~D-A181 AND MODELLING THE UNCLASSIFIED mEEIIEEIIEEE · .small correction nec- to be macle when a si...

27
~D-A181 168 MEASURING AND MODELLING THE TRANSITION LAYER DURING THE 1/1 DISSOLUTION OF GR (U) CORNELL UNIV ITHACA SCHOOL OF CHEMICAL ENGINEERING P D KRASICKY ET AL 29 MAY 87 UNCLASSIFIED TR-5 N88814-85-K-8474 F/G 7/ 6 NL mEEIIEEIIEEE

Transcript of ~D-A181 AND MODELLING THE UNCLASSIFIED mEEIIEEIIEEE · .small correction nec- to be macle when a si...

Page 1: ~D-A181 AND MODELLING THE UNCLASSIFIED mEEIIEEIIEEE · .small correction nec- to be macle when a si licon wafer i U se ( a s ihe s ubstrate mzate, ia 3 verA thin layer of Silicon

~D-A181 168 MEASURING AND MODELLING THE TRANSITION LAYER DURING THE 1/1DISSOLUTION OF GR (U) CORNELL UNIV ITHACA SCHOOL OFCHEMICAL ENGINEERING P D KRASICKY ET AL 29 MAY 87

UNCLASSIFIED TR-5 N88814-85-K-8474 F/G 7/ 6 NL

mEEIIEEIIEEE

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IIII1I455

- " U!~~I[ IIl ll

I~.81111.25 1111 ___

MICROCOPY RSL TIO TS CHAR'

p

w . -~ .IwV *p 1W -W

II

Q& m III

- A W Aj

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OTC FILE Cop

OFFICE OF NAVAL RESEARCH

Contract NOQO 1 4-85-K-0474

00W" Technical Report No. 5

MEASURING AND MODELLING THE00 TRANSITION LAYER DURING THE DISSOLUTION

OF GLASSY POLYMER FILMS

o by

P. D. Krasicky, R, J. Groele, and F. Rodriguez

Olin Hall, Cornell University

School of Chemical EngineeringIthaca, NY 14853

Prepared for presentation at theNational Meeting of the American Institute of Chemical Engineers

Boston, August 24-27, 1987

Reproduction in whole or in part is permittedfor orICILECTE

any purpose of the United States Government .\JUN 1 0 1987

*This document has been approved for public release%')and sale; its distribution is unlimited

67 6 4 ,J

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SECUf•ITY CLASSIFICATION OF THIS PAGE ("o.e Data Ensoteid)READ INSTRUCTIONS

REPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM1. REPORT NUMBER 2. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER

4. TITLE (and Subtitle) S. TYPE OF REPORT 6 PERIOD COVERED

Measuring and Modelling the Transition LayerDuring the Dissolution of Glassy Polymer Films Technical Report

6. PERFORMING ORG. REPORT NUMBER

7. AUTHOR(e) 6. CONTRACT OR GRANT NUMBER(@)

P. D. Krasicky, R. J. Groele, F. Rodriguez

S. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASKAREA I WORK UNIT NUMBERS

Cornell UniversityIthaca, NY 14853

It. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

Chemistry May 29, 1987Office of Naval Research 13. NUMBER OF PAGES

Arlington, VA _?_17__9

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UnclassifiedISa. DFCL ASSIFICATION DOWNGRADING

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Technical Report Distribution List, GEN/413-2.

For unlimited distribution and public release.

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Abstracts Distribution List, 356A/413-2.For unlimited distribution and public release.

III. SUPPLEMENTARY NOTES

Presented at National Meeting of American Institute of Chemical Engineers,August 24-27, 1986, Boston, M1Au ut,,. s ..

