Modeling anomalous depth dependent dissolution effects in

chemically amplified resists

Mosong Cheng, Jacek Tyminski*, Ebo Croffie, Andrew Neureuther

Electronic Research Laboratory

Department of Electrical Engineering and Computer Sciences

231 Cory Hall, University of California, Berkeley, CA 94720

Phone: (510)642-4590, Fax: (510)642-2739

*Nikon Precision Inc. 1399 Shoreway Rd, Belmont, CA 94002-4107

Phone: (650)508-4674, Fax: (650)508-4672

Abstract

A post exposure bake and dissolution model for JSR KRF-K2G resist has been

established for bake temperature and time effects from large area exposures on

production equipment. Data from TARC coated K2G resist were well behaved and

provided key understanding of the PEB processes. Data from K2G without TARC

showed inhibition of surface dissolution that is possibly due to photoacid evaporation.

Both processes showed an intrinsic thickness reduction of 50 nm in the first 30 seconds

of PEB and then a continued decrease of 4nm per minute of bake time. An algebraic

dissolution model for resist showing an “S-shape” in the logarithm dissolution rate versus

exposure dose is developed using a barrier model. This model was fit with the dissolution

rates deduced from the coated K2G as a function of activated site concentration. The

rates agree well with DRM data and the DRM data showed further details of depth

dependent effects. The methodology of large area exposure allowed the simulation

parameters for PEB temperature and time effects to be quantitatively determined very

effectively.

Keywords: chemically amplified resist, post exposure bake, dissolution rate

monitoring, dissolution model, fitting process, simulation

I. Introduction

Chemically amplified resists are based on the acid catalytic deprotection of a polymer

matrix. During the standard post exposure bake (PEB) step, several mechanisms are

involved, including a deblocking reaction, photoacid diffusion, acid loss, free volume

generation, polymer matrix densification, evaporation of small species such as acid and

volatile groups. Some of the systems also suffer from substrate or air contamination. As a

result, the dissolution rate distribution within resists is not uniform and can distort the

formation of final patterns after development [1].

Dissolution Rate Monitor (DRM) measurements have been widely used as a tool to

quantify development pattern formation process. While DRM data is a great input for

resist modeling, the data in Fig. 1 presents a formidable challenge. It shows that the

dissolution rate in JSR KRF-K2G resist depends on depth. However, this dependence is

anomalous in that the rate increases from the top of the resist to the bottom of the resist

when the exposure dose is low, while the exposure energy decreases from top to bottom.

Note that if a top anti-reflective coating (TARC) is applied before exposure, then this

anomalous behavior disappears, as shown in Fig 1 (b).

The goal of this paper is to establish a PEB and development model for JSR KRF-

K2G resist that accounts for PEB time and temperature effects. The approach is to utilize

the large area exposure methodology developed by M. Zuniga et al. [2] and to compare

result with the DRM data shown above. This paper begins with observation of intrinsic

compaction during PEB. Data on thickness loss versus exposure dose after development

are then presented. The data is then normalized using activated site concentration as a

common basis. The dissolution parameters of the resist are then fit and compared with

DRM data. Finally an isolated line profile simulation of the resist is presented.

II. Post exposure bake model

During the post exposure bake (PEB) process, several chemical and physical

reactions occur. Photoacid catalyses the deblocking/deprotection process [3], in which the

blocked polymer is converted to a soluble hydroxyl group and a volatile group. The

volatile group then generates free volume. Meanwhile, the photoacid can diffuse and its

diffusivity is enhanced by the amount of free volume. Furthermore, if the PEB

temperature approaches the glass transition temperature Tg, the deprotected polymer

matrix starts densifying, which reduces the acid diffusion [3]. As a result of PEB, the

evaporation of solvent / free volume can lead to compaction of resist. A model for these

effects is forth coming from collaboration work of S. Postinkov and E. Croffie [4].

Based on M. Zuniga’s work [6], and given the acid evaporation phenomena which

exists in some resists, we assume the following model:

(3)

(2) (x)CK- ).(

(1) )1(

asC0

ae2

1

eDD

CKCDt

C

CCKt

C

aaa

maas

as

=

=

=

Where Cas is the activated site concentration, Ca is the photo acid concentration, K1 is

the reaction rate constant, K2 is the acid loss rate within resist, Ke is the acid evaporation

rate at the surface, D0 is the acid diffusion coefficient in protected polymer and is a

constant.

