A Review Of IC Fabrication Technology - RIT

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Review of IC Fabrication Technology
MICROELECTRONIC ENGINEERING
ROCHESTER INSTITUTE OF TECHNOLOGY
A Review of IC Fabrication Technology
Dr. Lynn Fuller
Webpage: http://people.rit.edu/lffeee
Microelectronic Engineering
Rochester Institute of Technology
82 Lomb Memorial Drive
Rochester, NY 14623-5604
Tel (585) 475-2035
Email: [email protected]
Department webpage: http://www.microe.rit.edu
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
7-7-2014 Review.ppt
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Review of IC Fabrication Technology
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Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 2
Review of IC Fabrication Technology
OUTLINE
§
§
§
§
§
§
§
§
§
§
§
Constants
Periodic Table
Material Properties
Oxide Growth
Diffusion
Resistivity, Sheet Resistance, Resistance
Mobility
pn Junction
MOSFET Vt
Ion Implantation
Conclusion
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 3
Review of IC Fabrication Technology
CONSTANTS
Electronic charge
Speed of light in vacuum
Permittivity of vacuum
Free electron Mass
Planck constant
Boltzmann constant
Avogadro’s number
Thermal voltage
q
c
o
mo
h
k
Ao
kT/q
1.602 E -19 Coulomb
2.998E8 m/s
8.854 E -14 F/cm
9.11E-31 Kg
6.625E-34 J s
1.38 E-23 J /°K = 8.625E-5 eV/°K
6.022E23 molecules/gm- mole
@ 300 °K = 0.02586
PLAY
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 4
Review of IC Fabrication Technology
1
PERIODIC TABLE OF THE ELEMENTS
1.0079
2
He
H
0.1787
Helium
0.0899
Hydrogen
3
6.914
4
Be
0.53
Lithium
1.85
Beryllium
1122.9898 12
Density
g/cm3
24.305
Na
Mg
0.97
Sodium
1.74
Magnesium
47.90
K
Ca
Sc
Ti
0.86
Potassium
1.55
Calcium
3.0
Scandium
4.50
Titanium
38
87.62
39
88.906
40
91.22
Sr
Y
Zr
1.53
Rubidium
2.8
Strontium
4.5
Yttrium
6.49
Zirconium
132.90
56
137.33
57 138.906 58
23 50.941 24
V
Rb
55
14
20.086
Si
Cr
7.19
5.8
Vanadium Chromium
41
92.906
Nb
178.49
51.996
42
95.94
25
54.938
180.95
183.85
27 58.9332 28
29
63.546
30
65.238
14.0067
8
15.9994
9 18.9984 10
20.179
B
C
N
O
F
Ne
2.34
Boron
2.62
Carbon
1.251
Nitrogen
1.429
Oxygen
1.696
Fluorine
0.901
Neon
13
58.70
7
12.011
26.9815
14
20.086
15 30.97376 16
32.06
17
35.453
18
39.948
Al
Si
P
S
Cl
Ar
2.70
Aluminum
2.33
Silicon
1.82
Phosphorous
2.07
Sulfur
3.17
Clorine
1.784
Argon
31
69.72
32
72.59
33 74.9216 34
78.96
35
79.904
36
83.80
Fe
Co
Ni
Cu
Zn
Ga
Ge
As
Se
Br
Kr
7.43
Manganese
7.86
Iron
8.90
Selenium
8.90
Nickel
8.96
Copper
7.14
Zinc
5.98
Gallium
5.32
Germanium
5.72
Arsenic
4.80
Selenium
3.12
Bromine
3.74
Krypton
43
Mo
60
55.847
6
10.81
Mn
98
Tc
8.55
10.2
11.5
Niobium Molybdenum Technetium
59
26
5
Name
2.33
Silicon
19 39.0983 20 40.08 21 44.9559 22
85.468
Atomic Weight
Symbol
Atomic Number
9.01218
Li
37
4.0026
61
186.207
44
101.07
45 102.9055 46
47
106.4
107.868
48
112.41
49
114.82
50
118.69
51
121.75
26
55.847
26
127.60
54
131.30
Ru
Rh
Pd
Ag
Cd
In
Sn
Sb
Te
Fe
Xe
12.2
Rhodium
12.4
Rhodium
12.0
Palladium
10.5
Silver
8.65
Cadmium
7.31
Indium
7.30
Tin
6.68
Antimony
6.24
Tellurium
7.86
Tellurium
5.89
Xenon
76
77
78
84
85
190.2
192.22
195.09
79 196.9665 80
200.59
81
204.37
82
207.2
83
206.980
209
210
86
222
Cs
Ba
La
Hf
Ta
W
Re
Os
Ir
Pt
Au
Hg
Tl
Pb
Bi
Po
At
Rn
1.87
Cesium
3.5
Barium
6.7
Lanthanum
13.1
Hafnium
16.6
Tantalum
19.3
Tungstem
21.0
Rhenium
22.4
Osmium
27.16
Iridium
21.4
IPlatinum
19.3
Gold
13.53
Mercury
11.85
Thallium
11.4
Lead
9.8
Bismuth
9.4
Polonium
???
