Semiconductor Device
Modeling and Characterization
EE5342, Lecture 1-Spring 2002
Professor Ronald L. Carter
ronc@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.
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• 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
2
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
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•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
3
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
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•
•
•
•
•
•
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
4
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 handwritten page of
notes. Calculator OK.
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3. There will be no
make-up, or early
exams given. Attendance is required for
all tests.
4. See Americans
with Disabilities Act
statement
5. See academic dishonesty statement 6
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
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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=q2/4peor2,
q=1.6E-19 Coul, eo=8.854E-14 Fd/cm
• Quantization L = mvr = nh/2p
• En= -(mq4)/[8eo2h2n2] ~ -13.6 eV/n2
• rn= [n2eoh]/[pmq2] ~ 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
1
Tmax  mv 2  h f  fo   qVstop
2
• 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) constant
h = 6.625E-34 J-sec
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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 = 2p /l
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Wave-particle
Duality
• Compton showed Dp = hkinitial - hkfinal, 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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Newtonian Mechanics
• Kinetic energy, KE = mv2/2 = p2/2m
Conservation 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 waveparticle 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 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.
2y x  8p2m
 2 E V ( x )  y x   0
2
x
h
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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.

*
y
 x y x dx  1
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
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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
np x 

y x  
sin 
, n = 1,2,3,...
a
 a 
h 2n 2 h 2k 2
h hk
En 

,p  
2
2
l 2p
8ma
4p
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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 , and
evanescent 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
y(x+L) = y(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
y(x) = A exp(jbx) + B exp (-jbx)
b = [8p2mE/h]1/2
• Between ions region, a < x < (a + b) = L
y(x) = C exp(ax) + D exp (-ax)
a = [8p2m(Vo-E)/h2]1/2
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K-P Impulse Solution
• Limiting case of Vo-> inf. and b -> 0,
while a2b = 2P/a is finite
• In this way a2b2 = 2Pb/a < 1, giving
sinh(ab) ~ ab and cosh(ab) ~ 1
• The solution is expressed by
P sin(ba)/(ba) + cos(ba) = cos(ka)
• Allowed values of LHS bounded by +1
• k = free electron wave # = 2p/l
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K-P Solutions*
x
x
P sin(ba)/(ba) + cos(ba) vs. ba
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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.
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