Equation (1) describes the deblocking reaction and (2) describes the acid diffusion

and acid loss process. There are several mechanisms, which contribute to acid loss. One

is free volume loss mechanism given by K2. Another is surface evaporation described by

Ke. Here we assumed the acid concentration in air is 0, and therefore the evaporation rate

is only proportional to the resist surface acid concentration. Equation (3) gives the acid

diffusion coefficient which is assumed to increase exponentially with the concentration of

activated site.

III. Dissolution model

“S-shape” dissolution rate versus dose curve has been observed and reported for poly-

vinyl phenol [7] which is the resin in K2G.. When dose is low, R is flat. When dose

reaches some threshold, R increases dramatically, which causes a high contrast. And with

dose increasing, R approaches its saturation value. Since there are no models in the

literature which give such an “S-shape” dissolution rate curve, we begin by establishing

an algebraic model.

KRF-K2G consists of poly(p-vinyl)phenol partially blocked with a blocking group

and a photoacid generator [5]. Fig. 2 from [8] depicts how protected groups prevent

penetration of developer as a basis for a model for positive DUV chemically amplified

resist. We assume three mechanisms are involved in the development of a positive

chemically amplified resist: the penetration of developer into the surface layer of resist,

the reaction of the developer with the resist and the transportation of the product back

into the bulk developer. A block group can prevent the penetration of developer into the

resist, hence blocks the dissolution.

To establish a model, we assume that the rate limiting step is the penetration of the

developer which is governed by a barrier effect with activation energy Eu for unprotected

sites and activation energy Ep for fully protected sites. We assume for partially

deprotected sites, the activation energy is a linear combination (1-Cas)Eu+Cas.Ep, where

Cas is the normalized amount of deprotected sites. Therefore the developer penetration

rate in partially deprotected polymer is

Here D and Ds are the developer concentration in the bulk developer and at the surface of

polymer, respectively, D>Ds. T is the temperature.

Also, Rp0 is the intrinsic penetration rate without depreotection, Rp2 and w are the

deprotection enhanced penetration components. Both of them are functions of T.

The dissolution rate is also given by the surface reaction rate of polymer with the

developer, also the dissolution rate, and is

(4) )D-)(D())((R s20/))((

10paspuasu wC

ppskTEECE

pp eRRDDeRR +=+=

(5) ss kDR =

Here k is the removal rate of polymer.

At steady state, Rs=Rp. After substitution of (4) to (5) and denoting new parameters,

the dissolution rate can be simplified as

Here Cas is the activation level, r0 is the development rate for the unexposed resist, a,

b and w are constant. The parameters r0, a, b and w have temperature dependence. This

model predicts a “S-shape” curve for a logarithm of dissolution rate versus Cas or dose.

IV. Experiment

Large area exposures of JSR KRF-K2G were made on a Nikon exposure tool. The

nominal processing conditions were: softbake 90oC, 90sec; resist thickness 750nm; post

exposure bake 100 oC, 60sec; developed with 0.261N TMAH, 21 oC, 60sec.

The large-area exposures were followed by post exposure bake at different

temperatures. Wafers with and without TARC were exposed with doses varying from 6

to 35 mJ/cm2, and baked for the matrix of bake times and temperatures shown in Table 1.

Note that a star pattern of various bake temperature for fixed bake time and then varying

bake time for fixed temperature was used.

Table I. PEB conditions for the experiment

Temp. oC 20 40 60 80 90 100 110 120 100 100 100 100

Time(sec) 60 60 60 60 60 60 60 60 30 120 240 480

After PEB and development, the remaining resist thickness in the exposed and

unexposed areas was measured.

(6) 1

)1(R 0

wCas

wCas

be

aer

++

=

V. Results and Analysis

We now proceed to establish a quantitative model for the effects of PEB and

dissolution on the thickness of resist developed. However, we noticed a considerable

thickness change of even unexposed resist which could not be accounted for by

development. Thus we begin in section 1 with an intrinsic compaction. We then

temporarily assume a threshold model in section 2 to estimate reaction parameters. In

section 3, with these reaction parameters, a non-threshold model for calculating resist

thickness loss is then developed and used to extract dissolution rate parameters. Finally in

section 4, DRM curves are fit to obtain the acid diffusion parameters.

1. Intrinsic compaction

Significant resist thickness changes were observed during PEB and before

development. We call this change “intrinsic compaction”. The resist thicknesses are

shown in Fig 3 and Fig 4 for unexposed regions after development. It can be seen that the

resist thickness is decreased. The thickness reduction is about the same for both top-

coated and non-top-coated resists. The resist thickness loss is fairly linear with PEB time.

