LithographicOptimizationUsingPhotoresistContrastBy Chris A. Mack, SEMATECH, Austin, Texas

Optimizing photoresist contrast is oneof the oldest and most commonly usedtechniques for improving a lithographicprocess. Unfortunately, this method hasnumerous problems and in many casesyields incorrect results. An example isthe use of contrast to optimize a surfac-tant developer process. The resultingcontrast values have little or no relation-ship to resolution or process latitude.The alternative is to perform linewidthversus focus and exposure experimentsas a function of the parameters to beoptimized, a time-consuming and expen-sive process.

This article explores the relationshipbetween photoresist contrast and theproperties of a lithographic processwhich need to be optimized. Using ameaningful definition of contrast, tech-niques for measuring contrast will beevaluated. The conventional method,resist thickness versus exposure, givesan accurate measure only under certainconditions and fails to consider the

dependence of contrast on exposureenergy. A more general technique will begiven. Byunderstanding the relationshipbetween the measured and actual con-

trast, the appropriateness of using con-trast can be evaluated.

BackgroundThe use of "contrast" to describe the

response of a photosensitive materialdates back one hundred years whenHurter and Driffield measured the

optical density of photographic negativeplates as a function of exposure [1]. The"perfect negative" was one which exhib-ited a linear variation of optical densitywith the logarithm of exposure. A plot ofoptical density versus log-exposureshowed that a good negative exhibited a"wide period of correct representation",as is shown in the Hurter-Driffield (H-D)curve in Fig. 1. Hurter and Driffieldcalled the slope of this curve in thelinear region y, the "development con-

..-,

stant". Negatives with high values of ywere said to be "high contrast" nega-tives because the photosensitive emul-sion quickly changed from low to highoptical density when exposed. Ofcourse, high contrast film is not alwaysdesirable since it easily saturates.

Photolithography evolved from photo-graphic science and borrowed many ofits concepts and terminology. Whenexposing a photographic plate, the goalis to change the optical density of thematerial. In lithography, the goal is toremove resist. Thus, an analogous H-Dcurve for lithography plots resist thick-ness after development versus log-expo-sure. The lithographic H-Dcurve isusually a portion of the complete H-Dcurve shown in Fig. 1. Because the goalis to completely remove unwanted pho-toresist, there is usually a range of ener-gies for which all of the photoresist isremoved and thus the H-Dcurve wouldshow no response. If, however, a verythick photoresist and/or a short devel-opment time were used so that theresist was not completely removed, theresult would be a complete H-Dcurve.This concept is illustrated in Fig.2,where the relationship between thelithographic H-Dcurve of a negativeresist and its hypothetical completecurve is shown. It is common practice tonormalize the initial resist thickness toone, so that the H-Dcurve displays therelative thickness remaining.

Following the definition of y fromHurter and Driffield, the photoresist"contrast" has traditionally been definedas the slope of the lithographic H-Dcurve at the point where the thicknessgoes to zero. Thus,

r=+~AI- T dIn E E = Eo

where "C is the resist thickness remainingafter development, T is the resist thick-ness before development, E is thenominal exposure energy, and Eois the

36 JANUARY 1991 MICROELECTRONICS MANUFACTURING TECHNOLOGY

energy at which 't reaches zero. Eo iscalled the clearing dose for positive pho-toresists and the gel dose for negativesystems. The positive sign in equation(1) is used for negative resists and theminus sign is used for positive systemsin order to keep the value of y positive.For the remainder of this paper, positivesystems will be discussed. The results,however, can easily be applied to nega-tive photoresists as well. (Note that abase-lO logarithm often is used in equa-tion (1) rather than the naturalloga-rithm. This article will always employthe natural log.)

Following the tradition of the photo-graphic sciences, a high contrast pho-toresist is one which makes a quick tran-sition from being an "under exposed"resist (which does not dissolve) to an"over exposed" resist (which dissolvescompletely). The traditional definition inequation (1) seems to fit this concept.Furthermore, it is analogous to the pho-

Figure 1: The original H-Dcurve ofHurter and Driffield showing theoptical density of two negative photo-graphic plates as a function of log

3.0

2.0~'iicG)Q

1.0

(1)

0.0

Log Exposure

~

tographic contrast as defined by Hurterand Driffield. The slope of opticaldensity (which is a logarithm of trans-mittance) versus log-exposure is similarin form to the slope of relative thickness(which is like a log-thickness) versuslog-exposure. Thus, it would seem that asuitable definition has been used.

