© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 1
MICROELECTRONIC ENGINEERINGROCHESTER 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
3-3-2009 Technology.ppt
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 2
OUTLINE
§ Oxide Growth§ Diffusion§ Resistivity, Sheet Resistance, Resistance§ Mobility§ pn Junction§ MOSFET Vt§ Ion Implantation§ Conclusion
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 3
OXIDE GROWTH
Oxide ThicknessXox
Original SiliconSurface
0.46 Xox Silicon Consumed
PLAY
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 4
WET OXIDE GROWTH CHART
1 10 10010-2
10-1
1
10
t, Time, (min)
Xox ,(um)
1300 C
1200
1100
9001000
PLAY
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 5
DRY OXIDE GROWTH CHART
10 100 1,000
10
10-2
10-1
1
t, Time, (min)
xox ,(um)
PLAY
1300 C
1200
1100
9001000
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 6
OXIDE GROWTH CALCULATOR
ROCHESTER INSTITUTE OF TECHNOLOGY OXIDE.XLS ZIPMICROELECTRONIC ENGINEERING 7/28/98
CALCULATION OF OXIDE THICKNESS LYNN FULLER
To use this spreadsheed change the values in the white boxes. The rest of the sheet isprotected and should not be changed unless you are sure of the consequences. Thecalculated results are shown in the purple boxes.
CONSTANTS VARIABLES CHOICESK 1.38E-23 J/K 1=yes, 0=no(Bo/Ao) dry 5760000 µm/hr Temp= 1100 °C wet 1Ea (dry) 2 eV time= 48 min dry 0(Bo/Ao) wet 71000000 µm/hr <100>Ea (wet) 1.96 eV Xint= 500 Å <111>Bo dry 9.40E+02 µm2/hrEa (dry) 1.24 eVBo wet 250 µm2/hrEa (wet) 0.74 eV
CALCULATIONS:
Xox (Oxide thickness)=(A/2){[1+(t+Tau)4B/A^2]^0.5 -1} = 5788 Å
B = Bo exp (-Ea/KTemp) 0.484600523 µm2/hrB/A = (Bo/Ao) exp (-Ea/KTemp) 4.64E+00 µm/hrA 0.104407971 µmTau = (Xi2+AXi)/B 0.01593147 hr
SiliconXox
0.46 Xox (silicon consumed)
Origional SiliconSurface Prior toOxide Growth
Oxide SiO2
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 7
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.
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 8
DIFFUSION FROM A CONSTANT SOURCE
N(x,t) = No erfc (x/2 Dt )
SolidSolubilityLimit, No
xinto wafer
Wafer Background Concentration, NBC
N(x,t)
Xj
p-type
n-type
PLAY STOP
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 9
ERFC FUNCTION
10-6
10-5
10-4
10-3
10-1
10-2
10-7
10-10
10-11
10-0
10-8
10-9
3.01.0 2.0 4.00.0 α = x / 4DtCon
cent
ratio
n/Su
rfac
e C
once
ntra
tion
= N
/No
PLAY
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 10
DIFFUSION CONSTANTS AND SOLID SOLUBILITY
DIFFUSION CONSTANTSBORON PHOSPHOROUS PHOSPHOROUS BORON PHOSPHOROUS
TEMP DRIVE-IN PRE DRIVE-IN SOLID SOLIDSOLUBILITY SOLUBILITY
NOB NOP900 °C 1.07E-15 cm2/s 2.09e-14 cm2/s 7.49E-16 cm2/s 4.75E20 cm-3 6.75E20 cm-3950 4.32E-15 6.11E-14 3.29E-15 4.65E20 7.97E201000 1.57E-14 1.65E-13 1.28E-14 4.825E20 9.200E201050 5.15E-14 4.11E-13 4.52E-14 5.000E20 1.043E211100 1.55E-13 9.61E-13 1.46E-13 5.175E20 1.165E211150 4.34E-13 2.12E-12 4.31E-13 5.350E20 1.288E211200 1.13E-12 4.42E-12 1.19E-12 5.525E20 1.410E211250 2.76E-12 8.78E-12 3.65E-12 5.700E20 1.533E21
PLAY
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 11
