EE 5340 Semiconductor Device Theory Lecture 01 – Spring 2011 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc

Web Pages Review the following R. L. Carter’s web page www.uta.edu/ronc/ EE 5340 web page and syllabus www.uta.edu/ronc/5340/syllabus.htm University and College Ethics Policies www.uta.edu/studentaffairs/conduct/ www.uta.edu/ee/COE%20Ethics%20Statement%20Fall%2007.pdf ©rlc L01 18Jan2011

First Assignment Send e-mail to ronc@uta.edu On the subject line, put “5340 e-mail” In the body of message include email address: ______________________ Your Name*: _______________________ Last four digits of your Student ID: _____ * Your name as it appears in the UTA Record - no more, no less ©rlc L01 18Jan2011

Quantum Concepts Bohr Atom Light Quanta (particle-like waves) Wave-like properties of particles Wave-Particle Duality ©rlc L01 18Jan2011

Bohr model for Hydrogen atom Electron (-q) rev. around proton (+q) Coulomb force, F = q2/4peor2, q = 1.6E-19 Coul, eo=8.854E-14Fd/cm Quantization L = mvr = nh/2p, h =6.625E-34J-sec ©rlc L01 18Jan2011

Bohr model for the H atom (cont.) En= -(mq4)/[8eo2h2n2] ~ -13.6 eV/n2 rn= [n2eoh2]/[pmq2] ~ 0.05 nm = 1/2 Ao for n=1, ground state ©rlc L01 18Jan2011

Bohr model for the H atom (cont.) En= - (mq4)/[8eo2h2n2] ~ -13.6 eV/n2 * rn= [n2eoh2]/[pmq2] ~ 0.05 nm = 1/2 Ao * *for n=1, ground state ©rlc L01 18Jan2011

Energy Quanta for Light Photoelectric Effect: Tmax is the energy of the electron emitted from a material surface when light of frequency f is incident. fo, frequency for zero KE, mat’l spec. h is Planck’s (a universal) constant h = 6.625E-34 J-sec ©rlc L01 18Jan2011

Photon: A particle -like wave E = hf, the quantum of energy for light. (PE effect & black body rad.) f = c/l, c = 3E8m/sec, l = wavelength From Poynting’s theorem (em waves), momentum density = energy density/c Postulate a Photon “momentum” p = h/l = hk, h = h/2p wavenumber, k = 2p /l ©rlc L01 18Jan2011

Wave-particle duality Compton showed Dp = hkinitial - hkfinal, so an photon (wave) is particle-like ©rlc L01 18Jan2011

Wave-particle duality DeBroglie hypothesized a particle could be wave-like, l = h/p ©rlc L01 18Jan2011

Wave-particle duality Davisson and Germer demonstrated wave-like interference phenomena for electrons to complete the duality model ©rlc L01 18Jan2011

Newtonian Mechanics Kinetic energy, KE = mv2/2 = p2/2m Conservation of Energy Theorem Momentum, p = mv Conservation of Momentum Thm Newton’s second Law F = ma = m dv/dt = m d2x/dt2 ©rlc L01 18Jan2011

Quantum Mechanics Schrodinger’s wave equation developed to maintain consistence with wave-particle duality and other “quantum” effects Position, mass, etc. of a particle replaced by a “wave function”, Y(x,t) Prob. density = |Y(x,t)• Y*(x,t)| ©rlc L01 18Jan2011

Schrodinger Equation Separation of variables gives Y(x,t) = y(x)• f(t) The time-independent part of the Schrodinger equation for a single particle with Total E = E and PE = V. The Kinetic Energy, KE = E - V ©rlc L01 18Jan2011

Solutions for the Schrodinger Equation Solutions of the form of y(x) = A exp(jKx) + B exp (-jKx) K = [8p2m(E-V)/h2]1/2 Subj. to boundary conds. and norm. y(x) is finite, single-valued, conts. dy(x)/dx is finite, s-v, and conts. ©rlc L01 18Jan2011

Infinite Potential Well V = 0, 0 < x < a V --> inf. for x < 0 and x > a Assume E is finite, so y(x) = 0 outside of well ©rlc L01 18Jan2011

References *Fundamentals of Semiconductor Theory and Device Physics, by Shyh Wang, Prentice Hall, 1989. **Semiconductor Physics & Devices, by Donald A. Neamen, 2nd ed., Irwin, Chicago. ©rlc L01 18Jan2011