I9. KEY WORDS (Continue on rev*ree ade It n*coddea-y nd identify by block nu.mber)

Poly (methyl methacrylate)Dissolut ionTransition layersMicrolithography

V 0. ABSTRACT (Continue ?*ver*e *ide If necoeOery and Identi y by block number)

--he technique of laser interferometry is now routinely used by the micro-electronics industry for the measurement of the dissolution rates of thinpolymer films. In addition to the rate of dissolution, laser interferometrycan also provide quantitative information on the thickness of the transitionlayer between the dissolving glassy polymer and the liquid solvent. This paperdescribes how observed patterns of reflected light intensity may be analyzed

- to calculate the thickness of the transition layer for polymers that dissolve

DD , jAN 7,1473 EDITION oF I NOV 6 IS OBSOLETES/N 0102-LF-014-6601

SECURITY CLASSIFICATION OF THIS PAGE (When Date Entered)

.%

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SECURITY CLASSIFICATION OF THIS PAGE (Mlong Dot& Entored)

with little or no swelling. The technique required knowledge of the shapeof the concentration profile in the transition layer. However, by assumingvarious simple model profiles one may obtain a reasonable estimate.Experimental measurements of PMiA films dissolving in methyl ethyl ketoneindicate transition layers of thicknesses 0 to 0.1 pm for PMMA of molecularweights M n 37,000 to 1,400,000

~ F~r

r, ibut ion/-... .

.... : try Codes

,.st Spocial

i'iD

a L

SIC~uIlT'r C.ASSUICATIONi OF'TMIS PAOI (W~o n Data Enelred)

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MEASURINGAND MODELLING THETRA~NSITION LA~YER DURING THE DISSOLUTION

OF GLA~SSY POLYMER FILMS

P.D. Krasicky, R.3. Groele, F. RodriguezSchool of Chemical Engineering, Olin Hall

Cornell UniversityIthaca, NY 14853

I N'tROI)U:T I ON

Over the past few ye'ars "there has been a renew~ed interest in

+-~d/ of plolYmer- selling and dissolution behavior. Most

' t I. I rnod elI havo c conc en t.r ated on diffusion and swjel-

100 nc h t somre uo T-v 5s ,o be~n do i-e onT- d 1s sol-jt ion. T me

.N-ie v~irif-ty of observed phenomena is indicative of the complexi-

t y o)f the problem. E.:-per mental 1y, many techniques and samplp

qpomnetrie-, have been uised." Optical rnicroscop"I' has proven

11seful i-1 the study o1 Sw~elling and dissnlution behavior since

~t Z31l1ows measurement of the rate of dissoluLtion and observation

,.F the concentration profile i n the dissolving surface layer.

10.)wever. microscopy wor~s best wjhen the dimensions being observed

* - e I C H,7) o-r greater. Rutherford 2ackscattering Spectroscopy,

ma,, b r used to mak-e mea,;urxement,s on inuc(h smallepr dimensions, but

3neit cannot be don in rsE r itu and reursspecial sample

rrpraiT procedures-, i t. i' lim iteri to the study of sw~elling

o n I Y.

This p-ipor- was pre-'-nted in part at the National

V Meetingi nf the Amer. Inst. of Chem. Engs., Boston,

'Auts 2- -7. !qG6.

/f

.~~ ~ ~ .'% .. .. . .

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Of particular interest to the microelectronics industry is

the dissolution of a 1 Hm thick polymer film on a silicon

substrate. Thr technique of laser interferometry,"I is now

routinely used for the screening of new polymer-solvent systems

and for the optimization of processing conditions. Not so

obvious in the use of laser iriterferometry is the quantitative

information it can provide on the dissolving surface layer for

rolymers that dissolve with little or no swelling.

DISSOLUTION RATE MEASUREMENT USING LASER INTERFEROMETRY

Laser interferometry is popular as the method of dissolution

,-ate measurement since the sample geometries and substrate

materials of typical microlithographic processes can be used. The

basic: apparatus for laser interferometry is shown in figure I . A

silicon wafer that has been coated with a 0.5 to 1.5 Hm thic:

film of polymer is suspended in a transparent cylindrical

container filled with the developing solvent. The solvent

container includes a magnetic stirrer and a heating/cooling coil

convnected to a temperature bath. The beam from Hn unpolarized '-le--

Ne laser of wavelength 6328 A is directed ohliquely at the roated

ubstrate with an incident angle of typically 100. The reflected

beam is collected by a silicon photocell and the recorded signal

represents the reflected intensity as a function of time. A more

(-omp I Ct e description of the technique is gi vV h Kras I y

et. al..'

