Physics — Solid State · maximum-surface-resistance
Problem
Maximum surface resistance. Consider a square sheet of side L, thickness d, and electrical resistivity ρ. The resistance measured between opposite edges of the sheet is called the surface resistance: Rsq=ρL/Ld=ρ/d, which is independent of the area L2 of the sheet. (Rsq is called the resistance per square and is expressed in ohms per square, because ρ/d has the dimensions of ohms.) If we express ρ by (44), then Rsq=m/nde2τ. Suppose now that the minimum value of the collision time is determined by scattering from the surfaces of the sheet, so that τ≈d/vF, where vF is the Fermi velocity. Thus the maximum surface resistivity is Rsq≈mvF/nd2e2. Show for a monatomic metal sheet one atom in thickness that Rsq≈ℏ/e2=4.1kΩ.