In the last ten years, however,workers in the field of photolithographyhave found numerous circumstancesunder which the definition in equation(1) does not meet expectations of whatcontrast stands for. It is well known thatadding a dye to a photoresist decreasesthe measured value of contrast, usuallywithout reducing exposure latitude [2].The use of surfactant laden developersdramatically increases measured con-trast values [3], although often resolu-tion and exposure latitude are notimproved. What causes these apparentdiscrepancies between the behavior ofthe measured contrast and our conceptof how contrast affects lithography? Isthere a problem with the definition orthe measurement technique? Thesequestions can be answered by puttingthe concept of contrast on a firm theo-retical foundation and applying rigorousanalysis to the observed behavior.

Definition ofPhotoresist ContrastWith the advantage of retrospect, let uslook at the evolution of the traditionaldefinition of contrast and perhapsprovide a slightly different definition. In

Figure 2: Conventiooal photoresist H-D curve for a negative resist with thehypothetical "complete curve" alsoshown (dashed) for comparison.

...cCD'i:z:;'.IIII:

/

//

/

//

//

10 100

Energy (mJ/cm2)

photography, the desired effect of expo-sure is a change in the transmittance o.fthe photographic negative. In pho-tolithography, the desired effect is achange in development rate. Thischange in development rate is manifestas a change in resist thickness afterdevelopment. Analogous to the photo-graphic H-Dcurve, let us plot log-devel-opment rate versus log-exposure energy.Fig.3 shows the results for a typicalphotoresist. Note that this graph gives acomplete H-Dcurve and does not cut offat some energy Eo' We can now state adifferent definition of contrast, which Ishall call the theoretical contrast, Yth:

dInR

Yth==dIn E

where R is the development rate. (Thisdefinition is not very new, dating back atleast to Kaplan and Meyerhofer in 1979[4]. It is also commonly used in electron-beam lithography.) We shall now usethis theoretical contrast to quantify theeffect of contrast on a lithographyprocess and to compare it to the stan-dard measured value of contrast.

The goal of lithographic exposure isto turn a gradient in exposure energy(an aerial image) into a gradient indevelopment rate. From equation (2), itis very easy to express this effect as [5],

aIn R aInI-=y; -ax th ax

where I is the aerial image intensity and

Figure 3: The variation of developmentrate with energy (plotted in a way anal-ogous to the H-Dcurve). The slope ofthis curve is the theoretical contrast.

100

i.5: 10~..I:IIED-o'i 1=Q

10000.1

1 10 100Energy (mJ/cm2)

1000

(2)

x is the horizontal distance from thecenter of the feature being printed. Theleft hand term is the spatial gradient ofdevelopment rate. To differentiatebetween exposed and unexposed areas,it is desirable to have this gradient aslarge as possible. The right hand side ofequation (3) contains the log-slope ofthe aerial image. This term representsthe quality of the aerial image, or alter-natively, the amount of information con-tained in the image about the position ofthe mask edge. The photoresist contrast"amplifies" the information content ofthe image and transfers it into the pho-toresist as a development rate gradient.This expression quite clearly illustratesthe role of contrast in defining the"goodness" of a photoresist process.

The theoretical definition of contrast

now can be compared to the convention-al measured contrast, which now will becalled Ym' The thickness remainingafterdevelopment for the conventional H-Dcurve measurement can be described bythe following equation:

tdev

~ = T - f Rdt0

(4)

where t devis the final development time.Differentiating this equation withrespect to log-exposure yields:

(3)d"C tdevdR

dInE = - fdInE dt()

(5)

Dividing by the resist thickness and sub-stituting in the definition of Ythgives:

1- dx 1 'dev

T dIn E =- T J YihRd t0

(6)

Ifthe development rate is constant fromtop to bottom of the resist film, the con-trast can be taken out of the integral. Ifequation (6) is evaluated at the energyEo,the integral becomes one and:

-1- dxT dInE = Ym= y,.<Eo}= dlnR IdIn E E()

(7)

Thus, the measured contrast matchesthe theoretical contrast under the

important restriction of constant devel-opment rate through the resist film.

