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: Lynn.Fuller@rit.edu
Department webpage: http://www.microe.rit.edu
Rochester Institute of Technology
Microelectronic Engineering
© March 3, 2009 Dr. Lynn Fuller, Professor
3-3-2009 Technology.ppt
Page 1
Review of IC Fabrication Technology
OUTLINE
§
§
§
§
§
§
§
§
Oxide Growth
Diffusion
Resistivity, Sheet Resistance, Resistance
Mobility
pn Junction
MOSFET Vt
Ion Implantation
Conclusion
Rochester Institute of Technology
Microelectronic Engineering
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 2
Review of IC Fabrication Technology
OXIDE GROWTH
Oxide Thickness
Xox
Original Silicon
Surface
Silicon Consumed
0.46 Xox
PLAY
Rochester Institute of Technology
Microelectronic Engineering
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 3
Review of IC Fabrication Technology
WET OXIDE GROWTH CHART
10
1
Xox ,(um)
10-1
C
0
0
3
1
0
120
0
110
0
0
0
1
900
10-2
1
10
Rochester Institute of Technology
Microelectronic Engineering
t, Time, (min)
100
PLAY
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 4
Review of IC Fabrication Technology
DRY OXIDE GROWTH CHART
10
1
xox ,(um)
10-1
10-2
10
C
0
0
3
1
0
120
0
110
0
0
0
1
900
100
1,000
t, Time, (min)
Rochester Institute of Technology
Microelectronic Engineering
© March 3, 2009 Dr. Lynn Fuller, Professor
PLAY
Page 5
Review of IC Fabrication Technology
OXIDE GROWTH CALCULATOR
ROCHESTER INSTITUTE OF TECHNOLOGY
MICROELECTRONIC ENGINEERING
OXIDE.XLS
7/28/98
CALCULATION OF OXIDE THICKNESS
LYNN FULLER
ZIP
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
K
1.38E-23 J/K
(Bo/Ao) dry
5760000 µm/hr
Ea (dry)
2 eV
(Bo/Ao) wet
71000000 µm/hr
Ea (wet)
1.96 eV
Bo dry
9.40E+02 µm2/hr
Ea (dry)
1.24 eV
Bo wet
250 µm2/hr
Ea (wet)
0.74 eV
VARIABLES
Temp=
time=
Xint=
1100 °C
48 min
wet
dry
<100>
<111>
500 Å
CHOICES
1=yes, 0=no
1
0
CALCULATIONS:
Xox (Oxide thickness)=(A/2){[1+(t+Tau)4B/A^2]^0.5 -1} =
B = Bo exp (-Ea/KTemp)
B/A = (Bo/Ao) exp (-Ea/KTemp)
A
Tau = (Xi2+AXi)/B
Xox
0.484600523
4.64E+00
0.104407971
0.01593147
µm2/hr
µm/hr
µm
hr
Oxide SiO2
Rochester Institute ofSilicon
Technology
Microelectronic Engineering
5788 Å
Origional Silicon
Surface Prior to
Oxide Growth
0.46 Xox (silicon consumed)
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 6
Review of IC Fabrication Technology
OXIDE GROWTH 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
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 7
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
Microelectronic Engineering
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 8
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
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 9
α=x/
4Dt
Review of IC Fabrication Technology
DIFFUSION CONSTANTS AND SOLID SOLUBILITY
DIFFUSION CONSTANTS
BORON
PHOSPHOROUS PHOSPHOROUS
TEMP
DRIVE-IN
PRE
900 °C
950
1000
1050
1100
1150
1200
1250
1.07E-15 cm2/s 2.09e-14 cm2/s
4.32E-15
6.11E-14
1.57E-14
1.65E-13
5.15E-14
4.11E-13
1.55E-13
9.61E-13
4.34E-13
2.12E-12
1.13E-12
4.42E-12
2.76E-12
8.78E-12
BORON
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
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 10
PHOSPHOROUS
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
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 11
Review of IC Fabrication Technology
DIFFUSION FROM A LIMITED SOURCE
N(x,t) = Q’A(tp) Exp (- x2/4Dt)
π Dt
for erfc predeposit
Q’A (tp) = QA(tp)/Area = 2 No
PLAY
for ion implant predeposit
Q’A(tp) = Dose
PLAY
(Dptp) / π = 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
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 12
Review of IC Fabrication Technology
DIFFUSION MASKING CALCULATOR
Select
Boron or Phosphorous
Enter
Temperature and Time
Rochester Institute of Technology
Microelectronic Engineering
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 13
Review of IC Fabrication Technology
DIFFUSION MASKING
From: Hamilton and Howard
Rochester Institute of Technology
Microelectronic Engineering
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 14
Review of IC Fabrication Technology
DIFFUSION AND DRIVE IN CALCULATIONS
Starting Wafer Resistivity
Starting Wafer Type
Rho =
n-type = 1
p-type = 1
Pre Deposition Temperature
Pre Deposition Time
Drive-in Temperature
Drive-in Time
CALCULATE
Solid Solubility at Temperature of Pre Deposition
Diffusion Constant at Temperature of Pre Deposition
Diffusion Constant at Temperature of Drive-in
10
1
0
950
15
1100
480
VALUE
4.65E+20
3.93E-15
1.43E-13
ohm-cm
1 or 0
1 or 0
°C
min
°C
min
UNITS
cm-3
cm/sec
cm/sec
CALCULATION OF DIFFUSION CONSTANTS
D0 (cm2/s)
Boron
Phosphorous
NOB = 3.5E17 (T) + 1.325E20
NOP = 2.45E18(T) - 1.53E21
0.76
3.85
EA (eV)
3.46
3.66
CALCULATIONS
Substrate Doping = 1 / (q µmax Rho)
Ratio of Nsub/Ns =
Approximate inverse erfc from erfc(u)~=e
VALUE
UNITS
4.42E+14 cm-3
9.51E-07
-u2
/(u(pi)^0.5)
RESULTS
xj after pre deposition =( (4Dp tp)^05)*(inv_erfc(Nsub/Ns))
