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Introduction to Semiconductor Device Modeling and Characterization (EE5342) - Spring 2005

Join Professor Ronald L. Carter in EE5342: Semiconductor Device Modeling and Characterization. This course covers foundational concepts in semiconductor physics, including quantum mechanics, carrier statistics, and dynamic behavior of carriers. Key topics include the Bohr model of the atom, wave-particle duality, Schrödinger’s equation, and the Kronig-Penney model. Prepare for advanced topics in semiconductor devices and ensure familiarity with university ethics policies. For more information about course materials and assignments, visit [Professor Carter's webpage](http://www.uta.edu/ronc/).

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Introduction to Semiconductor Device Modeling and Characterization (EE5342) - Spring 2005

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  1. Semiconductor Device Modeling and CharacterizationEE5342, Lecture 1-Spring 2005 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

  2. 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

  3. 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.

  4. A Quick Review of Physics • Review of • Semiconductor Quantum Physics • Semiconductor carrier statistics • Semiconductor carrier dynamics

  5. 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

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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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)|

  12. 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.

  13. 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.

  14. 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

  15. 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.

  16. 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

  17. 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

  18. K-P Potential Function*

  19. 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

  20. 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

  21. x x K-P Solutions* P sin(ba)/(ba) + cos(ba) vs.ba

  22. K-P E(k) Relationship*

  23. 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.

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