*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*

**DOI:**10.54647/physics14498 74 Downloads 4225 Views

**Author(s)**

**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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