It shrinks about 50nm within the first 30sec of PEB. Then it continues to shrink with the

rate of 3 – 4nm per minute as can be seen in Fig. 4. Note that the resist thickness

decreases sharply when the PEB temperature is above 100oC.

Since this thickness loss is very large for unexposed films while the dissolution rate

for unexposed resist is only 0.15nm/s, we believe this effect is due to a shrinkage of the

materials. Possible mechanism for this intrinsic compaction is resist densification in

which the residual solvent and/or free volume are driven out by PEB, which could be

considered as a continuation of the soft bake. The effect of high temperature can be

explained by the thermal decomposition effect. When the PEB temperature is high, some

deprotection of the resin can take place that results in free volume and subsequent

compaction.

2. Extraction of reaction parameters K1,K2 and m

An example of the photoacid concentration as a function of depth after exposure is

shown in Fig. 5. This plot was obtained by using the BLEACH program in SAMPLE3D

with the Dill’s parameters A=-0.16 m-1, B=0.91 m-1, C=0.0013mJ-1, the resist layer

thickness 750nm, refractive index n=1.56, k=-0.02.

To obtain the reaction/acid loss rates of the resist, the method described by M. Zuniga

et al. [2] was used which is based on a threshold of activated site concentration for

development. Ignoring diffusion and assuming uniform acid concentrations in resist, the

relationship between acid concentration and bake time to achieve a given activation level

is given by

Or

Fig. 6 shows the resist thickness after development versus dose for different PEB

temperatures and times for both TARC and non-TARC processes. It can be seen that JSR

KRF-K2G has a very high contrast. When the PEB temperature is below 80oC, almost no

deprotection process occurs even at high exposure doses. Also, varying the temperature

by 10oC from the nominal 100oC temperature will vary the dose-to-clear by about 1

mJ/cm2. Given the nominal dose-to-clear of 16 mJ/cm2, this means the sensitivity is

(7) 0K if )1ln()]exp(1[C 21

22

ma = asthC

K

mKtmK

(8) 0K if )1ln(

.C 21

ma ==

K

Ct asth

varied by about 6%. When the PEB time is doubled, the dose-to-clear is reduced by 1

mJ/cm2 which corresponds to a sensitivity increases of about 5%.

Assuming identical resist thickness loss corresponding to identical Cas, and using

average acid concentration obtained from BLEACH as the initial Ca, we calculated the

different amount of Ca to achieve a certain resist thickness loss for different bake times.

Then fitting these Ca and times with equation (7), we were able to obtain the reaction

rate. We fitted the reaction parameters to the thickness developed in the ranges from

50nm to 450nm and obtained the reaction parameters at a PEB temperature of 100oC. The

values in Table II show a difference primarily in the K2 value.

Table II. reaction parameters when PEB temperature is 100oC.

K1 (sec-1 ) K2 (sec-1 ) m

No TARC 5.57 0.07 1

TARC 5.40 0.05 1

This indicates acid evaporation exists. As a first order approximation, the evaporation

rate Ke is the difference and is 0.02 sec-1.

Given the resist thickness loss at other PEB temperatures [6], we have obtained the

reaction parameters, which are shown in Table below.

Table III. Reaction parameters

LnK1 (sec-1) EK1 (eV) lnK2 (sec-1) EK2 (eV) m Ke (sec-1)

5.6 0.13 -0.6 0.13 1 0.02

3. Extraction of dissolution parameters

Having obtained the reaction parameters in section 2, we then extracted the

dissolution parameters by fitting the resist thickness developed versus Cas data with

equation (6) for 100oC, 60sec PEB. Note that when Cas reaches 0.9 which is enough to

clear the resist, the experimental dissolution rate saturates at 700nm/60sec 12nm/sec.

We fitted the data in the region Cas<0.9 with an optimization program that is on the basis

of Method of Feasible Direction and can reach the global optimum with certain

constraints. Finally we obtained the following dissolution parameters:

Table IV. Dissolution parameters

r0 (nm/s) a b w

3.54 2.1*10-5 0 18.12

For TARC-coated, PEB 100oC and 60sec, The resist thickness curve versus Cas

generated by the above parameters and the experimental data are both shown in Fig 7.

In order to justify the model, Fig 8 shows the thickness developed versus exposure

dose curves from experimental data and simulation with the above parameters for 100oC,

30 sec PEB, TARC-coated process. It can be seen that the two curves fit at low, moderate

and high doses. However, the transition of the experimental curve is higher

exponentially.

