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

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Presentation on theme: "Graduate Lecture Series 29 June – 3 July, 2009 Prof Ngee-Pong Chang Lecture 2 Fermi Gas."— Presentation transcript:

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

2 Enrico Fermi Paul Dirac

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

5

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 T=0 T > 0

12 Probability of Occupancy

13 Energy in units Filling up the Fermi Sea In One Dimensional Box 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

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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

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24 3-Dimensional Density of States

25 2-Dimensional Density of States

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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

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36 Woodward Yang harvard lecture notes

37 CBO =conduction band offset

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39 2-Dimensional Density of States

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42 Quantum Wire

43 2005/Lectures/Matveev/Boulder%20lecture.pdf

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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 Conductance

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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

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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!


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