Download presentation

Presentation is loading. Please wait.

Published byRuth Hardy Modified over 2 years ago

1
Graduate Lecture Series 29 June – 3 July, 2009 Prof Ngee-Pong Chang Lecture 2 Fermi Gas

2
Enrico Fermi 1901 - 1954 Paul Dirac 1902 - 1984

3
Ionisation Energy of Sodium 5.14 eV Band Theory of Metals Start with isolated Sodium Atom

4
Ionisation Energy of Sodium 5.14 eV Band Theory of Metals

6
Splitting of 3s level with 2 Sodium atoms Bring two Sodium Atoms together

7
Band Theory of Metals Splitting of 3s level with 6 Sodium atoms Bring six Sodium Atoms together

8
Band Theory of Metals Splitting of 3s levels with Sodium atoms in crystalline solid

9
Band Theory of Metals

10
Fermi-Dirac Distribution electrons holes

11
Probability of Occupancy 1.0 0.0 T=0 T > 0

12
Probability of Occupancy

13
Energy in units Filling up the Fermi Sea In One Dimensional Box 10 20 30 ² F

14
1-Dimensional Box

15
1-Dimensional Fermi Gas Sum Over Spins

16
1-Dimensional Fermi Gas Single Spin Orientation Fermi Surface dependence on number of electrons

17
2-Dimensional Fermi Gas Single Spin Orientation Fermi Surface dependence on number of electrons

18
3-Dimensional Fermi Gas Single Spin Orientation Fermi Surface dependence on number of electrons

20
1-Dimensional Fermi Gas Single Spin Orientation Total Energy

21
2-Dimensional Fermi Gas Single Spin Orientation Total Energy

22
3-Dimensional Fermi Gas Single Spin Orientation Total Energy

24
3-Dimensional Density of States

25
2-Dimensional Density of States

26
http://upload.wikimedia.org/wikipedia/en/c/c5/DOS_multdim.jpg

27
3-Dimensional Fermi Gas Density of States

28
2-Dimensional Fermi Gas Density of States

29
1-Dimensional Fermi Gas Density of States

30
Conduction Band Valence Band

36
Woodward Yang harvard lecture notes

37
CBO =conduction band offset

39
2-Dimensional Density of States

42
Quantum Wire

43
http://boulder.research.yale.edu/Boulder- 2005/Lectures/Matveev/Boulder%20lecture.pdf

45
A graphene nanoribbon field-effect transistor (GNRFET). Here contacts A and B are at two different Fermi levels E F1 and. E F2Fermi levels

46
Ballistic Conductor

47
i i’ t’ t Landauer formula 1927 - 1999 Conductance

49
µ Gas Pressure on the Wall A cos θ v δ t A θ

50
Pressure due to Non-Relativistic Degenerate Fermi Gas Equation of state for Fermi Gas since at T = 0 We have for a metal

51
White dwarf as seen by Hubble Space Telescope

53
What's Inside a White Dwarf? To say that white dwarfs are strange is an understatement. An earth-sized white dwarf has a density ofdensity 1 x 10 9 kg/m 3. In comparison, the earth itself has an average density of only 5.4 x 10 3 kg/m 3. That means a white dwarf is 200,000 times as dense!

Similar presentations

OK

Electrons in Solids Simplest Model: Free Electron Gas Quantum Numbers E,k Fermi “Surfaces” Beyond Free Electrons: Bloch’s Wave Function E(k) Band Dispersion.

Electrons in Solids Simplest Model: Free Electron Gas Quantum Numbers E,k Fermi “Surfaces” Beyond Free Electrons: Bloch’s Wave Function E(k) Band Dispersion.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on as 14 amalgamation of companies Ppt on any famous personality Ppt on event handling in javascript what is the syntax Ppt on biodegradable and non biodegradable resources Ppt on product specification definition Ppt on introduction to object-oriented programming languages Ppt on democracy in contemporary world class 9 Ppt on maggi in india Ppt on aravind eye care system Ppt on product advertising in cartoons