C-

%2

FW,

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As the polymer film 'dissolves, the reflected intensity

should oscillate due to thin film interference effects. The

quantity of interest is the reflectance R which is defined as

the ratio of the reflected light intensity to the incident light

intensity. A sufficiently accurate expression for the reflectance

H = r,,, - cr,:-,r> . ( l-r;.. ':cos(,. ( ]

Here r, a a-e the F-esnel reflet on coefficierrts for the

polymer/suLIstratE, alrd SIvent/po iymer interfac :s, respect ve--

1,- y. The phase angle 0- is the diFference io phase between light

rays reflected frem the two inter-faces. The phase angle is given

4rT d 4 r ;' -

Where d is the thickness; o- the polymer tilm, is the tree

'space avnlergth of thc 1 iht (h t is t",e irrcf dent agie o+ thc

light, 3nd n -rd n are t P -,e-fr:arti%,e iIdires ot the s - .'e,)t

ard oDIymer. Figure P is a ,ketch of a tylpiral observed -etlert-

r-d in te FrI .t y pat t er n. A 7 P fx)er(-t e thp r ~e IF-(-t ed. it (- IIt

nsc1llates sinusoidally until the film is completely dilssolvd.

after wahich th- ref lectance from the bare substrate I s ,:orItaTt

"From a reflectance-time trare such as finjure a. meash em ont of

LA

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the reflectance ratio a/b arfd the period of oscillation T allows

calculation of the dissolution rate of the polymer film and the

polymer's !efractive index. Values of the refractive indices of

the substrate and soIvent, the wavelength of light, and the

inc:ident anole must also be known.

fhe above a.na 1 ycis applies only if the solv rnt/polymer

iterface )s 1'erf e(tIy sharp. For some polymer-solvent systems

this interface is not perfectly sharp, but is expanded into a

-cntito,js t-ansition layer of nonzero thickness. The appropriate

* prescIro,1 to- th reflectance is now

F , . " + :'fr ,:.r;,,( L-r; ,'c- ,< ?

1 'I , is osI tire factor less than unity mult plyinq the

jie (tn ,- (ro f nr: t r and t 0',. + ,,,. B t, f 'id t

:ae ang1e 0, deoe,-,d on the thickness and s!hape ot toe

?rotratiron profile in the transition layer. The effect of the

t-ans 1'.on layer in t.o reduce the amplituCde of the -efl Iectance

Sse: 1 Ii at n,-. t by The factor f while preservin the average value

of the r f Ior t aTre aTd to ,h Ift the ns, i 1 1 at ins phase, tby

, IT, ittd , , edur ton factor 1 is measLirerd a -- 3)a)

,ffs t r--r f,) td-d bet-eF'n the maximum value of ref lect-ance ii thc-

I -r I at io--; c)nd rte reflectance of the bare substratfe after the

f Im has completely dlissolved (see figur e 3).

a -b+ s) (b

(a -' s) - (b3 - s,)

-4

- #

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The phase angle IS isMeaSUIr9-d in terms of the time interval tol

between the observed endpoint of dissolution and the next

ex-pec-ted maximum relative to the period for a Complete oscilla-

t i On.

L,'rrection for Si Iicon Oxide Laver

.small correction nec- to be macle when a si licon wafer i

U se ( a s ihe s ubstrate mzate, ia 3 verA thin layer of Silicon

ox ide i s 'always Present and c~an account for- an additional phase

shift qiven approximately by

where d.. is the thickness o-f the silicon oxide layer, n_ s it s

refractive index.. -and e\ is th-~ w~avlength of light used. Fcr

the silI icon substrates used in this work the thickness ot the

nat i vn oF 0d1e IlayerT wa rqeA U r eel by elI i pslomeitry to be ahoci t

Pl A. 1his can 3CClrut tor)T a phas5e s h 1ft n f _7.,O vihich Mu t heL-

,uttrar ted fr-om the mrasutred value of 0, to get the phase Ihif t

Otue to thp transit ion) layer alu net-

- - .~.. ' ~ -;~-.**~*-* *~"~~9I-V ~ " *' - V

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Sur face Roughness

One might wonder whether an alternate explanation for the

apparent reduction in the amplitude of the reflectance oscilla-

tions could he roughness on the dissolving pol-ymer surface.

