Effects of the overlap between wave functions of impurity centers on the activation energy of hopping conduction

Abstract

The hopping conductivity σ₃ has been studied in samples of slightly counterdoped crystalline Si: B with a boron concentration of 2×10¹⁶ cm⁻³<N<10¹⁷ cm⁻³ and a compensation of 10⁻⁴≤K≤10⁻². It is found that at K≤10⁻³ the activation energy ε₃ is not lower (as it must be according to classical notions at finite K) but larger than the value ε_N=e ² N ^1/3/κ, where e is the electronic charge and κ is the dielectric constant. With decreasing N, the energy ε₃ drops slower and, with decreasing K, grows faster than follows from the standard theory. At K≤10⁻⁴, ε₃ is higher than ε _N by a factor of 1.5–2. The result is explained by the effect of the overlap between wave functions of neighboring impurity centers on the structure of the impurity band.