EE 5340 Semiconductor Device Theory Lecture 01 – Spring 2011

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

2. 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

3. 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

4. Quantum Concepts • Bohr Atom • Light Quanta (particle-like waves) • Wave-like properties of particles • Wave-Particle Duality

5. Bohr model forHydrogen 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

6. 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

7. 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

8. 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

9. 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

10. Wave-particle duality • Compton showed Dp = hkinitial - hkfinal, so an photon (wave) is particle-like

11. Wave-particle duality • DeBroglie hypothesized a particle could be wave-like, l = h/p

12. Wave-particle duality • Davisson and Germer demonstrated wave-like interference phenomena for electrons to complete the duality model

13. 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

14. 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)|

15. 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

16. 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.

17. 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

18. 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.