To examine what happens when therate is not constant through the resistfilm it is convenient to put equation (4)in a different form. An equivalent expres-sion governing the dissolution is [5]:

MICROELECTRONICSMANUFACTURINGTECHNOLOGYJANUARY1991 37

T-T

fdz

tdev= R(z)0

Proceeding as before, we take thederivative of both sides with respect tolog-exposure and get:

(8)

o-]r~~- 1 ~- 0 dInE R2(z) R(T - 'l') dInE

(9)

Rearranging:

1 d'l'--T dIn E

R(T - 'l')

T

T-r

fdlnR dz

dInE R(z)0(10)

Evaluating this expression at E =Eo(Le.,r = 0) and using the definitions of mea-sured and theoretical contrast:

T

R(T)J

~Ym= T Yth R(z)

0

(11)

Ifthe development rate does not varythrough the resist thickness, it is easyto show that equation (11) predicts thatmeasured and theoretical contrast

values are equal. Other conditions, suchas surface inhibition and resist absorp-tion, can be handled using this equationand will be described in a subsequentsection. Equation (11) states that themeasured contrast is an average of thetheoretical contrast weighted by oneover the development rate.

We can now explore the properties of

TABLE1PARAMETERSUSED FORCALCULATINGRESISTCONTRAST

Wavelength=436nm

Rmax= 100nm/s

Rmin= 0.1 nm/s

mth= -10

Developerselectivity n = 4

Exposure Rateconstant= 0.015cm2/mJResistindex of refraction = 1.65

the theoretical contrast and in particularits variation with exposure energy.

Exposure Dependenceon Resist ContrastTo study the behavior of the theoreticalcontrast, we will pick the following spe-cific development rate expression whichmatches experimentally determineddevelopment rates for high resolutionresists:

nR ='max (1- m) + 'min

where n is the relative photoactive com-pound (PAC)concentration and m is aterm called the developer selectivity.This equation is a simplification of a pre-viously proposed kinetic model [6] withm thequal to a large negative number.Fig. 3 is a plot of this rate expressionwith the PACconcentration calculatedusing standard first order kinetics of theexposure reaction:

m =e - cE

where c is the exposure rate constant.The values of all parameters used togenerate Fig. 3 are shown in Table I. Thetheoretical contrast can now be derivedby differentiating equation (12) withrespect to log-exposure, giving:

= (- mlnm )(1- r min)Yth n 1- m R

This equation has been derived previ-

Figure 4: Energy dependence of thetheoretical contrast, Yth,for differentdeveloper selectivities n.

5.0

4.0

«13.0

~«Ic"

2.0

1.0

l

0.01 100010 100

Energy (mJ/cm2)

ously for the case of rmin= 0 by applyingthe development rate expression (12)into the conventional contrast measure-ment equation (4) and making theassumption of constant developmentrate through the film [7]. Note that thetheoretical contrast is directly propor-tional to the developer selectivity n. Theterms in parentheses give the exposuredependence of YthoThe dependence ofcontrast on energy is shown in Fig.4.

(12)Comparing Measuredand Theoretical ContrastWe will now use equation (11) to predictthe effects of absorption and surfaceinhibition on the measured contrast. Butfirst, we will describe another method ofpredicting the measured contrast, usingan enhanced version of the PROLITH/2optical lithography model. Based on theprogram PROLITH[8], it simulates theexposure and development of positiveand negative photoresists with firstorder exposure kinetics and has theability to automatically generate stan-dard H-Dcurves and calculate the mea-sured contrast using the standard defini-tion in equation (1). An example of theoutput is shown in Fig.5. PROLITH/2cannow be used as a check against equation(11). The results should be identicalunder identical conditions. Fig.6 showsthe variation of the measured contrastwith exposure energy for the simplestpossible case of a non-absorbing pho-toresist with no surface inhibition on anon-reflecting substrate. In this case, the

(13)

(14)

Figure 5: H-Dcurve as predicted byPROLITH/2.

PROLITH/2

The Positive Resist Optical LithographyModel, v2.xx

Data sent to contrast dat.

Relative Resist Thickness. 1.0

0.8

0.6

j Base e gamma =0.4 1.123

0.2 Dose to Clear =79.26mJ/cm2

0.01.00 2.00 3.00 4.00 5.00 6.00

In(Exposure Energy (mJ/cm2»

measured and theoretical contrasts arethe same. One can see that PROLITH/2and equation (11) give the same results.

