Question

Consider a one-dimensional crystal (similar to a carbon nanowire) with length 10 um and lattice spacing 0.1 nm.

RequireD:
a. What is the Fermi level assuming one electron per atom?
b. What is the density of states as a function of electron energy?

Answer 1

Answer:

a)  Fermi level = 600 electron-volts

b) $\frac{2.04 * 10^{13} }{\sqrt{E} }$

Explanation:

Given data:

length of one-dimensional crystal = 10 um

Lattice spacing = 0.1 nm

A) Determine the Fermi level assuming one electron per atom

Total length = 10 um

Interatomic separation of a = 0.1 nm

in this case the Atom has one electron therefore the number of electrons = 10^5  and the number of states Ns = gsN = 2 * 10^5  ( attached below is some part of the solution )

hence : Fermi level = 600 electron-volts

B) Determine the density of states as a function of electron energy

attached below is the detailed solution