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Semiconductor Device Modeling and Characterization EE5342, Lecture 1-Spring 2002

Semiconductor Device Modeling and Characterization EE5342, Lecture 1-Spring 2002. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/. http://www.uta.edu/ronc/5342sp02

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Semiconductor Device Modeling and Characterization EE5342, Lecture 1-Spring 2002

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  1. Semiconductor Device Modeling and CharacterizationEE5342, Lecture 1-Spring 2002 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

  2. http://www.uta.edu/ronc/5342sp02 Obj: To model and characterize integrated circuit structures and devices using SPICE and SPICE-like descriptions of the devices. Prof. R. L. Carter, ronc@uta.edu, www.uta.edu/ronc, 532 Nedderman, oh 11 to noon, T/W 817/273-3466, 817/272-2253 GTA: TBD Go to web page to get lecture notes EE 5342, Spring 2002

  3. Text-Semiconductor Device Modeling with SPICE, by Antognetti and Massobrio - T. Ref:Schroder (on reserve in library) S Mueller&Kamins D See assignments for specific sections Spice References: Goody, Banzhaf, Tuinenga, Herniter, PSpiceTM download from http://www.orcad.com http://hkn.uta.edu. Dillon tutorial at http://engineering.uta .edu/evergreen/pspice Texts and References

  4. Grading Formula: 4 proj for 15% each, 60% total 2 tests for 15% each, 30% total 10% for final (req’d) Grade = 0.6*Proj_Avg + 0.3*T_Avg + 0.1*F Grading Scale: A = 90 and above B = 75 to 89 C = 60 to 74 D = 50 to 59 F = 49 and below T1: 2/19, T2: 4/25 Final: 800 AM 5/7 Grades

  5. Project Assignments • Four project assignments will be posted at http://www.uta.edu/ronc/5342sp02/projects • Pavg={P1 + P2 + P3 + P4 + min[20,(Pmax-Pmin)/2]}/4. • A device of the student's choice may be used for one of the projects (by permission) • Format and content will be discussed when the project is assigned and will be included in the grade.

  6. 1. This syllabus may be changed by the instructor as needed for good adademic practice. 2. Quizzes & tests: open book (no Xerox copies) OR one hand-written page of notes. Calculator OK. 3. There will be no make-up, or early exams given. Atten-dance is required for all tests. 4. See Americans with Disabilities Act statement 5. See academic dis-honesty statement Notes

  7. 5 (con’t.) All work submitted must be original. If derived from another source, a full bibliographical citation must be given. 6. If identical papers are submitted by different students, the grade earned will be divided among all identical papers. 7. A paper submitted for regrading will be compared to a copy of the original paper. If changed, points will be deducted. Notes

  8. Review of • Semiconductor Quantum Physics • Semiconductor carrier statistics • Semiconductor carrier dynamics

  9. 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

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

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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)|

  16. 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.

  17. 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.

  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

  19. 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.

  20. 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

  21. 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

  22. K-P Potential Function*

  23. 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

  24. 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

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

  26. K-P E(k) Relationship*

  27. 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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