Absorption and Exposure in Positive Photoresist

Absorption and exposure in positive photoresist

Chris A. Mack

A review of the theory of absorption on microscopic and macroscopic levels is given. This theory is thenapplied to the absorption of UV light by diazo-type positive photoresist during exposure. A formal treatmentof the properties of polychromatic light is given. Using these analyses, the effects of polychromatic exposureof a photoresist are derived. Finally, experimental verification of Beer's law and determination of theexposure quantum efficiency of a particular photoresist is given.

1. Introduction

The phenomenon of absorption can be viewed on amacroscopic or a microscopic scale. On the macro-level, absorption is described by the familiar Lambert-Beer law which gives a linear relationship betweenabsorbance and path length times the concentration ofthe absorbing species. On the microlevel, a photon isabsorbed by an atom or molecule, promoting an elec-tron to a higher energy state. Both methods of analy-sis yield useful information needed in describing theeffects of light on a photoresist.

If the light used to expose this photoresist is poly-chromatic, one must be careful to define what is meantby the intensity of light. Usually, intensity is mea-sured by some detector. Different detectors will, ingeneral, give different readings for the intensity ofpolychromatic light. Thus, a formal definition of theactual intensity must be established along with amethod of relating the actual intensity to the measuredintensity. Once this has been done, a treatment of theexposure of photoresist by polychromatic light can besimilarly formalized.

11. Macroscopic Absorption

The basic law of absorption is an empirical one withno known exceptions. It was first expressed by Lam-bert in differential form as

dI PI (1)dz

where I is the intensity of light traveling in the zdirection through a medium, and a is the absorption

The author is with U.S. Department of Defense, Fort Meade,Maryland 20755-6000.

Received 31 December 1987.

coefficient of the medium and has units of inverselength. In a homogeneous medium (i.e., a is not afunction of z), Eq. (1) may be integrated to yield

I(z) = IO exp(-az), (2)

where z is the distance the light has traveled throughthe medium and Io is the intensity at z = 0. If themedium is inhomogeneous, Eq. (2) becomes

I(z) = Io exp(-abs), (3)

where abs = a(z')dz' = the absorbance.When working with electromagnetic radiation, it is

often convenient to describe the radiation by its com-plex electric field vector. The electric field can implic-itly account for absorption by using a complex index ofrefraction n such that

n = n - iK. (4)

The imaginary part of the index of refraction, some-times called the extinction coefficient, is related to theabsorption coefficient by

a = 47rK/X. (5)

In 1852 Beer showed that for dilute solutions theabsorption coefficient is proportional to the concen-tration of the absorbing species in the solution:

asolution = ac, (6)

where a = molar absorption coefficient;= aMW/p;

MW = molecular weight;p = density; andc = concentration.

The stipulation that the solution be dilute expresses afundamental limitation of Beer's law. At high concen-trations, where absorbing molecules are close together,the absorption of a photon by one molecule may affectthe ability of another molecule to absorb light.' Sincethis interaction is concentration dependent, it causes

1 December 1988 / Vol. 27, No. 23 / APPLIED OPTICS 4913

deviation from the linear relation (6). Also, an appar-ent deviation from Beer's law occurs if the index ofrefraction changes appreciably with concentration.

For an N component homogeneous solid, the overallabsorption coefficient becomes

NAT = Eajcj.

j=1(7)

Of the total amount of light absorbed, the fraction oflight which is absorbed by component i is given by

IAi = aAc

IAT \aT/(8)

where IAT is the total light absorbed by the film, and IAiis the light absorbed by component i.

We will now apply the concepts of macroscopic ab-sorption to a typical positive photoresist. A diazo-naphthoquinone positive photoresist (such as AZ1350J)is made up of four major components; a base resin Rwhich gives the resist its structural properties, a pho-toactive compound M (abbreviated PAC), exposureproducts P generated by the reaction of M with ultravi-olet light, and a solvent S. Although photoresist dry-ing during prebake is intended to drive off solvents,thermal studies have shown that a resist may contain10-20% solvent after a 30-min 1000C prebake.2 3 Theabsorption coefficient a is then

a = aMM + aP + aRR + aSS. (9)

If MO is the initial PAC concentration (i.e., with no UVexposure), the stoichiometry of the exposure reactiongives

P=M M. (10)

Equation (9) may be rewritten as4

a= Am +B, (11)

where A = (aM - ap)MO;B = apMO + aRR + aS; andm = M/Mo.