The effect of absorption can readilybe seen from equation (11). Absorptionincreases the exposure of the top of thephotoresist relative to the bottom. Thus,the development rate at the top of theresist will be greater than at the bottom.The average development through thefilm will be greater than that at thebottom and equation (11) predicts ameasured contrast lower than the theo-retical. The results are shown in Fig. 7.As expected, the measured contrast issignificantly less when only a moderateamount of absorption is added, eventhough the theoretical contrast staysthe same. Note that the PROLITH/2simu-lation has some experimental error asso-ciated with determining the slope from alimited number of simulated data points.Increasing the number of points simulat-ed would increase the accuracy of theslope, but the number was left intention-ally small to illustrate the difficulty ofdetermining the slope of experimentaldata. The simulation contained morepoints than most people would measurein a real experiment, and the accuracy ofthe thickness values in the simulation isgreater. One should expect a fair amountof error in determining the measuredcontrast from experimental data, evenwith a high linear regression correlationcoefficient. The effect of bleaching onthe measured contrast is similar to thatof absorption, but the peak contrastshifts to a higher energy.

Figure 6: Comparison of measuredcontrast, calculated with equation (11)(solid line) and simulated withPROLITH/2 (squares), for the case of anon-absorbing resist on a non-reflect-ing substrate.

4.0

3.0

«IEE2.0«Ic"

1.0

0.01 10 100

Energy (mJ/cm2)1000

MICROELECTRONICSMANUFACTURINGTECHNOLOGYJANUARY1991 39

From equation (11), one can see thatthe effect of surface inhibition is oppo-site to that of absorption. A reducedaverage development rate, relative tothat of the bottom of the resist, wouldresult in a measured contrast higherthan the theoretical contrast. Fig.8shows that, indeed, the measured con-trast is much higher than the theoreticalcontrast when surface inhibition is

included. This would explain the obser-vation that arbitrarily high measuredcontrast values for surfactant ladendevelopers did not translate intoimproved resolution or process latitude.

Other processes which affect themeasured contrast can also be

explored, such as reflecting substratesand post-exposure bakes. For thesemore complicated situations, usingPROLITHj2to predict measured con-trast is very convenient. Fig.9 showsthe measured contrast simulated for asilicon substrate with a post-exposurebake for two different resist thickness-

es. In this figure, a slight change wasmade in the method of determining themeasured contrast. Rather than usingthe slope of the H-Dcurve at zero thick-ness remaining, a linear regression wasperformed on the H-Dcurve betweenthe 10%and 70%thickness points. Thismethod was used in order to facilitatecomparison of these results with previ-ously published experimental data, asexplained below.

Waldo and Helbert [9] andLuehrmann and Goodwin [10] used con-trast in the conventional way as a

Figure 7: Comparison of measuredcontrast, calculated with equation (11)(solid line) and simulated withPROLITH/2(squares), for the case of anabsorbing resist (8=0.5 Ilm-1)on a non-reflecting substrate.

2.0

1.5

.EE 1.0.(!J

0.5

0.01 10 100

Energy (mJ/cm2)1000

..,,\

means of optimizing a photoresistprocess. One interesting (and to many,unexpected) result was a periodic varia-tion of measured contrast with resistthickness due to thin film interference

effects. PROLITHj2was used to simu-late this phenomenon for a particulardevelopment time (100 seconds). Theresults, shown in Fig. 10, show the samebehavior as was reported [9,10]. Theanalysis given in this paper, with aknowledge of the standing wave effect,can be used to explain this behaviorand its significance.

As is well known, changing the thick-ness of a photoresist on a reflecting sub-strate results in a periodic change in thereflectivity of the film stack due to thinfilm interference effects. The period ofthis changing reflectance (in this case132nm) is the wavelength divided bytwice the index of refraction of the pho-toresist. This change in reflectivity is, ofcourse, accompanied by a change in theamount of light transmitted into the pho-toresist. When the resist thickness issuch that the reflectance of the stack is

at a maximum, the amount of lightcoupled into the photoresist is at aminimum. Thus, the incident exposureenergy must be increased to make up forthe reduced coupling in order to get thesame effective exposure. This can beseen in Fig. 10as a periodic change in Eowith resist thickness. It can also be seenin Fig.9. The two resist thicknessesshown were chosen to be at a minimumand a maximum coupling. The result is asimple shift of the curve to a higher

Figure 8: Comparison of measuredcontrast, calculated with equation (11)(solid line) and simulated withPROLITH/2 (squares), for the case withsurface inhibition (relative surface rate=0.0001, inhibition depth =0.1 11m).