Usng simple scattering theory it can be shown that the presence

o!a rough surface at the polymer/solvent interface would result

in a reduction of the amplitude of the reflectance oscillations,

hut the average value of the reflectance would also he reduced.

1I surface roughness were present one would calculate an er-

roneous polymer refract ve index when applying the equat ioi,

cleri ved for the' presence of a transition layrer. For the po yme-rs

used in th-s study the refractive index Was ver!fied to be

correct by other means. Thus it appears the formation of a

transition layer is the correct explanation for the' observed

havor.

IUANTITATIVE ANALYSIS OF THE TRANSITION LAYER

The magnitude of the observed amplitude reductinr: factu: m.

h)Fe, used Is a gauge of the thickness of the tri tJ7, 1 y-,

.,etweero the solvent and the glassy polymer . A value of =

,oUld correspond to a perfectly sharp interface, i.e. a t7 1-

t in laynr of zero thickness. Values of f 1 correspond to

thirhLer transitinn layers. A more quantitative analysis is ,l

JuucV ihlO. In principle, one can ralculate an absol,,te thiu kness

V LW

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of the transition layer, provided the shape of the concentration

prmof ile is krnown. For simpl ic ity, this prof ile may be expressed

in term5i of refractive index (as in figure 4). It can be shown

'hat the variation in refractive index through the transition

ilyer is to -a good aporoximation proportional to the variation i-

concv:en tr a tion. I t i s assumed that the transition 1-ye has a

f iite th i ckness 6S and that the refractive indlex in the laver-

va~ries only in the direction perpendicular to the surface, IFcI

v'hich the- distance variable ;-s 7. The profile may be simplified

1u r t he b y scal I rig th -* v ar i a b Ie s o f th1 rk ne ss arri r efra t

d e' (sP fig u rE 5.

Q(U) - --- ) -----

Th- resulting expressions that quantify the tr-an-,i ton lay-v c r

be der ived fI-o m opt i CalI t heo ry. of i nhomogerieou-s layers. T 1)

I pi tude reduc tion factor- f i S equa I to thFe maqrnlfude O-f 1-

complex quantity F(Y) aind the phase angle V, i- the co'Trl>'pva

<wq o f F (I~'

0, arjF('Y)}

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where

Si -dg(u)-e - du (11)

do

TT n, .c o S"',.

n.. 4- n'

(n -i (

cosi = [ - )35

Equation 11 for F(Y) results when the reflection coefficient of

the transition layer is calculated using the Rayleigh-Gans or

Born approximation.I;'' 1. Physically, this amounts to treating

the transition layer as a continuous weakly reflecting region

in which the local differential reflection coefficient is

I n I!/2n, 'where Vn is the gradient of refractive index.

Weakly reflecting meaTs that the total change in refractive index

is small rompared with the average refractive index and that

m iltiple reflections within the layer can be neglected. The

overall reflection coefficient nf the layer is found by integrat-

ing the differential reflection coefficient while incorporating

the appropriate phase factor to account for propagation through

I8

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the layer. Scaling the parameters then gives F(C) in equation

Il. Thus, one only needs to know something about the shape of

the refractive index profile g(u) in order to calculate directly

its thickness S from the measured values of f and 0,.. If

knoLledoe about the profile is incomplete, then a fitting

-procedure needs to be used to match the thickness S to the

masured f and 0,

FXPERIMENTAL RESULTS

Measurements were made on various molecular weights of PMMA

dissolvinQ in MEK at 20 0 C. As in figure 3, the presence of the

transitiorn laver is evident by the reduction in the amplitude of

the reflectance oscillations. Also, the endpoint of dissolution

rften ccrS significantly ahead of the next extrapolated maximum

in intensity. Because the reflectance is not observed to deviate

from its sinusoidal variation until the endpoint of dissolution,

it is postulated that this point represents the "leading edqe" of

the transition layer. Once this point reaches the substrat

surface thp rmaining transition layer dissolves away rapidly.

