Dc conductivity of arsenic-doped silicon near the metal-insulator transition.

Abstract

dc conductivity measurements have been made on uncompensated Si:As in the concentration range 6.85\ifmmode\times\else\texttimes\fi{}${10}^{18}$32.8\ifmmode\times\else\texttimes\fi{}1${0}^{18}$R ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ for 0.5T77 K, although three samples were studied in a dilution refrigerator. Insulating samples exhibited variable-range hopping (VRH) behavior of the form \ensuremath{\sigma}(T)=${\ensuremath{\sigma}}_{0}$(1/T${)}^{s}$ exp[-(${T}_{0}$/T${)}^{p}$] for 0.86${N}_{c}$0.99${N}_{c}$ for T8 K. The most satisfactory overall fit to the data is p\ensuremath{\sim}(1/4 and s\ensuremath{\sim}0, namely Mott VRH. A new criterion is given to decide the temperature regimes where Mott or Efros-Shklovskii VRH (p=(1/2) should be observed. The characteristic Mott temperature ${T}_{0}$\ensuremath{\propto}(1-N/${N}_{c}$${)}^{3\ensuremath{\nu}}$ yielded 0.77\ensuremath{\nu}0.97. Strong deviations from VRH behavior were observed for N0.84${N}_{c}$. Metallic samples showed a \ensuremath{\sigma}(n,T)=\ensuremath{\sigma}(n,0)+m(n)${T}^{1/2}$ dependence at sufficiently low temperatures. The results yield \ensuremath{\sigma}(n,0)=${\ensuremath{\sigma}}_{0}$(n/${n}_{c}$${\mathrm{\ensuremath{-}}1)}^{\ensuremath{\mu}}$ with ${\ensuremath{\sigma}}_{0}$=376 S/cm, 8.55${n}_{c}$8.60\ifmmode\times\else\texttimes\fi{}${10}^{18}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$, and \ensuremath{\mu}=0.60\ifmmode\pm\else\textpm\fi{}0.05. The coefficient m(n) shows behavior similar to that for Si:P, but shows a second sign crossing for n/${n}_{c}$\ensuremath{\sim}2.4. The m(n) results seem to confirm the dominance of the Hartree interaction for the many-valley case.