High-Field Effects in Degenerate Nonparabolic Semiconductors: Collision Integral and Isotropic Distribution Function

Physica Status Solidi (b)

1971

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A solution of the kinetic equation for the piezoelectric mode of electron-lattice interaction has been obtained by retaining the higher-order terms in the orthonormal expansion of the distribution function a t high electric fields. It is seen that at low temperatures and moderately high elcctric fields, the inclusion of the higher-order terms significantly changes the isotropic part of the distribution function of electrons in piezoelectric semiconductors with low electron dcnsities (for which thc analysis is relevant).Eine Losung dcr kinetischen Gleichung fur die piezoelektrischc Mode der Elektron-GitterWechselwirkung wurde durch Beriicksichtigung der Terme hijherer Ordnung in der orthonormalen Entwicklung der Verteilungsfunktion bei hohen elektrischen Feldern erhalten. Es wird gezeigt, daS bci niedrigen Tempcraturen und nicht zu hohcn elektrischen E'eldern der EinschluB hoherer Terme den isotropen Anteil der Verteilungsfunktion der Elektronen in piezoelektrischcn Halbleitern mit niedriger Elektronendichte (fur die die Analyse relevant ist) wesentlich iindert.

Section: Theoretical Formulation and Discussionmentioning

confidence: 99%

Validity of the electron energy distribution function for piezoelectric scattering at high electric fields

Sodha

Physica Status Solidi (b)

1971

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Distribution function of degenerate hot carriers in nonparabolic semiconductors: Electromagnetic heating

Sodha

1971

Phys. Stat. Sol. (a)

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Expressions for the collision integrals corresponding to various modes of carrier–lattice interaction for a few nonparabolic semiconductors (viz. InSb, InAs, etc.), using more accurate carrier wave functions which are assumed to be unaffected in form by the application of a strong radiation field, have been derived for different cases of interest; the realistic nonparabolic energy band structure for an arbitrary degree of degeneracy of transport carriers has been taken into account. These expressions are then used to obtain the isotropic part of the carrier energy distribution function in the presence of a strong electromagnetic field arbitrarily oriented to a steady magnetic field. It is shown that the distribution functions not only depend on the electromagnetic field strength but also upon how the electromagnetic energy is split into its component waves. The normalization of distribution functions for piezoelectric and polar optical scatterings for any finite value of the applied electromagnetic field strength has been discussed in terms of the nonparabolicity of energy bands, and the significant changes owing to the use of more accurate carrier wave functions rather than plane waves are clearly brought out. The present investigation can directly be used to study the effect of electromagnetic heating on various kinetic effects in semiconductors and may thus provide new additional means for obtaining information about semiconductor parameters.

Non‐normalizability of the hot electron distribution function for piezoelectric scattering

Physica Status Solidi (b)

1972

Piezoelectric semiconductors have recently gained a new importance due to the various kinds of acousto-electric instabilities associated with them at high electric fields (1) thus lending significance to the study of the distribution function before the onset of these instabilities. Laikhtman (2) first derived an expression for the distribution function of electrons in a parabolic conduction band assuming the piezoelectric mode of electron-lattice interaction to be the only scattering mechanism.The expression obtained by him can be written a s follows:where C is the electron energy, -. A(E,TWe, however, wish to point out in the present communication that the distribution function given by equation (1) is inherently unstable at all electric fields, i.e. for 1 physica (b)