Chapter 1: Pierret
Dr. Jeff Davis
ECE 3040
FALL 2007
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References
• Prof. Alan Doolittle’s Notes
– users.ece.gatech.edu/~alan/index_files/ECE3040index.htm
• Prof. Farrokh Ayazi’s Notes
– users.ece.gatech.edu/~ayazi/ece3040/
• Figures for Require Textbooks
– (Pierret and Jaeger)
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ECE 3040-B: Microelectronic Circuits (3-0-3)
PREREQUISITES: ECE 2030 and ECE 2040 and Math 2403 and Chem 1211
DESCRIPTION: Basic concepts of microelectronic materials, devices and circuits
TIME: MWF 10:35-11:55AM
CLASSROOM: Van Leer C240
CREDITS: Four Hours
PROFESSOR:
Jeffrey Davis, Office Klaus 3314
Phone:
894-4770
E-mail:
j eff.davis@ece.gatech.edu
OFFICE HOURS: MW 1:30-3; FRI 1:30-2:00
ASSIGNMENTS & G R A D I N G :
Homework
Class
Problems
Participation
(10%)
(5%)
Quiz
I
(18%)
Quiz
II
(18%)
Quiz
III
(18%)
Final
Exam
(31%)
Final grades will be assigned according: A = [90, 100] ; B = [80,90) ; C = [70,80) ; D =[50,70) ; F = [0,50]
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MISSING TESTS OR QUIZES: If you must miss a test or quiz for a serious condition, you must let me know
as soon as you know that you cannot attend. Any excused absence must be accompanied by proper documentation.
For example, if you have a f lat tire, I would like to see the dated receipt to fix the t ire. If you have a death in the
family, I would like to see a copy of the death certificate. If you are in an auto accident, I would like to see a copy of
the police report. If you oversleep, I will let you take a make up exam, BUT the highest grade you can receive is a C.
FORMULA SHEET FOR TEST: You may have a f ormula sheet for each test according to the following criteria:
1) single 8 x 11 page ;2) front side only; 3) formulas only; 4) handwritten; 5) do N OT cop y homework, class
examples, or old exam problems solution to your formula sheet ; 6) no graphs or pictures allowed.
TEXTBOOKS:
Jaeger, Microelectronic Circuit Design, McGraw Hill, 2003. ISBN 00763649503 (required)
Pierret, Semiconductor Device Fundamentals, Addison Wesley, 1996. ISBN 0-201-54393-1 (required)
TA: Sarah Bryan (sarahb4671@gatech.edu)
HOMEWORKS: Assigned and due every Monday (except on weeks that we have a test). They will be graded by the
T.A.
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Sign Honor Code Agreement
• "Plagiarizing is defined by Webster’s as “to steal and pass off (the ideas or words of another) as
one's own: use (another's production) without crediting the source.” If caught plagiarizing, you
will be dealt with according to the GT Academic Honor Code." †
• Copying homework from "word" or using "word" to complete your homework will be considered
plagiarism.
• “You are allowed (and encouraged) to work toge ther with other students on homework; however,
you should NOT copy another persons homework. If you are working in groups you must be able
to reproduce the homework problem on your without assistance from another person. You are also
allowed (and encouraged) to ask me and the TA questions, although you should try to think abou t
the problems before asking. I strongly encourage you to work on extra problems from the book on
your own.” †
• Cheating off of another person’s test or quiz is unethical and unacceptable. Cheating off of anyone
else’s work is a direct violation of the GT Academic Honor Code, and will be
dealt with
accordingly.
• “For any questions involving these or any other Academic Honor Code issues, please consult me,
my teaching assistants, or www.honor.gatech.edu.” †
I, _______________________________________ , understand what are considered violations of the
honor code in this class. I will abide by these rules. Failure to do so will result in either receiving a failing
grade for this class and will result in being turned over to the Dean of Students for academic misconduct.
_______________________________
Sign your name.
†
These statements were taken for a new website by the Dean of Students which can be found at the
following URL: http://www.honor.gatech.edu/faculty/syllabus_checklist.html
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What is this course about?
PN Junction Diodes
Bipolar Junction Transistors (BJT)
Metal Oxide Semiconductor Field
Effect Transistor (MOSFET)
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What is this course about?
Basic Semiconductor Physics
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What is this course about?
