# Lecture2 - 2 LECTURE2:EnergyBandsand EECS170A...

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10/14/2010 1 LECTURE 2: Energy Bands and Charge Carriers in Semiconductors EECS 170A 10/14/2010 1 In this part of the lecture we will discuss the band theory of solids and how they effect the electrical conduction. Topic is cumbersome for a 50minutes lecture and needs review of basic postulates of quantum mechanics Here we will discuss the basic findings and discuss how they affect our understanding at microscopic level. The first thing we need to remember from our basic physics 10/14/2010 2 classes is the blackbody radiation theory which states that “a material at a constant temperature absorbs and emits energy where total rate of radiation generation is equal to rate of absorption.” The release and absorption of energy is not random and they are absorbed/radiated at in discrete packets: , (Max Planck, 1901) (concept of energy quantization) Hence, energy levels are discrete E n h Bohr’s model: electrons occupy circular orbits around the nucleus and carry angular momentum: Combining with Planck’s theory we end up conclusion that says electron occupy certain orbits with energy state: (how many chocolate bars?) Here L is the angular momentum at n’th orbit, m 0 is the electron mass at rest and r n is the radius of the orbit Results work for Hydrogen atom and fails for others 10/14/2010 3 0 2 n n h L n r n 4 19 0 2 2 0 13 6 , 1 1.6 10 , 1 0.239 2(4 ) n m q E eV eV J J calories n n    Next comes the Schrodinger’s wave mechanics that states that electrons in atom can occupy only certain energy states with fixed principal quantum number, n, azimuthal quantum 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 a specific state is a statistical value No one can localize the electron and give exact information on their momentum, energy, etc. (uncertainty principle) 19 1 1.6 10 ( ) 1 1 1 1 / ( ) 1 eV J in energy eV electron V eV e or q V Multi electron atoms: Finding an electron at a specific state is a statistical value You can calculate the probability of finding electron at specific distance, r, from nucleus where a 0 is here is the Bohr radius 10/14/2010 4 2 0 3 0 0 5 92 1 4 2. 0 n a m m q   You can extend the analysis to find the probability of finding electrons at certain energy levels and states.

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10/14/2010 2 Multi electron atoms: Si Silicon has 14 electrons: At an isolated state, they occupy 1s, 2s, 2p, 3s, and 3p states. Electrons at the outer shell are valance electrons that contribute bonding with other atoms Valance has 8 states but only 4 are occupied: 4 more electrons can also occupy the same energy level 10/14/2010 5 Since exclusion principle says that no more than one electron can occupy the same energy level at the same state bringing 2 atoms close to each other will cause overlap in the energy band.
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• Fall '10