TibIe I lists the measured values of f and Q, for the va rious

molecular weights of PMMA dissolving in MEK. These values are

plotted in figure 6.

..

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Thickness Calculations

In order to calculate directly the thickness of the transi-

tion layer it is necessary to know the shape of its refractive

index profile. Unfortunately, the exact shape of this profile is

not known for these types of polymer-solvent systems. However,

it i'- still instrjctiv\,- to calculate the thickness based on some

:imnle model profiles. The profile shapes (figure 7) of linear,

cosine, step-linear, and step-exponential were chosen to approxi-

mate a realistic profiie shape and still allow an analytical

solution to the intearai in Equation 11. The functional form of

these proj I es and the1ir der i vat i ves as they would appear in

equation 11 are listed in Table 2.

The thickness of the transition layer can be calculated to

match the measured values of f and 0i . The linear and cosine

orofiles contain only one adjustable parameter: the normalized

transition layer thickness ', so in genera] the observed values

of f arid 0, cannot both be satisfied at the same time. The

stEp-linear and step-exponential profiles contain two adjustable

parameters: I and the step fraction q. For the latter tteo

profiles it is assumed that the observed endpoint of controlled

uniform dissoltition occurs when the step edge of the transition

layer reaches the substrate surface. The occurrence of these

step-like profiles has been observed on a much larger scale by

Ieberreiter"' in the dissolution of polystyrene.

In principle one could perform the above analysis for any

profile shape, although it might require numerical integration

1 0

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and tedious iteration to sblve for the transition layer thick-

ness. In practice it is convenient to use a graphical pro-

cedure. As an example, figure 8 is a chart of transition layer

thickness as a function of phase shift for the step-linear

profile, with '6 and q as adjustable parameters. In this case one

only needs to read off the unique values of normalized trnickness

and step fraction q for measured values of f and C.A

Table 3 lists the calculated thicknesses of the transition

layer of PMMA for the four model profi les. Although not entirely

obvious from the values given in Table 3 the actual physical

thicknesses arTe very close for all four model orofiles. This can

be seen more clearly in figure 9 where the actual profiles have

been plotted on the same scale for one molecular w.,eight of PMMA.

Despite deviations at the tail ends the profiles overlap remark-

ably wel 1. Thus, even though the exact profile shape is not

known, it is reasonable to conclude that the transition layer

thickness calculated by any of the model profiles is not far from

the actual thickness. The same kind of consistency in overall

thickness has been obtained elsewhere by fitting a fami ly f

one-parameter refractive index profiles to photometry data from

the reflection of light from an interface separating the liquid

and vapor phases of a fluid near its critical point.'

.1g

4-,i

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CONCLUSIONS

The technique just described is useful for approximating the

thickness of the transition layer for polymers that dissolve with

little or no swelling. Because the calculated thickness does not

depend strongly on the assumed concentration profile shape it is

reasonable that a calculated thickness will closely approximate

the actual thickness. However, for the same reason experimental

measurements are not likely to distinguish among various

theoretical models based on profile shape alone. Application of

this technique to polymer-solvent systems that exhibit both

swelling and dissolution is not as straightforward since these

systems are generally characterized by a non-uniform dissolution

rate and damped reflectance oscillations, i.e. T and f are not

constant. However, at least some qualitative information about

the profile may be obtainable in such cases.

The reflectance of the dissolving film is not observed to

deviate from its sinusoidal shape until the leading edge of the

transition layer reaches the substrate surface. At that time the

remaining transition layer dissolves away rapidly. It appears

that the rate of the dissolution process is governed primarily by

what is happening near the leading edge -- the interface with the

solid polymer -- rather than by what is happening elsewhere in

the transition layer. Although it does not provide direct

detailed information about the shape of the concentration profile

in the transition layer, this technique may be helpful in the

12

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development of theoretical models for- the dissolution o zvr

*by reveal ing the lenoth scales over which the o'ssolJut icn -2ce

takes place.

