The AC Conductivity in n-Type Silicon Below the Metal-Insulator Transition

Abstract

In recent decades there have been many important developments, both experimental and theoretical, which have clarified our understanding of the various physical processes responsible for impurity band DC transport in doped semiconductors. In particular, the studies of Fritzsche and coworkers¹⁻³ have distinguished the various thermally activated processes [σ_DC(T)=Σσ_i exp(−ε_i/kT)] responsible for phonon-induced hopping conduction on the insulating side of the metal-insulator (MI) transition. These DC transport studies of impurity-band conduction have been reviewed by Fritzsche⁴. One result for weakly-compensated Ge and Si was the demonstration that the activation energy ε₂ scaled to zero as the donor density (n-type) or acceptor density (p-type) approached a critical value N_c (the MI transition) for the onset of a finite σ_DC(N,T=0)” ^Nc is reliably given⁵, for a wide range of impurity-host systems, by the Mott criterion N_c ^1/3a*= 0.26±0.05 where a* is an effective Bohr radius. The activation energy ε₂=(E_C–E_F) where E_C is the mobility edge within the Anderson localization approach; ε₂ is the energy difference between upper and lower Hubbard bands within the Hubbard model. More recently, the scaling theory predictions of Abrahams et. al.⁶ for σ_DC(N,T=OK) for metallic samples have been experimentally confirmed for Si:P⁷, Ge:Sb⁸, and Si:As^{9, 10} and other systems. The experimental results for these impurity-host systems show σ_DC(N>N_C, T→OK)^α (N/N_c−1)^υ but with different critical exponents¹¹ for different systems. The uncompensated systems Si:P, Ge:Sb, and Si:As show υ≃0.5 rather than the Anderson localization prediction⁶ of υ≃1.