Thermodynamics in Chip
Processing
Terry Ring
Silicon Wafers
Chip Feature Scaling
Moore’s Law
• please see
http://developer.intel.com/update/archive/issue2/focus.htm
What is a semiconductor?
• Conductor
– Metal
• Insulator
– Ceramic (oxides)
• Semiconductor
–
–
–
–
–
Diamond
Silicon
Germanium
Gallium Arsenide
Host of others
Intrinsic Silicon
• Silicon has four valence electrons. When a
group of Silicon atoms bond together to
produce a pure lattice structure, the
material is referred to as Intrinsic Silicon.
Si
Si
Si
Si
Si
Si
Si
Si
Si
Silicon Doping
• This pure silicon configuration (intrinsic
silicon) is a poor conductor because none of
its electrons are available to serve as carriers
of electric charge.
• The fabrication of integrated circuits requires
that the substrate (the wafer surface) be
somewhat conductive.
• This process is known as doping. Boron (B),
Phosphorus (P), and Arsenic (As) are the
most common dopant atoms used in the
industry.
The Periodic Table of Elements
x: All isotopes are radioactive.
1
Atomic Number
Atomic Weight
Aymbol of Element
1.008
H
Hydrogen
(1)*
IA
Period
1
*
Name of Element
1.008
H
1
3
6.941
4
Li
Be
Beryllium
11
22.99
12
Na
Mg
Magnesium
19
39.10
5
Representative Transition Inner-Transition Noble
Gases
Elements
Elements
Elements
20
40.08
10.81
13
24.31
Sodium
3
(18)
Noble
Gases
2
21
44.96
22
(6)
VI B
(5)
VB
(4)
IV B
(3)
III B
47.90
23
50.94
24
52.00
(7)
VII B
25
54.94
(8)
26
55.85
27
58.93
(11)
IB
(10)
(9)
VIII B
28
58.71
29
63.55
(12)
II B
30
65.37
6
12.01
(16)
VI A
(15)
VA
(14)
IV A
(13)
III A
9.012
Lithium
2
Number in ( ) heading each column
represents the group designation
recommended by the ACS Committee
on Nomenclature.
(2)
II A
Hydrogen
7
14.01
8
16.00
(17)
VII A
9
19.00
4.003
He
Helium
10
20.18
B
C
N
O
F
Ne
Boron
Carbon
Nitrogen
Oxygen
Fluorine
Neon
26.98
14
28.09
15
30.97
16
32.06
17
35.45
18
39.95
Al
Si
P
S
Cl
Ar
Aluminum
Silicon
Phosphorous
Sulfur
Chlorine
Argon
31
69.72
32
72.59
33
74.92
34
78.96
35
79.90
36
83.80
K
Ca
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
Ga
Ge
As
Se
Br
Kr
Potassium
Calcium
Scandium
Titanium
Vanadium
Chromium
Manganese
Iron
Cobalt
Nickel
Copper
Zinc
Gallium
Germanium
Arsenic
Selenium
Bromine
Krypton
4
37
85.47
38
1.008
39
88.91
40
91.22
41
92.91
42
95.94
43
98.91
Rb
Sr
Y
Zr
Nb
Mo
Tc
Strontium
Yttrium
Zirconium
Niobium
Molybdenum
Technetium
74
75
55
132.9
56
137.3
57
138.9
72
178.5
73
180.9
183.9
44
x
Rubidium
5
186.2
101.1
45
102.9
46
106.4
47
107.9
48
112.4
49
114.8
50
118.7
51
121.8
52
127.6
Pd
Ag
Cd
In
Sn
Sb
Te
I
Xe
Palladium
Silver
Cadmium
Indium
Tin
Antimony
Tellurium
Iodine
Xenon
76
190.2
77
192.2
78
195.1
79
197.0
80
200.6
81
204.4
82
207.2
83
209.0
84
(210)
W
Re
Os
Ir
Pt
Au
Hg
Tl
Pb
Bi
Po
Cesium
Barium
Lanthanum
Hafnium
Tantalium
Tungsten
Rhenium
Osmium
Iridium
Platinum
Gold
Mercury
Thallium
Lead
Bismuth
Polonium
226.0
89
(227)
x
Rax
Ac
Francium
radium
Actinium
104
(261)
Unq
58
x
140.1
Cerium
90
232.0
Th
x
Thorium
(262)
Unpx
59
140.9
106
(263)
Unhx
60
144.2
Nd
Pr
Ce
Lanthanides
Actinides
105
Praseodymium Neodymium
91
231.0
Pa
x
Protactinium
92
238.0
x
U
Uranium
107
(262)
Uns
61
x
(147)
108
(265)
Uno
62
x
150.4
109
85
(210)
x
Astatine
Radon
(266)
152.0
64
157.3
65
158.9
66
162.5
67
164.9
68
167.3
69
168.9
70
173.0
71
175.0
Pmx
Sm
Eu
Gd
Tb
Dy
Ho
Er
Tm
Yb
Lu
Promethium
Samarium
Europium
Gadolinium
Terbium
Dysprosium
Holmium
Erbium
Thulium
Ytterbium
Lutetium
93
237.0
94
(244)
x
Npx
Pu
Neptunium
Plutonium
95
(243)