The quantities A and B are experimentally measur-able4 and can be easily related to typical resist absor-bance curves, measured using an UV spectrophotome-ter. When the resist is fully exposed, M = 0 and

a°exposed =B- (12)

Similarly, when the resist is unexposed, m = 1 (M =Mo) and

aunexposed = A + B. (13)

From this A may be found by

adiff = afunexposed - exposed = A. (14)

Thus, A(X) and B(X) may be determined from the UVabsorbance curves of unexposed and completely ex-posed resist (Fig. 1).

Ill. Microscopic Absorption

On a microscopic level, the absorption process can bethought of as photons being absorbed by an atom ormolecule causing an outer electron to be promoted to a

300 400 500Wavelength (nm)

Fig. 1. Photoresist absorption parameters A and B as a function ofwavelength for AZ1350J.

higher energy state. This phenomenon is especiallyimportant for the photoactive compound since it is theabsorption of UV light which leads to the chemicalconversion of M to P.

M n E P. (15)

This concept is stated in the first law of photochemis-try: only the light which is absorbed by a molecule canbe effective in producing photochemical change in themolecule.

Einstein first quantified absorption on a microscop-ic scale by using probabilities. Consider a substanceM being exposed to radiation of intensity I and spec-tral power density J(X) [where J(X)d\ is defined as theintensity of the radiation with wavelengths between Xand X + d so that I = J(X)dX, see the followingsection]. Einstein's relation for photon absorption is5

AI = NMBE(X)J(X)dX, (16)

where AIbM = the number of photons with wave-lengths between X and X + dX absorbedper second by M;

NM = the number of molecules of M; andBE(X) = Einstein's coefficient of absorption.

[Originally, Einstein's relation involved an energy den-sity u(v) instead of J(X). The original Einstein coeffi-cient Bnm is related to BE(X) by Bnm = BE(X)c/n, wherec is the speed of light and n is the index of refraction ofthe medium.] The total number of photons absorbedper second by M at all wavelengths can be found byintegrating Eq. (16) over wavelength

4m= NM BE(X)J(X)dX. (17)

To relate Eq. (16) to measurable quantities, onemust relate the microscopic theory to macroscopic ob-servations. Consider an elemental volume containingsome amount of substance M (Fig. 2). The light ab-sorbed by the volume (with wavelengths between X and

+ d) is IO - IT. The light absorbed by M can befound using Eq. (8):

IAM = (IO IT) (aMM) (18)

4914 APPLIED OPTICS / Vol. 27, No. 23 / 1 December 1988

Io = Jo(A)dA

+

Az

Relative Intensity (or response)1.2 . .. .. .. .. .. .. .. .. .. .

/Area = S .8

.6

IT = J7(A)dAFig. 2. Geometry used to compare macroscopic and microscopic

absorption.

Intensity can be converted to photons absorbed by Mper second (between X and X + dX) by

AB X = aM (MIT) ( )

hc (a) (19)

where h is Planck's constant. Now Eqs. (16) and (19)can be equated:

Xs (aM)h (IO - IT) NMBE(X)J(X)dX. (20)

Dividing both sides of the equation by the volume SAzand by Avogadro's number NA,

aMMX /'0 -IT ) MBE(X)J(X)dX. (21)NAhca'\ ~Az (1

Letting Az go to 0,

lim ( T dI = L (22)Az-0 Az dz

Recalling that, in this case, I = J(X)dX, Eq. (21) be-comes

amXNAhc MJ(X)dX = MBE(A)J(X)dX. (23)

Einstein's coefficient of absorption can now be relatedto the molar absorption coefficient of M:

BE() = aM (24)

Recalling Eqs. (4) and (5),

BE(A) = 4 r(MW)M KM. (25)

Thus, Einstein's coefficient of absorption is propor-tional to the imaginary part of the index of refractionof the photoactive compound, KM.

Einstein's coefficient for spontaneous emissionAE(X) can be related to BE(X) by

8-rhc2n2

AE(W = 5 BE(). (26)

Integrating over wavelength gives the overall AE,

AE=8 nJ am dX. (27)

.4

0 is - - - - -1 a._1rw ,-,, I ,sX_ I.......