ACKNOWLEDGEMENTS

This work was supported in p'tb the fce O

Researc:h. The cooPerati.orejthe National Research-

Fac iilt\ for Submicron Struct;ures a+. Cornel i -h sL-ns--

* NSF) also is aCknoiOLIe -ged.

REFERENCES

1. A.H. Windle, in "Polymer Permeability," ed. J. Comyn,

Elsevier Applied Science Publishers,1 London (i985).

2. J.S. Vrentas, J.L. Duda, and A.-C. Hou, Journal of App.

Polymer Science, 29, 399 (1984).

3. C. Gostoli, and G.C. Sarti, Polym. Eno. Sci.. 22. 1016

(1982).

4. R.C. Lasky, PhD Thesis, Cornell University (1986).

5. A.C. Quano, in "Polymers in Electronics," ACS Symposium~

Series, 242, ed. T. Davidson, ACS, Washington D.C.(14)

6. D.S. Soong, SPIE Proceedings, 539, ed. L.F. Thompson.

(March, 1985).

7. E.E Parsonage, N.A. Peppas, and P.I. Lee, paper to be

published, Journal of Vacuum Science and Tech., B.

8. F. Rodriguez, P.D. Krasicky, and R.J. Groele, Solid State

Technology, 28, 125 (May, 1985).

'3

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9. K. Ueberreiter, in "Diffusion in Polymers," ed. J. Crank

and G.S. Park, Academic Press, New York (1968).

10. A.C. Ouano, Y.O Tu, and J.A. Carothers, in "Structure-

Solubility Relationships in Polymers," ed. F.W. Harris

and R.B. Seymour, Academic Press, New York (1977).

11. P.D. Krasicky, R.J. Groele, and F. Rodriguez, paper to be

published, Chem. Eng. Comm..

12. Lord Rayleigh, Proc. Roy. Soc. A 86, 207 (1912).

13. R. Gans, Ann. Physik 47, 707 (1915).

14. W. Geffcken, Ann. d. Phys. (5) 40, 385 (1941).

15. R. Jacobsson, Progress in Optics 5, 247 (1965).

16. J.S. Huang and W.W. Webb, J. Chem. Phys. 50, 3677 (1969).

TABLE I : Am t tude reduction factor f an phase _i i

ancle O., due to the transition layer for

various molecular weights oF PMM4 dissolvinoin MEK at 200G.

Molecular Weioht

p M_. M_. f (dre)

27 10-3 37 xi0 !.0 4

29 52 1.03_ 61 i.0

35 63 0.9-7

67 13L 0 9397 170 0. 90 i

100 150 o.S ic -0160 320 0.89 P 5180 270 0.88 !5

220 500 0.85 24

220 500 0.87 30

360 950 0.79 30360 950 0.80 33

1000 1400 0.71 35

14

Lztk*S.,..

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TABLE 2

MOD.EL TRANSITION LAYER COCNRAT737-4

PROPILE SHAPE g(ei)

i. L 1NEAR 1-u

2. COSINE 0.5(1 + cor ~ 0.-s-r

3. S TEP -LI NE AR q(1 u)- -

4. STEP-EXPONENTIAL e-c - -

-Note - thazt here S(,-) represents the raczi 4 t a

,-ees-r to account T4 or re--Featicn

tra i 0o 1i -- aer e~cness -9 e I sewhc- t

T. -9;-E 3: Calculated transition ',a"v- t-li-:-=

and step fr-action q, 7e =-

mcdel profile shapes. -zs Z. e

MoeflrWeight L in e ar Cosine Se~-1-

0' ' iO- 07:±0 0 0 C

2= 52 0 0Ci0 0

5: 3 0.031 0.04100/ 340.047 0.063 C0!f Z .

Q7170 0.057 0.075 .o CB *-

150 0.060 0.079 0.7. .CC_

0~ 320 0.060 0.079 0 05 C

180 270 0.062 0.083 0 .065 -'4~ C. 0 s C.

