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Molecular dynamics simulation of gel formation and acid diffusion in negative tone chemically amplified resists
ELSEVIER
Microelectronic Engineering 46 (1999) 359-363
M O L E C U L A R DYNAMICS S I M U L A T I O N OF GEL F O R M A T I O N AND ACID D I F F U S I O N IN N E G A T I V E T O N E C H E M I C A L L Y A M P L I F I E D RESISTS G. P. Patsis"' and N. Glezos Institute of Microelectronics, NCSR Demokritos, Aghia Paraskevi, 15310, Attiki, Greece '"e-mail: patsis @cyclades.nrcps-ariadne-t.gr The knowledge of the structural changes that occur during the lithographic process using chemically amplified resists (CARs) is of great importance in process and resist optimization. Molecular dynamics (MD) is a suitable method for the simulation of these microscopic changes. A detailed description of the lithographic procedure including reaction propagation, acid diffusion, cage effects, free volume effects and developer selectivity can be included in such a model. The comparison of contrast curve data and acid diffusion measurements with MD modeling, leading to the evaluation of microscopic parameters are presented in this paper. 1. I N T R O D U C T I O N In the case of lithography using chemically amplified resists (CARs) it is of importance to determine and control the parameters that affect acid creation and acid diffusion. During the post exposure bake stage (PEB) the acid produced during exposure diffuses through the polymer chains and induces cross-linking or site de-protection depending on the nature of the resist system. This complex phenomenon is modeled using a non-linear coupled system of equations involving the reaction rate and the acid diffusion rate. In the case of CARs based on the crosslinking mechanism, acid mobility is controlled by the cross-link density of the environment (cage effect). In order to take into account this effect some authors j'2 have assumed the reaction rate K as a decreasing function of the cross-link density O. In previous papers by the same group 3'4'5 the diffusion coefficient D was assumed as a function of the cross-link density ® and various functional forms where tried out in specific cases. The parameters of the functional laws where deduced by comparison with experimental results based on e-beam point exposures. Exponential laws best fitted experimental results in most of the cases examined.
0167-9317/99/$ - see front matter PII: S0167-9317(99)00104-5
Contrast curve analysis has been also used in order to investigate the cage effec('. The decrease in acid mobility as the PEB time increases is demonstrated by a Charlesby-Pinner representation of the corresponding contrast curves. A new interpretation has been given to the Charlesby gel formation theory 7'8 in the case of CARs. However these analytic models fail to describe accurately the gel point transition of the resist film. This can be attributed to the absence of parameters that describe explicitly the effect of chain reaction and acid propagation paths. Molecular Dynamics (MD) is a suitable method for the simulation of microscopic changes occuring during PEB. Acid diffusion, cross- linking and free volume effects can be effectively described through percolation theory . Such modeling work in the field of lithography for the simulation of the effect of amine additives and T-top formation has already been reported 9'1° In this work, percolation theory is used in order to study non-linear diffusivity of the acid produced during PEB. The diffusion coefficient D depends upon the density of the reacted sites ® which in its turn depends upon the radiation dose d. A direct relation D(d) between diffusion coefficient and dose is obtained.
© 1999 Elsevier Science B.V. All rights reserved.
G.P. Patsis, N. Glezos I Microelectronic Engineering 46 (1999) 359-363
360
2. T H E M O L E C U L A R D Y N A M I C S M O D E L Electron beam exposure results with the experimental epoxy based resist EPR j~ have been used for modeling. EPR is a two component system consisting of fractionated cresol epoxy novolac polymer chains and hexafluoroantimonate tryphenylsulphonium salt as the photoacid generator molecules. In the case examined the concentation of the photoacid generator is 10%. For the simulation, a 3D square lattice is considered , with lattice constant equal to the monomer radius. In a rough approximation , taking into account the ionic r a d i u s , the bond length and the possible molecular conformations, a monomer molecule occupies a spherical volume of radius - 1 0 A ° as shown in figure 1.
(3). Each lattice site can be occupied by no more than one monomer and one initiator molecule. (4). Periodic boundary conditions where considered. Chains that extend out of the boundaries of an edge of the lattice are inserted from the opposite side. ;::
I
I ~P~f
I V
I '~'~l'
I
I
Cross linked
I
r \
F i g u r e 2. A 2D representation of the lattice model for the EPR resist system.
