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MAS.020UF Introduction to Solid State Physics
Course outline
Crystal structure
Crystal structure
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Unit cell
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Bravais lattices
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Miller indices
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Wigner Seitz cell
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Drawing Wigner-Seitz cells in two dimensions
Drawing Wigner-Seitz cells in three dimensions
Asymmetric unit
Examples of crystal structures
simple cubic
,
fcc
,
bcc
,
hcp
,
diamond
,
silicon
,
zincblende
,
ZnO wurzite
,
NaCl
,
CsCl
,
perovskite
,
graphite
,
sugar
More crystal structures, CIF files, and programs to visualize crystal structures
The AFLOW standard encyclopedia of crystallographic prototypes
Symmetries
Point groups
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Table of crystal classes and their associated point groups
Flowchart to determine the point group of a crystal
Space groups
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Space Group → Bravais Lattice, Point Group
Crystal physics
SGTE data for pure elements
- The Gibbs energy as a function of temperature for many elements.
Stress and strain
Einstein notation for tensors
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Equilibrium thermodynamic properties
Internal energy, Helmhotz free Energy, Gibbs free energy, Enthalpy, Specific heat, Pyroelectricty
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, Pyromagnetism, Piezoelectricty
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, Piezomagnetism
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, Electrocaloric effect
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, Electrostriction
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, Magnetostriction
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, Thermal expansion
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Nonequalibrium properties
Electrical conductivity, thermal conductivity, Seebeck effect, Peltier effect, Hall effect, Enrst Effect, Ettingshausen effect
Intrinsic symmetries
Maxwell relations
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Symmetric and asymmetric tensors
Crystal diffraction
Periodic functions
Fourier series
Fourier series in 1-D
Reciprocal lattices
Fourier series in 2-D
Fourier series in 3-D
Plane waves and reciprocal space
Interference of scattered waves
Intensity of the scattered waves
Plotting the intensity of the scattered waves
Laue condition $\Delta\vec{k}=\vec{G}$
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The number of diffraction peaks observed
Ewald sphere
Brillouin zones
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Brillouin zones of 2D Bravais lattices
Brillouin zones of 3D Bravais lattices
Drawing 3D Brilouin zones
Symmetry points and lines:
Simple Cubic
,
Face Centered Cubic
,
Body Centered Cubic
,
Hexagonal
,
Rhombohedral
,
Simple Tetragonal
,
Body Centered Tetragonal
,
Simple Orthorhombic
,
Base Centered Orthorhombic
,
Face Centered Orthorhombic
,
Body Centered Orthorhombic
,
Simple Monoclinic
,
Base Centered Monoclinic
,
Triclinic
Symmetry points of 2D lattices:
Square
,
Hexagonal
,
Rectangular
,
Centered Rectangular
,
Oblique
Atomic form factors
X-ray atomic form factors
Electron atomic form factors
Structure factor
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Bragg diffraction
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The reciprocal lattice vector
G
hkl
is orthogonal to the (
hkl
) plane.
