Fermi Energy of a 1D Electron Gas
المؤلف:
Sidney B. Cahn, Gerald D. Mahan And Boris E. Nadgorny
المصدر:
A GUIDE TO PHYSICS PROBLEMS
الجزء والصفحة:
part 2 , p 32
29-8-2016
1141
Fermi Energy of a 1D Electron Gas
Calculate the Fermi energy for a one-dimensional metal with one free electron per atom and an atomic spacing of 2.5 A at T = 0.
SOLUTION
For a one-dimensional gas the number of quantum states in the interval dp is
where g = 2s + 1 = 2 and L is the “length” of the metal. The total number of electrons N (which in this case is equal to the number of atoms) is
(1)
Therefore,
where d is the atomic spacing. The Fermi energy
(2)
where m is the electron mass.
(3)
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