BondLength- - l - ~
[
Conformations ~
~ l
I, _8Ac
%*.-16A°,,~ F i g u r e 1. EPR monomer molecule Polymer chains and initiator's molecules where placed randomly on that lattice under the following restrictions • (1). The chains should be self avoiding and populate tile lattice as possible. (2). The polymerization length was assumed a uniform distribution in a numerical interval which successfully describe the experimental polymerization length of EPR.
The radiation induced effects whe,'e simulated through the use of an initiation probability attributed to each of the initiator's molecules. The formation of a cross-link should satisfy the following requirements: (1). The cross-linked monomers belong to different chains (no cyclization effects are allowed in accordance with experimental evidence in the specific case considered). (2). The cross-linked monomers should be "near" i.e. within one lattice constant from an active initiator's molecule. The effects of chain r e a c t i o n , cage formation , diffusion range and post exposure bake temperature where considered through the use of a parameter describing the range (length) of each site excitation propagation.
G.P. Patsis, N. Glezos / Microelectronic Engineering 46 (1999) 359-363 The problem of coverage of the cubic lattice by monomer and photo-initiator molecules randomly together with the knowledge of connectness within the formed network can be conveniently described using graph theory 17_ A graph is a finite set of points , some of which are connected by lines. The points on which lines are connected are termed nodes and the lines themselves, edges. An example of a bi-directed graph is shown in figure 3. This graph is formed by 14 nodes some of which remain fi'ee.
361
The implementation of the inter-chain connections is based on the formation of a sparse array using linked lists. Each node in this representation is a head of list which contains information about the chain and links to its monomers (see figure 4). In order to determine the characteristics of the clusters that are tbrmed during PEB , the cycles in the graph have to be evaluated.
Figure 4. Implementation of a sparse array using doubly linked lists. 3. RESULTS The whole code for the simulations was integrated in a graphical environment that can run on PC under win95. It is also available for unix based systems with a C++ compiler. The input parameters Figure 3 : An example of a bidirected graph In each simulation what is needed is first to make a mathematical abstraction of the real system under a mathematical - physical model and then to translate this model into the computer's language using suitable programming techniques. Each monomer is represented by a node in a graph and the lines connecting different monomers-nodes represent the links between monomers in a chain. In computer language each node is a structure containing information about the position in the lattice and the chain identity.
are
;
1. the lattice size, 2. the number of chains, 3. the maximum number of monomers per chain (polymerization length), the acid diffusion range, 5. the reaction initiation probability, 6. the reaction propagation probability, 7. the reaction probability, 8. the maximum number of cross-links per monomer (functionality). ,
362
I.
2. 3. 4. 5. 6. 7. 8. 9.
G.P. Patsis, N. Glezos I Microelectronic Engineering 46 (1999) 359-363
The output quantities are : the chain and monomer density, the reaction yield, the cross-link density, the cluster density, the gel fraction, the fi'ee volume fraction, the cluster size distribution, the number / weight average molecular weight, the dispersivity.
Developer selectivity is controlled by determining the mininmm cluster size removed by the developer. The most important information obtained using MD includes the contrast curve, the cluster size and cluster number distributions around the gel point and the weight and number average molecular weights as well as the dependence of cross-link density upon the radiation dose. In figure 5 simulation results are shown the case of three characteristic initiation probabilities. Each probability corresponds to a different dose. The initiator's molecules activation probability is related to the radiation dose through a relation of the form : Pi,,itia,io,~ =
] -exp{-Kd
}
The sensitivity parameter K is obtained from experimental contrast curve data of EPR under the same initiator concentration as in the case of the simulation. Such a fit is shown in figure 6. , where experimental contrast curve for a 50keV exposure of EPR is compared with MD modeling results for different acid diffusion ranges. The best fit is obtained for a number of acid diffusion steps R = I 0 which corresponds to D=10-Vpme/sec in accordance with results obtained by other methods 3 It is also obvious fl'om these two figures that the model can both qualitatively and quantitatively describe the gel point transition which is especially useful for such a system that exhibits high contrast and low sensitivity.
