Lecture 10.0Lecture 10.0

Photoresists/Coating/Lithography

Semiconductor FabSemiconductor Fab

Land $0.05 BillionBuilding $0.15 BillionTools & Equipment $1 BillionAir/Gas Handling Sys$0.2 BillionChemical/Electrical Sys $0.1 BillionTotal $1.5 Billion10 year Amortization ~$1 Million/day

80nm Line width with 80nm Line width with =193 nm =193 nm LithographyLithography

Photoresist -Photoresist -Sales $1.2 billion/yr. in 2001 Sales $1.2 billion/yr. in 2001 Resins

– phenol-formaldehyde, I-lineSolventsPhotosensitive 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

PhotoresistPhotoresist

Spin Coat waferDry solvent out of filmExpose to LightDevelop Quench developmentDissolve resist (+) or developed

resist (-)

Spin CoatingSpin Coating

Cylindrical Coordinates– Navier-Stokes– Continuity

Navier-StokesNavier-Stokes

Spin Coating DynamicsSpin Coating Dynamics

Newtonianr

V

z

V

rg

gz

r

rz

VV

r

VV

t

V

gzz

VV

r

VV

t

V

StokesNavierz

V

r

rV

r

Continuity

zrrz

r

zrzz

zz

rz

rrzr

zr

rr

zr

,

)(1

0)()(1

2

Newtonian Fluid-Newtonian Fluid-non-evaporatingnon-evaporating

2/1

22

322

32

0

22

2

3

41)(

)0(..

3

1

)(3

),(@0

0@0

.'.

thhth

solution

hthCB

hrrr

qrrrt

h

thdzvq

trhaz

v

zv

sCB

rz

v

oo

o

h

r

r

r

r

If hois a constant film is uniformFor thin films, h -1 t-1/2

Evaporation Model - Evaporation Model - Heuristic ModelHeuristic Model

CN non-volatile, CV volatile

e= evaporationq= flow rate

Spin Coater - Heuristic ModelSpin Coater - Heuristic Model

Flow Rate, h is thickness

Evaporation rate due to Mass Transfer

Spin Coating SolutionSpin Coating Solution

Dimensionless Equations

Viscosity as a function of composition

Viscosity increases with loss of Viscosity increases with loss of solventsolventViscosity of pure

Resin is very high

Viscosity of Solvent is low

0 0.02 0.041 10 5

1 10 4

1 10 3

0.01

Volume Fraction Vapor Component

Vis

cosi

ty(m

^2/s

ec) 1.521 10 3

1 10 5

x( )

x o0 x

Spin CoatingSpin Coating

Thickness RPM-1/2 o1/4

Observed experimentally

ResultsResults

Effect of Mass Transfer = dimensionless

Mass transfer Coefficient

– Increase MT Increase in Film Thickness

– MT increases viscosity and slows flow leading to thicker film

Dimensionless Film Thickness

Dissolve edge of photoresistDissolve edge of photoresist

So that no sticking of wafer to surfaces takes place

So that no dust or debris attaches to wafers

Wafer with Photoresist

LithographyLithography

Light passes thru die mask

Light imaged on wafer

Stepper to new die location

Re-image Wafer with Photoresist

Mask

Light Source

ReductionLens

LithographyLithography

Aspect Ratio (AR)=3.5– AR=Thickness/Critical Dimension

• Critical Dimension=line width• Thickness= photoresist thickness

Lateral Resolution (R)– R=k1 /NA

Numerical Apparature (NA)– NA is a design parameter of lens

Depth of Focus (DOF)– DOF= k2 /NA2

Lithography - PhotoreactionLithography - Photoreaction

– Photo Reaction Kinetics• dC(x,t)/dt = koexp(-EA/RT) C(x,t) I(x,)

– Beer’s Law• I(x, )/Io=exp(- () C(x,t) x)

() = extinction coefficient

– Solution?• dC(x,t)/dt = koexp(-EA/RT) C(x,t) Io exp(- () C(x,t) x)

– C=Co at t=0, 0<x<L

Drying solvent out of LayerDrying solvent out of Layer

Removal of Solvent– Simultaneous Heat and Mass Transfer– In Heated oven– Some shrinkage of layer

PhotoresistPhotoresist

Positive– Light induced reaction

• decomposes polymer into Acid + monomers

– Development• Organic Base (Tri

Methyl ammonium hydroxide) + Water

• neutralizes Acid group

• Dissolves layer – Salt + monomer

Negative– Light induced reaction

• Short polymers crosslink to produce an insoluble polymer layer

– No Development needed

– Dissolution of un-

reacted material

Photoresist DevelopmentPhotoresist Development

Boundary Layer Mass TransferPhotoresist DiffusionChemical ReactionProduct diffusion, etc.

Reaction Plane

Reactant ConcentrationProfileProduct

ConcentrationProfile

Rate Determining StepsRate Determining Steps

X

Dissolution of Uncrosslinked PhotoresistDissolution of Uncrosslinked Photoresist

Wafers in CarriagePlaced in SolventHow Long??Boundary Layer MT

is Rate Determining– Flow over a leading

edge for MT– Derivation & Mathcad

solutionAlso a C for theConcentration profile

Mass transfer correlation Mass transfer correlation - flow over leading edge- flow over leading edge

Sh=Kgx/DAB

Kg= DAB / C

Sc=/DAB

Re=V x/

Global Dissolution Rate/TimeGlobal Dissolution Rate/Time

Depends on–Mass Transfer• Diffusion Coefficient• Velocity along wafer surface• Size of wafer

– Solubility– Density of Photoresist Film

Local Dissolution Rate/TimeLocal Dissolution Rate/Time

Depends on–Mass Transfer• Diffusion Coefficient• Velocity along wafer surface• Size of wafer

– Solubility– Density of Photoresist Film– Position on the wafer