NNSE508_EM-L10-statistics

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

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
NNSE 508 EM Lecture #10 1 Lecture contents Density of states Statistics Metals: transport
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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 z z z y y y x x x n L k n L k n L k 2 2 2 • Electrons are waves ! • Large 3D box (L is large, n is large) with Born-von Karman boundary Conditions: ikr Ae 3D : 2D : 1D :   3 2 V N • Free electron approximation: ( , , ) ( , , ) same for y and z x x L y z x y z   0 L x V(x) x V 0   z y x z y x z y x n n n L L L k k k 3 2   2 2 S N 2 kL N Number of states:
Background image of page 2
NNSE 508 EM Lecture #10 3 Density of states m k V E 2 2 2 0 In the interval k to k+ k number of states : 2 kL N 3D :      2 1 0 2 1 V E m k In the interval E to E+dE number of states per unit “volume” (spin included): 2D : 1D : m k k E 2   3 2 V N   2 2 2 2 k N   3 3 2 2 4 k N 2 ) ( m E N   2 1 0 2 1 2 ) ( V E m E N E N V E N 1 ) (   2 1 0 3 2 2 3 2 ) ( V E m E N
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
NNSE 508 EM Lecture #10 4 Density of states and dimensionality From Singh, 2003
Background image of page 4
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   2 1 0 3 2 2 3 * 2 ) ( V E m E N 3D density of states * * c dos m m
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 15

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

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online