TEMPERATURE DEPENDENCE OF DIFFUSION CONSTANTS
Temperature Dependence:
D = D0 Exp (-EA/kT) cm2/sec k = 8.625E-5 eV/°K T in Kelvins
Boron D0 = 0.76 Phosphorous D0 = 3.85EA = 3.46 EA = 3.66
Temperature Dependence of the Solid Solubility ofBoron and Phosphorous in Silicon
NOB = 3.5E17T + 1.325E20 cm-3 T in CelsiusNOP = 2.45E18T - 1.53E21 cm-3 T in Celsius
PLAY
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 12
DIFFUSION FROM A LIMITED SOURCE
for erfc predepositQ’A (tp) = QA(tp)/Area = 2 No (Dptp) / π = Dose
for ion implant predepositQ’A(tp) = Dose
N(x,t) = Q’A(tp) Exp (- x2/4Dt)
π Dt
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
PLAY
PLAY
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 13
DIFFUSION MASKING CALCULATOR
SelectBoron or Phosphorous
Enter Temperature and Time
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 14
DIFFUSION MASKING
From: Hamilton and Howard
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 15
DIFFUSION AND DRIVE IN CALCULATIONS
Starting Wafer Resistivity Rho = 10 ohm-cmStarting Wafer Type n-type = 1 1 1 or 0
p-type = 1 0 1 or 0Pre Deposition Temperature 950 °CPre Deposition Time 15 minDrive-in Temperature 1100 °CDrive-in Time 480 min
CALCULATE VALUE UNITSSolid Solubility at Temperature of Pre Deposition 4.65E+20 cm-3Diffusion Constant at Temperature of Pre Deposition 3.93E-15 cm/secDiffusion Constant at Temperature of Drive-in 1.43E-13 cm/sec
CALCULATION OF DIFFUSION CONSTANTS D0 (cm2/s) EA (eV)Boron 0.76 3.46Phosphorous 3.85 3.66NOB = 3.5E17 (T) + 1.325E20NOP = 2.45E18(T) - 1.53E21
CALCULATIONS VALUE UNITSSubstrate Doping = 1 / (q µmax Rho) 4.42E+14 cm-3Ratio of Nsub/Ns = 9.51E-07
Approximate inverse erfc from erfc(u)~=e-u2
/(u(pi)^0.5) 3.47
RESULTS VALUE UNITSxj after pre deposition =( (4Dp tp)^05)*(inv_erfc(Nsub/Ns)) 0.13 µmPre deposition Dose, QA= 2No (Dp tp/π)^0.5 9.87E+14 atoms/cm2xj after drive-in = ((4 Dd td/QA) ln (Nsub (πDdtd)^0.5))^0.5 4.03 µmaverage doping Nave = Dose/xj 2.45E+18 atoms/cm3mobility (µ) at Doping equal to Nave 109 cm2/V-sSheet Resistance = 1/(q (µ(Nave))Dose) 58 ohmsSurface Concentration After Drive-in = Dose/ (pDt)^0.5 8.68E+18 cm-3
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 16
DIFFUSION FROM A LIMITED SOURCE
GIVEN VALUE UNITSStarting Wafer Resistivity Rho = 10 ohm-cmStarting Wafer Type n-type = 1 1 1 or 0
p-type = 1 0 1 or 0
Pre Deposition Ion Implant Dose 4.00E+15 ions/cm2
Drive-in Temperature 1000 °CDrive-in Time 360 min
CALCULATE VALUE UNITSDiffusion Constant at Temperature of Drive-in 1.43E-14 cm/sec
CALCULATION OF DIFFUSION CONSTANTS D0 (cm2/s) EA (eV)Boron 0.76 3.46Phosphorous 3.85 3.66
CALCULATIONS VALUE UNITSSubstrate Doping = 1 / (q µmax Rho) 4.42E+14 cm-3
RESULTS VALUE UNITSPre deposition Dose 4.00E+15 atoms/cm2xj after drive-in = ((4 Dd td/QA) ln (Nsub (πDdtd)^0.5))^0.5 1.25 µmaverage doping Nave = Dose/xj 3.21E+19 atoms/cm3mobility (µ) at Doping equal to Nave 57 cm2/V-sSheet Resistance = 1/(q (µ(Nave))Dose) 27.6 ohmsSurface Concentration = Dose/ (pDt)^0.5 1.28E+20 cm-3
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 17
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?
