1 Prof. Junqiao Wu Department of Materials Science and Engineering, U.C. Berkeley 322 HMMB, 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 Rm350, HMMB. Website:

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 General trends in semiconductors covalent ionic

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

5 You won’t regret visiting

6 n-doped p-doped Fermi Si

7 Defects in semiconductors

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9 Band offsets

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 Ohmic contact Work function

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

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

15 Hot carriers resistivity mobility

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

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

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  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  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 Absorptions in Semiconductors Absorption coefficient (cm -1 ) Photon energy (eV) Wavelength (  m) bandgap exciton deeper-bands free carrier phonons (lattice vibration) local impurity vibration impurity electronic cyclotron, spin, magnon core levels CB VB

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 illumination 1 6

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