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
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4. 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: R = pL/ Ld = p/d, which is independent of the
area 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/ndet. Suppose now that the minimum value of the
collision time is determined by scattering from surfaces of the sheet, so that
Td/v, where v is the Fermi velocity. Thus the maximum surface resistivity is
Rmvp/nd²e². Show for a monatomic metal sheet one atom thickness that
sq
Rħ/e² = 4.1k, where lkn is 10³ ohms.
sq](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d2fdd51-a813-4b36-89e9-f9581acfc2ee%2F9485fc98-0213-42c5-99e3-ed7142f44e7c%2Fr0p1b4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:sq
4. 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: R = pL/ Ld = p/d, which is independent of the
area 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/ndet. Suppose now that the minimum value of the
collision time is determined by scattering from surfaces of the sheet, so that
Td/v, where v is the Fermi velocity. Thus the maximum surface resistivity is
Rmvp/nd²e². Show for a monatomic metal sheet one atom thickness that
sq
Rħ/e² = 4.1k, where lkn is 10³ ohms.
sq
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