Upload
calvin-evans
View
224
Download
1
Embed Size (px)
Citation preview
L1 January 15 1
Semiconductor Device Modeling and CharacterizationEE5342, Lecture 1-Spring 2002
Professor Ronald L. [email protected]
http://www.uta.edu/ronc/
L1 January 15 2
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, [email protected], 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
L1 January 15 3
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
L1 January 15 4
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 15 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.
L1 January 15 6
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 15 7
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 15 8
•Review of – Semiconductor Quantum
Physics– Semiconductor carrier statistics– Semiconductor carrier dynamics
L1 January 15 9
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
L1 January 15 10
Quantum Concepts
• Bohr Atom• Light Quanta (particle-like waves)• Wave-like properties of particles• Wave-Particle Duality
L1 January 15 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) constanth = 6.625E-34 J-sec
stopomax qVffhmvT 2
21
L1 January 15 12
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 15 13
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
L1 January 15 14
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
L1 January 15 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”, (x,t)
• Prob. density = |(x,t)• (x,t)|
L1 January 15 16
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 ( )
L1 January 15 17
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
L1 January 15 18
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
L1 January 15 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 , andevanescent solutions for E < Vo
• A reflection coefficient can be def.
L1 January 15 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
L1 January 15 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 (x+L) = (x) exp(jkL), Bloch’s Thm
L1 January 15 23
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
L1 January 15 24
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/