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UT Arlington EE 5340 - Semiconductor Device Theory

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Slide 1Web PagesFirst AssignmentQuantum ConceptsBohr model for Hydrogen atomSlide 6Bohr model for the H atom (cont.)Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Quantum MechanicsSchrodinger EquationSolutions for the Schrodinger EquationInfinite Potential WellReferencesEE 5340Semiconductor Device TheoryLecture 01 – Spring 2011Professor Ronald L. [email protected]://www.uta.edu/ronc©rlc L01 18Jan20112Web 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 18Jan20113First Assignment•Send e-mail to [email protected]–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 18Jan20114Quantum Concepts•Bohr Atom•Light Quanta (particle-like waves)•Wave-like properties of particles•Wave-Particle Duality©rlc L01 18Jan20115Bohr 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©rlc L01 18Jan20116Bohr model for the H atom (cont.)•En= -(mq4)/[8eo2h2n2] ~ -13.6 eV/n2•rn= [n2eoh2]/[pmq2] ~ 0.05 nm = 1/2 Aofor n=1, ground state©rlc L01 18Jan20117Bohr 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 18Jan20118Energy 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) constanth = 6.625E-34 J-sec stopomaxqVffhmvT 221©rlc L01 18Jan20119Photon: 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 18Jan201110Wave-particle duality•Compton showed Dp = hkinitial - hkfinal, so an photon (wave) is particle-like©rlc L01 18Jan201111Wave-particle duality•DeBroglie hypothesized a particle could be wave-like, l = h/p©rlc L01 18Jan201112Wave-particle duality•Davisson and Germer demonstrated wave-like interference phenomena for electrons to complete the duality model©rlc L01 18Jan201113Newtonian Mechanics•Kinetic energy, KE = mv2/2 = p2/2m Conservation of Energy Theorem•Momentum, p = mvConservation of Momentum Thm•Newton’s second Law F = ma = m dv/dt = m d2x/dt2©rlc L01 18Jan201114Quantum 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 18Jan201115Schrodinger Equation•Separation of variables givesY(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  22280xxmE V x x  h2( )©rlc L01 18Jan201116Solutions 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.    1dxxx©rlc L01 18Jan201117Infinite 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 2,88E1,2,3,...=n ,sin2222222nhkhpmkhmanhaxnax©rlc L01 18Jan201118References *Fundamentals of Semiconductor Theory and Device Physics, by Shyh Wang, Prentice Hall, 1989. **Semiconductor Physics & Devices, by Donald A. Neamen, 2nd ed., Irwin,


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