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 σ on metalloid concentration x are derived. In amorphous metal-metalloid alloys the metal-insulator transition (M-I transition) characterized by the transition from σ>0 to σ=0 at temperature $T=0$ at x=xc takes place in the phase separated regime. The M-I transition in S_1-xMₓ alloys is determined by the conduction band (phase A), whereas in N_1-xMₓ, and in many T_1-xMₓ 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 xc are characteristic features for S_1-xMₓ 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-xGeₓ 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 σₘᵢₙ(c*∕6)(e²∕h)(1∕d) and mobility edges at density of states 4c*m∕h²d, 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∕2π is Plancks constant).