THE DIAGRAM TECHNIQUE FOR CALCULATION OF TRANSPORT CONSTANTS OF RANDOM INHOMOGENEOUS MATERIALS .1. THE AC EFFECTIVE CONDUCTIVITY

Diagram methods are applied for evaluating the ac effective conductivity sigma-*(omega) of a disordered semiconductor (e.g., a highly doped compensated semiconductor, a composite, etc.). Expressions for sigma-*(omega) are obtained in a number of approximations - the cumulant approximation, the self-consistent moment approximation, and the effective medium approximation. For a random binary mixture which consists of two materials with conductivities sigma-1 and sigma-2 the dependences of real and imaginary parts of sigma-*(omega) on the frequency omega of the external electric field, volume fraction x of the most conducting material and the ratio of the conductivities sigma-2/sigma-1 are presented for all approximations mentioned. For a metal insulator mixture (sigma-2 = 0) on the onset of percolation the cumulant and effective medium approximations predict the following behaviour of sigma(MI)*(omega): sigma(MI)*(0) approximately (x - x(c))t, sigma(MI)*(omega) approximately omega(s), here t = 1, s = 1/2. The results, obtained for sigma(MI)*(omega) are compared with those of computer simulation in the model of fully penetrating spheres (Balberg and Binenbaum). The cumulant approximation is in good agreement with the computer results.