Metal-insulator transition in boron-ion-implanted diamond

Abstract

We have observed the metal-insulator transition in single crystal, high-purity type-IIa diamond which has been implanted at $77\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ with boron ions in multiple steps and annealed at high temperatures between implants. Electrical conductivity measurements made at temperatures in the range $1.5--300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ have shown that, for boron concentrations below the critical concentration ${n}_{c}$ which we estimate as $3.9\ifmmode\times\else\texttimes\fi{}{10}^{21}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$, Efros-Shklovskii hopping conduction occurs at sufficiently low temperatures. At the highest concentrations, just-metallic behavior is found, with the low-temperature conductivity governed by the relation $\ensuremath{\sigma}(\mathrm{T})=\ensuremath{\sigma}(0)+b{T}^{m}$. The conductivity critical exponent $\ensuremath{\mu}$ is estimated to be 1.7, with a fairly large uncertainty because of the limited number of concentrations on the metallic side of the transition. The high $\ensuremath{\mu}$ value found for this wide bandgap, uncompensated $p$-type system contrasts with the value $\ensuremath{\mu}\ensuremath{\approx}\frac{1}{2}$ reported for $p$-type $\mathrm{Si}$ and other uncompensated semiconductors.