Maximum surface resistance. Consider 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: Rq=pL/Ld = p/d, which is independent of the area L² of the sheet. (R is called the resistance per square and is expected in ohms per square, because p/d has the dimensions of ohms.) If we express p by p=m/ne²t, then Rq = m/nde²t. Suppose now that the minimum value of the collision time is determined by scattering from surfaces of the sheet, so that T≈d/ve, where v is the Fermi velocity. Thus the maximum surface resistivity is Rmv/nd²e². Show for a monatomic metal sheet one atom thickness that Rh/e² = 4.1k, where lk is 10³ ohms. sq

Maximum surface resistance. Consider 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: Rq=pL/Ld = p/d, which is independent of the area L² of the sheet. (R is called the resistance per square and is expected in ohms per square, because p/d has the dimensions of ohms.) If we express p by p=m/ne²t, then Rq = m/nde²t. Suppose now that the minimum value of the collision time is determined by scattering from surfaces of the sheet, so that T≈d/ve, where v is the Fermi velocity. Thus the maximum surface resistivity is Rmv/nd²e². Show for a monatomic metal sheet one atom thickness that Rh/e² = 4.1k, where lk is 10³ ohms. sq