Astatine
9.91
Radon
89
104 261 105 262 106 263
87
223
88
226.02
Fr
Ra
???
Francium
5
Radium
227.02
Ac
PLAY
Unq Unp Unh
10.07
????
Unnilpentium
????
Actinium Unnilquadium
Unnilhexium
58 140.12 59 140.91 60
Ce
Pr
144.24
Nd
61 145
Pm
62 150.4 63 151.96 64 157.25
Sm
6.78
6.77
7.00
6.475
7.54
Cerium PraseoymiumNeodymium Promethium Samarium
90 232.0
Th
91 231 92 238.02
Pa
U
93 237
Np
11.7
15.4
18.90
20.4
Rochester
Institute
of Technology
Thorium Protactinium Uranium
Neptunium
Microelectronic Engineering
94
237
Eu
Gd
5.26
7.89
Europium Gadolinium
95 243
96
247
65 158.92
66
162.5
67 164.93
68 167.26
69 169.93
70
173.04
71
174.97
Tb
Dy
Ho
Er
Tm
Yb
Lu
8.27
Terbium
8.54
Dysprosium
8.90
Holmium
9.06
Erbium
9.33
Thulium
6.98
Ytterbium
9.84
Lutetium
97 247
98
251
99 252
Pu Am
Cm
Bk
Cf
Es
19.8
13.6
PlutoniumAmericium
13.511
Curium
????
Berkelium
????
Californium
????
Einsteinium
© July 7, 2014 Dr. Lynn Fuller, Professor
100 257 101
Fm
258
Md
????
????
Fermiumr Mendelevium
Page 5
102
259
103
260
No
Lr
????
Nobelium
????
Lawrencium
Review of IC Fabrication Technology
MATERIAL PROPERTIES
Symbol
Atoms per unit cell
Atomic Number
Atomic weight
Lattice constant
Atomic density
Density
Energy Gap 300°K
Relative permittivity
Index of refraction
Melting point
Specific heat
Thermal diffusivity
Coefficient expansion
Intrinsic carrier conc
Electron Mobility
Hole Mobility
Density of States conduction
Density of States valance
Breakdown Electric Field
Effective mass electron
Effective mass hole
Electron affinity
Z
MW
ao
No
d
Eg
r
n
Tm
Cp
K
Dth
ni
µn
µp
Nc
Nv
E
mn*/mo
mp*/mo
qX
Units
g/g-mole
nm
cm-3
g cm-3
eV
°C
J (gK)-1
w(cmK)-1
K-1
cm-3
cm2/Vs
cm2/Vs
cm-3
cm-3
V/cm
eV
Rochester Institute of Technology
Microelectronic Engineering
Si
8
14
28.09
0.54307
5.00E22
2.328
1.124
11.7
3.44
1412
0.70
0.87
2.5E-6
1.45E10
1417
471
2.8E19
1.04E19
3E5
1.08
0.81
4.05
Ge
8
32
72.59
0.56575
4.42E22
5.323
0.67
16.0
3.97
937
0.32
0.36
5.7E-6
2.4E13
3900
1900
1.04E19
6.0E18
8E4
0.55
0.3
4.00
GaAs
8
31/33
144.64
0.56532
2.21E22
5.316
1.42
13.1
3.3
1237
0.35
0.44
5.9E-6
9.0E6
8800
400
4.7E17
7.0E18
3.5E5
0.068
0.5
4.07
GaP
8
31/15
100.70
0.54505
2.47E22
4.13
2.24
10.2
3.3
1467
SiO2
Si3N4
14/8
60.08
14/7
140.28
0.775
1.48E22
3.44
4.7
7.5
2.0
0.004
5.3E-6
2.20E22
2.19
8~9
3.9
1.46
1700
1.4
0.32
5E-6
300
100
20
10E-8
6~9E6
0.5
0.5
4.3
1.0
From Muller and Kamins
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 6
0.17
2.8E-6
Review of IC Fabrication Technology
OXIDE GROWTH
Oxide Thickness
Xox
0.46 Xox
Original Silicon
Surface
Silicon Consumed
Dry oxide O2 only
Wet oxide O2 bubbled through water
Steam burn H2 in O2 to make H20 (steam)
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
PLAY
Page 7
Review of IC Fabrication Technology
WET OXIDE GROWTH CHART
10
1
Xox ,(um)
10-1
10-2
1
10
Rochester Institute of Technology
Microelectronic Engineering
t, Time, (min)
100
PLAY
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 8
Review of IC Fabrication Technology
DRY OXIDE GROWTH CHART