6.0

4.0.EE.(!J

2.0

0.01 10 100

Energy (mJ/cm2)1000

40 JANUARY 1991 MICROELECTRONICS MANUFACTURINGTECHNOLOGY

energy. One might expect that thechange in Eowith resist thickness wouldtrack the shift in the r (E) curve, result-ing in a measured contrast which is inde-pendent of resist thickness (except forany bulk effects). Obviously this is notthe case. In fact, the measured contrastshows a periodic dependence on resistthickness which is 90° out of phase withrespect to the Eo curve. The reason forthis strange behavior is far fromobvious, but can be explained by under-standing the effects of the post-exposurebake on the standing wave pattern.

The standing wave effect causes asinusoidal variation in the concentration

of photoactive compound with depthinto the photoresist, m(z). Fig. llashows an example of this for a 1.06 /lmresist film.Also shown in this figure isthe PACdistribution after a post-expo-sure bake. As expected, the bake simplysmooths out the standing wave pattern.Fig. 11b shows the same type of behav-ior, but for a resist thickness of 1.09/lm.This thickness was chosen to be halfway between a maximum and a minimumof energy coupled into the resist. Notethat the resist no longer contains aneven number of cycles. As a result, thetop of the resist contains, on average, ahigher concentration of PAC.When thepost-exposure bake diffuses out the PACvariation, the top of the resist contains aregion of relatively higher PACconcen-tration. This results in a slower develop-ment rate in this top region, creating, ineffect, a small surface inhibition effect.This effective surface inhibition due to a

"A

Figure 9: Contrast simulated withPROLITH/2 for the case of a bleachableresist (A =0.6 Ilm-1, 8=0.05 Ilm-1) on asilicon substrate with a post-exposurebake (diffusion length =40 nm). Solidline is 1.00 11m thick resist and dashedIine is 1.06 11m th ick.

1.2

1.0

0.8.EE.(!J0.6

0.4

0.2 -

1 10 100

Energy (mJ/cm2)

1000

. locallyhigherPACconcentrationwillcause the measured contrast to be.

higher. As Fig. 10shows, this is the casefor a 1.09!lm thick resist. Similarly, a1.03!lm resist film will have a locallylower PACconcentration at the top ofthe film, resulting in an increase in thedevelopment at the top of the resist.This in turn will cause the measured

. contrast to be lower.lt is importanttonote that the theoretical contrast is notaffected by the thin film interferenceeffect. The periodic change in measuredcontrast is nothing more than an artifactof the measurement technique and isanother example of how the measuredcontrast deviates from the theoreticalcontrast.

Using Contrast toOptimize a ProcessThe preceding sections have outlinednumerous circumstances where themeasured contrast deviates significantlyfrom the theoretical contrast. In order totrust the use of contrast to optimize alithography process, we must answertwo questions: (1) how does the theoret-ical contrast relate to the quality of ourprocess? and (2) can we measure con-trast with enough confidence to use theresults? In the following section I willsuggest alternate measurement methodsfor contrast which will improve the useof measured contrast. But first, shouldwe even bother with contrast at all?

The justification for using contrastcan be found in equation (3). Increasing

Figure 10: PROLITH/2 simulation of Eo(solid line) and y m {Eo}(dashed line) asa function of resist thickness for expo-sure on a silicon substrate.

110 1.20

1.15100

1..!t90

~

' I ,E ,/- . /

:I 80

US: 700Q

1.10

'"E

1.05 E'", I-'

J

"\ / ,'~~ 1.00

60 0.95

501.0

0.901.41.1 1.2 1.3

Resist Thickness (jlm)

contrast increases the development gra-dient in the resist. Equation (3) is onlyone part of the story, however, beingmerely a snapshot of what is happeningin the development cycle. Let us takethe example of finding the optimumexposure energy. Figs. 6-9clearly showthat there is an optimum energy whichgives the maximum contrast (call it Emax)'Should one use this energy as thebest nominal exposure dose? Doing sowould expose the center of any clearareas at the optimum energy, but theregion near the mask edge would get sig-nificantly less energy. Typically, theaerial image has an energy of about 30%of the nominal dose at the mask edge.Thus, the line edge would have a con-trast far less than the maximum. Shouldone triple this dose so that the photore-sist at the mask edge receives an energyof E max? Doing so would ignore theimportance of the development processup to the line edge. The answer is proba-bly somewhere between these twoextremes, but looking at contrast aloneprovides no clue as to the answer.