300 320 340 360 380 400 420 440 460 480 500

Wavelength (nm)

Fig. 3. Typical mercury arc lamp spectrum and a detector responsecurve.

intensity of the light involves using a detector thatinvariably does not have a flat response over this range.The question then arises, how does the measured lightintensity IM relate to the actual total intensity IT for apolychromatic light source? Let us first define a spec-tral power density J(X) such that

IT =f J(X)dX. (28)

Consider now a hypothetical experiment. The lightintensity of some source is measured over a very nar-row range of wavelengths between X0 and X0 + AX byinserting a filter with a transmission function t(X) de-fined as having a transmittance T within the givenwavelength range and zero outside the range. Equa-tion (28) becomes

1(Xo) = t(X)J(X)dX, (29)

where I(X0) is the measured intensity from our hypo-thetical experiment. If AX is sufficiently small, J(X)can be assumed constant over this range giving

I(,\) = TJ(X0 )AX. (30)

The measured I(X0) is often normalized so that it hasa value of 1 at some wavelength. For the case of amercury arc lamp, one often uses the wavelength X =365 nm. Thus, a relative intensity IR(X) can be de-fined:

IR(XO) I(X,)/I(365 nm) = J(Xo)/J(365 nm), (31)

where the second equality comes as a result of Eq. (30).A graph of IR(X) vs X is known as the spectral output ofthe light source. Figure 3 shows the spectral output ofa typical mercury arc lamp. From Eq. (31), the spec-tral density J(X) is proportional to this graph:

J(W) = IR(X)J(365 nm).

IV. Polychromatic Light

The light used to expose photoresists is generally inthe 300-500-nm wavelength range. Measuring the

Consider now the original problem of relating a mea-sured intensity to the actual intensity. When a detec-tor is used to measure light intensity, Eq. (28) can bemodified to read


(32)

W

I = S,(X)J(X)dX,

where SD(X) is the spectral response of the detector.Figure 3 shows a typical UV radiometer responsecurve. Figure 4 shows the product of the two curves inFig. 3 and can be thought of as the portion of the sourceoutput that is seen by the detector. Equation (32) canbe used to remove J(X) giving

Im = J(365 nm) J SD(X)IR(X)dX,

Relative Intensity(33) 1.2 .. ...

.8

.6

.4

(34)

.2

Solving this equation for J (365 nm) and substitutingback into Eq. (32) gives

J() = -IMIR(X)

JA SDG()IR(X)dX

(35)

This can now be used in Eq. (28) to give IT in terms ofIM:

J IR(X)dX

ITS=IM XfJ S,(X)I,(X)dX

0300 320 340 360 380 400 420 440 460 480 500

Wavelength (nn)

Fig. 4. Part of the mercury arc lamp spectrum that is seen by thedetector in Fig. 3.

J exp[-a(X)z]IR(X)dX

fT SD(X)IR(X)dX(39)

(36)

Each integral can be evaluated using standard numeri-cal integration techniques and is a constant for a givensource/detector system.

One should note that this method of determining ITis sensitive to variations in the source spectral outputIR. In the example given, only wavelengths near the365-nm peak are measured due to the narrow responseof the detector. If the relative heights of the threemajor peaks change (due to lamp aging, for example6),the measured intensity will not reflect this change.7This problem is alleviated by using a detector with awider spectral range. Obviously, if SD(X) has a valueof one over the range for which J(X) is nonzero, the twointegrals in Eq. (36) are equal and IT will equal IM.

Equation (36) relates the actual total intensity oflight in an isotropic, nonabsorbing medium (such asair) to the measured intensity. If, however, the medi-um in question is absorbing, IT is a function of thedistance the light has traveled, z, and therefore isdependent on the position of measurement. Equation(28) can be modified to handle this case by letting thespectral density be a function of position as well aswavelength:

IT(Z) = J J(z,X)dX. (37)

Consider an absorbing isotropic film in which thereare no standing waves (e.g., a very thick film or a filmon an optically matched substrate) illuminated by nor-mally incident plane waves. For such a case, we canwrite

J(z,X) = Jo(X)Tl2 exp[-a(X)z], (38)

where T12 is the transmittance of the air-film interfaceand Jo(X) is the incident spectral density, i.e., thesource spectral density. Equations (31)-(35) will ap-ply to J0 (X) so that Eq. (36) will become

If a is not wavelength dependent, the exponential termcan come out of the integral giving the standard inte-grated form of the Lambert law of absorption:

IT(Z) = Io exp(-az), (40)

where

I = IMT12XSD()IR()d

Any similar problem can be solved if a suitable J(z,X)can be defined. For the problem of standing wavescaused by exposing a photoresist on a reflecting sub-strate with a plane wave (e.g., during projection print-ing), J(z,X) can be defined by8

J(z,X) = JO(X)TI2lexp(-ikz) + P23tD exp(ikz)2

11 + P12P23T I

where pij is the reflection coefficient between media iandj, k is the propagation constant of the film, TD is theinternal transmittance of the film, and the subscripts1,2,3 represent air, resist, and substrate, respectively.