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 18
RESISTANCE, RESISTIVITY, SHEET RESISTANCE
Resistance = R = ρ L/Area = ρs L/w ohms
Resistivity = ρ = 1/( qµnn + qµpp) ohm-cm
Sheet Resistance = ρs = 1/ ( q µ(N) N(x) dx) ~ 1/( qµ Dose) ohms/square
L Area
R
wt
ρs = ρ / t I
V
slope = 1/Rq = 1.6E-19 coul
PLAY
PLAY
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 19
EXACT CALCULATION OF CARRIER CONCENTRATIONS
B 1.11E+03h 6.63E-34 Jsec Nd = 3.00E+16 cm-3 Donor Concentrationεo 8.85E-14 F/cm Ed= 0.049 eV below Ecεr 11.7 Na = 8.00E+15 cm-3 Acceptor Concentrationni 1.45E+10 cm-3 Ea= 0.045 eV above EvNc/T^3/2 5.43E+15Nv/T^3/2 2.02E+15 Temp= 300 °K
Donor and Acceptor Levels (eV above or below Ev or Ec)Boron 0.044
Phosphorous 0.045Arsenic 0.049
CALCULATIONS: (this program makes a guess at the value of the fermi level and trys to minimizethe charge balance)
KT/q 0.026 VoltsEg=Ego-(aT^2/(T+B)) 1.115 eVNc 2.82E+19 cm-3Nv 1.34E+01 cm-3Fermi Level, Ef 0.9295 eV above Evfree electrons, n = Nc exp(-q(Ec-Ef)KT) 2.17E+16 cm-3Ionized donors, Nd+ = Nd*(1+2*exp(q(Ef-Ed)/KT))^(-1) 2.97E+16 cm-3holes, p = Nv exp(-q(Ef-Ev)KT) 3.43E-15 cm-3Ionized acceptors, Na- = Na*(1+2*exp(q(Ea-Ef)/KT))^(-1) 8.00E+15 cm-3Charge Balance = p + Nd+ - n - Na- 3.22E+12 cm-3
Click on Button to do Calculation
Button
Button
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 20
RESISTIVITY OF SILICON VS DOPING
1021
1020
1014
1015
1016
1019
1018
1017
1013
100 101 102 103 10410-3 10-2 10-110-4
Boron
Phosphorous
ρ = 1/(qµ(N)N)
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)
Impu
rity
Con
cent
ratio
n, N
, cm
-3
Resistivity, ohm-cm
PLAY
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 21
ELECTRON AND HOLE MOBILITY
Total Impurity Concentration (cm-3)
0200400600800
1000120014001600
10̂13
10̂14
10̂15
10̂16
10̂17
10̂18
10̂19
10̂20
ArsenicBoronPhosphorus
Mob
ility
(cm
2 / V
sec
)
electrons
holes
Parameter Arsenic Phosphorous Boronµmin 52.2 68.5 44.9µmax 1417 1414 470.5Nref 9.68X10^16 9.20X10^16 2.23X10^17α 0.680 0.711 0.719
µ(N) = µ mi+ (µmax-µmin)
{1 + (N/Nref)α}
Electron and hole mobilitiesin silicon at 300 K as functions of the total dopantconcentration (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:
From Muller and Kamins, 3rd Ed., pg 33
PLAY
PLAY
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 22
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) =
µp (T,N) =
88 Tn-0.57
54.3 Tn-0.57
Where Tn = T/300From Muller and Kamins, 3rd Ed., pg 33
1250 Tn-2.33
407 Tn-2.33
1 + [ N / (1.26E17 Tn 2.4)] ^0.88 Tn -0.146
1 + [ N / (2.35E17 Tn 2.4)]^ 0.88 Tn -0.146
+
+
PLAY
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 23
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 isprotected and should not be changed unless you are sure of the consequences. Thecalculated results are shown in the purple boxes.