As an example, the ratio of the devel-opment rate at the center of a feature tothe rate at the edge of the feature deter-mines the resist profile slope [5]. Fig. 12shows how this ratio has an optimumenergy. In this case the optimum isalmost exactly twice E max' the energywhich gives the maximum contrast.Thevariation of contrast with exposureenergy is very important, but contrastalone cannot be used to determine the

optimum exposure energy.

Figure 11: PAC concentration beforeand after a post-exposure bake for (a)1.06 11mthick resist, and (b) 1.09 11mthick resist.

1.0

c 0.8~'"~0.6

(e) ~c30.4

~0.2

0.00 200 400 600 800 1000

Depth into Resist (nm)

1.0

c 0.8~~0.6c

(b) 3cc3 0.4U

f 0.2

0.00 200 400 600 800 1000

Depth into Resist (nm)

Optimizing exposure energy is tricky,since the aerial image effectively variesthe exposure energy dramatically over asmall distance. Can contrast be used forother variables? Any parameter whichaffects contrast uniformly from thecenter of the space to the line edge canbe optimized using contrast. As asecond example, consider the commontask of comparing two photoresistsusing contrast. Suppose resist A is infact a higher contrast resist (with aselectivity n =4) compared with resist B(with n =2). Since contrast is directlyproportional to n, it seems obvious thatcontrast measurements would point tothe better resist. However, closer exami-nation of Fig. 4 shows that this is notnecessarily the case. If the energy usedfor the measurement were too low,resist B would have the higher contrastand appear to be the better resist. Thisbrings out an extremely important pointabout using contrast to optimize somevariable - to be confident of theresults, it is necessary to measure con-trast as a function of energy.

Measuring ContrastTheabovediscussionshows the difficul-ty of using the theoretical contrast as ameans of optimizing a lithographyprocess. On top of this, we add the diffi-culty of being sure our measured con-trast accurately reflects the theoreticalcontrast. It is possible to use equation(11) to extract the theoretical contrastfrom the measured contrast, but only if

Figure 12: Using the ratio of center-to-edge development rates to find theoptimum exposure energy (for the caseof a non-absorbing resist on a non-reflecting substrate).

40

E

~30~'"II:QIti 20II:

~QI

ECI.,g 10

~Q

10000

1 10 100

Energy (mJ/cm2)

MICROELECTRONICSMANUFACTURING TECHNOLOGY JANUARY 1991 41

Ii

the variation of development ratethrough the film is known. In somesimple cases, such as absorption in theresist, this may be possible. The mostcritical problem is the presence ofsurface inhibition. Even a small amountof surface inhibition can make the result-ing measured contrast totally useless.Therefore, any parameter whichchanges the amount of surface inhibitioncannot be optimized using measuredcontrast. Is there a better way tomeasure contrast?

The ideal method of determining Y th(E) is with a development rate monitor(DRM).A DRMcan measure R (E,z)directly allowing calculation of the theo-retical contrast from its definition, equa-tion (2). One must still remember thatthe value of E used is the actual energydeposited in the film at position z, notthe incident energy. Using a DRMsignifi-cantly complicates the process of mea-suring contrast. It is, however, the onlyfoolproof method.

It is possible to improve on the con-ventional measurement technique forcontrast using our definition of theoreti-cal contrast as a guide. We desire anapproximate method of measuringdevelopment rate without using a DRM.Rather than using the thickness remain-ing after development, let us use thethickness removed after development,which is proportional to the develop-ment rate. Since the true contrast is

determined by plotting log-developmentrate versus log-exposure, we will plotlog-thickness removed versus log-expo-sure. Finally, in order to obtain as closeto a complete H-Dcurve as possible, wewill make our development time used inthe measurement as short as possible.The resulting data allows us to deter-mine measured contrast as a function of

energy, rather than at one energy Eo'The new measured contrast is definedas:

d In 'f,.

Ym = dInE

where Yr is the thickness removed. Ofcourse, this new method of measuringcontrast still suffers from the sameproblems of development varyingthrough the resist film and can berelated to the theoretical contrast usingthe same equation (11). However, sincecomparing two resist processes usingcontrast can be accomplished only bymeasuring Y(E), this new measurementtechnique is significantly more useful.