V. Exposure Kinetics

The chemical reaction (15) can be rewritten in gen-eral form as

k, k,M sk M* P.

k2(42)

where M = the photoactive compound (PAC);M* = molecule in an excited state;

P = the carboxylic acid (product); andkl,k 2,k3 = the rate constants for each reaction.

Simple kinetics can now be used. The proposed mech-anism (42) assumes that all reactions are first order.Thus, the rate equation for each species can be writtenas


dM = k2M* - kM,

dM*dt=kM - (k + k)M*,

k2 is the sum of the rate constants of these three mech-anisms:

(43) k2 = A, + kq + J BE(X)J(X)dX, (52)

dP= k3M*.

A system of three coupled linear first-order differen-tial equations can be solved exactly using Laplacetransforms and the initial conditions

M(t = 0) = MO,(44)

M*(t = 0) = P(t = 0) = 0.

However, if one uses the steady-state approximationthe solution becomes much simpler. This approxima-tion assumes that in a very short time the excitedmolecule M* comes to equilibrium, i.e., M* is formedas quickly as it disappears. In mathematical form,

dM*d =0. (45)dt

A previous study has shown that M* does indeed cometo equilibrium quickly, of the order of 10-8 s.9 Thus,

dM=K--KM,

where

K-klk 3k2 + k3

Assuming K remains constant with time,

M = Mo exp(-Kt).

(46)

where AE = Einstein's coefficient of spontaneousemission;

BE(X) = Einstein's coefficient of induced emission= BE(X); and

kq = rate constant for the quenching reaction.Under normal circumstances (i.e., not a laser) the

amount of induced emission is very small. In fact, anorder of magnitude analysis using typical resist parame-ters gives AE to be 108 times greater than f BE(X)J(X)dXfor a light intensity of 1 mW/cm2 . Thus, ignoring in-duced emission and assuming no quenching, the con-stant k2 becomes

k2 = AE. (53)

The overall rate constant K can now be written as

K = J C(X)J(X)dX, (54)

where

C( = k3 4(X)BE(X) '1YX)BEG\)AE + k,

and cLT iS the overall quantum efficiency of the formu-lation of product P. Equation (47) now becomes

M = MO exp[-t J C(X)J(X)dX ] (55)(47)

The overall rate constant K is a function of theintensity of the exposure radiation. The exact func-tionality can be determined by analyzing the phenom-enon of absorption. In the previous section, an ex-pression was given for the number of photons absorbedby M per second. If we define a quantum efficiency Psuch that

For monochromatic light, this expression simplifies to

M = Mo exp-(CIt). (56)

A study of absorption was used to relate BE(X) tomeasurable quantities [Eq. (24)]. This equation canbe used to relate the quantum efficiency (PT(X) to mea-surable quantities:

= molecules of M converted to M*number of photons absorbed by M

(48)

Eq. (17) becomes

dM (generated) = M | b(X)B,(X)J(X)dX. (49)dt Jo

But, the rate of generation of M* is equal to kjM.Thus,

k= J (X)B,(X)J(X)dX. (50)

The reverse reaction,

M* ::>Ml (51)

can occur by three different paths: M* can spontane-ously give off a photon, reverting to M; it can react withsome molecule in the photoresist (called quenching);or M* can undergo induced emission due to the con-tinuing bombardment of photons. The rate constant

4YX) = NAhc (X)am(X)X(57)

A kinetic analysis of the exposure of a positive pho-toresist has led to the integrated rate Eq. (55). Inderiving this equation we have assumed that J(X) (or Ifor monochromatic light) was constant within the re-sist during the exposure. This, however, is not true ingeneral due to the changing chemical composition ofthe resist as it is being exposed. This problem can bedealt with, however, if 1(t) is known.'( Thus, Eq (55)or (56) forms the backbone of an optical lithographyexposure model. Of course, the usefulness of theseequations depends on the ability to measure the con-stant C. Fortunately, a simple experiment can be usedto measure C in a straightforward and fairly accuratemanner.4

When exposing a photoresist, the resist acts as thedetector. There is only a certain range of wavelengthsto which the resist is sensitive. If we define SR(X) asthe spectral sensitivity of the resist,

1, December 1988 / Vol. 27, No. 23 / APPLIED OPTICS 4917

Absorpotion Parameter A (lm-l)1.6 . .. . . . . . . . .