10
1
xox ,(um)
10-1
10-2
10
100
1,000
t, Time, (min)
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
PLAY
Page 9
Review of IC Fabrication Technology
OXIDE GROWTH CALCULATOR
OXIDE.XLS
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 10
Review of IC Fabrication Technology
EXAMPLES
1. Estimate the oxide thickness resulting from 50 min.
soak at 1100 °C in wet oxygen.
2. If 1000 Å of oxide exists to start with, what is
resulting oxide thickness after an additional 50 min.
soak at 1100 °C in dry oxygen.
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 11
Review of IC Fabrication Technology
OXIDE THICKNESS COLOR CHART
Thickness
500Å
700
1000
1200
1500
1700
2000
2200
2500
2700
3000
3100
3200
3400
3500
3600
3700
3900
4100
4200
4400
4600
4700
Color
Tan
Brown
Dark Violet - Red Violet
Royal Blue
Blue
Light Blue - Metallic Blue
Metallic - very light Yellow Green
LIght Gold or Yellow - Slightly Metallic
Gold with slight Yellow Orange
Orange - Melon
Red Violet
Blue - Violet Blue
Blue
Blue
Blue - Blue Green
Light Green
Green - Yellow Green
Yellow Green
Yellow
Light Orange
Carnation Pink
Violet Red
Red Violet
Violet
Blue Violet
Thickness
4900
5000
5200
5400
5600
5700
5800
6000
6300
6800
7200
7700
8000
8200
8500
8600
8700
8900
9200
9500
9700
9900
10000
Color
Blue
Blue
Blue Green
Green
Yellow Green
GreenYellow
Yellow -"Yellowish"(at times appears to be Lt gray or matellic)
Light Orange or Yellow - Pink
Carnation Pink
Violet Red
"Bluish"(appears
violet red, Blue Green, looks grayish)
Blue
Blue
Blue Green - Green
"Yellowish"
Orange
Salmon
Dull, LIght Red Violet
Violet
Blue Violet
Blue
Blue
Blue
Blue Green
Dull Yellow Green
Yellow - "Yellowish"
Orange
Carnation Pink
Nitride Thickness = (Oxide Thickness)(Oxide Index/Nitride Index)
Eg. Yellow Nitride Thickness = (2000)(1.46/2.00) = 1460
Rochester Institute of Technology
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Blue
PLAY
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 12
Review of IC Fabrication Technology
DIFFUSION FROM A CONSTANT SOURCE
PLAY STOP
N(x,t) = No erfc (x/2 Dt )
N(x,t)
Solid
Solubility
Limit, No
p-type
n-type
Wafer Background Concentration, NBC
Xj
Rochester Institute of Technology
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© July 7, 2014 Dr. Lynn Fuller, Professor
Page 13
x
into wafer
Review of IC Fabrication Technology
Concentration/Surface Concentration = N/No
ERFC FUNCTION
10-0
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
10-9
10-10
10-11
0.0
Rochester Institute of Technology
Microelectronic Engineering
1.0
2.0
3.0
4.0
PLAY
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 14
 = x / 4Dt
Review of IC Fabrication Technology
DIFFUSION CONSTANTS AND SOLID SOLUBILITY
DIFFUSION CONSTANTS
BORON
TEMP
DRIVE-IN
900 °C
950
1000
1050
1100
1150
1200
1250
1.07E-15 cm2/s
4.32E-15
1.57E-14
5.15E-14
1.55E-13
4.34E-13
1.13E-12
2.76E-12
PHOSPHOROUS PHOSPHOROUS
PRE
2.09e-14 cm2/s
6.11E-14
1.65E-13
4.11E-13
9.61E-13
2.12E-12
4.42E-12
8.78E-12
BORON
