02+QM+_+Band+Structure

02+QM+_+Band+Structure - Last Lecture: Crystal...

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Unformatted text preview: Last Lecture: Crystal Structures… Lattice Unit Cell a Determining Miller Indices for plane: Find the intercepts Take reciprocal Multiply by lowest common denominator In a cubic lattice, the vector perpendicular to (h k l) plane is [h k l] direction Last Lecture: Electrical Conduction Scattering Æ Ohm’s Law Classical Model (Drude Model) AJR IR V = = A L A L R σ ρ = = Nucleus Core electrons Valence electrons qnv J = = E σ n q v qn µ σ = = E “Free” valence electrons contribute to conductivity E µ = v µ , electron mobility • Determine how atomic structure affects electrons in the material • Note that we will need to invoke principles of quantum mechanics. EECS 320 Quantum Mechanics Brief Overview Waves and Particles: Classical Pictures What is particle? Examples? - Described by Newton’s Law What is wave? Examples?- Described by wave equations. Waves-Particles Duality Particle wave-like Wave particle-like Double-slit Experiment Photoelectric Effect d e t e c t h e r e d e t e c t h e r e Incident light Electron >h ν Material t • Light shining on a metal can “knock” electrons out of atoms. • Maximum kinetic energy of released electrons proportional to frequency of light, instead of intensity. • Light comes in packets called Photons: E = h f, h=6.626 X 10-34 J·s Electrons have wave-like properties Principles Of Quantum Mechanics Wave-Particle Duality Uncertainty Principle Waves show particle-like behavior (photon-light) Particles show wave-like behavior (electron-wave) p h = λ de Broglie Wavelength h ≥ ∆ ∆ x p h ≥ ∆ ∆ t E Uncertainty in position/momentum of particle and energy/momentum of wave Describe using probability Energy Quanta Emitted radiation takes on discrete energies Photoelectric Effect Incident light Electron >h ν Material Ejection depends on E, not intensity Energy Quantization: Hydrogen Atom...
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02+QM+_+Band+Structure - Last Lecture: Crystal...

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