*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 67 Downloads 2137 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

**References**

[ 1 ] | N. F. Mott, “Metal-Insulator Transitions,” London: Taylor and Francis, 1974. |

[ 2 ] | A. Pergament, “Metal-insulator transition: the Mott criterion and coherence length,” J. Phys.: Condense Matter, vol. 15, pp. 3217-3223, 2003. |

[ 3 ] | P. P. Edwards et al., “The metal-insulator transition: a perspective,” Phil. Trans. R. Soc. London A , vol. 356, pp. 5-22, 1998. |

[ 4 ] | C. Kittel, “Introduction to Solid State Physics, pp. 84-100. Wiley, New York (1976). |

[ 5 ] | H. Van Cong et al., “Size effect on different impurity levels in semiconductors,” Solid State Communications, vol. 49, pp. 697-699, 1984; H. Van Cong, “Effects of impurity size and heavy doping on energy-band-structure parameters of various impurity-Si systems,” Physica B, vol. 487, pp. 90-101, 2016. |

[ 6 ] | H. Van Cong, and G. Debiais, “A simple accurate expression of the reduced Fermi energy for any reduced carrier density. J. Appl. Phys., vol. 73, pp. 1545-15463, 1993. |

[ 7 ] | H. Van Cong, “Effects of donor size and heavy doping on optical, electrical and thermoelectric properties of various degenerate donor-silicon systems at low temperatures,” American Journal of Modern Physics, vol. 7, pp. 136-165, 2018; H. Van Cong et al., “28.68% (29.87%)- Limiting Highest Efficiencies obtained in Crystalline Silicon Junction Solar Cells at 300K, Due to the Effects of Heavy (Low) Doping and Impurity Size, “SCIREA J. Phys., vol.7, pp. 160-179, 2022; H. Van Cong et al., “30.76% (42.73%)- Limiting Highest Efficiencies obtained in Crystalline GaAs Junction Solar Cells at 300K, Due to the Effects of Heavy (Low) Doping and Impurity Size, “SCIREA J. Phys., vo.7, pp. 180-199, 2022. |

[ 8 ] | M. A. Green, “Intrinsic concentration, effective density of states, and effective mass in silicon,” J. Appl. Phys., vol. 67, 2944-2954, 1990. |

[ 9 ] | J. Wagner and J. A. del Alamo, J. Appl. Phys., vol. 63, 425-429, 1988. |