1.4

1.2

.8

.6

.4

00 .05 .1 .15 .2 .25 .3 .35 .4

Weight Fraction PAC

Fig. 5. Verification of Beer's law for an experimental positive pho-toresist.

Ieff(z) = J SR(X)J(zX)dX, (58)

where Ieff is the effective light intensity used by theresist per unit depth into the resist. SR(X) can befound by a fundamental analysis of the absorption oflight, as given above:

SR(X) = 1T(X)aM(X)M = NAhCM CX) (59)X

Thus, the sensitivity of the resist is proportional to C/Xand the PAC concentration.

Using the results of the previous section, we can putEq. (55) in terms of measurable quantities:

m = exp(-CeffIMt), (60)

where

J C(X)IR(X)dX

Ceff=°

f" S,(X)IR(X)dX

Knowing C(X), SD(X), and IR(X), the effective constantCeff can be calculated. One should note the similaritybetween Eqs. (60) and (56). Polychromatic exposurecan be treated in a manner identical to monochromaticexposure.

As was mentioned, a technique exists for measuringC(X).4 The method involves exposing a photoresistcoated glass wafer with light of wavelength X and mea-suring the transmitted light with time. Alternatively,if polychromatic light is used, Ceff will be measured.Again, this value will be dependent on the particularsource/detector combination used to make the mea-surements.

VI. Experimental Results

As mentioned previously, Beer's law is empirical innature and, thus, should be verified experimentally.

In the case of positive photoresists, this means formu-lating resist mixtures with differing photoactive com-pound to resin ratios. Using Varcum 29-808 resin 1

and Fairmount 1010 photoactive compound,1 2 photo-resists were made with 30% by weight solids content incellosolve acetate solvent. Of the 30% solids, the PACto resin weight ratio was varied in different formula-tions. A total of six formulations were made: 10%,15%, 20%, 25% 30%, and 35% PAC by weight. Higherpercentages of PAC were found to be insoluble at roomtemperature. The resist mixtures were spin-coatedonto quartz wafers to a thickness of -1 Agm and hot-plate baked for 3 min at 1000C. The values of theabsorption parameters A and B and the exposure rateconstant C were measured for each resist at the g, h,and i lines of the mercury spectrum using the tech-nique described by Dill et al.

4 The results shown inFig. 5 show quite clearly a linear dependence of absorp-tion on concentration and extrapolation to zero ab-sorption for zero concentration, in support of Beer'slaw. The slope of these curves is am and is related toaM by the density and molecular weight of the PAC.Further, using the measured value of C for this resist,the overall quantum efficiency can be determined, aswell as BE(X). These values are given in Table I wherethe density of the resist was 1.2 g/cm3 and the molecu-lar weight of the PAC was estimated to be 368 g/mol.

Finally, values of the resist absorption parameters Aand B and the exposure rate constant C were measuredfor a variety of commercially available photoresists.The results are shown in Table II.

VII. Conclusions

Two theoretical approaches to absorption by a pho-toresist have been described. The Lambert-Beer lawgives us absorption in terms of measurable quantities.The Einstein relation describes abosorption in termsof individual photons, which becomes important whendetermining a theoretical exposure rate. It has alsobeen shown that these methods of analysis are equiva-lent, and the Einstein coefficients can be related tomeasurable quantities found in the Lambert-Beer law.From the point of view of optical lithography, theprinciples of macroscopic absorption were used in de-termining the intensity of light in the resist duringexposure. The theory of microscopic absorption wasused when determining the effects of absorption onresist chemistry.

The problems associated with describing polychro-matic radiation can be solved using the methods dis-

Table 1. Measured and Calculated Parameters for an ExperimentalPhotoresist

Wavelength AM C BE(nm) (Pm-') (cm2/mJ) T (cm2/mJ)

365 3.38 0.0118 0.373 0.0316

405 4.32 0.0292 0.651 0.0449

436 2.17 0.0133 0.548 0.0243


Table II. Absorption and Exposure Parameters for Commercial Photoresists

365 nm 405 nm 436 nm

ResistA B C A B C A B C

(pm-l) (pm-1) (cm2/mJ) (pm-i) (pm-l) (cm2/mJ) (pm-) (pm-) (cm2/mJ)-- - t 7 __ A Y arrn A^_ALIJOUJ