Pre deposition Dose, QA= 2No (Dp tp/ π)^0.5
xj after drive-in = ((4 Dd td/QA) ln (Nsub (πDdtd)^0.5))^0.5
average doping Nave = Dose/xj
mobility (µ)
at Doping
equal to Nave
Rochester
Institute
of Technology
Sheet
Resistance
=
1/(q
(µ(Nave))Dose)
Microelectronic Engineering
Surface Concentration After Drive-in = Dose/ (pDt)^0.5
© March 3, 2009 Dr. Lynn Fuller, Professor
3.47
VALUE
0.13
9.87E+14
4.03
2.45E+18
109
58
8.68E+18
UNITS
µm
atoms/cm2
µm
atoms/cm3
cm2/V-s
ohms
cm-3
Page 15
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
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 (π 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
UNITS
4.00E+15 atoms/cm2
1.25 µm
3.21E+19 atoms/cm3
57 cm2/V-s
27.6 ohms
1.28E+20 cm-3
Rochester Institute of Technology
Microelectronic Engineering
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 16
Review of IC Fabrication Technology
DIFFUSION EXAMPLES
1. A predeposit from a p-type spin-on dopant into a 1E15 cm-3
wafer is done at 1000°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 4 hours at 1100 °C. What is the new junction depth?
Rochester Institute of Technology
Microelectronic Engineering
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 17
Review of IC Fabrication Technology
RESISTANCE, RESISTIVITY, SHEET RESISTANCE
Resistance = R = ρ L/Area = ρs L/w
Resistivity = ρ = 1/( qµnn + qµpp)
ohms
ohm-cm
PLAY
Sheet Resistance = ρs = 1/ ( q µ(N) N(x) dx) ~ 1/( qµ Dose) ohms/square
PLAY
ρs = ρ / t
I
q = 1.6E-19 coul
L
slope = 1/R
Area
w
t
V
R
Rochester Institute of Technology
Microelectronic Engineering
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 18
Review of IC Fabrication Technology
EXACT CALCULATION OF CARRIER CONCENTRATIONS
B
h
εo
εr
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 cm-3
0.049 eV below Ec
8.00E+15 cm-3
0.045 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
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
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 19
Review of IC Fabrication Technology
RESISTIVITY OF SILICON VS DOPING
Impurity Concentration, N, cm-3
1021
ρ = 1/(qµ(N)N)
1020
1019
Because µ is a function of N
and N is the doping, the
relationship between resistivity
ρ and N is given in the figure
shown, or calculated from
equations for µ(N)
1018
Boron
1017
1016
Phosphorous
1015
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
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 20
Review of IC Fabrication Technology
1600
1400
1200
1000
800
600
400
200
0
PLAY
electrons
holes
10
^1
3
10
^1
4
10
^1
5
10
^1
6
10
^1
7
10
^1
8
10
^1
9
10
^2
0
Mobility (cm2/ V sec)
ELECTRON AND HOLE MOBILITY
Electron and hole mobilities
in silicon
at 300 K as
Arsenic
functions
Boron
of the total dopant
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)α}
From Muller and Kamins, 3rd Ed., pg 33
Rochester Institute of Technology
Microelectronic Engineering
Parameter
µmin
µmax
Nref
α
© March 3, 2009 Dr. Lynn Fuller, Professor
Arsenic
52.2
1417
9.68X10^16
0.680
Page 21
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
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 22
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=
163 cm2/(V-sec)
Rochester Institute of Technology
Microelectronic Engineering
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 23
Review of IC Fabrication Technology
EXCELL WORKSHEET TO CALCULATE RESISTANCE
Rochester Institute of Technology
Microelectronic Engineering
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 24
Review of IC Fabrication Technology
ION IMPLANT EQUATIONS
Gaussian Implant Profile
N’
-(X-Rp)2
N(x) =
exp [
]
2π ∆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) = 2π ∆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
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 25
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
© March 3, 2009 Dr. Lynn Fuller, Professor
1,000
PLAY
Page 26
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)
© March 3, 2009 Dr. Lynn Fuller, Professor
1,000
PLAY
Page 27
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 - No in white boxes
ENERGY
60
0
1
0
0
Thickness to Mask >1E15/cm3 Surface Concentration
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
Lance Baron, Fall 2004
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 28
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
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 29
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
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 30
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 = ρs = 1/ ( q µ(N) N(x) dx) ~ 1/( qµ Dose) ohms/square
(µmax-µmin)
µ(N) = µ min +
α}
{1
+
(N/N
)
ref
for Boron
µmin
µmax
Nref
α
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
© March 3, 2009 Dr. Lynn Fuller, Professor
π Dt
Page 31
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
© March 3, 2009 Dr. Lynn Fuller, Professor
Page 32