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HW4_Fa11_solutions - MatE153:HW4:Solutions Reading Kasap...

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MatE 153: HW 4: Solutions Reading Kasap: 4.1-4.8, 5.1 and 5.2 Be sure to look over the reading review notes on D2L. This will help you prepare for the final. Total Points: 80 1. Why is the bandgap of GaAs larger than that of Si? (5 points) GaAs is predominantly ionically bonded (where Ga gains an electron from As). This ionic bonding is stronger than the covalent bonding in Si so it takes more energy to move an electron away from this bonding (out of the valence band to the conduction band). 2. What assumptions are different between Boltzmann and Fermi-Dirac probability functions? (5 points) The key difference in assumptions is that Boltzamm statistics assumes that the site the electron is moving into is empty. Fermi-Dirac has more complicated math because it checks to make sure the site is empty (by using the probability of it being empty). 3. Using Excel, generate a plot of the density of states, g(E), in the valence band for copper from the bottom to the half way point in band. Assume the Fermi energy is the half way point in the band. (5 points) This would be a plot of g(E) from E=0 eV to E= 7eV. You need to have your units in Joules in order for everything to cancel out. ( ) ) J ( E Js 10 626 . 6 kg 10 1 . 9 2 8 ) J ( E h m 2 8 ) E ( g 2 / 3 2 34 31 2 / 3 2 e × × π = π = ( ) 3 4 2 4 2 4 3 2 3 3 2 2 3 3 3 3 3 3 2 / 1 2 / 3 2 2 m J 1 m kg 1 s J 1 s J m kg kg s m s J kg kg s kgm s J kg Nm s J kg J s J kg : units the of check a s ' Here = = = = = h 6.63E- 34 m 9.10E- 31
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