PHOSPHOROUS
DRIVE-IN
SOLID
SOLUBILITY
NOB
7.49E-16 cm2/s 4.75E20 cm-3
3.29E-15
4.65E20
1.28E-14
4.825E20
4.52E-14
5.000E20
1.46E-13
5.175E20
4.31E-13
5.350E20
1.19E-12
5.525E20
3.65E-12
5.700E20
PLAY
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 15
SOLID
SOLUBILITY
NOP
6.75E20 cm-3
7.97E20
9.200E20
1.043E21
1.165E21
1.288E21
1.410E21
1.533E21
Review of IC Fabrication Technology
TEMPERATURE DEPENDENCE OF DIFFUSION
CONSTANTS
PLAY
Temperature Dependence:
D = D0 Exp (-EA/kT) cm2/sec
Boron
D0 = 0.76
EA = 3.46
k = 8.625E-5
eV/°K
T in Kelvins
Phosphorous D0 = 3.85
EA = 3.66
Temperature Dependence of the Solid Solubility of
Boron and Phosphorous in Silicon
NOB = 3.5E17T + 1.325E20 cm-3
NOP = 2.45E18T - 1.53E21 cm-3
T in Celsius
T in Celsius
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 16
Review of IC Fabrication Technology
DIFFUSION FROM A LIMITED SOURCE
N(x,t) = Q’A(tp) Exp (- x2/4Dt)
 Dt
for erfc predeposit
Q’A (tp) = QA(tp)/Area = 2 No
PLAY
for ion implant predeposit
Q’A(tp) = Dose
PLAY
(Dptp) / Dose
Where D is the diffusion constant
at the drive in temperature and t is
the drive in diffusion time, Dp is
the diffusion constant at the
predeposit temperature and tp is the
predeposit time
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 17
Review of IC Fabrication Technology
DIFFUSION MASKING CALCULATOR
Select
Boron or Phosphorous
Enter
Temperature and Time
Rochester Institute of Technology
Microelectronic Engineering
From: Hamilton and Howard
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 18
Review of IC Fabrication Technology
DIFFUSION MASKING
Phosphorous Masking
Boron Masking
From: Hamilton and Howard
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 19
Review of IC Fabrication Technology
DIFFUSION AND DRIVE IN CALCULATIONS
DIFFUSION.XLS
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 20
Review of IC Fabrication Technology
DIFFUSION FROM A LIMITED SOURCE
GIVEN
Starting Wafer Resistivity
Starting Wafer Type
VALUE
Rho =
n-type = 1
p-type = 1
Pre Deposition Ion Implant Dose
UNITS
10 ohm-cm
1 1 or 0
0 1 or 0
4.00E+15 ions/cm2
Drive-in Temperature
Drive-in Time
1000 °C
360 min
CALCULATE
Diffusion Constant at Temperature of Drive-in
VALUE
UNITS
1.43E-14 cm/sec
CALCULATION OF DIFFUSION CONSTANTS
IonImplt.xls
D0 (cm2/s) EA (eV)
0.76
3.46
3.85
3.66
Boron
Phosphorous
CALCULATIONS
Substrate Doping = 1 / (q µmax Rho)
VALUE
UNITS
4.42E+14 cm-3
RESULTS
Pre deposition Dose
xj after drive-in = ((4 Dd td/QA) ln (Nsub (Ddtd)^0.5))^0.5
average doping Nave = Dose/xj
mobility (µ) at Doping equal to Nave
Sheet Resistance = 1/(q (µ(Nave))Dose)
Surface Concentration = Dose/ (pDt)^0.5
VALUE
4.00E+15
1.25
3.21E+19
57
27.6
1.28E+20
UNITS
atoms/cm2
µm
atoms/cm3
cm2/V-s
ohms
cm-3
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 21
Review of IC Fabrication Technology
EXAMPLE
1. A predeposit from a p-type spin-on dopant into a 1E15 cm-3
wafer is done at 1100°C for 10 min. Calculate the resulting
junction depth and dose.
