NNSE508_EM-L10-statistics

# NNSE508_EM-L10-statistics - 1 Lecture contents Density of...

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NNSE 508 EM Lecture #10 1 Lecture contents Density of states Statistics Metals: transport

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NNSE 508 EM Lecture #10 2 Density of states How to fill the states in almost free electron band structure ? 1. Calculate number of states per unit energy per unit volume 2. Use Pauli exclusion principle and distribution function to fill the bands Electrons are waves ! Large 3D box (L is large, n is large) with Born-von Karman boundary Conditions: 3D : 2D : 1D : Free electron approximation: 0 Lx V(x) x V0 Number of states: z z z y y y x x x n L k n L k n L k π 2 2 2 = = = ikr Ae ± = ψ ( 29 3 2 V N = ( , , ) ( , , ) same for y and z x x L y z x y z + = ( 29 z y x z y x z y x n n n L L L k k k = = = 3 2 ( 29 2 2 S N Σ = 2 kL N =
NNSE 508 EM Lecture #10 3 Density of states In the interval k to k+ k number of states : 3D : In the interval E to E+dE number of states per unit “volume” (spin included): 2D : 1D : m k V E 2 2 2 0 + = π 2 kL N = ( 29 ( 29 [ ] 2 1 0 2 1 V E m k - = m k k E = 2 ( 29 3 2 V N = ( 29 2 2 2 2 kL k N = ( 29 3 3 2 2 4 kL k N = 2 ) ( m E N = ( 29 2 1 0 2 1 2 ) ( - - = V E m E N E N V E N = 1 ) ( ( 29 2 1 0 3 2 2 3 2 ) ( V E m E N - =

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NNSE 508 EM Lecture #10 4 Density of states and dimensionality From Singh, 2003
NNSE 508 EM Lecture #10 5 Density of states in 3D and DOS effective mass Valence band density of states for Si (calculations) Effective mass density of states

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## This note was uploaded on 11/08/2011 for the course NNSE 508 taught by Professor Sergeoktyabrsky during the Spring '11 term at SUNY Albany.

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NNSE508_EM-L10-statistics - 1 Lecture contents Density of...

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