# TEST1 - GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL OF...

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ECE 3080: Test #1, Solution June 21, 2005 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 2005, Test #1 SOLUTIONS Short Questions (20 questions, 3 points each): 1. What is the difference between an indirect and a direct bandgap semiconductor? In a direct band gap semiconductor (e.g. GaAs), the minimum of the conduction band and the maximum of the valence band are located at the same k-vector of the E(k) relationship, thus only energy needs to be supplied to excite an electron from the valence to the conduction band. In an indirect semiconductor (e.g. Si), the minimum of the conduction band and the maximum of the valence band are not located at the same k-vector, thus both energy and momentum must to be supplied to excite an electron from the valence to the conductions band. 2. Which E(k) band structure exhibits a smaller curvature? The one for heavy holes or the one for light holes? Justify your answer. The effective mass is inversely proportional to the curvature of the band structure: 1 m * " # \$ % ij = 1 ! 2 d 2 E ( k ) dk i dk j As a result, a smaller curvature means a larger effective mass, thus the E(k) band structure associated with the heavy holes exhibits a smaller curvature. 3. What is known as the Pauli principle and what role does it play in semiconductor physics? 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. 4. The solution of the Schrodinger wave equation is the wave function ! ; what is the physical meaning of the product !! * ? The integral !! *dV """ gives the probability to find a particle in a given volume element dV.

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## This note was uploaded on 08/28/2010 for the course ECE 3080 taught by Professor Staff during the Fall '08 term at Georgia Tech.

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TEST1 - GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL OF...

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