ee 5340 semiconductor device theory lecture 01 – spring 2011 professor ronald l. carter...
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EE 5340Semiconductor Device TheoryLecture 01 – Spring 2011
Professor Ronald L. [email protected]
http://www.uta.edu/ronc
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Web Pages
* Review the following• R. L. Carter’s web page
– www.uta.edu/ronc/• EE 5340 web page and syllabus
– www.uta.edu/ronc/5340/syllabus.htm• University and College Ethics Policies
– www.uta.edu/studentaffairs/conduct/– www.uta.edu/ee/COE%20Ethics%20Statement%20Fall%2007.p
df
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First Assignment
• Send e-mail to [email protected]– On the subject line, put “5340 e-mail”– In the body of message include
• email address: ______________________• Your Name*: _______________________• Last four digits of your Student ID: _____
* Your name as it appears in the UTA Record - no more, no less
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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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Bohr model forHydrogen atom• Electron (-q) rev.
around proton (+q)
• Coulomb force, F = q2/4peor2, q = 1.6E-19 Coul, eo=8.854E-14Fd/cm
• Quantization L = mvr = nh/2p, h =6.625E-34J-sec
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Bohr model for the H atom (cont.)• En= -(mq4)/[8eo
2h2n2] ~ -13.6 eV/n2
• rn= [n2eoh2]/[pmq2] ~ 0.05 nm = 1/2 Ao
for n=1, ground state
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Bohr model for the H atom (cont.)En= -
(mq4)/[8eo2h2n2] ~
-13.6 eV/n2 *
rn= [n2eoh2]/[pmq2] ~ 0.05 nm = 1/2 Ao *
*for n=1, ground state
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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/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 = 2 p / l
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Wave-particle duality
• Compton showed Dp = hkinitial - hkfinal, so an photon (wave) is particle-like
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Wave-particle duality
• DeBroglie hypothesized a particle could be wave-like, l = h/p
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Wave-particle duality
• 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 = p2/2m Conservation of Energy Theorem
• Momentum, p = mvConservation 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”, Y(x,t)
• Prob. density = |Y(x,t)• Y*(x,t)|
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Schrodinger Equation
• Separation of variables givesY(x,t) = y(x)• f(t)
• The time-independent part of the Schrodinger equation for a single particle with Total E = E and PE = V. The Kinetic Energy, KE = E - 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
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.
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
y(x) = 0 outside of well
2,
88E
1,2,3,...=n ,sin2
2
22
2
22
nhkh
pmkh
manh
axn
ax
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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.