2. The spin-on dopant is removed and the Boron is driven in
for 2 hours at 1100 °C. What is the new junction depth?
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 22
Review of IC Fabrication Technology
RESISTANCE, RESISTIVITY, SHEET RESISTANCE
Resistance = R =  L/Area = s L/w
Resistivity = 1/( qµnn + qµpp)
ohms


PLAY
ohm-cm
Sheet Resistance s = 1/ ( q µ(N) N(x) dx) ~ 1/( qµ Dose) ohms/square
PLAY
s =  / t
I
q = 1.6E-19 coul
L
slope = 1/R
Area
w
t
V
R
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 23
Review of IC Fabrication Technology
CALCULATION OF CARRIER CONCENTRATIONS
B
h
o
r
ni
Nc/T^3/2
Nv/T^3/2
1.11E+03
6.63E-34 Jsec
8.85E-14 F/cm
11.7
1.45E+10 cm-3
5.43E+15
2.02E+15
Nd =
Ed=
Na =
Ea=
Temp=
3.00E+16
0.049
8.00E+15
0.045
cm-3
eV below Ec
cm-3
eV above Ev
Donor Concentration
Acceptor Concentration
300 °K
Donor and Acceptor Levels (eV above or below Ev or Ec)
Boron
0.044
Phosphorous
0.045
Arsenic
0.049
carrier_conc.xls
CALCULATIONS: (this program makes a guess at the value of the fermi level and trys to minimize
the charge balance)
KT/q
0.026 Volts
Eg=Ego-(aT^2/(T+B))
1.115 eV
Nc
2.82E+19 cm-3
Nv
1.34E+01 cm-3
Fermi Level, Ef
0.9295 eV above Ev
free electrons, n = Nc exp(-q(Ec-Ef)KT)
2.17E+16 cm-3
Ionized donors, Nd+ = Nd*(1+2*exp(q(Ef-Ed)/KT))^(-1)
2.97E+16 cm-3
holes, p = Nv exp(-q(Ef-Ev)KT)
3.43E-15 cm-3
Ionized acceptors, Na- = Na*(1+2*exp(q(Ea-Ef)/KT))^(-1)
8.00E+15 cm-3
Charge Balance = p + Nd+ - n - Na3.22E+12 cm-3
Rochester Institute of Technology
Microelectronic Engineering
Click on Button to do Calculation
Button
Button
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 24
Review of IC Fabrication Technology
RESISTIVITY OF SILICON VS DOPING
Impurity Concentration, N, cm-3
1021
1/(qµ(N)N)
1020
1019
Because µ is a function of N
and N is the doping, the
relationship between resistivity
 and N is given in the figure
shown, or calculated from
equations for µ(N)
1018
Boron
1017
1016
1015
Phosphorous
1014
1013
10-4
10-3
10-2
10-1 100
Rochester Institute of Technology
Microelectronic Engineering
101
102
103
104
PLAY
Resistivity, ohm-cm
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 25
Review of IC Fabrication Technology
PLAY
electrons
20
10
^
19
10
^
18
10
^
17
10
^
16
10
^
15
10
^
14
holes
10
^
13
1600
1400
1200
1000
800
600
400
200
0
10
^
Mobility (cm2/ V sec)
ELECTRON AND HOLE MOBILITY
Electron and hole mobilities
in silicon
at 300 K as
Arsenic
functions
of the total dopant
Boron
Phosphorus
concentration
(N). The
values plotted are the results
of the curve fitting
measurements from several
sources. The mobility curves
can be generated using the
equation below with the
parameters shown:
Total Impurity Concentration (cm-3)
(µmax-µmin)
PLAY
µ(N) = µ mi+
{1 + (N/Nref)}
Institute of Technology
FromRochester
Muller
and Kamins, 3rd Ed., pg 33
Microelectronic Engineering
Parameter
µmin
µmax
Nref

© July 7, 2014 Dr. Lynn Fuller, Professor
