Possible solution of the conductivity exponent puzzle for the metal-insulator transition in heavily doped uncompensated semiconductors

Abstract

The electrical conductivity \ensuremath{\sigma} (extrapolated to T=0) of uncompensated Si:P indicates a crossover as a function of P concentration N at ${\mathit{N}}_{\mathrm{cr}}$ slightly above the metal-insulator transition at ${\mathit{N}}_{\mathit{c}}$. For N>${\mathit{N}}_{\mathrm{cr}}$ the exponent of \ensuremath{\sigma}\ensuremath{\sim}(N-${\mathit{N}}_{\mathit{c}}$${)}^{\mathrm{\ensuremath{\mu}}}$ is \ensuremath{\mu}\ensuremath{\approxeq}0.64, while \ensuremath{\mu}\ensuremath{\approxeq}1.3 for ${\mathit{N}}_{\mathit{c}}$N${\mathit{N}}_{\mathrm{cr}}$. At ${\mathit{N}}_{\mathrm{cr}}$ d\ensuremath{\sigma}/dT changes sign from negative for N>${\mathit{N}}_{\mathrm{cr}}$ to positive for N${\mathit{N}}_{\mathrm{cr}}$. $sigma--- in a magnetic field also yields \ensuremath{\mu}\ensuremath{\approxeq}1. The apparent discrepancy between uncompensated and compensated semiconductors is traced back to a difference in the (nonuniversal) width of the critical region.