Conduction at low temperature in ion-implanted silicon

The electrical conductivity in a 4 x 1014 cm-2, 130 keV phosphorus implanted layer is studied, after annealing, in the temperature range 4.2 K to 6 mK. The annealing (at 600 0C) is such that most of the phosphorus ions become electrically active and are only partially compensated by the remaining defects. The analysis of σ versus T indicates that three different regimes of conductivity are operating, depending on the temperature range. Between 4.2 K and approximately 100 mK the results find a reasonable interpretation in terms of three-dimensional variable range hopping (VRH), which follows Mott's law: σ proportional to exp(Tsup(-1/4). When T decreases, between approximately 100 and approximately 50 mK the hopping range becomes larger than the thickness of the implanted layer and a two-dimensional VRH regime, in which σ is proportional to exp(Tsup(-1/3)), takes place. At low temperature, below approximately 50 mK, σ varies as exp(Tsup(-1/2)); a tentative explanation of this behaviour is proposed, in terms of correlation effects. (author)