A realistic analysis of the phonon growth characteristics in a degenerate semiconductor using a simplified model of Fermi-Dirac distribution

• Published in: The Journal of physics and chemistry of solids 2017-01, Vol.100, p.9-13
• Main Authors: Basu, A., Das, B., Middya, T.R., Bhattacharya, D.P.
• Format: Article
• Language: English
• Subjects: Degenerate semiconductor; Low temperature; Model distribution; Phonon growth
• ISSN: 0022-3697; 1879-2553
• DOI: 10.1016/j.jpcs.2016.09.004

The phonon growth characteristic in a degenerate semiconductor has been calculated under the condition of low temperature. If the lattice temperature is high, the energy of the intravalley acoustic phonon is negligibly small compared to the average thermal energy of the electrons. Hence one can traditionally assume the electron-phonon collisions to be elastic and approximate the Bose-Einstein (B.E.) distribution for the phonons by the simple equipartition law. However, in the present analysis at the low lattice temperatures, the interaction of the non equilibrium electrons with the acoustic phonons becomes inelastic and the simple equipartition law for the phonon distribution is not valid. Hence the analysis is made taking into account the inelastic collisions and the complete form of the B.E. distribution. The high-field distribution function of the carriers given by Fermi-Dirac (F.D.) function at the field dependent carrier temperature, has been approximated by a well tested model that apparently overcomes the intrinsic problem of correct evaluation of the integrals involving the product and powers of the Fermi function. Hence the results thus obtained are more reliable compared to the rough estimation that one may obtain from using the exact F.D. function, but taking recourse to some over simplified approximations. •Phonon growth by a degenerate ensemble of non-equilibrium electrons is analyzed.•Some of the features of low lattice temperature are considered.•Fermi-Dirac distribution for the carriers is approximated by a well tested model.•The model yields analytical results without using oversimplified approximations.•The results are more reliable and serve as useful data for device technologists.