4. Fitting DRM data and extracting acid diffusion parameters

With the reaction rate and dissolution rate parameters obtained above, we can now fit

the dissolution rate versus depth with the DRM data and also extract the possible acid

diffusion parameters with reaction and dissolution parameters fixed. For this purpose, a

fast program capable of simulating 1-dimensional transportation-reaction systems was

developed. And the MFD optimization program described in section 3 was also applied.

Table V summaries the diffusion parameters obtained from the fitting process. Fig. 9

shows the simulation results for no-TARC resist, PEB 100oC, 60sec, it fits considerably

well with the DRM data.

Table V Diffusion parameters

D0 (nm2/s)

250 6

VI. Resist profile simulation

This anomalous behavior of JSR KRF-K2G resist without TARC may cause severe

distortion of pattern during development of the resist. An example is “T-top”. To

overcome this effect, a TARC is applied to the resist and Fig 10 shows the resist profile

after development, for TARC-coated, dose 7mJ/cm2, PEB 100oC, 60sec, develop 10sec.

VII. Conclusion

In this paper a methodology for extracting PEB and dissolution parameters is used to

deduce a model for the JSR KRF-K2G resist. PEB reaction rate and dissolution rate

versus chemical state parameters were extracted from large-area exposure and resist

thickness measurements. The simulated dissolution rate curves were then compared to the

DRM data and this allowed further modeling of acid evaporation.

Intrinsic compaction of the resist during PEB process is described. A linear scale

transform of space coordinate system is suggested for modeling this compaction

phenomenon. We also quantified the PEB temperature and time effects on resist

sensitivity. A 10 oC increase of bake temperature causes a 6% increase on sensitivity.

Doubling the bake time only increases the sensitivity by 5%. The “S-shape” dissolution

rate versus dose curve is developed using energy barrier model, which is able to explain

the dissolution of poly-vinyl phenol. Since DRM data provide very detailed information

about both PEB and dissolution effects, fitting DRM data could be a solid basis for

extracting and calibrating bake and dissolution models. The parameters extracted from

large area exposures agree with DRM data but the DRM data was independently matched

in attempting to model depth dependent effects.

Reference:

[1] H. Miyamoto, et al., “Study for the design of high resolution Novolak-DNQ

photoresist: the effects of low molecular weight phenolic compounds on resist systems”,

Proc. SPIE, Vol. 2438, 1995

[2] M. Zuniga, A. Neureuther, “Post Exposure Bake Characterization and Parameter

Extraction for Positive Deep-UV Resists through Broad Area Exposure Experiments”,

Proc. of the SPIE, Vol. 2724, 1996.

[3] B. Mortini, S. Tedesco, B. Dal’Zotto, P. Paniez, “Specific behavior of chemically

amplified systems with low activation energy under electron-beam exposure:

implementation of 248 and 193 nm resists”, J. Vac. Sci. Technol. B, 15(6), Nov/Dec

1997, pp2534-2540

[4] See papers by S. Postinkov and E. Croffie in this proceedings.

S. Postinkov et al, “A study of resolution limit due to intrinsic bias in chemically

amplified resists”,

E. Croffie et al, “New moving boundary transport model for acid diffusion in

chemically amplified resists”.

[5] A. Tritchkov, R. Jonckheere, L. Van den hove, “Use of positive and negative

chemically amplified resists in electron-beam direct-write lithography”, J. Vac. Sci.

Technol. B, 13(6), Nov/Dec 1995, pp2986-2993

[6] M. Zuniga, A. Neureuther, “Reaction Diffusion Modeling and Simulation in

Positive Deep Ultraviolet Resists”, J. Vac. Sci. Tech. B, Dec 95 (2957).

[7] T. Itani, H. Iwasaki, M. Fujimoto, K. Kasama, Proc. SPIE, 2195, 126(1994)

[8] T. Itani, H. Iwasaki, H. Yoshin, M. Fujimoto, K. Kasama, Proc SPIE, 2438,

91(1995)

[9] M. Cheng, E. Croffie, A. Neureuther, “Methodology of Modeling and simulating

line-end shortening effects in deep-UV resist”, Proc. SPIE, Vol 3678 (1999)

[10] J. Sheats, B. Smith, “Microlithography: science and technology”, Marcel Dekker

Inc., 1998

(a)

(b)

Fig. 1 Dissolution rate vs depth into JSR KRF-K2G resist. In (a), the resist is coated onbare silicon without ARC, in (b), resist is coated with top ARC.

