Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ Semiconductor Device Modeling and Characterization EE5342, Lecture 1-Spring 2005 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ L1 January 18

Web Pages Bring the following to the first class R. L. Carter’s web page www.uta.edu/ronc/ EE 5342 web page and syllabus www.uta.edu/ronc/5342/syllabus.htm University and College Ethics Policies http://www.uta.edu/studentaffairs/judicialaffairs/ www.uta.edu/ronc/5342/Ethics.htm L1 January 18

First Assignment e-mail to listserv@listserv.uta.edu In the body of the message include subscribe EE5342 This will subscribe you to the EE5342 list. Will receive all EE5342 messages If you have any questions, send to ronc@uta.edu, with EE5342 in subject line. L1 January 18

A Quick Review of Physics Semiconductor Quantum Physics Semiconductor carrier statistics Semiconductor carrier dynamics L1 January 18

Bohr model H atom Electron (-q) rev. around proton (+q) Coulomb force, F=q2/4peor2, q=1.6E-19 Coul, eo=8.854E-14 Fd/cm Quantization L = mvr = nh/2p En= -(mq4)/[8eo2h2n2] ~ -13.6 eV/n2 rn= [n2eoh]/[pmq2] ~ 0.05 nm = 1/2 Ao for n=1, ground state L1 January 18

Quantum Concepts Bohr Atom Light Quanta (particle-like waves) Wave-like properties of particles Wave-Particle Duality L1 January 18

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 L1 January 18

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 L1 January 18

Wave-particle Duality Compton showed Dp = hkinitial - hkfinal, so an photon (wave) is particle-like DeBroglie hypothesized a particle could be wave-like, l = h/p Davisson and Germer demonstrated wave-like interference phenomena for electrons to complete the duality model L1 January 18

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 L1 January 18

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)| L1 January 18

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 KE = E and PE = V. L1 January 18

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. L1 January 18

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 L1 January 18

Step Potential V = 0, x < 0 (region 1) V = Vo, x > 0 (region 2) Region 1 has free particle solutions Region 2 has free particle soln. for E > Vo , and evanescent solutions for E < Vo A reflection coefficient can be def. L1 January 18

Finite Potential Barrier Region 1: x < 0, V = 0 Region 1: 0 < x < a, V = Vo Region 3: x > a, V = 0 Regions 1 and 3 are free particle solutions Region 2 is evanescent for E < Vo Reflection and Transmission coeffs. For all E L1 January 18

Kronig-Penney Model A simple one-dimensional model of a crystalline solid V = 0, 0 < x < a, the ionic region V = Vo, a < x < (a + b) = L, between ions V(x+nL) = V(x), n = 0, +1, +2, +3, …, representing the symmetry of the assemblage of ions and requiring that y(x+L) = y(x) exp(jkL), Bloch’s Thm L1 January 18

K-P Potential Function* L1 January 18

K-P Static Wavefunctions Inside the ions, 0 < x < a y(x) = A exp(jbx) + B exp (-jbx) b = [8p2mE/h]1/2 Between ions region, a < x < (a + b) = L y(x) = C exp(ax) + D exp (-ax) a = [8p2m(Vo-E)/h2]1/2 L1 January 18

K-P Impulse Solution Limiting case of Vo-> inf. and b -> 0, while a2b = 2P/a is finite In this way a2b2 = 2Pb/a < 1, giving sinh(ab) ~ ab and cosh(ab) ~ 1 The solution is expressed by P sin(ba)/(ba) + cos(ba) = cos(ka) Allowed values of LHS bounded by +1 k = free electron wave # = 2p/l L1 January 18

K-P Solutions* x P sin(ba)/(ba) + cos(ba) vs. ba L1 January 18

K-P E(k) Relationship* L1 January 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. L1 January 18