As a final note on measuring con-trast, the use of a lithography simula-

tion tool can be an extremely valuableaid. The model can be used to predictthe log-thickness removed versus log-exposure curve. The values of thedevelopment rate parameters used inthe model, in particular the developerselectivity n, can be adjusted to get thebest fit to experimental data. It is thevalue of n which can provide usefulcomparisons of different photoresistprocesses.

ConclusionsThe use of measured contrast to opti-mize a photoresist process is fraughtwith pitfalls. As the preceding analysishas shown, the measured contrast candeviate significantly from the true con-trast. However, equation (11) for thefirst time gives us a tool which can helpus understand these deviations and, insome cases, correct for them. Further-more, an enhanced measurementmethod has been proposed which pro-vides information about the energydependency of the contrast. The carefulapplication of the enhanced measure-ment method with the understanding ofequation (11) can, in some circum-stances, lead to an accurate determina-tion of the true contrast.

Once the contrast has been deter-

mined, care must be used in applyingthis information to optimize a resistprocess. It is essential to measure con-trast as a function of energy andcompare the entire curves to determineif one process is better than another.Finally, although the variation of con-trast with exposure is extremely impor-tant, it cannot be used to optimize expo-sure energy.

(15)

References1. F. Hurter and V.c. Driffield, "Photo-Chemical Investigations and a NewMethod of Determination of the Sensi-tiveness of Photographic Plates," Journalof the Society of Chemical Industry, (May31, 1990)pp. 455-469.2. AV. Brown and W.H.Arnold, "Opti-mization of Resist Optical Density forHigh Resolution Lithography on Reflec-tive Surfaces," Advances in Resist Tech-nology and Processing/I,Proc.,SPIEVol.539 (1985) pp. 259-266.3. V. Marriott, "HighResolution PositiveResist Developers: A Technique forFunctional Evaluation and Process Opti-mization," Optical Microlithography /I,Proc., SPIE,Vol. 394 (1983) pp. 144-151.4. M. Kaplan and D. Meyerhofer,"Response of Diazoquinone Resists to

42 JANUARY 1991 MICROELECTRONICS MANUFACTURINGTECHNOLOGY

Optical and Electron-Beam Exposure," .'RCA Review, Vol. 40 (June, 1979) pp.166-190.

5. C.A Mack, "Photoresist Process Opti-mization," KTI Microelectronics Seminar

Interface /87(1987) pp. 153-167.6. C.A Mack, "Development of PositivePhotoresist," Journal of the Electrochemi-cal Society, Vol. 134, No.1 (Jan. 1987)pp. 148-152.7. P. Trefonas and B.K. Daniels, "New

Principle for Image Enhancement inSingle Layer Positive Photoresists,"Advances in Resist Technology and Pro-cessing IV, Proc., SPIEVol. 771 (1987) pp.194-210.

8. C.A Mack, "PROLITH: A Comprehen-sive Optical Lithography Model," Optical

Microlithography IV, Proc., SPIE Vol. 538(1985)pp. 207-220.9. W.G. Waldo and J.N. Helbert, "Stand-

ing Wave Interference Effects on Pho-toresist Contrast," Journal of the Electro-

chemical Society, Vol. 137, No.4 (Apr.1990) pp. 1311-1313.10. P. Luehrmann and G. Goodwin, "Pho-toresist Process Optimization and

Control Using Image Contrast," KTIMicroelectronics Seminar Interface /89

(1989) pp. 279-292.

Chris A. Mack received Bachelor of Science

degrees in Physics, Chemistry, ElectricalEngineering, and Chemical Engineering fromRose-Hulman Institute of Technology in 1982,and a Master of Science degree in ElectricalEngineering from the University of Marylandin 1989. He joined the MicroelectronicsResearch Laboratory of the Department ofDefense in 1983 and began his work in opticallithography research. He has authorednumerous papers in the area of opticallithog-raphy, regularly teaches courses on thistopic, and has developed the lithography sim-ulation programs PROLITH and PROLITH/2.He is currently on assignment at SEMATECH.

This article is based on a paper presented bythe author at the KTI MicrolithographySeminar, November, 1990,San Diego, Califor-nia.

For additional information on any aspect ofthis article, the author can be reached atSEMATECH, 2706 Montopolis Drive,Austin, Texas 78741.Telephone 1512356.3458.

Article Interest PollTo assistus in the presentationof usefulinformationin interesting,easy-toassimilateform, pleaseexpressyourevaluationof this article'smerit bycirclingtheappropriatenumberon the ReaderServicecard.High 704 Average705 Low 706