K2G on Bare Silicon

0

10

20

30

40

50

60

70

80

90

0 100 200 300 400 500 600 700 800

z-Position [ nm ]

Dev

elo

pm

ent

Rat

e [

nm

/sec

]

0

0.7

1.4

2.1

2.8

3.5

3.7

4

4.3

4.6

4.9

5.2

5.5

5.8

6.1

6.4

6.7

7

7.3

7.6

8.8

K2G; ARC

0

100

200

300

400

500

600

700

0 100 200 300 400 500 600 700 800

z-Positon [ nm ]

Dev

elo

pm

ent

Rat

e [

nm

/sec

]

0

0.7

1.4

2.1

2.8

3.5

3.7

4

4.3

4.6

4.9

5.5

5.8

6.1

6.4

7

7.3

7.6

8.5

8.8

9.1

31.3

(a) (b)

Fig. 2 A proposed dissolution model for positive DUV chemically amplified resist. Twosituations are considered: (a) before deblocking where TMAH penetration is preventedby block group. (b) after deblocking where TMAH penetration is enhanced by absence ofblock group.

TMAH

BlockGroup

BlockGroup

BlockGroup

BlockGroup

BlockGroup

TMAH

BlockGroup

BlockGroup

Fig. 3 Unexposed resist thickness vs. PEB temperature

Unexposed resist thickness reduction varying PEB temperature

620640660680700720740760

80 90 100 110 120

Bake temperature(C)

Th

ickn

ess

(nm

)

w/o TARCw/ TARC

Ref

Fig. 4 Unexposed resist thickness vs PEB time

Unexposed resist thickness reduction varying PEB time

620640660680700720740760

30 60 120 240 480

Bake time(sec)

Th

ickn

ess

(nm

)

w/o TARC

w/ TARC

Ref

Fig 5 Acid concentration in resist, the exposure dose is 8mJ/cm2, note that there is verylittle difference between TARC-coated and non-TARC-coated layers.

0

0.005

0.01

0.015

0.02

0.025

0

68.9

138

207

276

344

413

482

551

620

689

Depth(nm)

No

rmal

ized

aci

d c

on

cen

trat

ion

w/o TARC

w/ TARC

(a) (b)

(b) (d)

Fig. 6. Resist thickness after development versus dose. The curves in (a)and (c) are for different bake temperatures. The curves in (b) and(d) are for different bake times at 100oC.

Resist thickness after develop, varying bake temperature, no TARC

0100200300400500600700800

6 10 14 18 22 26 30 34

Dose(mJ/cm^2)

Th

ickn

ess(

nm

) 20C

40C

60C

80C

90C

100C

110C

120C

Resist thickness after develop, varying bake time, no TARC

0

200

400

600

800

6 10 14 18 22 26 30 34

Dose(mJ/cm^2)

Res

ist

thic

knes

s(n

m)

30s

60s

120s

240s

480s

Resist thickness after develop, varying bake temperature, with TARC

0100200300400500600700800

6 10 14 18 22 26 30 34

Dose(mJ/cm^2)

Th

ickn

ess(

nm

) 20C

40C

60C

80C

90C

100C

110C

120C

Resist thickness after develop, varying bake time, with TARC

0

200

400

600

800

6 10 14 18 22 26 30 34

Dose(mJ/cm^2)

Res

ist

thic

knes

s(n

m)

30s

60s

120s

240s

480s

Fig. 7 Resist thickness vs Cas, PEB 100oC, 60sec. Experimental data are marked with “*”and simulated results are marked with “o”.

Dissolution rate vs. normalized activated site concentration

1

10

100

1000

10000

0.46

1451

1

0.67

3353

6

0.80

1878

9

0.87

9833

5

0.92

7115

3

0.95

5793

2

normalized activated site concentration

dis

solu

tio

n r

ate(

nm

/s)

Calculate

Experimental

Fig. 8 Resist thickness loss vs. dose curves, PEB 100oC, 30sec.

Resist thickness loss vs. dose

1

10

100

1000

6 10 14 18 22 26 30 34

Dose(mJ/cm̂ 2)

Th

ickn

ess

dev

elo

ped

(nm

)

Calculation

Experimental

Fig 9 DRM date, experimental and simulation. PEB 100oC, 60sec, dose 6.7mJ/cm2.

K2G without TARC

0

2

4

6

8

10

12

14

16

18

0 100 200 300 400 500 600 700 800

z-Position [ nm ]

Dev

elo

pm

ent

Rat

e [

nm

/sec

]

Simulation for dose6.7mJ/cm^2

DRM curve for dose6.7mJ/cm^2

Fig. 10 Resist profile simulation