New dielectric constant, due to the impurity size effect, and determined by an effective Bohr model, affecting strongly the Mott criterion in the metal-insulator transition and the optical band gap in degenerate (Si, GaAs, InP)-semiconductors

H. Van Cong, Université de Perpignan Via Domitia, Laboratoire de Mathématiques et Physique (LAMPS), EA 4217, Département de Physique, 52, Avenue Paul Alduy, F-66 860 Perpignan, France.

Abstract
In the n(p)-type degenerate semiconductors, our expression for the relative static dielectric constant, \varepsilon\left(r_{d\left(a\right)}\right), is determined by an effective Bohr model, r_{d\left(a\right)} being the donor (acceptor) d(a)-radius, suggesting that, for an increasing r_{d\left(a\right)}, both \varepsilon\left(r_{d\left(a\right)}\right) and the effective Bohr radius a_B\left(r_{d\left(a\right)}\right), due to such the impurity size effect, decrease (\searrow), according to the increase (\nearrow) in: (i)the effective d(a)-ionization energy E_{d(a)}\left(r_{d\left(a\right)}\right) in absolutes values, (ii) the effective band gap E_{gn(gp)}\left(r_{d\left(a\right)}\right), and also (iii) the critical density N_{CDn(CDp)}\left(r_{d(a)},\ \ 0.25\ley\le1\right) in the MIT, as those showed in Tables 2-4, for the n(p)-type (Si, GaAs, InP)-semiconductors, in which the empirical parameter y has been chosen as: y=0.25 and 0.271. One notes here that y=0.25 was given in the Mott criterion: a_B\timesN_{CD}^{1/3}\approxy=0.25. Further, if denoting the d(a)-density by N, the physical condition given for such degenerate semiconductors (or for the metallic phase) is found to be given by: N\geqN_{CDn(CDp)}. Then, in such the important physical condition, our numerical results of optical band gap (OBG), due to the effects of impurity size and heavy doping, are also investigated and given in Tables 6-8.In summary, our new expression for \varepsilon\left(r_{d\left(a\right)}\right), due to such an impurity size effect, strongly affects a_B\left(r_{d\left(a\right)}\right), N_{CDn(CDp)}\left(r_{d(a)},\ \ \ y\right), and the OBG, obtained in the n(p)-type (Si, GaAs, InP)- degenerate semiconductors.

Keywords
Keywords: effects of impurity size and heavy doping; degenerate semiconductors; static dielectric constant; critical density in metal-insulator transition; optical band gap

Cite this paper
H. Van Cong, New dielectric constant, due to the impurity size effect, and determined by an effective Bohr model, affecting strongly the Mott criterion in the metal-insulator transition and the optical band gap in degenerate (Si, GaAs, InP)-semiconductors , SCIREA Journal of Physics. Volume 7, Issue 5, October 2022 | PP. 221-234. 10.54647/physics14498

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