Critical behavior of the zero-temperature conductivity in compensated silicon, Si:(P,B)

Abstract

The zero-temperature electrical conductivity, σ(0), of samples of Si:(P,B) has been obtained by extrapolation from measurements at temperatures of 100 mK and above. The compensation ratio K, defined as the ratio of acceptor to donor concentrations, ranges from 0.2 to 0.5. Naturally occurring gradients in the electron concentration n and values of K in melt-grown crystals provide sets of samples whose properties vary smoothly through the metal-insulator transition. Following a single-parameter scaling theory of localization, we analyze our data in terms of a relation σ(0)=${\sigma }_0$(n/$n_c$ ${\mathrm{-}1)}^{\mu }$. Alternatively, we use the experimental variable σ(296), the room-temperature conductivity, in place of the electron concentration n. Values of the conductivity exponent μ for three crystals range from 0.79 to 0.91, with estimated errors of ±0.08. No clear evidence for a dependence of μ on the compensation ratio K is found in the range of K covered by our samples.