AZ1318sfd

AZ1512

AZ4110

AZ5214

Kodak 820

Ultramac PR64

Ultramac PR914

Utramac PR914AR

Shipley 1400-27

Shipley 1400-27D1

Shipley 1813

OFPR-800

OFPR-800 AR-15

EPR-5000

HPR 204

HPR 256

HPR 1182

Xanthochrome

U.Ubb

0.898

0.916

0.512

0.563

1.000

0.982

1.032

1.052

1.018

0.919

0.996

0.812

0.768

0.909

1.189

1.015

0.787

0.639

U.275

0.310

0.292

0.107

0.056

0.106

0.252

0.232

0.632

0.271

0.357

0.281

0.284

0.384

0.306

0.216

0.322

0.157

0.597

0.013

0.015

0.015

0.017

0.013

0.019

0.020

0.020

0.021

0.019

0.019

0.016

0.015

0.014

0.020

0.025

0.018

0.934

0.949

0.917

0.468

0.517

1.045

1.026

1.036

1.012

1.068

0.967

1.078

0.772

0.932

0.971

1.162

1.058

0.802

0.824

0.053

0.121

0.100

0.070

0.018

0.088

0.064

0.064

0.775

0.061

0.153

0.073

0.105

0.224

0.088

0.053

0.097

0.035

0.096

0.023

0.030

0.028

0.023

0.021

0.028

0.029

0.028

0.032

0.029

0.036

0.019

0.029

0.026

0.032

0.031

0.027

0.028

0.579

0.573

0.556

0.266

0.029

0.563

0.536

0.601

0.592

0.601

0.534

0.592

0.475

0.606

0.563

0.655

0.517

0.458

0.520

0.037

0.202

0.077

0.044

0.020

0.052

0.041

0.066

1.110

0.066

0.252

0.059

0.073

0.241

0.076

0.036

0.094

0.031

0.057

cussed above. One must know the spectral output ofthe illumination source and the spectral response ofthe detector in order to relate the measured intensity(detector reading) to the actual intensity. If one alsoknows the wavelength dependence of a photoresistexposure rate constant C, the process of exposure canbe treated in a straightforward manner. The constantC can be related to other physical properties of theresist or can be measured experimentally.

The results of the above analysis have been incorpo-rated into an overall lithography model called PRO-LITH (the positive resist optical lithography model)which can model polychromatic exposure of photore-sist, for example, during contact printing.1 0

The author wishes to thank Edward Grauch andAaron Radomski for their help in measuring the ABCparameters.

References

1. D. A. Skoog and D. M. West, Fundamentals of AnalyticalChemistry (Holt, Rinehart, & Winston, New York, 1976), pp.509-510.

2. J. M. Koyler et al., "Thermal Properties of Positive Photoresistand Their Relationship to VLSI Processing," in Proceedings,Kodak Microelectronic Interface '79 (Oct. 1979), pp. 150-165.

3. J. M. Shaw, M. A. Frisch, and F. H. Dill, "Thermal Analysis ofPositive Photoresist Films by Mass Spectrometry," IBM J. Res.Dev. 21, 219 (1977).

4. F. H. Dill et al., "Characterization of Positive Photoresist,"IEEE Trans. Electron Dev. ED-22, 445 (1975).

5. W. J. Moore, Physical Chemistry (Prenctice Hall, EnglewoodCliffs, NJ, 1972), pp. 753-755.

6. G. Bachur, "Development of Optical Measurement and ControlSystems for Photolithography," Proc. Soc. Photo-Opt. Instrum.Eng. 80, 2 (1976).

7. A. Minvielle and R. Rice, "Spectral Output Variations in Per-kin-Elmer Micraligns," in Proceedings, Kodak MicroelectronicInterface '79 (Oct. 1979), pp. 60-65.

8. C. A. Mack, "Analytical Expression for the Standing WaveIntensity in Photoresist," Appl. Opt. 25, 1958 (1986).

9. J. Albers and D. B. Novotny, "Intensity Dependence of Photo-chemical Reaction Rates for Photoresists," J. Electrochem. Soc.127, 1400, (1980).

10. C. A. Mack, "PROLITH: A Comprehensive Optical Lithogra-phy Model," Proc. Soc. Photo-Opt. Instrum. Eng. 538, 207(1985).

11. Reichhold Chemicals, Inc., Warren, NJ 07060.12. Fairmount Chemical Co., Inc., Newark, NJ 07105.

0


0.016

0.014

0.0130.013

<0.001

0.013

0.014

0.016

0.013

0.017

0.015

0.011

0.016

0.014

0.015

0.012

0.014

0.016

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Absorption and Exposure in Positive Photoresist