Final Exam Spring 09
Phys 175A
Dr. Ray Kwok
SJSU
1. It is said that crystal structure = lattice + basis. If so,
how would you describe a honeycomb?
a1
a
Parallelograms lattice with 2-pt basis
a1 = a2 = 2 (a cos30o) = 1.73 a
a2
r
a1 = 1.73a ( x cos 30o + y
Mid-Term 2
Phys 175A Dr. Ray Kwok SJSU
1. Phonon Heat Capacity
M
a m m
M
m
m
M
Consider a linear chain of 3N atoms with equal spacing, but different masses (M and m) as distributed below. What is the thermal energy of this lattice at low T? At high T? Ske
Mid-Term 2
Phys 175A
Dr. Ray Kwok
SJSU
1. Phonon Heat Capacity
Honeycomb
Consider an ideal 2D N x N array of atoms (N along the a1 direction, and N along the a2
direction as shown) with nearest neighbor interaction only. The distance between all nearest
n
Phys 175A
Mid-Term 1, Spring 12
Dr. Ray Kwok
Name: _
Honeycomb
Consider an ideal 2D infinite array of atoms (shown) with nearest neighbor interaction only. The
distance between all nearest neighbor is a with effective force constant C.
s
a2
a1
1) Describe
Review Exercise 1
Phys 175A Dr. Ray Kwok SJSU
Question:
Consider a monatomic divalent 2D rectangular lattice as shown. Find the total specific heat of the crystal. Is the crystal a metal or insulator?
Phys 175A
Mid-Term 1, Spring 09
Dr. Ray Kwok
Name: _
Body-Centered Rectangles
Consider an ideal 2D infinite lattice (shown) with nearest neighbor interaction only.
a
2a
1) Describe the lattice properties.
a) Define the primitive vectors.
b) What is the ce
Phys 175A
Final Exam, Spring 09
Dr. Ray Kwok
Name : _
1.
It is said that crystal structure = lattice + basis. If so, how would you describe a honeycomb?
Phys 175A
2.
Final Exam, Spring 09
Dr. Ray Kwok
Consider the planes with indices (100), the lattice is
Chapter 2 Motion and Recombination
of Electrons and Holes
2.1 Thermal Motion
3
2
1
2
2
Average electron or hole kinetic energy = kT = mvth
vth =
3kT
=
meff
3 1.38 10 23 JK 1 300K
0.26 9.110 31 kg
= 2.3 105 m/s = 2.3 10 7 cm/s
Modern Semiconductor Devices
Chapter 1 Electrons and Holes
in Semiconductors
1.1 Silicon Crystal Structure
Unit cell of silicon crystal is
cubic.
Each Si atom has 4 nearest
neighbors.
Modern Semiconductor Devices for Integrated Circuits (C.
Hu)
Slide 1-1
Silicon Wafers and Crystal Pl
Chapter 9 Fermi Surfaces & Metals
Phys 175A Dr. Ray Kwok SJSU
Definition of Metals
A crystal with a Fermi Surface
E
NFE
ky
E
kF
kx
FEG
Eg E+
EF kz
a
a
kx
Fermi sphere
Electrons near Fermi surface
2kT
Heat capacity
N() N()f()
need vacant states even if n
Chapter 2
Reciprocal Lattice
Phys 175A
Dr. Ray Kwok
SJSU
Crystal Lattice
Periodic f(r + T) = f(r) for any observable
functions such as electronic density,
electric potential.etc. which means they
are all periodic functions because of the
translational pr
Chapter 1
Crystal Structure
Phys 175A
Dr. Ray Kwok
SJSU
Ideal Crystal
Infinite periodic structure
No edge
No impurity
Translational invariance for all observables
Crystal = Lattice + Basis
basis
lattice
crystal
Translational invariance cfw_a
With a set of
Chapter 5
Phonons Thermal Properties
Phys 175A
Dr. Ray Kwok
SJSU
Heat capacity of metal
Metal, treated as ideal electronic gas, should
carry KE = (3/2)NkT = U (internal energy)
C = U/T = (3/2)Nk = constant at low T
A more advanced model of metal suggested
Chapter 7
Energy Bands
Phys 175A
Dr. Ray Kwok
SJSU
Nearly Free Electron Model
atomic potential
U
FEG
U=0
U
x
U0
U1
NFE model
small perturbation, U1
2x
U ( x) = U 0 + U1 cos
a
U 0 < U1 < 0
=a
Electronic Wave in NFE model
Consider the following cases:
U1
Chapter 3
Crystal Binding
Phys 175A
Dr. Ray Kwok
SJSU
4 basis categories
Molecular Bonds Introduction
To understand the crystal binding, one should
understand how molecules bind together
The bonding mechanisms in a molecule are
fundamentally due to electr
Chapter 6
Free Electron Fermi Gas
(FEFG)
Phys 175A
Dr. Ray Kwok
SJSU
Classification of Solids
Many ways to classify solids
(a) lattice structure and
(b) crystal bonding
(c) measurable properties
One of the easiest and earliest properties
observed is the d
Chapter 4
Crystal Vibrations
Phys 175A
Dr. Ray Kwok
SJSU
Lattice dynamics
Thermal motion of atoms about their
equilibrium positions gives rise to many
interesting physics of a crystal
Consider motions as linear combinations of all
natural resonance Fourie