Inhomogeneity and the metal-insulator transition for disordered systems

The effect of both macroscopic stress inhomogeneity and doping inhomogeneity on the critical behavior of the conductivity in the vicinity of the metal-insulator transition are calculated. For the uniaxial stress case the inhomogeneity is calculated from the bending deflection d(z) of a column under compression. It is the transverse variation in doping or stress S that can produce a substantial increase in the scaling exponent t of the T-->0 conductivity and change the critical stress S-c to an apparent critical stress S-c(*). It is demonstrated the calculated results can explain the experimental results of uniaxial stress experiments for Si:P and Si:B. In these cases when sigma(S,T-->0) is sufficiently large sigma(S,T=0)proportional to\S/S-c-1\(t) with tsimilar to1/2, but when sigma(S,T=0) is sufficiently small sigma(S,T=0)proportional to\S/S-c(*)-1\(t)(eff) with t(eff) between 1 and 1.6 dependent on geometrical factors. For the doping inhomogeneity case both uncorrelated dopant density variations and correlated linear dopant variations are considered. Correlated cases can either increase or decrease n(c) depending on the geometry of the doping gradients. An uncorrelated broad distribution can mask scaling behavior with an exponent t=1/2 and change the exponent to tsimilar to1. This suggests that the microscopic physics may be the same for crystalline doped semiconductors Si:P, Ge:Ga, and the amorphous semiconductor-metal cases and that the difference in scaling exponents of the conductivity results from the breadth and shape of the distribution P(n(r)-n). A large width of P(n(r)-n) for a-S1-xMx alloys helps explain why the conductivity prefactors are comparable to Si:P; etc., even though the electron density is 10(3) larger.