# Solid State Physics in a Nutshell

## Video Lectures

Displaying all 35 video lectures.
I. Bonding and Crystal Structure
Lecture 1

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Covalent Bonding
Lecture 2

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Dipole Interactions
We begin by discussing metallic bonding and relating it to the electron in a box model. From there we tackle dipole and induced dipole interactions, including the London dispersion force and Van der Waals bonding.
Lecture 3

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Lattice and Basis
We focus on the microscopic structure of crystals in this video. We first introduce the translational symmetry of the crystal called the lattice and the description of the crystal chemistry called the basis. We then discuss different types of lattices including the primitive and conventional cells.
Lecture 4

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Slices
We discuss the slices technique and its utility in understanding the structure of various crystals, including the Perovskite structure.
Lecture 5

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Crystal Structure Types
Today, we discuss different types of centering in cubic system. We also delve into the similarities between the fcc and the diamond structure. Finally, we compared two types of close packed structures.
Lecture 6

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Miller Indices
Today, we discuss the utility of Miller indices in labeling different planes and how this can be used to better understand crystal structure.
II. Elastic Diffraction
Lecture 7

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Fourier Series
This video discusses Fourier series and how they can be used to build complex functions from simple periodic functions, like sines and cosines.
Lecture 8

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General Theory of Diffraction
We discuss the general theory of diffraction and build an expression for intensity which can be tested experimentally. We also build a delta k vector which is critical to our understanding of diffraction.
Lecture 9

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Scattering Density
We discuss scattering density and create a mathematical description of this concept.
Lecture 10

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Structure Factor
We now discuss how, given a structure and a basis, we can predict the spacing, position and magnitude of the intensity. We find that, in practice, we have no idea where atoms sit in a lattice. So we take a guess, use the structure factor to calculate the intensity and compare that to experimental data. We also go through the structure factor and how to use it mathematically.
Lecture 11

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Centered Lattices
We briefly discuss centered lattices and the information they can give us.
III. Elastic Scattering
Lecture 12

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Ewald Sphere
In this video we discuss the Ewald sphere which is a geometric interpretation of the interference condition that our change in wave vector, k, must be equal to our reciprocal lattice vector, G.
Lecture 13

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Powder Diffraction
We begin this video by connecting the intensity to reciprocal space for polycrystalline materials using a concentric sphere model. We then show that one can measure this using omega two theta scans which radially grow a change in wave vector so it crosses different reflections. We also show that the distance between these spheres depends on the crystal system which gives rise to different intensity patterns.
Lecture 14

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Omega Rocking Curves
We begin this video by examining reciprocal space for epitaxial thin films on a substrate. We then introduce omega rocking curves which give us information about out of plane orientation quality.
Lecture 15

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Psi Scans
Today, we discuss psi scans which rotate the sample about its normal and give information about the in plane alignment of a thin film grown on a substrate.
IV. Phonon Dispersions and Transport & Thermal Properties
Lecture 16

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Introduction to Phonons
We begin today with a one dimensional crystal and we treat the bonds between the atoms as springs. We then develop an expression for the force acting on one particular atom. Using a plane wave approximation for the displacement we then develop an equation relating the wave vector and the frequency of oscillation.
Lecture 17

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Nyquist Frequency and Group Velocity
In this video we find the physically significant values of q, our wave vector. We then use our dispersion to find group and phase velocities. In addition, we define the Nyquist frequency in conjunction with our physically significant q values.
Lecture 18

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Phonon Quantization
Today we first introduce phonons to describe vibrations in a lattice and discuss their analogous behavior to photons. We then discuss how phonons behave like simple harmonic oscillators and gain their energy expression from this. Finally, we discuss why phonons have kinetic energy but no linear momentum.
Lecture 19

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Phonon Density of States
In this video we first look at how the q-space is discrete for a finite solid and has a finite range. We then examine the phonon density of states.
Lecture 20

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Planck Distribution and Einstein Heat Capacity
We first introduce the Planck distribution which describes the population of phonons as a function of temperature. We then applied Einstein's model of isolated oscillators to the heat capacity of phonons.
Lecture 21

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Heat Capacity with the Debye Model
We discuss the Debye model which invokes a linear, isotropic dispersion and uses that to solve for the heat capacity of a solid.
Lecture 22

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Thermal Conductivity
Today, we delve into thermal conductivity and look at how it is related to heat capacity.
Lecture 23

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Phonon-Phonon Scattering
Today, we look at phonon-phonon scattering of two different types. First, we handle the easier form, normal scattering, and then we move on to the more difficult form, Umklapp scattering.
Lecture 24

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Thermal Conductivity & Temperature Dependence
In this video we go through the connection between thermal conductivity and temperature. We end this video with an analysis of the thermal conductivity of different varieties of silicon.
V. Inelastic Scattering
Lecture 25

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Inelastic Scattering Theory
We begin this video by describing scattering density as a function of time as well as position in order to describe inelastic scattering. We then go through and define our time dependence of other factors to build an expression for constructive interference. We wrap up with an example based on the scattering of visible light.
VI. Free Electron Model: Density of States & Heat Capacity
Lecture 26

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Free Electron Model
We begin this video by approximating our system as one electron in an infinite square well. We then develop a dispersion relation for the electron. We continue by looking at both fixed and periodic boundary conditions to develop a solution for the wave function.
Lecture 27

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Density of States and Fermi Dirac Distribution
Today we come up with an expression for the electronic density of states and apply Fermi Dirac statistics to see how these states are filled.
Lecture 28

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Heat Capacity
Today, we develop an expression for heat capacity that depends linearly on temperature. We then use this model and show how it gives insight into the electronic density of states at the fermi level.
Lecture 29

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Screening
Today, we show that the free electron model works well for solids because screening is so high that the conduction electrons don't feel the potential from all the other atoms. Shielding is the concept that free electrons will not see the nucleus of an atom because all of the core electrons are in the way.
VII. Weak Potential and Band Structures
Lecture 30

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Bloch Theorem and the Central Equation
We start by introducing Bloch's theorem as a way to describe the wave function of a periodic solid with periodic boundary conditions. We then develop the central equation and find a relation between the Fourier coefficients associated with the wave vectors, k minus G, over all space.
Lecture 31

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Vanishing Potential and Brillouin Zones
Today, we extend Bloch's theorem into two dimensions and develop some vocabulary for labeling points withing the brillouin zone. We also go through band structure using spaghetti diagrams.
Lecture 32

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Band Structures of Metals and Insulators
In this video we introduce metals, semi metals, semiconductors and insulators. We also go through classifying these materials, especially using experimentally obtained dispersion diagrams.
VIII. Intrinsic Semiconductors
Lecture 33

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Thermal & Optical Excitations
Today, we develop a description of thermal and optical excitations in intrinsic semiconductors. We consider both direct and indirect transitions.
Lecture 34

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Effective mass and holes
In this video, we look back to the impact of an electric field on electrons in a metal and extend these ideas to a semiconductor. From this, the ideas of an effective mass and holes emerge.
Lecture 35

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Fermi Level
In this video, we consider how the density of states alters the temperature dependence of the Fermi level and establish the n*p product rule.