The metal-semiconductor transition in amorphous Si_1-x Cr_x films: phenomenological model for the metallic region

Abstract

A detailed phenomenological re-analysis of previously published conductivity data, σ(T, x), is presented. It was shown in [1] that the cusp-like low-temperature contribution can be described by$\bar \beta (x) \cdot T^p$ wherep=0.19±0.03. Starting from this result, two furtherT dependent contributions are separated: The high-temperature region is dominated by a positive contribution σ_ht (T, x), which is approximately independent ofx, nearly linear inT above 100 K and nearly quadratic inT below 30 K. ForT≲ 4 K, there is a small deviation, increasing withT, from the superposition of the above mechanisms. The relation between$\bar \beta$, being negative, and theT independent part,$\bar \alpha$, exhibits a singularity,$\bar \beta \sim (\bar \alpha - \bar \alpha _0 )^\vartheta$ where$\bar \alpha _0 = 270 \pm 50 \Omega ^{ - 1} cm^{ - 1}$ andϑ=0.68±0.05 −(p−0.19). This singularity should be related to the metal-semiconductor transition, taking place atT _c ≈0.14. The quantity$\bar \alpha _0$ should be interpreted as minimum metallic conductivity. The limitingT dependences asx→x _c +0 agrees quantitatively with that one obtained previously for the activated region,x→x _c −0. Extrapolation of the phenomenological model obtained leads to the hypothesis that the interplay of$\bar \beta \cdot T^p$ and σ_ht could be the main origin of the temperature coefficient changing its sign in the Mooijregion, at σ _tc=0. The model enables several trend predictions concerning the value of σ _tc=0.