Solid State Physics in a Nutshell
Video Lectures
Displaying all 35 video lectures.
I. Bonding and Crystal Structure | |
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Lecture 1 Play Video |
Covalent Bonding |
Lecture 2 Play Video |
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 Play Video |
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 Play Video |
Slices We discuss the slices technique and its utility in understanding the structure of various crystals, including the Perovskite structure. |
Lecture 5 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
Scattering Density We discuss scattering density and create a mathematical description of this concept. |
Lecture 10 Play Video |
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 Play Video |
Centered Lattices We briefly discuss centered lattices and the information they can give us. |
III. Elastic Scattering | |
Lecture 12 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
Thermal Conductivity Today, we delve into thermal conductivity and look at how it is related to heat capacity. |
Lecture 23 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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. |