96
(247)
97
(247)
x
Amx
Cmx
Bk
Americium
Curium
Berkelium
98
(251)
Cf
x
Californium
99
(254)
Es
x
Einsteinium
100
(257)
Fm
x
Fermium
101
(258)
x
102
(255)
x
Md
No
Mendelevium
Nobelium
(222)
Rnx
Unex
63
86
At
x
Ta
88
131.1
Rh
Hf
Frx
54
Rhodium
La
(223)
126.0
Ru
Ba
87
53
Ruthenium
Cs
6
7
( ) Indicates mass number of isotope
with longest known half-life.
103
(256)
Lrx
Lawrencium
Dopant Chemistry
• By looking at the Periodic Table, we can
determine the number of electrons that
Boron and Phosphorus have in their outer
orbit.
B
P
N-Type
P
Si
Si
Si
Si
P
Si
Si
Si
Si
P-Type
B
Si
Si
Si
Si
B
Si
Si
Si
Si
Anatomy of a
Memory Chip
One Die or Chip
Building Blocks of the
DRAM memory cell
READ
WRITE
Basic DRAM memory cell - 1T
Row or Wordline
Column or Bitline
DRAM memory Array
MOSFET-Gate, Source, Drain
Metal-Oxide-Semiconductor-Field-Effect-Transistors
• A MOSFET is composed of three main components; a gate, a
source, and a drain. The gate is a physical structure built on the
wafer surface to control the opening and closing of a source-todrain channel. To create this structure, a metal and oxide layer
are formed on a semiconductor surface (MOS). The source and
drain regions are just highly doped, shallow pockets in the
wafer surface next to the gate.
The Transistor(continued)
• Doing the dishes requires that we access a
Source (or reservoir) of water.
• Channel (or pipe) connects the reservoir to the
sink. Don’t want a continuous flow of water to
our drain (or sink). . .
•
Need a gate (or valve) to block the water flow.
Source
Closed
Gate
Source
Reservoir
Water
Open
Gate
Reservoir
Water
External
Energy
(voltage)
Drain
Drain
Channel
Gate
Sink
Gate
Sink
Lithography
• Light passes thru
die mask
• Light imaged on
wafer
• Stepper to new die
location
• Re-image
Light Source
Mask
Reduction
Lens
Wafer with Photoresist
MS&E vs ChE
• How is a Materials Science and Engineering
Education Different from Chemical Engineering
Education?
– Focus on Solids Processing
• What Crystal Structure
– Higher Purity Materials
– Impurities Control Properties
• Semiconductors
• Grain Boundaries
– Where atoms are in structure determines properties
Where Thermodynamics Comes
into Chip Processing
•
•
•
•
Evaporation Rate during Spin Coating
Evaporation Rate during Photoresist Drying
Metal Physical Deposition
Chemical Vapor Deposition
– Feed of TEOS
– Rxn of TEOS
• Etching - SiF4 vapor pressure
• CMP Solution Equilibria
– Dissolution/Precipitation
Lithography
• Light passes thru
die mask
• Light imaged on
wafer
• Stepper to new die
location
• Re-image
Light Source
Mask
Reduction
Lens
Wafer with Photoresist
PhotoLythography
PhotoResist
UV light
=193 nm
80 nm Line
Photoresist -Sales $1.2 billion/yr. in
2001
• Resins
– phenol-formaldehyde, I-line
• Solvents
• Photosensitive compounds
– Polymethylmethacrylate or poly acrylic acid
• = 638 nm RED LIGHT
– diazonaphthoquinone
• Hg lamp, = 365 nm, I-line
– o-nitrobenzyl esters – acid generators
• Deep UV, = 248 nm, KrF laser
– Cycloolefin-maleic anhydride copolymer
– Poly hydroxystyrene
• =193 nm gives lines 100 nm
• = 157 nm F laser
• Additives
Photoresist
•
•
•
•
•
•
Spin Coat wafer
Dry solvent out of film
Expose to Light
Develop
Quench development
Dissolve resist (+) or developed resist (-)
Spin Coating
• Cylindrical Coordinates
– Navier-Stokes
– Continuity
Newtonian Fluidnon-evaporating
 2 vr
 2    2 r
z
B.C.' s
vr  0 @ z  0
vr
 0 @ a  h( r, t )
z
 2
q   vr dz 
h (t )3
3
0
h
h
1 
 2  2 3
qr  