CONSTANTS VARIABLES CHOICESTn = T/300 = 1.22 1=yes, 0=no
Temp= 365 °K n-type 1N total 1.00E+18 cm-3 p-type 0
<100>
Kamins, Muller and Chan; 3rd Ed., 2003, pg 33mobility= 163 cm2/(V-sec)
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 24
EXCELL WORKSHEET TO CALCULATE RESISTANCE
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 25
ION IMPLANT EQUATIONS
after implant
Approximationused in Vtcalculations
after anneal at950 C, 15 min
-(X-Rp)2
2(∆Rp2+Dt)ApproximationN’ = Ni xi
After Anneal
N(x) = exp [ ]N’
2π ∆Rp2 + 2Dt
Gaussian Implant Profile
N(x) = exp [ ]
Rp = Range∆Rp = Straggle
From Curves}
-(X-Rp)2
2∆Rp2N’
2π ∆Rp
N’ = Dose = dtI
mqA
Ni
xi
where D is diffusion constant at the anneal temperaturet is time of anneal
xco
ncen
tratio
n cm
-3
PLAY
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 26
ION IMPLANT RANGE
10 100 1,00010-2
10-1
1
Implantation Energy (KeV)
Pro
ject
ed R
ang
e, R
p,(
um
)
B
P
As
Sb
PLAY
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 27
ION IMPLANT STANDARD DEVIATION
0.001
0.01
0.1
10 100 1,000Implantation Energy (KeV)
Sta
nd
ard
Dev
iati
on
, ∆R
p,(
um
)
B
P
As
Sb
PLAY
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 28
ION IMPLANT MASKING CALCULATOR
Rochester Institute of Technology Lance BarronMicroelectronic Engineering Dr. Lynn Fuller
11/20/2004
IMPLANT MASK CALCULATOR Enter 1 - Yes 0 - No in white boxes
DOPANT SPECIES MASK TYPE ENERGYB11 1 Resist 0 60 KeVBF2 0 Poly 1P31 0 Oxide 0
Nitride 0
Thickness to Mask >1E15/cm3 Surface Concentration 4073.011 Angstroms
This calculator is based on Silvaco Suprem simulations using the Dual Pearson model.
Lance Baron, Fall 2004
In powerpoint click on spread sheet to change settings for a new calculation
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 29
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.
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 30
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.
PLAY
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 31
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.
N(x,t) = Q’A(tp) Exp (- x2/4Dt)
π Dt
Sheet Resistance = ρs = 1/ ( q µ(N) N(x) dx) ~ 1/( qµ Dose) ohms/square
µ(N) = µ min + (µmax-µmin)
{1 + (N/Nref)α}
Let Q’A(tp) = 5.633E15 cm-2D= 1.55E-13 cm2/s
t = 1 hourfor Boronµmin 44.9µmax 470.5Nref 2.23X10^17α 0.719
© March 3, 2009 Dr. Lynn Fuller, Professor
Rochester Institute of TechnologyMicroelectronic Engineering
Review of IC Fabrication Technology
Page 32
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.
xxj
NBC
N(x)