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ME 381R Lecture 13: Semiconductors Dr. Li Shi Department of Mechanical Engineering The University of Texas at Austin Austin, TX 78712 www.me.utexas.edu/~lishi [email protected] 1 Free Electron Bands Free electron band • Origin of Energy Bands R 0 3p V(r) ˜ -1/r Discrete Electronic Energy States Atom 2 Atom 1 Energy (eV) -5 3s -10 -25 R Split Energy Levels -30 -35 Atom 1 Atom 2 Pauli’s Exclusion Principle 2p 0 3.67 5 10 Interatomic Distance (Å) Na: 1s22s22p63s1 2 Semiconductors X (real space) 3 K Space Semiconductor Forbidden gap Metal E k k 4 Band Gap Energy: Eg 5 How is the Band Gap formed? •For free electron in metals: U 0 because of high electron density and short electrostatic screening length •Electron wavefunction scattered by periodic potentialstanding wave when K= np/a (think about interference of light) 6 Multiple Bands 7 Bandgap Formation 8 Bandstructure of Si and GaAs 9 Electrons and Holes 10 Charge Carrier Density Parabolic approx (free electron): Electron: Hole: m*: effective mass 11 f(E) and D(E) Intrinsic Semiconductor Doped Semiconductor 12 Law of mass action: 13 Intrinsic Semiconductors 14 Doped Semiconductors 15 Dopant Energy Level 16 Carrier Densities in Doped Semiconductors “Law of Mass Action” for semiconductors Charge accounting: 17 Charge Density in Doped Semiconductors Charge neutrality (accounting): Occupation of donors by electrons: Occupation of acceptors by holes: From now on: pure n-type semiconductor (pure p-type is similar) Approximation = 0 (Only one type of dopant at a time) 18 where 19 Temperature Dependance of Carrier Concentration I) Low temperature limit Carrier freeze-out II) Higher temperature limit Saturation III) Muy caliente limit: n ~ ni intrinsic region 20 Carrier Density vs. Temperature HOT COLD 21 Carrier Transport in Semiconductors • Current Density: • Mobility: • Electrical Conductivity: • Drift Velocity: 22 Carrier Scattering Carrier Scattering Mechanisms • Defect Scattering • Phonon Scattering • Boundary Scattering (Film Thickness, Grain Boundary) Grain Grain Boundary 23 Carrier Scattering •Intra-valley •Inter-valley •Inter-band 24 Defect Scattering (i) Ionized defects Perturb potential periodicity Charged defect (ii) Neutral defects 25 Scattering from Ionized Defects (“Rutherford Scattering”) •Average Carrier Velocity in Semiconductors (not the drift velocity): •Mean Free Time: 1/ <v>-3 T-3/2 •Mobility: 26 Carrier-Phonon Scattering • Phonon modulates the periodic potential 1/ph~ Carrier scattered by moving potential 27 Mobility 28 Electrical Conductivity 29