Arsenic
52.2
1417
9.68X10^16
0.680
Page 26
Phosphorous
68.5
1414
9.20X10^16
0.711
Boron
44.9
470.5
2.23X10^17
0.719
Review of IC Fabrication Technology
TEMPERATURE EFFECTS ON MOBILITY
Derived empirically for silicon for T in K between 250 and 500 °K and for
N (total dopant concentration) up to 1 E20 cm-3
µn (T,N) = 88 Tn-0.57 +
1250 Tn-2.33
1 + [ N / (1.26E17 Tn 2.4)] ^0.88 Tn -0.146
PLAY
µp (T,N) = 54.3
Tn-0.57
Rochester Institute of Technology
Microelectronic Engineering
407 Tn-2.33
+
1 + [ N / (2.35E17 Tn 2.4)]^ 0.88 Tn -0.146
Where Tn = T/300
From Muller and Kamins, 3rd Ed., pg 33
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 27
Review of IC Fabrication Technology
EXCELL WORKSHEET TO CALCULATE MOBILITY
MICROELECTRONIC ENGINEERING
3/13/2005
CALCULATION OF MOBILITY
Dr. Lynn Fuller
To use this spreadsheed change the values in the white boxes. The rest of the sheet is
protected and should not be changed unless you are sure of the consequences. The
calculated results are shown in the purple boxes.
CONSTANTS
Tn = T/300 = 1.22
VARIABLES
Temp=
N total
365 °K
1.00E+18 cm-3
n-type
p-type
<100>
CHOICES
1=yes, 0=no
1
0
Kamins, Muller and Chan; 3rd Ed., 2003, pg 33
mobility=
Rochester Institute of Technology
Microelectronic Engineering
163 cm2/(V-sec)
mobility.xls
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 28
Review of IC Fabrication Technology
EXCELL WORKSHEET TO CALCULATE RESISTANCE
Resistors_Poly.xls
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 29
Review of IC Fabrication Technology
UNIFORMLY DOPED PN JUNCTION
P+ Phosphrous donor atom and electron
P+ Ionized Immobile Phosphrous donor atom
BB-
Ionized Immobile Boron acceptor atom
+
Space Charge Layer
n = ND
p = NA
B-
+
B-
+
B-
p-type
Boron acceptor atom and hole

B-
B-
charge density, 
qNA W1 =qND W2
P+
P+
P+ P+
P+
P+
P+
P+
P+
+VR
n-type
+qND
-W1
x
W2
-qNA
Electric Field,

Potential, 
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
+VR
Page 30
Review of IC Fabrication Technology
UNIFORMLY DOPED PN JUNCTION
Built in Voltage:
= KT/q
ln (NA ND /ni2)
ni = 1.45E10 cm-3
Width of Space Charge Layer, W: with reverse bias of VR volts
WW1W2= [ (2q+VR) (1/NA 1/ND)]1/2
W1 width on p-side
W1= W [ND/(NA ND)]
W2 width on n-side
W2= W [NA/(NA ND)]
Maximum Electric Field:
=
- [(2q/+VR) (NA ND/(NA ND))]1/2
Junction Capacitance per unit area:
Cj’rW= r[(2q+VR) (1/NA 1/ND)]1/2
Rochester Institute of Technology
Microelectronic Engineering
o r = 8.85E-12 (11.7) F/m
= 8.85E-14 (11.7) F/cm
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 31
Review of IC Fabrication Technology
EXAMPLE
Example: If the doping concentrations are Na=1E15 and Nd=3E15
cm-3 and the reverse bias voltage is 0, then find the built in voltage,
width of the space charge layer, width on the n-side, width on the pside, electric field maximum and junction capacitance. Repeat for
reverse bias of 10, 40, and 100 volts.
