FYS Vår 2012 (Kondenserte fasers fysikk)

Transcription

1 FYS Vår 2012 (Kondenserte fasers fysikk) Based on Introduction to Solid State Physics by Kittel Course content Periodic structures, understanding of diffraction experiment and reciprocal lattice Imperfections in crystals: diffusion, point defects, dislocations Crystal vibrations: phonon heat capacity and thermal conductivity Free electron Fermi gas: density of states, Fermi level, and electrical conductivity Electrons in periodic potential: energy bands theory classification of metals, semiconductors and insulators Semiconductors: band gap, effective masses, charge carrier distributions, doping, pn-junctions Metals: Fermi surfaces, temperature dependence of electrical conductivity Andrej Kuznetsov, Dept of Physics and Centre for Material Science and Nanothechnology Postboks 1048 Blindern, 0316 OSLO Tel: , e-post: andrej.kuznetsov@fys.uio.no visiting address: MiNaLab, Gaustadaleen 23b

2 Ukenplan for FYS3410; moduler 1, 2, 3, og 4 undervisas respektive i uker 3-4, 5-6, 7-8, og 9-10 ojämna uker förelasningar oppgaver obliger måndag kl 9-12, Ø394 tilbakemeldning kl 16 tisdag kl 8-10, Ø443A kl 14-16, Ø394 onsdag kl 12-14, Ø443A torsdag kl 10-12, Ø443A kl 14-16, Ø394 * släpps ut kl 16 fredag kl 13-15, Ø443A jämna uker förelasningar oppgaver obliger måndag kl 10-12, Ø394 * tisdag onsdag torsdag levereringsfrist kl 16 fredag * Notera att i nagra enstaka dagar pagar gruppeundervisningen i Ø443A istallet (se kursens det officiella tidsplannen).

3 FYS3410 lectures: Spring 2012 MODULE 1 Crystals (Kittels chapters 1, 2, 3, and 20) 16/01/2012: Introduction and motivation, chemical bonding in solids, periodicity, lattices, index system for crystal planes 17/01/2012: Reciprocal space, Laue condition, Ewald construction, interpretation of a diffraction experiment 3h 2h 18/01/2012: Ideas of Fourier analysis, Bragg planes, and Brillouin zones 2h 19/01/2012: Defects and diffusion in crystals 2h 20/01/2012: Mechanical properties and elastic waves in crystals 2h

4 Lecture 5: Mechanical properties and elastic waves in crystals crystal binding elastic and plastic deformation analysis of elastic strain elastic waves in cubic crystals

5 Lecture 5: Mechanical properties and elastic waves in crystals crystal binding elastic and plastic deformation analysis of elastic strain elastic waves in cubic crystals

6

7 Crystals of Inert Gases

8 Covalent Crystals H 2

9

10 Lecture 5: Mechanical properties and elastic waves in crystals crystal binding elastic and plastic deformation analysis of elastic strain elastic waves in cubic crystals

11 stress strain = load W area A = increase in length x original length L ε ij =S ij σ ij Hooke s law σ ij =C ij ε ij See Eqs 37 and 38 in Kittel, p.77 Is there a good reason to introduce complications with so many different indexes as in p.73-80? Yes there is, because, for example elastic waves in crystals often propagate in different directions, specifically can be longitudinal or transverse waves

12 Elastic deformation 1. Initial 2. Small load 3. Unload bonds stretch return to initial F Elastic means reversible!

13 Plastic deformation 1. Initial 2. Small load 3. Unload F Plastic means permanent! linear elastic plastic linear elastic

14 Elastic/plastic deformation

15 Elastic/plastic deformation E E Youngs Modulus or Modulus of Elasticity

16 How is strain applied to the electronic chips? Strained Si 45 nm Si 1-x Ge x Si 1-x Ge x p-type MOSFET

17 Evolution of x-ray diffraction k k

18 Evolution of x-ray diffraction k k 2θ

19 Evolution of x-ray diffraction k k 2θ

20 Evolution of x-ray diffraction k k 2θ n 2d sin 2θ

21 Evolution of x-ray diffraction k k 2θ n 2d sin 2θ

22 Evolution of x-ray diffraction k k 2θ n 2d sin 2θ

23 Lecture 5: Mechanical properties and elastic waves in crystals crystal binding elastic and plastic deformation analysis of elastic strain elastic waves in cubic crystals

24 Analysis of elastic strain Newton s 2 nd law: ik Cik jl ujl 2 u 2 t 1 C 2 ui 2 t i ik x2 2 k u u l j x xu x x C ik jl k jjl k l ik jl xk C ik jl 2 ul x x k j u1 u 1 u2 u 3 u1 u 1 C C12 C44 C t x1 x1x 2 x1x 3 x2 x u2 u 2 u3 u 1 u2 u 2 C C12 C44 C t x2 x2x3 x2x1 x1 x u3 u 3 u2 u 1 u3 u 3 C C12 C44 C t x3 x3x2 x3x1 x2 x1

25 Lecture 5: Mechanical properties and elastic waves in crystals crystal binding elastic and plastic deformation analysis of elastic strain elastic waves in cubic crystals

26 Elastic waves in cubic crystals