Abstract
In various degenerate donor-silicon systems, taking into account the effects of donor size and heavy doping and using an effective autocorrelation function for the potential fluctuations expressed in terms of the Heisenberg uncertainty relation and also an expression for the Gaussian average of <img width="32" height="20" src="http://article.sciencepublishinggroup.com/journal/122/1221186/image001.png" />, a ≥ 1 <img width="18" height="20" src="http://article.sciencepublishinggroup.com/journal/122/1221186/image002.png" /> being the kinetic energy of the electron, calculated by the Kane integration method (KIM), we investigated the density of states, the optical absorption coefficient and the electrical conductivity, noting that this average expression calculated by the KIM was found to be equivalent to that obtained by the Feynman path-integral method. Then, those results were expressed in terms of <img width="55" height="20" src="http://article.sciencepublishinggroup.com/journal/122/1221186/image003.png" /> for total electron energy <img width="42" height="20" src="http://article.sciencepublishinggroup.com/journal/122/1221186/image004.png" />, vanished at the conduction-band edge: <img width="42" height="20" src="http://article.sciencepublishinggroup.com/journal/122/1221186/image005.png" />, and for <img width="42" height="20" src="http://article.sciencepublishinggroup.com/journal/122/1221186/image006.png" /> exhibited their exponential tails, going to zero as <img width="120" height="20" src="http://article.sciencepublishinggroup.com/journal/122/1221186/image007.png" />, and presenting the maxima, in good accordance with an asymptotic form for exponential conduction-band tail obtained by Halperin and Lax, using the minimum counting methods. Further, in degenerate d-Si systems at low temperatures, using an expression for the average of <img width="19" height="20" src="http://article.sciencepublishinggroup.com/journal/122/1221186/image008.png" />, p ≥ 3/2, calculated using the Fermi-Dirac distribution function, we determined the mobility, electrical conductivity, resistivity, Hall factor, Hall coefficient, Hall mobility, thermal conductivity, diffusion coefficient, absolute thermoelectric power, Thomson coefficient, Peltier coefficient, Seebeck thermoelectric potential, and finally dimensionless figure of merit, which were also compared with experimental and theoretical results, suggesting a satisfactory description given for our obtained results.
Highlights
Donor-silicon d (a)-Si system at a given temperature T, doped with a given d (a)-density N, assuming that all the impurities are ionized, is the base material of modern semiconductor devices [1,2,3,4,5,6]
In the Appendix A of our recent paper [12], basing on an effective Bohr model, such a compression occurring in various donor (d)-Si systems was investigated, suggesting that the effective dielectric constant, < (" ), decreases with increasing ". This donor size (" )-effect affects the changes in all the energy-band-structure parameters or the electronic properties of various donor-Si systems, expressed in terms of < (" ), as those investigated in our recent paper [12], noting that < (r5) = 11.4
Using the effective autocorrelation function for potential fluctuations W, developed in Eq (B.6) of the Appendix B, expressed in terms of the Heisenberg uncertainty relation given in Eq (B.5), and an expression for the Gaussian average of, 〈 〉Šëì, obtained in Eq (20) by the Kane integration method (KIM), we developed the expressions for density of states, optical absorption coefficient, and electrical conductivity, obtained in various degenerate d-Si systems, being due to the effects of donor-size and heavy doping, as given respectively in Eqs. (36, 49, 72)
Summary
Donor (acceptor)-silicon d (a)-Si system at a given temperature T, doped with a given d (a)-density N, assuming that all the impurities are ionized, is the base material of modern semiconductor devices [1,2,3,4,5,6].
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