Single Transistor Amplifiers
Operational Amplifiers
Digital CMOS circuits
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Questions to answer in this
lecture!
• What is a semiconductor?
• How do we described x-tal structure?
• How do we produce pure Silicon x-tals?
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What is a semiconductor?
10
Classifications of Electronic Materials
A high level description could be …
• Metals -- Highly conductive to current flow!
• Insulators -- Highly resistive to current flow!
• Semiconductors -- Somewhere in between!
Doping is a good thing!
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Classifications of Electronic Materials
Another could be based on bond strengths…
12
Classifications of Electronic Materials
Results in how conductive a material is…
Semiconductor Crystal
Metal Crystal
Metal atoms are ionized..
Electrons free to roam
(1022
cm-3)
Strong Bonds
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Classifications of Electronic Materials
The strength of the bonds determines
material properties
“The partially heteropolar [ionic&covalent]
bonds in GaAs are strong than the homopolar
[covalent] bonds in Si and Ge. It leads to a
smaller amplitude of the lattice vibrations (and
as a consequence to higher mobility), higher
melting point, and wider energy gapsӠ
†Michael
Shur, GaAs Devices and Circuits, 1987 Spring Publisher
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Energy Band Theory of Solids
Origin of Allowable Energy Bands…
Carbon (C) 1s22s22p2
‘N’ for this figure is the number of
atoms with overlapping electron
wavefunctions
sp3 hybrid orbitals
Energy split due to Pauli Exclusion Principle once
electron wave functions start to overlap.
Note - at zero temp all
electrons are in the valence
band!
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Reference:
Energy Band Theory of Solids
Energy necessary to break the electron from its bond is the bandgap energy.
Insulators
Semiconductors
Ec
Si
Ec
eInSb
SiO2
8.8eV
Ev
Ev
e- e- eEv
e- e- e- e- e-
“Silicon”
e-
Ec
1.12eV
e-
0.17eV
e- e- e-
e-
Indium
Antimonide
Remember: Metals have not forbidden region!
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Energy Band Theory of Solids
What is an electron volt?
• It is an ENERGY!
• 1eV = 1.6e-19 J
InSb
Ec
0.17eV
Amount of K.E. energy given to a electron passing
through an electrostatic potential of 1 volt
W = F ! "x
W = (qE) ! "x
V
W =q
"x = qV
"x
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Classification of Semiconductors
• Elementary Semiconductors Examples
– Si and Ge
• Compound Semiconductors Examples
– III-V Compound Semiconductors (GaAs)
– IV-IV Compound Semiconductors (SiC)
– II-VI Compound Semiconductors (CdS)
Average of 4 valence electrons per atom in outer subshell to produce covalent/ionic bonds!
GaAs = “Gallium Arsenide”
SiC = “Silicon Carbide”
CdS = “Cadmium Sulfide”
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To refer to compound semiconductors take root of second element and add “ide” as a suffix!
Classification of Semiconductors
• Alloys (substitutional vs. interstitial)
– Binary Alloys -- Si1-xGex
– Ternary Alloys -- AlxGa1-xAs
– Quaternary Alloys -- GaxIn1-xAs1-yPy
Remember: This fraction refers to the number of atoms!
Unlike compound semiconductors, composition amount of alloy
material can change to change bandgap.
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Classification of Semiconductors
Example
What percentage of atoms are Gallium in the ternary alloy Ga0.5In0.5N?
100* 0.5/(1+0.5+0.5) =25%
What percentage of atoms are Indium in the ternary alloy Ga0.5In0.5N?
100* 0.5/(1+0.5+0.5) =25%
What percentage of atoms are Nitrogen in the ternary alloy Ga0.5In0.5N?
100* 1/(1+0.5+0.5) =50%
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Classification of Semiconductors
Why is GaAs a compound semiconductor
and SiGe an semiconductor alloy?
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Classification of Semiconductors
Alloy composition changes x-tal
properties
reference
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Doping Semiconductors
OCCASIONALLY add in other elements to substitute for
silicon in x-tal to change conductivity of material!
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
“OCCASIONALLY” typically means 1 dopant atom in 1000 Silicon atoms to 1 dopant
atom in 100M Silicon atoms
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Doping Semiconductors
Si
silicon has
4 valence electrons
phosphorus has
5 valence electrons
Si
Si
Si
B
P
boron has
3 valence electrons
Si
Si
Si
4 covalent bonds
Si
P
Si
Si
Si
free electron
n-type dopant
Si
B
Si
Si
“hole”
p-type dopant
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How do we describe x-tal
structure?