F'
> - . :1::5 -:.{,'../
..........-
-LJ
P(lnitiation) = 0.(X)l
P(lnitiation)
Dose = 0.017 ,ItC/cln 2
D o s e = 0.167 pC/era"
= 0.01
P(lnitiation)
= O. I
D o s e = 1.294 ~lC'/Clll 2
Figure 5 . 20 x 20 lattice model for three different doses. 1 ......................................
7~
.-
....................... !
o~ i ''~R=l° 0 . 2 - : -'~-" R = 2 0
//
At/
o.1
1 Dose
lO
(pC/cm^2)
Figure 6 . Gel-Dose (Constrast) curve. In figure 7 the dependence of the simulated cross-link density upon the radiation dose for the different ranges that correspond to figure 6 is shown. 1 .................................................................................................................................. i l °~ ---R=s I . / ._-~--~ ii
,
~R=~oj
/ ~
1j
~ . . . . .
i l
,8 2
,3 1 0
i 05
i 1
i 15 Dose
i 2
(pC/cm^2)
Figure 7. Cross-link density vs Dose
i 25
i 3
G.P. Patsis, N. Glezos I Microelectronic Engineering 46 (1999) 359-363
The data from this chart are used in order to translate the D(®) into the D(d) relation. This relation is shown in figure 8 ,and it has the form : D = Do exp{-lt 6)} where the values of Do and It have been determined previously by fitting experimental point exposure data to the solution of a reaction diffusion system 5 . From this it is observed that the acid mobility decreases in regions, which have accepted higher doses.
Applied in the case of EPR, the MD model has provided acceptable values of the diffusion coefficient as well as a satisfactory simulation of the contrast curve, not obtained by other methods. The applicability of the method may be extended to lithographic resist systems based on dissolution mechanisms other than cross-linking. The knowledge of the detailed structure of the resist system is essential for the definition of the model. REFERENCES
I.
t~ <
E s-
0
05
1
15 Dose
2
25
3
(~C/cm^2)
Figure 8 . Diffusion Coefficient vs Dose. 4. C O N C L U S I O N S In this paper, a molecular dynamics model is used in order to determine the dependence of the diffusion length upon the crosslink density in the case of a chemically amplified resist. This information is important in the lithographic process. The main advantage of this method is that it gives the possibility to include in the model several microscopic events occurring during the PEB stage. The cross-link density, the diffusion length , the gel fraction and the ti"ee volume are among the results provided by this method. The critical computational procedure is the use of graph theory for the evaluation of cluster formation in the polymer system.
363
D.Seligson,S.Das,H.Gaw,P.Pianetta, JVST(B), 6(6), 2303, (1988). 2. N.N.Tam, R.A.Ferguson, and A.R.Neureuther, JVST B10, 2565 (1992) 3. N.Glezos, G.Patsis, I.Raptis and P.Argitis, JVST B 14(6), 4252 (1996). 4. G..P.Patsis, I.Raptis, N.Glezos, P.Argitis, M.Hatzakis, C.J.Aidinis, M.Gentili, and R.Maggiora , Microelectronic Engineering 35, 157-160, (1997). 5. N.Glezos, G.Patsis, A.Rosenbusch and Z.Cui, Microel. Eng. 41/42, 319 (1998) 6. G.Patsis, G.Meneghini, N.Glezos and P.Argitis, JVST B 15(6), 2561 (1997) 7. A.Charlesby, Proc. Roy. Soc. (London) A 2 2 2 , 542, (1954). 8. N.Atoda, and H.Kawakatsu , J. Electrochem. Soc. : Solid State Science and Technology , Vol. 123, No. 10, 1519,(1976). 9. K.Kamon, K.Nakazawa, A.Yamaguchi, N.Matsuzawa, T.Ohfuji, K.Kanzaki and S.Tagawa, JVST(B), 15(6), 2610 (1997). 10. T.Ushirogouchi,K.Asakawa,M.Nakase and A.Hongu, SPIE v2438, 609 (1995). 11. P.Argitis, I.Raptis, C.J.Aidinis, N.Glezos, M.Bacciochi, J.Everett and M.Hatzakis. JVST(B) 13(6) 3030 (1995). 12. Sara Baase , "Computer Algorithms : Introduction to Design and Analysis" , AddisonWesley.