20500 0.070 0.093 0.06-3 C.52 0.02--220 500 0.065 0.086 0.057 0.8 0.021 1.350 950 0.08E4 0.11 0.0 7 & 0. 55 0.020 0. 1350 950 0.08E1 0.11 0.07, 6.2 0.022= 0. ZO

1000 1400 0.10 0.13 0.07q .54 0,. 038 0.2

15 Copy avaUiabl. am &"O be tPganit hwly logibl Iseoftaobo

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Pw

20

LB

1. Interferometer for monitoring polymer dissolution. Beam from laser. L.is reflected at angle 0 from coated wafer, W, immersed in solvent bath. B.Reflected light is measured with photocell. P.

T-1- I1(I)C " -

a , I

a b

r 0 Time

2. Typical reflected Light intensity trace from polymer film with anegligible transition layer. This example used a personal computerinterfaced with the photocell to reproduce the signal. The period T andamplitudes a and b are used to calculate the dissolution rate.

C -T - T .-

-

a)ab

a.0Time

3. Trace of reflected light intensity when transition laver is present. Theadded features (beyond Fig. 2) are the offset. s, and the phase difference.

teI r e

Page 22: ~D-A181 AND MODELLING THE UNCLASSIFIED mEEIIEEIIEEE · .small correction nec- to be macle when a si licon wafer i U se ( a s ihe s ubstrate mzate, ia 3 verA thin layer of Silicon

n ?~(Po lyrne

n ni

((so/venl)z

4. Refractive index.n. profile in the transition laver of thicknesswhere z is distance

! a(u)

O0 u

5. Scaled refractive index profile where u and g(u) are given by equations7 and 8

7

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1.0- v vv 010 0' 0

" f -- TV o 0 00 °

0-8 0 Q

0.8 ~o o

v 200

0.6 0 C0

-0 00 1000

0 0

I ,, , II ,I i , * Q0°

0.01 0.05 0.1 0.5 I 2

VT. A.,'e. Molecular Wt., Mw xlO -6

6. Experimental results for P.MMA dissolving in MEk at 20C where f is the

Amplitude reduction fac-or and Ot is the Phase shift angle 'see equations 4

and 5 ).

SL_ neorStpLna

q(u) g(u) ......

0 00 U I 0 U

Cos• S/ep-Eponeni/

g(u) (u)q

I0~ 00 U I 0 U

7. Profiles for the four models of Table 2.

Page 24: ~D-A181 AND MODELLING THE UNCLASSIFIED mEEIIEEIIEEE · .small correction nec- to be macle when a si licon wafer i U se ( a s ihe s ubstrate mzate, ia 3 verA thin layer of Silicon

0.0 3000t 60 90

$~~~~~~~. Char ofrdcdtato ae hckes .a ucno h

0.5 A /S Li0ea

0 30 Sep -Epoe 0i0

indisinurdAite rmeauciothe facor.f anfourPmodels.iTheadata.usedhearaetfor q Ao take 9no30oute000 hag in cocetato at the

0.5 8- ' a

Page 25: ~D-A181 AND MODELLING THE UNCLASSIFIED mEEIIEEIIEEE · .small correction nec- to be macle when a si licon wafer i U se ( a s ihe s ubstrate mzate, ia 3 verA thin layer of Silicon

DL/413/83/01GEN/413-2

TECHNICAL REPORT DISTRIBUTION LIST, GEN

No. No.Copies Copies

Office of Naval Research 2 Dr. David YoungAttn: Code 413 Code 334800 N. Quincy Street NORDAArlington, Virginia 22217 NSTL, Mississippi 39529

Dr. Bernard Douda Naval Weapons CenterNaval Weapons Support Center Attn: Dr. Ron AtkinsCode 5042 Chemistry DivisionCrane, Indiana 47522 China Lake, California 93555

Commander, Naval Air Systems 1 Scientific AdvisorCommand Commandant of the Marine Corps

Attn: Code 310C (H. Rosenwasser) Code RD-1Washington, D.C. 20360 Washington, D.C. 20380

