Maximum surface resistance considers a square sheet of side L, thickness d, and electrical resistivity p. The

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Maximum surface resistance considers a square sheet of side L, thickness d, and electrical resistivity p. The resistance measured between opposite edges of the sheet is called the surface resistance: Rsq = pL/Ld = p/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 p/d has the dimensions of ohms.) If we express p 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 ≈ mvp/nd2e2. Show for a monatomic metal sheet one atom in thickness that Rsq ≈ h/e2 = 4.1kΩ

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