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X-tal properties
1. Si thin film transistors
1. Gate material of MOSFET
Most high-quality devices
2. Amorphous Si Solar Cells
2. Polycrystalline solar cells
are made of pure x-tal!
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Importance of Crystal (x-tal)
Structure
• Example - Carbon
– Graphite (conductor)
– Diamond (great insulator)
• We must have a working vocabulary to
describe different x-tal structures
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Unit Cell Definition
A portion of the crystal that could be used to reproduce
the entire x-tal… kind of like a “rubber stamp”
Examples of
unit cells
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Unit Cell Definition
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A unit cell can be used to recreate the entire x-tal lattice!
Unit Cell Definition
Is this a unit cell?
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A unit cell can be used to recreate the entire x-tal lattice!
Primitive Unit Cell
The smallest portion of the crystal that could be used to
reproduce the entire x-tal.
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3-D Cubic X-tal Cells
(BCC)
(FCC)
a = “lattice constant”
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Strictly speaking are these
pictures correct?
(BCC)
(FCC)
YES &NO!
1
2
4
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Diamond Lattice
One-quarter of diagonal length
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Zinc Blende
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Atomic Density
What is the atomic density of a BCC material with lattice constant
5.2 angstroms?
Number of Atoms per unit cell = 2
Volume of unit cell = a 3 = (5.2e ! 8 cm) 3 = 1.41e ! 22 cm3
Number of Atoms per unit cell
atoms
Density =
= 1.4e22
Volume of unit cell
cm337
X-tal planes
2a
a
a
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X-tal planes
a
a
a
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How do we specify x-tal
planes?
Answer: Miller Indices!
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What are miller indices?
(346)
For cubic lattice types, it is a vector that is perpendicular to the
given plane.
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How do I calculate vector
perpendicular to a plane?
zz! , xx! , yy!
vector 1 = zz! ! xx!
vector 2 = zz! ! yy!
x!
y!
vector1 " vector2 = !x 0
0 !y
divide by xyz
zy ! xz ! xy !
x+
y+
z
xyz
xyz
xyz
1 ! 1 ! 1!
x+ y+ z
x
y
z
Z
z!
z = zyx! + xzy! + xyz!
z
z
y
X
Y
x
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X-tal planes and Miller Indices
1. Identify Intercepts in x,y,z order
( 4a, -3a, 2a)
2. Divide by unit cell length in each
direction x,y,z order ( 4, -3, 2)
3. Invert the values (1/4, -1/3, 1/2)
4. Multiply by a number (12 in this
example) to give smallest whole
number set = 3, -4, 6
5. Place any minus signs over their index
and place set in parenthesis = (346)
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Examples: x-tal planes
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X-tal Directions using Miller
Indices
1. Find vector in the desired direction
2. Divide by the lattice constant
3. Convert vector to smallest possible whole number set
4. Use SQUARE BRACKETS around number set
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Certain planes are “equivalent” because
their atomic properties are not
distinguishable in a periodic lattice.
a
a
(100)
(010)
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Equivalent x-tal planes & directions
z
z
y
y
x
x
Planes
Directions
{100} =
<100> =
(100), (100)
(010), (010)
(001), (001)
[100], [100]
[010], [010]
[001], [001]
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Wafer Orientations
Secondary flat
(111) p-type
(111) n-type
Secondary flat
Secondary flat
(100) n-type
(100) p-type
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How do we produce silicon
x-tals?
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Producing ultra-pure silicon
start with Silica
(impure SiO2)
Chlorinated
impure Silicon
ultra-pure
SiCl4
heat Silica with
Carbon to remove
Oxygen
liquefied SiCl4
“silicon
tetrachloride”
heat SiCl4 in H2
atmosphere
(SiCl4+2H2 ⇒
4HCL+ Si )
very impure
silicon
distillation
purification
process
ultra-pure
polycrystalline
Silicon
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Ingot
Wafer
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Wafer Boat
300mm wafer
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Czochralski Crystal Growth
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54
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From your Chemistry Classes
be sure to review…
•
•
•
•
Ionic Bonds (NaCl)
Covalent Bonds ( Si, SiC)
Metallic Bonds
Van de Waals
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