Microelectronic Engineering 46 (1999) 359-363
M O L E C U L A R DYNAMICS S I M U L A T I O N OF GEL F O R M A T I O N AND ACID D I F F U S I O N IN N E G A T I V E T O N E C H E M I C A L L Y A M P L I F I E D RESISTS G. P. Patsis"' and N. Glezos Institute of Microelectronics, NCSR Demokritos, Aghia Paraskevi, 15310, Attiki, Greece '"e-mail: patsis @cyclades.nrcps-ariadne-t.gr The knowledge of the structural changes that occur during the lithographic process using chemically amplified resists (CARs) is of great importance in process and resist optimization. Molecular dynamics (MD) is a suitable method for the simulation of these microscopic changes. A detailed description of the lithographic procedure including reaction propagation, acid diffusion, cage effects, free volume effects and developer selectivity can be included in such a model. The comparison of contrast curve data and acid diffusion measurements with MD modeling, leading to the evaluation of microscopic parameters are presented in this paper. 1. I N T R O D U C T I O N In the case of lithography using chemically amplified resists (CARs) it is of importance to determine and control the parameters that affect acid creation and acid diffusion. During the post exposure bake stage (PEB) the acid produced during exposure diffuses through the polymer chains and induces cross-linking or site de-protection depending on the nature of the resist system. This complex phenomenon is modeled using a non-linear coupled system of equations involving the reaction rate and the acid diffusion rate. In the case of CARs based on the crosslinking mechanism, acid mobility is controlled by the cross-link density of the environment (cage effect). In order to take into account this effect some authors j'2 have assumed the reaction rate K as a decreasing function of the cross-link density O. In previous papers by the same group 3'4'5 the diffusion coefficient D was assumed as a function of the cross-link density ® and various functional forms where tried out in specific cases. The parameters of the functional laws where deduced by comparison with experimental results based on e-beam point exposures. Exponential laws best fitted experimental results in most of the cases examined.
0167-9317/99/$ - see front matter PII: S0167-9317(99)00104-5
Contrast curve analysis has been also used in order to investigate the cage effec('. The decrease in acid mobility as the PEB time increases is demonstrated by a Charlesby-Pinner representation of the corresponding contrast curves. A new interpretation has been given to the Charlesby gel formation theory 7'8 in the case of CARs. However these analytic models fail to describe accurately the gel point transition of the resist film. This can be attributed to the absence of parameters that describe explicitly the effect of chain reaction and acid propagation paths. Molecular Dynamics (MD) is a suitable method for the simulation of microscopic changes occuring during PEB. Acid diffusion, cross- linking and free volume effects can be effectively described through percolation theory . Such modeling work in the field of lithography for the simulation of the effect of amine additives and T-top formation has already been reported 9'1° In this work, percolation theory is used in order to study non-linear diffusivity of the acid produced during PEB. The diffusion coefficient D depends upon the density of the reacted sites ® which in its turn depends upon the radiation dose d. A direct relation D(d) between diffusion coefficient and dose is obtained.
© 1999 Elsevier Science B.V. All rights reserved.
G.P. Patsis, N. Glezos I Microelectronic Engineering 46 (1999) 359-363
360
2. T H E M O L E C U L A R D Y N A M I C S M O D E L Electron beam exposure results with the experimental epoxy based resist EPR j~ have been used for modeling. EPR is a two component system consisting of fractionated cresol epoxy novolac polymer chains and hexafluoroantimonate tryphenylsulphonium salt as the photoacid generator molecules. In the case examined the concentation of the photoacid generator is 10%. For the simulation, a 3D square lattice is considered , with lattice constant equal to the monomer radius. In a rough approximation , taking into account the ionic r a d i u s , the bond length and the possible molecular conformations, a monomer molecule occupies a spherical volume of radius - 1 0 A ° as shown in figure 1.
(3). Each lattice site can be occupied by no more than one monomer and one initiator molecule. (4). Periodic boundary conditions where considered. Chains that extend out of the boundaries of an edge of the lattice are inserted from the opposite side. ;::
I
I ~P~f
I V
I '~'~l'
I
I
Cross linked
I
r \
F i g u r e 2. A 2D representation of the lattice model for the EPR resist system.