Applications of diffraction
powder diffraction
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American Mineralogist Crystal Structure Database (contains diffraction data)
Neutron diffraction
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Electron diffraction
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LEED
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Lattice Vibrations and Phonons
Normal modes and phonons
Using complex numbers to represent sinusoidal oscillations
Linear chain
Linear chain with two different masses
fcc with linear springs to nearest neighbors
bcc with linear springs to nearest neighbors and next nearest neighbors
simple cubic with linear springs to nearest neighbors and next nearest neighbors
Jupyter python notebook for calculating phonon dispersion equations
Animations of some optical modes
Thermodynamic properties of phonons
Dispersion relation
Density of states
linear chain
linear chain with two masses
Ag-fcc
,
Al-fcc
,
AlN
,
Fe-bcc
,
GaN
,
Mg-hcp
,
Mo-bcc
,
Si-diamond
,
α-Sn
,
β-Sn
,
Ta-bcc
,
Tb-hcp
,
Ti-hcp
,
W-bcc
,
ZnO (rocksalt)
,
ZnO (zincblende)
,
ZnO (wurtzite)
,
Zr-hcp
Energy spectral density
u
(ω,
T
)
Internal energy density
u
(
T
)
Specific heat
c
v
(
T
)
Helmholtz free energy density
f
(
T
)
Entropy density
s
(
T
)
Table summarizing the thermodynamic properties of phonons
Kinetic theory
Thermal conductivity
Electron energy bands
Free electrons
Fermi function
Free electron density of states
Free electron model in 1-D
Free electron model in 2-D
Free electron model in 3-D
Table of thermodynamic properties of free electrons
Bloch theorem
One dimension
Bloch waves in one dimension
Kronig Penney Model
One-dimensional potentials
Empty lattice approximation:
simple cubic
,
fcc
,
bcc
,
hexagonal
,
tetragonal
,
body centered tetragonal
,
orthorhombic
,
simple monoclinic
Fermi surfaces
Fermi surface of a two-dimensional square lattice
Fermi surfaces of some three-dimensional lattices
Electronic band structure calculations
Plane wave method, central equations
Nearly free electron model
Tight binding
Table of tight binding band structure calculations
Some band structure calculations:
Cr
,
Li bcc
,
GaAs
,
GaN
,
GaP
,
Ge
,
InAs
,
6H SiC
,
V
Periodic table of electronic bandstructures
Separable square wave potentials
Materials Project
Metals, semimetals, semiconductors, insulators
Numerical determination of the thermodynamic properties of metals
Chemical potential μ(
T
)
Energy spectral density
u
(
E,T
)
Internal energy density
u
(
T
)
Specific heat
c
v
(
T
)
Helmholtz free energy density
f
(
T
)
Grand potential density φ(
T
)
Sommerfeld expansion
Calculated electron density of states
Al fcc
,
Au fcc
,
Cu fcc
,
Cr bcc
,
Li bcc
,
Na bcc
,
Pt fcc
,
W bcc
,
Si diamond
,
Fe bcc
,
Ni fcc
,
Co fcc
,
Mn bcc
,
Cr bcc
,
Gd hcp
,
Pd fcc
,
Pd
3
Cr
,
Pd
3
Mn
,
PdCr
,
PdMn
,
GaN
,
6H SiC
,
GaAs
,
GaP
,
Ge
,
InAs
,
V bcc
Experimental methods
Ultraviolet photoelectron spectroscopy (UPS)
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X-ray photoelectron spectroscopy (XPS)
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DE 3:18
Angle resolved photoemission spectroscopy (ARPES)
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3:37
Inverse photoemission spectroscopy
Kinetic theory
Ballistic transport
Diffusive transport
Drift and diffusion simulation
Ohm's law
Mattheissen's rule
Hall effect
Thermal conductivity
Wiedermann-Franz law
Lorentz number
Semiconductors
Role of semiconductors in technology
Band structure of semiconductors
Conduction band
E
c
, valence band
E
v
, band gap
E
g
Direct and indirect band gaps
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Absorption and emission of photons and phonons
Simplified band structures from the
NSM Archive
Direct band gap:
InAs
,
InP
,
GaAs
,
InN
,
GaN (zincblende)
,
GaN (wurtzite)
,
AlN
Indirect band gap:
Ge
,
Si
,
GaP
Silicon
,
SiC 4H
Electrons and holes
Effective mass
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Holes
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Ohm's law
Boltzmann approximation
Intrinsic semiconductors
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Effective density of states
N
c
,
N
v
The density of electrons in the conduction band
n
=
N
c
exp((μ -
E
c
)/k
B
T
)
The density of holes in the valence band
p
=
N
v
exp((
E
v
- μ)/
k
B
T
)
Law of mass action:
np = N
c
N
v
exp(-
E
g
/k
B
T
)
The intrinsic carrier density
n
i
=(
N
c
N
v
)
1/2
exp(-
E
g
/2
k
B
T
)
Chemical potential of intrinsic semiconductors
Thermodynamic properties of intrinsic semiconductors
Intrinsic semiconductors with a split-off band
Table summarizing the thermodynamic properties of semiconductors in the Boltzmann approximation
DE 3:18 3:37 
