New Critical Density in Metal-Insulator Transition, obtained in n(p)- Type Degenerate [ InAs1-xPx(Sbx), GaTe1-xAsx(Sbx,Px), CdTe1-xSx(Sex)]-Crystalline Alloys, 0≤x≤1, being just That of Carriers Localized in Exponential

Abstract

By basing on the same physical model and treatment method, as used in our recent works [1, 2], for  GaAs1-xTex(Sbx,Px) -crystalline alloys, 0≤x≤1 , we will investigate the critical impurity density in the metal-insulator transition (MIT), obtained now in n(p)-type degenerate X(x)=[InAs1-xPx(Sbx), GaTe1-xAsx(Sbx,Px), CdTe1-xSx(Sex)]- crystalline alloys, being due to the effects of the size of donor (acceptor) d(a)-radius, rd(a), and the x- concentration, assuming that all the impurities are ionized even at T=0 K. In such n(p)-type degenerate X(x)= -crystalline alloys, we will determine: (i)-the critical impurity density NCDn(CDp)(rd(a), x) in the MIT, as given in Eq. (8), by using an empirical Mott parameter  Mn(p)=0.25, and (ii)-the density of electrons (holes) localized in the exponential conduction (valence)-band tails (EBT), NEBTCDn(CDp)(rd(a),x), as given in Eq. (26), by using our empirical Heisenberg parameter, Hn(p)=0.47137, as given in Eq. (15), suggesting that: for given rd(a) and x,  NEBTCDn(CDp)(rd(a),x)=NCDn(CDp)(rd(a),x)  obtained with a precision of the order of  2.91x10-7, as observed in Tables 2-8. In other words, such the critical d(a)-density NCDn(CDp)(rd(a),x) is just the density of electrons (holes) localized in the EBT, NEBTCDn(CDp)(rd(a),x). So, if denoting the total impurity density by N, the effective density of free electrons (holes), N*  given in the parabolic conduction (valence) band of the n(p)-type degenerate - crystalline alloy, can thus be defined by: N*(N,rd(a),x)=N-NCDn(NDp)=N-NEBTCDn(CDp) , as that given in compensated crystals, needing to determine various optical, electrical, and thermoelectric properties in such n(p)-type degenerate X(x)-crystalline alloys, as those studied in n(p)-type degenerate crystals [3-7].