1. 1 Prof. Junqiao Wu Department of Materials Science and Engineering, U.C. Berkeley wuj@berkeley.eduwuj@berkeley.edu, 322 HMMB, 510-642-4391 Summer Lectures on Semiconductor Physics for Engineers Contents: 1.Semiconductor basis (2 lectures, 6/2, 6/4) General trends, k-space, band structure, density of states and Fermi distribution k  p theory, defects and effective mass approximation Quantum confinement and nanostructures 2.Electrostatics (2 lectures, 6/8, 6/11) Maxwell equations and Poisson’s equation Band bending and carrier equilibration 3.Electrodynamics (2 lectures, 6/16, 6/18) Drude’s model and classical dielectric theory Boltzmann transport theory 4.Thermal effects (2 lectures, 6/23, 6/25) Phonons and thermal physics Thermoelectrics 5.Optical effects (1 lecture, 6/30) Light-semiconductor interactions Device physics of light emitting diodes and solar cells Prerequisites: calculus, vectors, ordinary and partial differential equations, linear algebra, electromagnetism, optics basics, solid state physics basics, quantum mechanics basics Time and location: Tuesday and Thursdays 5:00-6:30PM, June 2009. Rm350, HMMB. Website: http://www.mse.berkeley.edu/~jwu/courses/semi.html

2. 2 s2p2s2p2 cation and anion Most common semiconductors: group IV (Si), III-V (GaAs), II-VI (CdSe), and their alloys Insulators : group I-VII (NaCl)

3. 3 General trends in semiconductors covalent ionic

4. 4 bandgap Conduction bands Valence bands simple cubicface-center cubiczincblende Brillouin zone (for fcc structure)

5. 5 You won’t regret visiting http://www.ioffe.ru/SVA/

6. 6 n-doped p-doped Fermi Si

7. 7 Defects in semiconductors

8. 8

9. 9 Band offsets

10. 10 Schottky Contact: example of M/nS with  M >  S qMqM qSqS qq E CB E VB E FM E FS before contact qMqM qSqS qq E CB E VB E FM E FS after contact qV i =q(  M -  S ) qV i qBqB - - W - - + + - + - + vacuum level - - + + - + - +

11. 11 Ohmic contact Work function

12. 12 net charge distribution SD nanowire oxide gate air Nano Lett.; 7, 2778 (2007). Si @ 300K

13. 13 p-n junction and depletion width ++++ + --- ---- - +++ EFEF - - + + ionized donor ionized acceptor free electron free hole + - + - + - + - - + + - + - - - - - - - + + + + + + - + n-type p-type NDND NANA + - + - + - + - + + - + - - - - - - + + + + + - diffusion current ++++ + ----- ---- - +++++ E Fn E Fp EDED EAEA EgEg qV 0 W for N D =N A drift current Total net current = 0 (unless externally biased)

14. 14 I V 0 forwardreverse Biasing a diode n p VfVf n p VrVr n p

15. 15 Hot carriers resistivity mobility

16. 16 Phonon spectrum 1D diatomic chain Wavevector q 2xTA 1xLA 1xLO 2xTO Si

17. 17 Phys. Rev. 98, 940 (1955) Bulk Si Seebeck coefficient

18. 18 Natural Si ( 28 Si=92% 29 Si=5% 30 Si=3%) enriched Si ( 28 Si=99.9%) Majumdar, Science (2004) Thermal conductivity and thermoelectric figure of merit

19. 19  Reflected –Same energy (h ) and wavelength ( ) –Specular:  1 ’ =  1  Refracted then Absorbed –Snell’s law: n 1 sin  1 =n 2 sin  2 –Frequency: 1 = 2 = =  /2  –Speed of light: n 1 c 1 = n 2 c 2 –Wavelength: n 1 1 =n 2 2 –Intensity: I  exp(-  d) –Absorption:  (h )  (h -E g ) 1/2  Transmitted –  3 =  1 – 3 = 1, 3 = 1  Scattered –Rayleigh scattering, h = h 1 –Raman and Brillouin scattering, h = h 1  ħ  –not directional  Emitted –not directional –h  E g incident reflected transmitted scattered absorbed emitted 11 22 1’1’ n1n1 n2n2 33 d Optical process in semiconductors

20. 20  ħħ rr ii 0 GaAs E1E1 E0E0 E2E2 R 0 R  ħħ E0E0 E1E1 E2E2   (E-E 0 ) 1/2 for direct bandgap semiconductors Dielectric Functions of Semiconductors

21. 21 Absorptions in Semiconductors Absorption coefficient (cm -1 ) Photon energy (eV) Wavelength (  m) 10 -3 10 -2 10 -1 10 0 10 1 10 0 10 2 10 4 10 6 10 3 10 2 10 1 10 0 10 -1 bandgap exciton deeper-bands free carrier phonons (lattice vibration) local impurity vibration impurity electronic cyclotron, spin, magnon core levels CB VB + - - + -

22. 22 Fundamentals of photovoltaics 1.“Red” loss 2.Thermalization loss (“blue loss”) 3.Junction loss 4.Contact loss 5.Recombination loss 6.Reflection loss usable qV 2 3 4 5 2 illumination 1 6

23. 23

24. 24 LED materials InGaN AlGaAs AlGaP AlGaInP GaAsP GaPN GaN ZnSe, AlN AlGaN GaAs