations theory of solids. Two simple relations between plasmon energy and heat of formation have been proposed. One is based on spectroscopic model of Phillips and Van Vechten and other is based on the best-fit data of heat of formation. The calculated values of heat of formation from both the equations are compared with the experimental values and the values reported by earlier workers. A fairly good agreement has been obtained between them.     

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.     

Influence of alloy composition on the diffusivity-mobility ratio in n-channel inversion layers on ternary semiconductors

An expression is derived for the diffusivity-mobility ratio of the carriers in n-channel inversion layers on semiconductors like the ternary compounds which have strongly non-parabolic energy bands. The dependence of the ratio on alloy composition is also studied under the weak-field limit taking n-channel Hg_1–xCd_x.Te as an example.On leave of absence fromthe Department of Physics, Patna University, Patna, India.     

Influence of band non-parabolicity on the oscillatory dependence of the Debye screening length in degenerate semiconductors on magnetic quantization

The Debye screening length in degenerate non-parabolic bands is shown to have an oscillatory dependence on a quantizing magnetic field as in degenerate parabolic bands. The period of oscillations is, however, found to decrease with increasing non-parabolicity which also is observed to have no effect on the amplitude of the same.On leave of absence fromthe Department of Physics, B.N. College, Patna University, Patna 800004.The authors are indebted to Prof. J. N.Bhar for his keen interest in the work.     

TDPAC investigations of the111Cd quadrupole interaction in ternary chalcopyrite semiconductors

The quadrupole interaction at room temperature of¹¹¹Cd in CdSiP₂, CdGeP₂, and CdSnP₂ is investigated by^111mCd-TDPAC. The results are compared with those of former¹¹¹In(¹¹¹Cd) measurements. We observed axially symmetric quadrupole interactions with identical quadrupole coupling constants provided that radiation damage was annealed. This proves that also In probes are positioned at Cd-sites (A-sites) in these ternary compounds.     

Band gap anomaly in ternary chalcopyrite semiconductors,the role of p-d hybridization

Summary The anomalous reductions in the energy band gap of the chalcopyrite semiconductors as compared to their relative binary analogs are estimated quantitatively by using a simple relation that involves quantum defect electronegativity scale and the average principal quantum number. The chemical and the structural contribution to this anomaly is discussed in details and it is shown that the relation can be easily extended to explain the variation in the band gap of some cross-substitutional alloys.

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Riassunto Le anomale riduzioni del gap di energia nei semiconduttori a struttura calcopirite rispetto ai loro analoghi binari sono stimate quantitativamente usando una semplice relazione che implica l’uso della scala delle elettronegatività e il numero quantico principale medio. Il contributo chimico e strutturale a questa anomalia è discusso ed è mostrato che la relazione può essere agevolmente estesa per spiegare la variazione del gap in alcune soluzioni solide.

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Резюме Количественно оцениваются аномальные уменьшения ширины запрещенной зоны в полупроводниках халькопирита, по сравнению с бинарными аналогами. Подробно обсуждается химичекий и структурный вклад в эту аномалию. Показывается, что предложенный подход можно легко обобщить для объяснения изменения ширины запрещенной зоны в некоторых кросс-замещенных сплавах.

     

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

Summary 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.     

Effect of magnetic quantization on the Einstein relation in Kane-type semiconductors

An attempt is made to formulate the Einstein relation for the diffusivity-mobility ratio of the carriers in degenerate semiconductors having Kane-type energy bands in the presence of a quantizing magnetic field, taking degenerate n-InAs as an example. It is found on the basis of the three-band Kane model, which is the most valid model for n-InAs, that the same ratio oscillates with changing magnetic field only under degenerate conditions and remains unaffected otherwise. The corresponding results for parabolic semiconductors are also obtained from the expressions derived.     

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.     

A simplified analysis of the electronic contribution to the elastic constants in ultrathin films of stressed semiconductors under magnetic quantization

An attempt is made to study the electronic contribution to the second- and third-order elastic constants in ultrathin films of strained semiconductors under magnetic quantization in the presence of broadening on the basis of a newly formulated electron dispersion law. It is found, taking stressed n-InSb as an example, that the carrier contribution to the second- and third-order elastic constants oscillates with increasing carrier degeneracy and decreasing film thickness, respectively, in different manners and the stress enhances their numerical values. A relationship between the said contributions and the thermoelectric power has been derived for quantum confined semiconductors having arbitrary dispersion laws and our analysis agrees quite well with the suggested relationship.     

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.     

Effect of a quantizing magnetic field on the diffusivity-mobility ratio of the carriers in n-channel inversion layers on small gap semiconductors

In the present work, an attempt is made to derive expressions for the diffusivity-mobility ratios of the carriers in n-channel inversion layers on small-gap semiconductors under both weak and strong electric field limits in the presence of a quantizing magnetic field. It is found, taking n-channel layers on p-type InSb as examples, that the ratios show spiky oscillations with charging magnetic field, the periods of oscillations being independent of the degree of band non-parabolicity.On leave of absence fromthe Department of Physics, University of Patna, Patna, India.The authors are indebted to Professor B. R. Nag for helpful discussion.     

On the diffusivity-mobility ratio of the carriers in n-channel inversion layers on ternaryChalcopyrite semiconductors

An attempt is made to study the Einstein relations for the diffusivity-mobility ratios of the carriers in n-channel inversion layers on ternary chalcopyrite semiconductors under both weak and strong electric field limits, taking n-channel inversion layers on CdGeAs₂ as an example. It is found, on the basis of newly derived 2D E-k_s dispersion relations of the conduction electrons for both the limits by considering the various types of anisotropies in the energy band, that the ratios increase with increasing surface electric fields for both the limits and the theoretical results are in qualitative agreement with the suggested experimental method of determining the Einstein relation in degenerate semiconductors having arbitrary dispersion law. The corresponding well-known results for isotropic twoband Kane model are also obtained from the expressions derived.     

Relationship between the thermal expansion coefficient, plasmon energy, and bond length of ternary chalcopyrite semiconductors

A simple relation between the average bond length and plasmon energy, that is, d=15.30(?ω_p)^−2/3, has been proposed for A^IIB^IVC^V₂ and A^IB^IIIC^VI₂ chalcopyrite semiconductors. The average linear thermal expansion coefficient (α_L) of these semiconductors has been calculated using plasmon energy data. The linear expansion coefficients (α_a) and (α_c) of the lattice parameters a and c, respectively, have also been calculated. The calculated values of d, α_L, α_a and α_c have been compared with the experimental values and the values reported by different workers. A fairly good agreement has been obtained between them.     

Two-valley model for studying the low temperature phases inn-type inversion layers of semiconductors

The low temperature phases of a two-valley model forn-type inversion layers are studied. If the coupling constants are in a certain range charge-density waves exist below a transition temperatureT _c. For reasonable values of the coupling constantsT _c is around 30 °K.