BondLength- - l - ~
[
Conformations ~
~ l
I, _8Ac
%*.-16A°,,~ F i g u r e 1. EPR monomer molecule Polymer chains and initiator's molecules where placed randomly on that lattice under the following restrictions • (1). The chains should be self avoiding and populate tile lattice as possible. (2). The polymerization length was assumed a uniform distribution in a numerical interval which successfully describe the experimental polymerization length of EPR.
The radiation induced effects whe,'e simulated through the use of an initiation probability attributed to each of the initiator's molecules. The formation of a cross-link should satisfy the following requirements: (1). The cross-linked monomers belong to different chains (no cyclization effects are allowed in accordance with experimental evidence in the specific case considered). (2). The cross-linked monomers should be "near" i.e. within one lattice constant from an active initiator's molecule. The effects of chain r e a c t i o n , cage formation , diffusion range and post exposure bake temperature where considered through the use of a parameter describing the range (length) of each site excitation propagation.
G.P. Patsis, N. Glezos / Microelectronic Engineering 46 (1999) 359-363 The problem of coverage of the cubic lattice by monomer and photo-initiator molecules randomly together with the knowledge of connectness within the formed network can be conveniently described using graph theory 17_ A graph is a finite set of points , some of which are connected by lines. The points on which lines are connected are termed nodes and the lines themselves, edges. An example of a bi-directed graph is shown in figure 3. This graph is formed by 14 nodes some of which remain fi'ee.
361
The implementation of the inter-chain connections is based on the formation of a sparse array using linked lists. Each node in this representation is a head of list which contains information about the chain and links to its monomers (see figure 4). In order to determine the characteristics of the clusters that are tbrmed during PEB , the cycles in the graph have to be evaluated.
Figure 4. Implementation of a sparse array using doubly linked lists. 3. RESULTS The whole code for the simulations was integrated in a graphical environment that can run on PC under win95. It is also available for unix based systems with a C++ compiler. The input parameters Figure 3 : An example of a bidirected graph In each simulation what is needed is first to make a mathematical abstraction of the real system under a mathematical - physical model and then to translate this model into the computer's language using suitable programming techniques. Each monomer is represented by a node in a graph and the lines connecting different monomers-nodes represent the links between monomers in a chain. In computer language each node is a structure containing information about the position in the lattice and the chain identity.
are
;
1. the lattice size, 2. the number of chains, 3. the maximum number of monomers per chain (polymerization length), the acid diffusion range, 5. the reaction initiation probability, 6. the reaction propagation probability, 7. the reaction probability, 8. the maximum number of cross-links per monomer (functionality). ,
362
I.
2. 3. 4. 5. 6. 7. 8. 9.
G.P. Patsis, N. Glezos I Microelectronic Engineering 46 (1999) 359-363
The output quantities are : the chain and monomer density, the reaction yield, the cross-link density, the cluster density, the gel fraction, the fi'ee volume fraction, the cluster size distribution, the number / weight average molecular weight, the dispersivity.
Developer selectivity is controlled by determining the mininmm cluster size removed by the developer. The most important information obtained using MD includes the contrast curve, the cluster size and cluster number distributions around the gel point and the weight and number average molecular weights as well as the dependence of cross-link density upon the radiation dose. In figure 5 simulation results are shown the case of three characteristic initiation probabilities. Each probability corresponds to a different dose. The initiator's molecules activation probability is related to the radiation dose through a relation of the form : Pi,,itia,io,~ =
] -exp{-Kd
}
The sensitivity parameter K is obtained from experimental contrast curve data of EPR under the same initiator concentration as in the case of the simulation. Such a fit is shown in figure 6. , where experimental contrast curve for a 50keV exposure of EPR is compared with MD modeling results for different acid diffusion ranges. The best fit is obtained for a number of acid diffusion steps R = I 0 which corresponds to D=10-Vpme/sec in accordance with results obtained by other methods 3 It is also obvious fl'om these two figures that the model can both qualitatively and quantitatively describe the gel point transition which is especially useful for such a system that exhibits high contrast and low sensitivity.
