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hw31102 - respectively Also the potential energy Ep is...

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EECE 7201 H.W. #3, Due February 8, 2011 Note: Many of these problems are very quick. The last two are more challenging! 1. What is the conductivity of a semiconductor (non-degenerate for those of you who know what this is) at T=0K? 2. What is the minimum energy an electron must gain in silicon before it can participate in conduction? 3. In intrinsic silicon at room temperature, do holes and electrons recombine (anahilate each other)? 4. We considered a crystal to be an infinite potential well for the purposes of calculating the density of states, and treated the electron as a wave for this purpose. If you think of the electron as a (free) particle inside a crystal, what happens as it approaches the surface at some velocity? 5. 1.19, text. 6. What is the name of the spectral series in hydrogen between the Lyman and Paschen Series? 7. 1.21, text. 8. 2.1, text. 9. A particle of mass ma and fixed energy E is confined to a two-dimensional infinite potential well, as discussed in class. The x and y side lengths of the well are a and b (or Lx and Ly or .
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Unformatted text preview: ..), respectively. Also, the potential energy, Ep, is constant everywhere inside the well. Assuming the side-lengths of the box are large, derive an expression for the density of states (S(E)) for the particle. This problem is covered both in Pierret and in our text, Appendix D. 10. (4.3, Pierret - reference) Link Here a, b, and c are equivalent to Lx, Ly, and Lz in our text. Part a is refering to the form of the solution for the energy levels (and wavefunctions) for this problem - is it the same here or different? Obviously the numbers are different, but is the form of the equations the same? Part b. is referring to how you would count the solutions up. This will be a hybrid of the 2-D and 3-D solutions. In d. the idea is to plot both the 3-D and the "2.5-D" solutions on the same axes for comparison. What you should see is that the 2.5-D result will approach the 3-D result as the third dimension (c or Lz) increases....
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