Disordered electronic systems. II. Phase separation and the metal-insulator transition in metal-metalloid alloys

The electronic transport in the phase separated regime is determined by both the different local band structure in the phases (called phases A and B) and electron redistribution (electron transfer) to the phase with the deeper average potential (phase B). Equations for the dependence of the electronic conductivity sigma on metalloid concentration x are derived. In amorphous metal-metalloid alloys the metal-insulator transition (M-I transition) characterized by the transition from sigma>0 to sigma=0 at temperature T=0 at x=x(c) takes place in the phase separated regime. The M-I transition in S(1-x)M(x) alloys is determined by the conduction band (phase A), whereas in N(1-x)M(x), and in many T(1-x)M(x) alloys, it is determined by the valence band (phase B) (N and T stand for a transition metal with completely and incompletely occupied d band, respectively, S for a simple metal as Al, Ga, In,..., and M for a metalloid element as Si or Ge). (1) Granular structure, (2) rapid decrease of the average metal grain size with increasing x, and (3) relatively small x(c) are characteristic features for S(1-x)M(x) thin films deposited under extreme deposition conditions and are caused by the fact that a considerable part of electrons transferred occupy surface states leading to charged phase boundaries. The fractal structure found in Al(1-x)Ge(x) alloys after annealing is related with the formation of a maximum of phase boundary faces for acceptance of the transferred electrons. For strong scattering in a single phase, there are a minimum metallic conductivity sigma(min)similar or equal to(c(*)/6)(e(2)/h)(1/d) and mobility edges at density of states 4c(*)m/h(2)d, where c(*)=1/4 (d is the average atomic distance. e and m are the elementary charge and effective mass of the electrons, respectively, and h=h/2 pi is Plancks constant).