Chapter 16, Insulator, Semiconductor, or Metal Video Solutions, The Oxford Solid State Basics

Problem 1

Metals and Insulators
Explain the following:
(a) sodium, which has two atoms in a bcc (conventional cubic) unit cell, is a metal;
(b) calcium, which has four atoms in a fcc (conventional cubic) unit cell, is a metal;
(c) diamond, which has eight atoms in a fce (conventional cubic) unit cell with a basis, is an electrical insulator, whereas silicon and germanium, which have similar structures, are semiconductors. (Try to think up several possible reasons!)
DWhy is diamond transparent?

Varsha Aggarwal

Numerade Educator

03:22

Problem 2

Fermi Surface Shapes
(a) Consider a tight binding model of atoms on a (two-dimensional) square lattice where each atom has a single atomic orbital. If these atoms are monovalent, describe the shape of the Fermi surface. (b) Now suppose the lattice is not square, but is rectangular instead with primitive lattice vectors of length $a_{x}$ and $a_{y}$ in the $x$ and $y$ directions respectively, where $a_{x}>a_{y}$. In this case, imagine that the hoppings have a value $-t_{x}$ in the $x$-direction and a value $-t_{y}$ in the $y$-direction, with $t_{y}>t_{x}$. (Why does this inequality match $a_{x}>a_{y} ?$ )
D.Write an expression for the dispersion of the electronic states $\epsilon(\mathbf{k})$.
D Suppose again that the atoms are monovalent, what is the shape of the Fermi surface now?

Chai Santi

Numerade Educator

10:43

Problem 3

More Fermì Surface Shapes*
Consider a divalent atom, such as Ca or Sr, that forms an fce lattice (with a single atom basis). In the absence of a periodic potential, would the Fermi surface touch the Brillouin zone boundary? What fraction of the states in the first Brillouin zone remain empty?

Hafiz Shahzaib

Numerade Educator