F'
> - . :1::5 -:.{,'../
..........-
-LJ
P(lnitiation) = 0.(X)l
P(lnitiation)
Dose = 0.017 ,ItC/cln 2
D o s e = 0.167 pC/era"
= 0.01
P(lnitiation)
= O. I
D o s e = 1.294 ~lC'/Clll 2
Figure 5 . 20 x 20 lattice model for three different doses. 1 ......................................
7~
.-
....................... !
o~ i ''~R=l° 0 . 2 - : -'~-" R = 2 0
//
At/
o.1
1 Dose
lO
(pC/cm^2)
Figure 6 . Gel-Dose (Constrast) curve. In figure 7 the dependence of the simulated cross-link density upon the radiation dose for the different ranges that correspond to figure 6 is shown. 1 .................................................................................................................................. i l °~ ---R=s I . / ._-~--~ ii
,
~R=~oj
/ ~
1j
~ . . . . .
i l
,8 2
,3 1 0
i 05
i 1
i 15 Dose
i 2
(pC/cm^2)
Figure 7. Cross-link density vs Dose
i 25
i 3
G.P. Patsis, N. Glezos I Microelectronic Engineering 46 (1999) 359-363
The data from this chart are used in order to translate the D(®) into the D(d) relation. This relation is shown in figure 8 ,and it has the form : D = Do exp{-lt 6)} where the values of Do and It have been determined previously by fitting experimental point exposure data to the solution of a reaction diffusion system 5 . From this it is observed that the acid mobility decreases in regions, which have accepted higher doses.
Applied in the case of EPR, the MD model has provided acceptable values of the diffusion coefficient as well as a satisfactory simulation of the contrast curve, not obtained by other methods. The applicability of the method may be extended to lithographic resist systems based on dissolution mechanisms other than cross-linking. The knowledge of the detailed structure of the resist system is essential for the definition of the model. REFERENCES
I.
t~ <
E s-
0
05
1
15 Dose
2
25
3
(~C/cm^2)
Figure 8 . Diffusion Coefficient vs Dose. 4. C O N C L U S I O N S In this paper, a molecular dynamics model is used in order to determine the dependence of the diffusion length upon the crosslink density in the case of a chemically amplified resist. This information is important in the lithographic process. The main advantage of this method is that it gives the possibility to include in the model several microscopic events occurring during the PEB stage. The cross-link density, the diffusion length , the gel fraction and the ti"ee volume are among the results provided by this method. The critical computational procedure is the use of graph theory for the evaluation of cluster formation in the polymer system.
363
D.Seligson,S.Das,H.Gaw,P.Pianetta, JVST(B), 6(6), 2303, (1988). 2. N.N.Tam, R.A.Ferguson, and A.R.Neureuther, JVST B10, 2565 (1992) 3. N.Glezos, G.Patsis, I.Raptis and P.Argitis, JVST B 14(6), 4252 (1996). 4. G..P.Patsis, I.Raptis, N.Glezos, P.Argitis, M.Hatzakis, C.J.Aidinis, M.Gentili, and R.Maggiora , Microelectronic Engineering 35, 157-160, (1997). 5. N.Glezos, G.Patsis, A.Rosenbusch and Z.Cui, Microel. Eng. 41/42, 319 (1998) 6. G.Patsis, G.Meneghini, N.Glezos and P.Argitis, JVST B 15(6), 2561 (1997) 7. A.Charlesby, Proc. Roy. Soc. (London) A 2 2 2 , 542, (1954). 8. N.Atoda, and H.Kawakatsu , J. Electrochem. Soc. : Solid State Science and Technology , Vol. 123, No. 10, 1519,(1976). 9. K.Kamon, K.Nakazawa, A.Yamaguchi, N.Matsuzawa, T.Ohfuji, K.Kanzaki and S.Tagawa, JVST(B), 15(6), 2610 (1997). 10. T.Ushirogouchi,K.Asakawa,M.Nakase and A.Hongu, SPIE v2438, 609 (1995). 11. P.Argitis, I.Raptis, C.J.Aidinis, N.Glezos, M.Bacciochi, J.Everett and M.Hatzakis. JVST(B) 13(6) 3030 (1995). 12. Sara Baase , "Computer Algorithms : Introduction to Design and Analysis" , AddisonWesley.