rh 
t
r r
3r r
B.C. h(t  0)  ho
solution
If hois a constant film is uniform
1 / 2
2
 4  2 
For thin films, h  -1 t-1/2
h(t )  ho 1 
ho t 
3


Evaporation Model - Heuristic Model
• CN non-volatile, CV volatile
• e = evaporation rate of volatile component
– ei = kMA(Psolvent-I - 0)
• q = flow rate
Evaporation Rate
• What is Psolvent-i in a mixture?
– Other solvents and non-volatile components
• fil = fiv
equilibrium condition
– fiv =yiP
– fil = γ i xi Pisat
– ln γ i =GiE/(RT)
Vapor Pressure of 2 solvent mix
• P =Σ γ i xi Pisat = γ 1 x1 P1sat + γ 2 x2 P2sat
• y1 =P1/P= γ 1 x1 P1sat /(γ 1 x1 P1sat + γ 2 x2 P2sat )
• Pisat obtained from Normal Boiling Point & Heat
of vaporization (Claperon Equation)

d
ln Psat
dT
• γ

HV( T)
Rg  T
2
See MathCad Example
• Vapor Pressure of Solvent Mix.mcd
• Binary Solvent Mixture
• Ternary mixture of Solvent plus Nonvolatile Resin
Next Step
Dissolve Edge of Photoresist
• So that no sticking of wafer to surfaces
takes place
– Wafers are stored in a rack on edge
• So that no dust or debris attaches to
wafers
Wafer with Photoresist
How would you set up this problem?
• fil = fis
– fis = γsi zi fsi
– fil = γli xi fli
– ln γl i =GiE/(RT)
equilibrium condition
same a previous example of solvent mix
• γli xi fli = zi γsi fsi
• γli xi = zi γsi Ψi
•
•
•
•
Ψi = exp{(ΔHisl/R)[(1/Tm) - (1/T)]}
ΔHisl =Heat of fusion, Tm melting temperature
zi γsi=1 for ideal solid (misicible)
zi= mole fraction of mix in solid
Break
• Second lecture is next
• What did we learn
• Calculate the partial pressure
– Used to calculate the evaporation rate of a
component of a solvent mixture
• Calculate the solubility of a solid in a
solvent mixture
Lecture 2
• Metal Deposition on the wafer
– Wires to connect the transistors and
capacitors
• To each other
• To outside world
– 2 Mb memory chip has
– > 1 km of wire
– 8 layers of wiring on top
Deposition Methods
• Growth of an oxidation layer
• Spin on Layer
• Chemical Vapor Deposition (CVD)
– Heat = decomposition T of gasses
– Plasma enhanced CVD (lower T process)
• Physical Deposition
– Vapor Deposition
– Sputtering
Physical Vapor Deposition
• Evaporation from
Crystal (metal)
• Deposition on Wall
Physical Deposition Reactor
• Wafers in Carriage
(Quartz)
• Carrier Gasses enter
• Pumped out via
vacuum system
• Furnace
Furnace
Vacuum
Chamber at lower Temp
– Metal evaporated
– Sublimation
• No liquid phase
P
s
l
V
v
Deposition Rate
• Ratei = Km A {Pi(TF) - Pi(TC)}
• What is the sublimation partial pressure of
metal as a function of temperature?
• fiv = fis
equilibrium condition
– fis = γsi zi fsi= γsi zi Pisat exp[VMi(P - Pisat)/(RT)]
»
– fiv =yiP
Poynting Factor
Metal Saturation Pressure
• Sublimation Vapor Pressure
– Claperon Equation

d
ln Psat
dT

HS( T)
Z Rg  T
2
• ΔHS is the heat of sublimation
• ΔHS = ΔHF + ΔHV
– solid to liquid then liquid to vapor
MathCad File
• Sublimation Vapor Pressure of Alloy.mcd