lecture4 - Lecture 4 Monday January 31 EE 332 Semiconductor...

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Lecture 4 Monday January 31 EE 332 Semiconductor Devices Problem Assignment 2.1, 2.4, 2.5, 2.8 Wave Velocity 2 v v and v v 1 v velocity Group then If v velocity Group v velocity Phase c c dk E d h E dk d ω k f p g p g g g p = = = = = = = = = = = h h ω ν ω νλ λ Effective Mass ( ) 2 2 2 2 2 2 2 2 2 2 1 / * * * 2 * 2 v * v * dk E d m m dk E d m k m p m E k m p h h h h = = = = = = = If we apply an electric field to a crystal the electrons may not accelerate as F=qE=ma. The difference is accounted for by an effective mass. GaAs Band Structure Minimum energies at about the same level. Larger mass
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Si Band Structure Minimum in X symmetry direction or [100] Effective mass Mass in perpendicular directions * m * // m Group Theory Symbols for High Symmetry Points Γ - Identifies the zone center where k=0 For the simple cubic and FCC lattice, two directions of high symmetry are: X - Denotes the zone end along the <100> direction L - Denotes the zone end along a <111> direction. Insight material Tables 2.1 and 2.2 Text Effective Mass Derivation Expand complicated band structure in a power series. For small energy band structure that of a free electron, or m k m p m E K 2 2 v 2 2 2 2 2 1 h = = =
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