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Semiconductor Device Modeling and Characterization EE5342, Lecture 1-Spring 2010. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/. 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 - PowerPoint PPT Presentation
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Semiconductor Device Modeling and CharacterizationEE5342, Lecture 1-Spring 2010
Professor Ronald L. Carterronc@uta.edu
http://www.uta.edu/ronc/
L1 January 20 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– http://www.uta.edu/ronc/5342/syllabus.htm
• University and College Ethics Policieswww.uta.edu/studentaffairs/conduct/www.uta.edu/ee/COE%20Ethics%20Statement%20Fall%2007.pdf
L1 January 20 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.
L1 January 20 4
A Quick Review of Physics
•Review of – Semiconductor Quantum
Physics– Semiconductor carrier statistics– Semiconductor carrier dynamics
L1 January 20 5
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 20 6
Quantum Concepts
• Bohr Atom• Light Quanta (particle-like waves)• Wave-like properties of particles• Wave-Particle Duality
L1 January 20 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) constanth = 6.625E-34 J-
sec
stopomax qVffhmvT 2
21
L1 January 20 8
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 20 9
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 20 10
Newtonian Mechanics• Kinetic energy, KE = mv2/2 =
p2/2m Conservation of Energy Theorem
• Momentum, p = mvConservation of
Momentum Thm• Newton’s second Law
F = ma = m dv/dt = m d2x/dt2
L1 January 20 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”, (x,t)
• Prob. density = |(x,t)• (x,t)|
L1 January 20 12
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 20 13
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 20 14
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 20 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 , andevanescent solutions for E <
Vo
• A reflection coefficient can be def.
L1 January 20 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
L1 January 20 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 (x+L) = (x) exp(jkL), Bloch’s Thm
L1 January 20 19
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 20 20
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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