= Vbi = KT/q ln (NA ND /ni2) =
WW1W2= [ (2/q) (+VR) (1/NA 1/ND)]1/2
=
W1 =
W2 =
Emax =
Cj =
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 32
Review of IC Fabrication Technology
EXAMPLE CALCULATIONS
PN.XLS
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 33
Review of IC Fabrication Technology
LONG CHANNEL THRESHOLD VOLTAGE, VT
Xox
Flat-band Voltage VFB = ms - Qss C’ox
p-type substrate
(n-channel)
Bulk Potential :
Work Function:
Difference
p = -KT/q
1
X (x) dx
C’ox 0 Xox
n-type substrate
(p-channel)
Qss = q Nss
n = +KT/q
ln (NA /ni)
M S = M - ( X + Eg/2q + [p]) M S = M
Maximum Depletion Width:
(Wdmax)
4 s[p]
qNa
Rochester Institute of Technology
Microelectronic Engineering
- ( X + Eg/2q - [n])
4 s[n]
qNd
Threshold Voltage:
VT = VFB + 2 [p] + 1
p-type substrate
C’ox
Threshold Voltage:
VT = VFB - 2 [n] n-type substrate
ln (ND /ni)
1
C’ox
2 s q Na ( 2[p])
2 s q Nd ( 2[n])
PLAY
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 34
Review of IC Fabrication Technology
LONG CHANNEL Vt
Gate work function, n+, p+, aluminum
Substrate doping, Nd or Na
Oxide thickness, Xox
Surface State Density, Nss or Qss
also
Substrate to Source voltage difference
Threshold Voltage
+3
+4
650Å
+2
+3
250Å
+1
+2
150Å
0
PLAY
+1
-1
n+ poly gate left scale
p+ poly gate right scale -2
Qf = 0
Vbs = 0
-3
implant dose = zero
Rochester Institute of Technology
Microelectronic Engineering
150Å
250Å
650Å
1014 1015 1016 1017
Substrate doping, Nd or Na
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 35
0
-1
-2
Review of IC Fabrication Technology
VT ADJUST IMPLANT
Assume that the total implant is shallow (within Wdmax)
+/- Vt = q Dose*/Cox’
where Dose* is the dose that is added to the Si
Cox’ is gate oxide capacitance/cm2
Boron gives + shift
Cox’ = or / Xox
Phosphorous gives - shift
Example: To shift +1.0 volts implant Boron through 1000 Å Kooi
oxide at an energy to place the peak of the implant at the
oxide/silicon interface. Use a Dose = Vt Cox’/q
=(1.0)(3.9)(8.85E-14)/(1.6E-16)=2.16E11 ions/cm2
but multiply by 2 since 1/2 goes into silicon
Rochester Institute of Technology
Microelectronic Engineering
PLAY
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 36
Review of IC Fabrication Technology
MOSFET THRESHOLD VOLTAGE CALCULATION
MOSFETVT.XLS
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 37
Review of IC Fabrication Technology
ION IMPLANT EQUATIONS
Gaussian Implant Profile
N’
-(X-Rp)2
N(x) =
exp [
]
2Rp
2Rp2
Rp = Range
Rp = Straggle
N’ = Dose =
} From Curves
I
mqA dt
concentration cm-3
after implant
after anneal at
950 C, 15 min
Ni
Approximation
used in Vt
calculations
After Anneal
x
N’
-(X-Rp)2
N(x) = 2Rp2 + 2Dt exp [ 2(Rp2+Dt) ]
xi
where D is diffusion constant at the anneal temperature
t is time of anneal
Rochester Institute of Technology
Microelectronic Engineering
PLAY
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 38
Approximation
N’ = Ni xi
Review of IC Fabrication Technology
ION IMPLANT RANGE
Projected Range, Rp ,(um)
1
As
10-1
B
P
Sb
10-2
10
100
Implantation Energy (KeV)
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
1,000
PLAY
Page 39
Review of IC Fabrication Technology
Standard Deviation, Rp ,(um)
ION IMPLANT STANDARD DEVIATION
0.1
B
0.01
P
As
Sb
0.001
10
Rochester Institute of Technology
Microelectronic Engineering
100
Implantation Energy (KeV)
© July 7, 2014 Dr. Lynn Fuller, Professor
1,000
PLAY
Page 40
Review of IC Fabrication Technology
ION IMPLANT MASKING CALCULATOR
Rochester Institute of Technology
Microelectronic Engineering
11/20/2004
IMPLANT MASK CALCULATOR
DOPANT SPECIES
B11
1
BF2
0
P31
0
Lance Barron
Dr. Lynn Fuller
Enter 1 - Yes
MASK TYPE
Resist
Poly
Oxide
Nitride
0
1
0
0
Thickness to Mask >1E15/cm3 Surface Concentration
0 - No in white boxes
ENERGY
60
KeV
4073.011 Angstroms
This calculator is based on Silvaco Suprem simulations using the Dual Pearson model.
