L1 January 151 Semiconductor Device Modeling and Characterization EE5342, Lecture 1-Spring 2002 Professor Ronald L. Carter

L1 January 152 EE 5342, Spring /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, Nedderman, oh 11 to noon, T/W 817/ , 817/ GTA: TBD Go to web page to get lecture notes

L1 January 153 Texts and References 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, PSpice TM download from Dillon tutorial at

L1 January 154 Grades 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

L1 January 155 Project Assignments Four project assignments will be posted at 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.

L1 January 156 Notes 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

L1 January 157 Notes 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.

L1 January 158 Review of –Semiconductor Quantum Physics –Semiconductor carrier statistics –Semiconductor carrier dynamics

L1 January 159 Bohr model H atom Electron (-q) rev. around proton (+q) Coulomb force, F=q 2 /4  o r 2, q=1.6E-19 Coul,  o =8.854E-14 Fd/cm Quantization L = mvr = nh/2  E n = -(mq 4 )/[8  o 2 h 2 n 2 ] ~ eV/n 2 r n = [n 2  o h]/[  mq 2 ] ~ 0.05 nm = 1/2 A o for n=1, ground state

L1 January 1510 Quantum Concepts Bohr Atom Light Quanta (particle-like waves) Wave-like properties of particles Wave-Particle Duality

L1 January 1511 Energy Quanta for Light Photoelectric Effect: T max is the energy of the electron emitted from a material surface when light of frequency f is incident. f o, frequency for zero KE, mat’l spec. h is Planck’s (a universal) constant h = 6.625E-34 J-sec

L1 January 1512 Photon: A particle -like wave E = hf, the quantum of energy for light. (PE effect & black body rad.) f = c/, c = 3E8m/sec, = wavelength From Poynting’s theorem (em waves), momentum density = energy density/c Postulate a Photon “momentum” p = h/  = hk, h = h/2  wavenumber, k =  2  /

L1 January 1513 Wave-particle Duality Compton showed  p = hk initial - hk final, so an photon (wave) is particle-like DeBroglie hypothesized a particle could be wave-like,  = h/p Davisson and Germer demonstrated wave-like interference phenomena for electrons to complete the duality model

L1 January 1514 Newtonian Mechanics Kinetic energy, KE = mv 2 /2 = p 2 /2m Conservation of Energy Theorem Momentum, p = mv Conservation of Momentum Thm Newton’s second Law F = ma = m dv/dt = m d 2 x/dt 2

L1 January 1515 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”,  (x,t) Prob. density = |  (x,t)   (x,t)|

L1 January 1516 Schrodinger Equation Separation of variables gives  (x,t) =  (x)  (t) The time-independent part of the Schrodinger equation for a single particle with KE = E and PE = V.

L1 January 1517 Solutions for the Schrodinger Equation Solutions of the form of  (x) = A exp(jKx) + B exp (-jKx) K = [8  2 m(E-V)/h 2 ] 1/2 Subj. to boundary conds. and norm.  (x) is finite, single-valued, conts. d  (x)/dx is finite, s-v, and conts.

L1 January 1518 Infinite Potential Well V = 0, 0 < x < a V --> inf. for x a Assume E is finite, so  (x) = 0 outside of well

L1 January 1519 Step Potential V = 0, x < 0 (region 1) V = V o, x > 0 (region 2) Region 1 has free particle solutions Region 2 has free particle soln. for E > V o, and evanescent solutions for E < V o A reflection coefficient can be def.

L1 January 1520 Finite Potential Barrier Region 1: x < 0, V = 0 Region 1: 0 < x < a, V = V o Region 3: x > a, V = 0 Regions 1 and 3 are free particle solutions Region 2 is evanescent for E < V o Reflection and Transmission coeffs. For all E

L1 January 1521 Kronig-Penney Model A simple one-dimensional model of a crystalline solid V = 0, 0 < x < a, the ionic region V = V o, 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  (x+L) =  (x) exp(jkL), Bloch’s Thm

L1 January 1522 K-P Potential Function*

L1 January 1523 K-P Static Wavefunctions Inside the ions, 0 < x < a  (x) = A exp(j  x) + B exp (-j  x)  = [8  2 mE/h] 1/2 Between ions region, a < x < (a + b) = L  (x) = C exp(  x) + D exp (-  x)  = [8  2 m(V o -E)/h 2 ] 1/2

L1 January 1524 K-P Impulse Solution Limiting case of V o -> inf. and b -> 0, while  2 b = 2P/a is finite In this way  2 b 2 = 2Pb/a < 1, giving sinh(  b) ~  b and cosh(  b) ~ 1 The solution is expressed by P sin(  a)/(  a) + cos(  a) = cos(ka) Allowed values of LHS bounded by +1 k = free electron wave # = 2  /

L1 January 1525 K-P Solutions* P sin(  a)/(  a) + cos(  a) vs.  a x x

L1 January 1526 K-P E(k) Relationship*

L1 January 1527 References *Fundamentals of Semiconductor Theory and Device Physics, by Shyh Wang, Prentice Hall, **Semiconductor Physics & Devices, by Donald A. Neamen, 2nd ed., Irwin, Chicago.