Semiconductor Device
Modeling and Characterization
EE5342, Lecture 1-Spring 2011
Professor Ronald L. Carter ronc@uta.edu
http://www.uta.edu/ronc/

* 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 Policies www.uta.edu/studentaffairs/conduct/ www.uta.edu/ee/COE%20Ethics%20Statement%20Fall%2007.pdf
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• 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.
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• Review of
– Semiconductor Quantum Physics
– Semiconductor carrier statistics
– Semiconductor carrier dynamics
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• Electron (-q) rev. around proton (+q)
• Coulomb force, F=q 2 /4 pe o r 2 , q=1.6E-19 Coul, e o
=8.854E-14 Fd/cm
• Quantization L = mvr = nh/2 p
• E n
• r n
= -(mq 4 )/[8 e
= [n 2 e o
©rlc L01 19Jan2011 h]/[ p o
2 mq h 2 n 2 ] ~ -13.6 eV/n 2
2 ] ~ 0.05 nm = 1/2 A for n=1, ground state o
5

• Bohr Atom
• Light Quanta (particle-like waves)
• Wave-like properties of particles
• Wave-Particle Duality
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T max

1 mv 2
 h  f
• Photoelectric Effect:
 f o
  qV stop
• 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
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7

• 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/2 p wavenumber, k = 2 p / l
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• Compton showed D p = hk initial
- hk final
, so an photon (wave) is particle-like
• DeBroglie hypothesized a particle could be wave-like, l = h/p
• Davisson and Germer demonstrated wave-like interference phenomena for electrons to complete the duality model
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• 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
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• 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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• Separation of variables gives
Y (x,t) = y (x)• f (t)
• The time-independent part of the
Schrodinger equation for a single particle with KE = E and PE = V.
 x
 
2 x

8 p h
2
2

 ( )  y    0
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• Solutions of the form of y (x) = A exp(jKx) + B exp (-jKx)
K = [8 p 2 m(E-V)/h 2 ] 1/2
• Subj. to boundary conds. and norm.
y (x) is finite, single-valued, conts.
d y (x)/dx is finite, s-v, and conts.
 y *     dx  1



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• V = 0, 0 < x < a
• V --> inf. for x < 0 and x > a
• Assume E is finite, so y (x) = 0 outside of well y   
2 a sin


 n p a x



, n =
E n
 h 2 n
8 ma
2
2
 h
4
2 p k
2
2
, p  h l
1,2,3,...
 hk
2 p
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• 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.
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• 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
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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 y (x+L) = y (x) exp(jkL), Bloch’s Thm
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• Inside the ions, 0 < x < a y (x) = A exp(j b x) + B exp (-j b x) b = [8 p 2 mE/h] 1/2
• Between ions region, a < x < (a + b) = L y (x) = C exp( a x) + D exp (a x) a = [8 p 2 m(V o
-E)/h 2 ] 1/2
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• Limiting case of V o
-> inf. and b -> 0, while a 2 b = 2P/a is finite
• In this way a 2 b 2 = 2Pb/a < 1, giving sinh( a b) ~ a b and cosh( a b) ~ 1
• The solution is expressed by
P sin( b a)/( b a) + cos( b a) = cos(ka)
• Allowed values of LHS bounded by +1
• k = free electron wave # = 2 p / l
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x x
P sin( b a)/( b a) + cos( b a) vs. b a
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*Fundamentals of Semiconductor
Theory and Device Physics, by Shyh
Wang, Prentice Hall, 1989.
**Semiconductor Physics & Devices, by Donald A. Neamen, 2nd ed., Irwin,
Chicago.
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