In powerpoint click on spread sheet to change settings for a new calculation
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
Lance Baron, Fall 2004
Page 41
Review of IC Fabrication Technology
REFERENCES
1. Basic Integrated Circuit Engineering, Douglas J. Hamilton, William
G. Howard, McGraw Hill Book Co., 1975.
2. Micro Electronics Processing and Device Design, Roy a. Colclaser,
John Wiley & Sons., 1980.
3. Device Electronics for Integrated Circuits, Richard S. Muller,
Theodore I. Kamins, Mansun Chan, John Wiley & Sons.,3rd Ed., 2003.
4. VLSI Technology, Edited by S.M. Sze, McGraw-Hill Book Company,
1983.
5. Silicon Processing for the VLSI Era, Vol. 1., Stanley Wolf, Richard
Tauber, Lattice Press, 1986.
6. The Science and Engineering of Microelectronic Fabrication, Stephen
A. Campbell, Oxford University Press, 1996.
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 42
Review of IC Fabrication Technology
HOMEWORK - REVIEW OF IC TECHNOLOGY
1. If a window is etched in 5000 Å of oxide and the wafer is oxidized again for 50 min in wet
O2 at 1050 °C what is the new thickness (where it was 5000 Å), the thickness in the etch
window, and the step height in the silicon if all the oxide is etched off the wafer. Draw a
picture showing original Si surface.
2. A Boron diffusion is done into 5 ohm-cm n-type wafer involving two steps. First a short
predeposit at 950 C for 30 min., followed by removal of the diffusion source and a drive in at
1100 C for 2 hours. Calculate the junction depth and the sheet resistance of the diffused layers.
Estimate the oxide thickness needed to mask this diffusion.
3. For a pn junction with the p side doping of 1E17 and the n side at 1E15 calculate, width of
space charge layer, width on p side, on n side, capacitance per unit area, max electric field.
4. Calculate the threshold voltage for an aluminum gate PMOSFET fabricated on an n-type
wafer with doping of 5E15, a surface state density of 7E10, and gate oxide thickness of 150 Å.
What is the threshold voltage if the surface state density is 3E11?
5. Calculate the ion implant dose needed to shift the threshold voltage found in the problem
above to -1 Volts.
Rochester Institute of Technology
Microelectronic Engineering
PLAY
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 43
Review of IC Fabrication Technology
HOMEWORK - EXACT CALCULATION OF SHEET
RESISTANCE FOR A DIFFUSED LAYER
1. A Boron p-type layer is diffused into an n-type silicon wafer
(1E15 cm-3) at 1100 °C for 1 hour. Calculate the exact value of the
sheet resistance and compare to the approximate value.
Sheet Resistance s = 1/ ( q µ(N) N(x) dx) ~ 1/( qµ Dose) ohms/square
(µmax-µmin)
µ(N) = µ min +
}
{1
+
(N/N
)
ref
for Boron

µmin
µmax
Nref

44.9
470.5
2.23X10^17
0.719
Let Q’A(tp) = 5.633E15 cm-2
D= 1.55E-13 cm2/s
t = 1 hour
N(x,t) = Q’A(tp) Exp (- x2/4Dt)
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
 Dt
Page 44
Review of IC Fabrication Technology
HW SOLUTION - EXACT CALCULATION OF SHEET
RESISTANCE FOR A DIFFUSED LAYER
Divide the diffused layer up into 100 slices and for each slice find
the doping and exact mobility. Calculate the sheet resistance from
the reciprocal of the sum of the conductance of each slice.
N(x)
NBC
x
xj
Rochester Institute of Technology
Microelectronic Engineering
© July 7, 2014 Dr. Lynn Fuller, Professor
Page 45
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