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Semiconductor Device Modeling and CharacterizationEE5342, Lecture 1-Spring 2002

Professor Ronald L. Carterronc@uta.edu

http://www.uta.edu/ronc/

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EE 5342, Spring 2002

• 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

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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,

•PSpiceTM download from http://www.orcad.com http://hkn.uta.edu.

•Dillon tutorial at http://engineering.uta .edu/evergreen/pspice

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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

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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.

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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

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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.

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•Review of – Semiconductor Quantum

Physics– Semiconductor carrier statistics– Semiconductor carrier dynamics

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Bohr model H atom

•Electron (-q) rev. around proton (+q)

•Coulomb force, F=q2/4or2, q=1.6E-19 Coul, o=8.854E-14

Fd/cm•Quantization L = mvr = nh/2•En= -(mq4)/[8o

2h2n2] ~ -13.6 eV/n2

•rn= [n2oh]/[mq2] ~ 0.05 nm = 1/2 Ao

for n=1, ground state

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Quantum Concepts

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

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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) constanth = 6.625E-34 J-sec

stopomax qVffhmvT 2

21

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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/

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Wave-particle Duality•Compton showed p = hkinitial - hkfinal,

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

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Newtonian Mechanics

•Kinetic energy, KE = mv2/2 = p2/2mConservation of Energy

Theorem•Momentum, p = mv

Conservation of Momentum Thm•Newton’s second Law

F = ma = m dv/dt = m d2x/dt2

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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)|

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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.

2

2

280

x

x

mE V x x

h2 ( )

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Solutions for the Schrodinger Equation• Solutions of the form of

(x) = A exp(jKx) + B exp (-jKx)K = [82m(E-V)/h2]1/2

• Subj. to boundary conds. and norm.(x) is finite, single-valued, conts.d(x)/dx is finite, s-v, and conts.

1dxxx

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Infinite Potential Well• V = 0, 0 < x < a• V --> inf. for x < 0 and x > a• Assume E is finite, so

(x) = 0 outside of well

248

2

2

22

2

22 hkhp,

kh

ma

nhE

1,2,3,...=n ,axn

sina

x

n

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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 , andevanescent solutions for E < Vo

• A reflection coefficient can be def.

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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

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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 (x+L) = (x) exp(jkL), Bloch’s Thm

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K-P Potential Function*

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K-P Static Wavefunctions• Inside the ions, 0 < x < a

(x) = A exp(jx) + B exp (-jx) = [82mE/h]1/2

• Between ions region, a < x < (a + b) = L (x) = C exp(x) + D exp (-x) = [82m(Vo-E)/h2]1/2

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K-P Impulse Solution• Limiting case of Vo-> inf. and b -> 0,

while 2b = 2P/a is finite• In this way 2b2 = 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/

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K-P Solutions*

P sin(a)/(a) + cos(a) vs. a

xx

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K-P E(k) Relationship*

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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.