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10/14/20101LECTURE 2: Energy Bands andCharge Carriers in SemiconductorsEECS 170A10/14/20101•In this part of the lecture we will discuss the band theory ofsolids and how they effect the electrical conduction.•Topic is cumbersome for a 50minutes lecture and needs reviewof basic postulates of quantum mechanics•Here we will discuss the basic findings and discuss how theyaffect our understanding at microscopic level.•The first thing we need to remember from our basic physics10/14/20102classes is the blackbody radiation theory which states that“amaterial at a constant temperature absorbs and emits energywhere total rate of radiation generation is equal to rate ofabsorption.”•The release and absorption of energy is not random and they areabsorbed/radiated at in discrete packets:,(Max Planck,1901) (concept of energy quantization)–Hence, energy levels are discreteEn h•Bohr’s model: electrons occupy circular orbits around the nucleus and carry angularmomentum:•Combining with Planck’s theory we end up conclusion that says electron occupycertain orbits with energy state:•(how many chocolate bars?)•Here L is the angular momentum at n’th orbit, m0is the electron mass at rest and rnisthe radius of the orbit•Results work for Hydrogen atom and fails for others10/14/2010302nnhLnrn419022013 6,11.610, 10.2392(4)nm qEeVeVJJcaloriesnn •Next comes the Schrodinger’s wave mechanics that states that electrons in atom canoccupy only certain energy states with fixed principal quantum number, n, azimuthalquantum number, l, and magnetic orbital quantum number, ±l, and a certain spin.•No more than one electron can occupy the same state.Finding an electron at aspecific state is a statistical value•No one can localize the electron and give exact information on their momentum,energy, etc. (uncertainty principle)1911.610()1111/()1eVJin energyeVelectronVeVeor qV•Multi electron atoms:Finding an electron at a specific state is astatistical value•You can calculate the probability of finding electron at specificdistance, r, from nucleus where a0is here is the Bohr radius10/14/2010420300592142.0namm q •You can extend the analysis to find the probability of findingelectrons at certain energy levels and states.
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