A Review of IC Fabrication Technology - RIT - People · PDF fileReview of IC Fabrication...

© March 3, 2009 Dr. Lynn Fuller, Professor

Rochester Institute of TechnologyMicroelectronic Engineering

Review of IC Fabrication Technology

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




OUTLINE

§ Oxide Growth§ Diffusion§ Resistivity, Sheet Resistance, Resistance§ Mobility§ pn Junction§ MOSFET Vt§ Ion Implantation§ Conclusion




OXIDE GROWTH

Oxide ThicknessXox

Original SiliconSurface

0.46 Xox Silicon Consumed

PLAY




WET OXIDE GROWTH CHART

1 10 10010-2

10-1

1

10

t, Time, (min)

Xox ,(um)

1300 C

1200

1100

9001000

PLAY




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




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




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.




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




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




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




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




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




DIFFUSION MASKING CALCULATOR

SelectBoron or Phosphorous

Enter Temperature and Time




DIFFUSION MASKING

From: Hamilton and Howard




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




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




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?




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




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




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




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




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




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)




EXCELL WORKSHEET TO CALCULATE RESISTANCE




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




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




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




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




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.




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




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




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)

A Review of IC Fabrication Technology - RIT - People · PDF fileReview of IC Fabrication...

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