Appearance of effective surface conductivity: An experimental and analytic study

Abstract

Surface conductance measurements on p-type doped germanium show a small but systematic change to the surface conductivity at different length scales. This effect is independent of the structure of the surface states. We interpret this phenomenon as a manifestation of conductivity changes beneath the surface. This hypothesis is confirmed by an analysis of the classical current flow equation. We derive an integral formula for calculating of the effective surface conductivity as a function of the distance from a point source. Furthermore we derive asymptotic values of the surface conductivity at small and large distances. The actual surface conductivity can only be sampled close to the current source. At large distances, the conductivity measured on the surface corresponds to the bulk value.

Fermi level pinning at the Ge(001) surface—A case for non-standard explanation

“…A more detailed analysis of the above relation may be found in Ref. 9. These formulas highlight the qualitative difference between the two-dimensional and threedimensional current flows, suffice it to say that σ 2 and σ 3 are expressed using different units.…”

Electric currents at semiconductor surfaces from the perspective of drift-diffusion equations

“…Thus, the conclusions of Ref. 12 are valid in any case; the current will have the three-dimensional character at sufficiently small and large distances from the source. Therefore, the confinement close to the surface may only appear at limited distances.…”

“…We begin with a brief résumé of the results published in Ref. 12. In that paper, it was pointed out that the theory may result in strange long-ranged behavior if d dz σ(0) = 0.…”

“…As such, it locally describes how the solutions satisfying the same boundary condition as σ(z)σ −1 (∞) behave near z = 0 for small k. Hence, ψ 2 (0; 0) = σ(0)σ −1 (∞) and the usual asymptotic behavior ϕ(r) ∼ (σ(∞)r) −1 holds for r → ∞. The arguments given in Ref 12. for k → ∞ remain valid in the case at hand as cos 2 Φ(k) → 1 for k → ∞.Appendix C: Absence of bound eigenstates ofL…”

“…However, in this case it is an approximate equation, neglecting terms of the order z/(r 2 + z 2 ) 3/2 , and hence valid close to the surface only. The local nature of the screened Poisson equation suggests that the solution at the surfaces is close to the all-inclusive solution.Appendix B: Boundary conditionsIn Ref 12. it was noted that the condition d dz σ(0) = 0 might result in the asymptotic behavior φ(r) ∼ r −3 for large values of r. It was based on the observation that generalized wavefunctions {cos(kz + Φ(k))} k>0 , where Φ vanish for z = 0 and k → 0.…”