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World Journal of Engineering Research and Technology

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An Official Publication of Society for Advance Healthcare Research (Reg. No. : 01/01/01/31674/16)

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Abstract

NEW CRITICAL IMPURITY DENSITY IN METAL-INSULATOR TRANSITION, OBTAINED IN N(P)- TYPE DEGENERATE HELIUM-FERMI LIQUID, BEING JUST THAT OF THE CARIERS, LOCALIZED IN EXPONENTIAL BAND TAILS. (IX)

Prof. Dr. Huynh Van Cong*

ABSTRACT

By basing on the same physical model and treatment method, as used in our recent work[1], we will investigate the critical impurity densities in the metal-insulator transition (MIT), obtained in n(p)-type degenerate Helium-Fermi Liquid (He-FL), being due to the effects of the size of donor (acceptor) d(a)-radius, r_(d(a)), and the high d(a)-density, N, assuming that all the impurities are ionized even at T=0 K. In such the n(p)-type He-FL, some important remarks are obtained and discussed in the following.(i)-In Tables 1a-1d in Appendix 1, the numerical results of the isothermal bulk modulus, B_(do(ao)), the pressure variation, [∆p(r_(d(a)))]_(n(p)), and the strain-energy variation, [∆σ(r_(d(a)))]_(n(p)), are obtained and computed, using Equations (2, 3). It should be noted that, for a given r_(d(a)), those increase with increasing reduced effective mass, m_(c(v))/m_o , in good agreement with Landau’s remarks on the Fermi Liquid.[2] (ii)-In Tables 2a-5d in Appendix1, the numerical results of the critical impurity density N_(CDn(CDp)) (r_(d(a))) in the metal-insulator transition (MIT), as that given in Eq. (8), by using an empirical Mott parameter M_(n(p))=0.25, are obtained and discussed. (iii)-Further, also in Tables 2a-5d in Appendix 1, for a given〖 r〗_d(a) , the numerical results of the density of electrons (holes) localized in the exponential conduction (valence)-band tails (EBT), N_CDn(CDp)^EBT (〖 r〗_d(a) ,x), are obtained, using Eq. (26), and taking the empirical Heisenberg parameter, H_(n(p))=0.47137, as that given in Eq. (15), giving raise to: N_CDn(CDp)^EBT (〖 r〗_d(a) )≅N_(CDn(CDp)) (r_(d(a))), with a precision of the order of 1.6859×〖10〗^(-6), as that given in Table 3a in Appendix 1. In other words, such the critical d(a)-density N_CDn(NDp) (r_(d(a)))), is just the density of electrons (holes) localized in the EBT, N_CDn(CDp)^EBT (〖 r〗_(d(a))), respectively.

[Full Text Article] [Download Certificate] https://doi.org/10.5281/zenodo.23038554