Naval Civil Engineering Laboratory I U.S. Army Research OfficeAttn: Dr. R. W. Drisko Attn: CRD-AA-IPPort Hueneme, California 93401 P.O. Box 12211

Research Triangle Park, NC 27709

Defense Technical Information Center 12 Mr. John BoyleBuilding 5, Cameron Station Materials BranchAlexandria, Virginia 22314 Naval Ship Engineering Center

Philadelphia, Pennsylvania 19112

DTNSRDC 1 Naval Ocean Systems CenterAttn: Dr. G. Bosmajian Attn: Dr. S. Yamamoto

Applied Chemistry Division Marine Sciences DivisionAnnapolis, Maryland 21401 San Diego, California 91232

Dr. William TollesSuperintendent 1Chemistry Division, Code 6100Naval Research LaboratoryWashington, D.C. 20375

, ,N

Page 26: ~D-A181 AND MODELLING THE UNCLASSIFIED mEEIIEEIIEEE · .small correction nec- to be macle when a si licon wafer i U se ( a s ihe s ubstrate mzate, ia 3 verA thin layer of Silicon

"L413/83/ 01356A/413-2

ABSTRACTS 0 STRIBUTION LIST, 356A

Naval Surface Weapons Center Professor J. K. GillhamAttn: Dr. J. M. Augl, Or. B. Hartman Department of ChemistryWhite Oak Princeton UniversitySilver Spring, Maryland 20910 Princeton, New Jersey 08540Professor Hatsuo Ishida Professor R. S. Roe

Department of Macromolecular Science Department of Materials ScienceCase Western Reserve University and Metallurgical EngineeringCleveland, Ohio 44106 University of Cincinnati

Cincinnati, Ohio 45221

Dr. Robert E. Cohen Professor L. H. SperlingChemical Engineering Department Department of Chemical EngineeringMassachusetts Institute of Technology -Lehigh UniversityCambridge, Massachusetts 02139 Bethlehem, Pennsylvania 18015

Dr. R. S. Porter Professor Brian NewmanDepartment of Polymer Science Department of Mechanics and

and Engineering Materials ScienceUniversity of Massachusetts Rutgers UniversityAmherst, Massachusetts 01002 Piscataway, New Jersey 08854

Professor A. Heeger Dr. C. E. HoyleDepartment of Chemistry Department of Polymer Science

- University of California University of Southern Mississippi* Santa Barbara, California 93106 Hattiesburg, Mississippi 39406

Dr. T. J. Reinhart, Jr., Chief Dr. Stuart L. CooperNonmetallic Materials Division Department of Chemical EngineeringDepartment of the Air Force University of WisconsinAir Force Materials Laboratory (AFSC) Madison, Wisconsin 53706Wright-Patterson AFB, Ohio 45433

Professor J. Lando Professor D. GrubbDepartment of Macromolecular Science Department of Materials Science.Case Western Reserve University and EngineeringCleveland, Ohio 44106 Cornell University

Ithaca, New York 14853

Professor C. Chung Dr. 0. B. CottsDepartment of Materials Engineering SRI InternationalRensselaer Polytechnic Institute 333 Ravenswood AvenueTroy, New York 12181 Menlo Park, California 94205

Professor J. T. Koberstein PLASTECDepartment of Chemical Engineering DRSMC-SCM-0(D), Bldg 351 NPrinceton University Armament Research & DevelopmentPrinceton, New Jersey 08544 Center

Dover, New Jersey 07801

Professor J. H. MagillDepartment of Metallurgical Professor C. H. Wang

and Materials Engineering Department of Chemistry

University of Pittsburgh University of UtahPittsburgh, Pennsylvania 15261 Salt Lake City, Utah 84112

Page 27: ~D-A181 AND MODELLING THE UNCLASSIFIED mEEIIEEIIEEE · .small correction nec- to be macle when a si licon wafer i U se ( a s ihe s ubstrate mzate, ia 3 verA thin layer of Silicon

vow

d~p

-O -M- u M s 3