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ECE 3080: Test #1, Solutions June 11, 2009 Page 1 of 6 G EORGIA I NSTITUTE OF T ECHNOLOGY S CHOOL OF E LECTRICAL AND C OMPUTER E NGINEERING ECE 3080: Semiconductor Devices for Computer Engineering and Telecommunication Systems Summer Semester 2009, Test #1 SOLUTIONS Short Questions (20 questions, 3 points each): 1. You confine an electron in a (geometrically) smaller and smaller potential well with infinitely high potential walls. Will the energy difference between neighboring energy states increase, decrease or stay the same as you decrease the dimensions of the potential well? Justify your answer. Once the potential well reaches atomic dimensions, we get discrete energy levels, i.e. the electron energy becomes quantized. With decreasing lateral dimension (width a) of the potential well, the energy difference between neighboring energy levels increases, as can be seen e.g. from the formula for the energy levels E n = 2 2m n π a 2 2. The solution of the Schrodinger wave equation is the wave function ψ ; what is the physical meaning of the product ψ ψ dV , where dV is a volume element? The integral ψψ *dV ∫∫∫ gives the probability to find a particle in a given volume element dV. 3. Briefly explain the concept of effective mass of an electron in a crystalline semiconductor. The concept of effective mass allows us to treat the movement of carriers in the crystalline semiconductor using classical Newtonian mechanics only by replacing the free electron mass with the effective mass. The complex interaction of the carriers with the crystal structure is “hidden” in the effective mass. 4. What is known as the Pauli exclusion principle? The Pauli exclusion principle states that no two fermions (e.g. electrons) in a system can occupy the same state with respect to all of its quantum numbers. In semiconductor physics, the Pauli principle causes the discrete energy levels of individual atoms to split up when forming a crystal, finally creating the band structures with allowed and forbidden energy regimes.
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ECE 3080: Test #1, Solutions June 11, 2009 Page 2 of 6 5. What is described by the density of states function?
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