Accurate expressions for optical coefficients, given in n(p)-type degenerate InP-crystals, due to the impurity-size effect, and obtained from an improved Forouhi-Bloomer parameterization model (FB-PM)

Volume 8, Issue 3, June 2023     |     PP. 223-247      |     PDF (1418 K)    |     Pub. Date: June 12, 2023
DOI: 10.54647/physics140553    72 Downloads     1972 Views  


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.

In the n(p)-type degenerate InP-crystals, at low temperature T and high d(a)-density N, our expression for the static dielectric constant, \varepsilon\left(r_{d\left(a\right)}\right), expressed as a function of the donor (acceptor) radius, r_{d\left(a\right)}, and determined by using an effective Bohr model, as that investigated in [1,2], suggests that, for an increasing r_{d\left(a\right)}, due to such the impurity size effect, \varepsilon\left(r_{d\left(a\right)}\right) decreases, affecting strongly the critical d(a)-density in the metal-insulator transition (MIT), N_{CDn(CDp)}(r_{d(a)}), determined by Eq. (3), and its values are reported in Table 1, and also our accurate expressions for optical coefficients, obtained in Equations (24, 25, 28, 29), and their numerical results are given in Tables 2-6. Furthermore, one notes that, as observed in Table 3c, our obtained results of those optical coefficients are found to be more accurate than the corresponding ones, obtained from the FB-PM [11], suggesting thus that our present model, used here to study the optical properties of the n(p)-type degenerate InP-crystals, is a good improved FB-PM, as observed in Table 3c.

Effects of the impurity-size and heavy doping; effective autocorrelation function for potential fluctuations; optical coefficients; critical photon energy

Cite this paper
H. Van Cong, Accurate expressions for optical coefficients, given in n(p)-type degenerate InP-crystals, due to the impurity-size effect, and obtained from an improved Forouhi-Bloomer parameterization model (FB-PM) , SCIREA Journal of Physics. Volume 8, Issue 3, June 2023 | PP. 223-247. 10.54647/physics140553


[ 1 ] 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 J. Phys., vol.7, pp. 221-234 (2022).
[ 2 ] H. Van Cong, “ Same maximum figure of merit ZT(=1), due to effects of impurity size and heavy doping, obtained in the n(p)-type degenerate InP-crystal (), at same reduced Fermi energy and same minimum (maximum) Seebeck coefficient , at which same, “SCIREA J. Phys., vol.8, pp. 91-114 (2023).
[ 3 ] 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); “Accurate expressions for optical coefficients, due to the impurity-size effect, and obtained in n(p)-type degenerate Si crystals, taking into account their correct asymptotic behavior, as the photon energy E (),” SCIREA J. Phys., vol.8, pp. 172-197 (2023).
[ 4 ] H. Van Cong et al., “A simple accurate expression of the reduced Fermi energy for any reduced carrier density. J. Appl. Phys., vol. 73, pp. 1545-15463, 1993; H. Van Cong and B. Doan Khanh, “Simple accurate general expression of the Fermi-Dirac integral and for j> -1,” Solid-State Electron., vol. 35, pp. 949-951(1992); H. Van Cong, “New series representation of Fermi-Dirac integral for arbitrary j> -1, and its effect on for integer j,” Solid-State Electron., vol. 34, pp. 489-492 (1991).
[ 5 ] C. Kittel, “Introduction to Solid State Physics, pp. 84-100. Wiley, New York (1976).
[ 6 ] M. A. Green, “Intrinsic concentration, effective density of states, and effective mass in silicon,” J. Appl. Phys., vol. 67, 2944-2954 (1990).
[ 7 ] H. Van Cong et al., “Optical bandgap in various impurity-Si systems from the metal-insulator transition study,” Physica B, vol. 436, pp. 130-139, 2014; H. Stupp et al., Phys. Rev. Lett., vol. 71, p. 2634 (1993); P. Dai et al., Phys. Rev. B, vol. 45, p. 3984 (1992).
[ 8 ] J. Wagner and J. A. del Alamo, J. Appl. Phys., vol. 63, 425-429 (1988).
[ 9 ] D. E. Aspnes, A. A. Studna, “Dielectric functions and optical parameters of Si, Se, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV”, Phys. Rev. B, vol. 27, 985-1009 (1983).
[ 10 ] L. Ding, et al., “Optical properties of silicon nanocrystals embedded in a matrix”, Phys. Rev. B, vol. 72, 125419 (2005).
[ 11 ] A. R. Forouhi, I. Bloomer, “Optical properties of crystalline semiconductors and dielectrics”, Phys. Rev., vol. 38, 1865-1874 (1988).
[ 12 ] G. E. Jr. Jellison, F. A. Modine, “Parameterization of the optical functions of amorphous materials in the inter-band region”, Appl. Phys. Lett., vol. 69, 371-373 (1996).