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Reaction-diffusion mechanisms for the chemical shrink process of nanofabrication
Chemical Physics Letters 414 (2005) 292–295 www.elsevier.com/locate/cplett
Reaction-diffusion mechanisms for the chemical shrink process of nanofabrication Tsung-Lung Li
a,*,1
, Jyh-Hua Ting
b
a
b
Department of Applied Physics, National Chia-Yi University, 300 Hsueh-Fu Road, Chiayi 60004, Taiwan National Nano Device Laboratories, 26 Prosperity Road I, Science-Based Industrial Park, Hsinchu 30078, Taiwan Received 15 May 2005; in final form 5 August 2005 Available online 9 September 2005
Abstract The effectiveness of reaction-diffusion mechanisms on the formation of nanoscale polymer films in the chemical shrink process is investigated by a two-dimensional model. The model includes three mechanisms: the catalytic cross-linking reaction of water-soluble polymers and cross-linkers, the diffusion of photoacids, and the trapping of photoacids by the cross-linked polymers. It is found that, although the cross-linking reaction is the vital mechanism for the chemical shrink process, it is much less effective on the formation of nanoscale polymer films than the photoacids diffusion and trapping mechanisms. 2005 Elsevier B.V. All rights reserved.
1. Introduction Modern manufacturing technology of advanced semiconductor devices involves the fabrication of patterns with sub-100 nm feature size. Different resolution enhancement techniques integrated with the conventional lithographic procedures have been developed, including the thermal flow process [1,2], the shrink assist film for enhanced resolution (SAFIER) process [3,4], and the resolution enhancement of lithography assisted by chemical shrink (RELACS) process [1,5]. To shrink patterns down to sub-100 nm regions, the RELACS process makes use of the nanoscale polymer films formed by the reaction-diffusion mechanisms occurring at the materials interfaces. As illustrated in Fig. 1, the RELACS process is a pattern shrinking process applied after the conventional lithographic process [1,5]. The RELACS process is also called the chemical shrink process. The material used for the process is called the chemical shrink. The chemical shrink process involves spin coating, mixing *
Corresponding author. Fax: +886 5 2717909. E-mail address: [email protected] (T.-L. Li). 1 This work is supported by National Science Council of Taiwan through Grant No. NSC93-2112-M-415-002. 0009-2614/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.08.078
bake, and rinsing steps. The chemical shrink film formed at the spin coating step is composed of water-soluble polymers and cross-linkers. In the mixing bake step, the residual photoacids around the edge of the pre-defined resist pattern diffuse to the chemical shrink film, and catalyze the cross-linking reaction of the water-soluble polymers and the cross-linkers. The cross-linked polymers become insoluble. Shrunken patterns are attained after the rinsing step. The chemical shrink process had been applied to the i-line [6], the 248 nm [5], the 193 nm [3], the 157 nm [1], and the electron-beam [7] lithography. Assisted by the chemical shrink process, the last three of the lithographic technologies mentioned above were demonstrated to shrink the contact holes down to sub-100 nm regions. Recently, the chemical shrink materials were optimized for various sub-100 nm manufacturing technologies [8,9]. Theoretical studies of the reaction-diffusion phenomena at the interface of resist and chemical shrink are important for material design and process integration [10], but are still lacking. In this work, a two-dimensional chemical shrink process simulator is developed to investigate the reaction-diffusion phenomena at the interface of the resist and chemical shrink. The three mechanisms built with the model are the catalytic cross-linking reaction, the photoacids diffusion, and the
T.-L. Li, J.-H. Ting / Chemical Physics Letters 414 (2005) 292–295
293
RESIST PATTER N
CHEMICAL SHRINK COATIN G
MIXING BAKE
WATER RINSE
a
b
c
d CA RESIST
CHEMICAL SHRINK
SUBSTRATE
Fig. 1. The chemical shrink process steps.
photoacids trapping by the cross-linked polymers. The catalytic cross-linking reaction is the vital mechanism for the formation of nanoscale polymer films at the interface. The photoacids diffusion and trapping mechanisms affect the supplies of the catalysts, the photoacids, to the cross-linking reaction. Each of the above three mechanisms is characterized by its corresponding activation energy and other parameters. To the extent that these modeling parameters are the approximate representation of the chemical shrink material properties, investigating the effects of the polymer activation energies on the chemical shrink process is equivalent to studying the effects of the reaction-diffusion mechanisms on the process. This will contribute to better understanding and application of the reaction-diffusion phenomena at the interface of the resist and chemical shrink. 2. Reaction-diffusion models As sketched in subplots of Fig. 1b,c, there are two types of materials on the substrate in the mixing bake step: the chemically amplified (CA) resist film and the chemical shrink film. These two films have different chemical compositions. The CA resist film contains residual photoacids resulted from the process steps prior to the chemical shrink process. The chemical shrink film mainly contains watersoluble polymers and cross-linkers. At the elevated temperatures of the mixing bake step, the residual photoacids in the CA resist diffuse to the chemical shrink materials and catalyze the cross-linking reaction of the water-soluble polymers and the cross-linkers, P þ C þ HA ! PC þ HA
ð1Þ
where P, C, HA, and PC denote the water-soluble polymers, the cross-linkers, the photoacids, and the crosslinked polymers, respectively. In the process of diffusion, some of the photoacids may be trapped by the cross-linked polymers and can no longer move to the proper sites for the next catalytic reaction. These trapped photoacids are considered to be inactivated. This photoacids trapping process is modeled by the reaction,
HA ! HAðtrappedÞ:
ð2Þ
During the mixing bake process, the water-soluble polymers, the cross-linkers, and the cross-linked polymers are assumed to be immobile, whereas the photoacids are diffusible due to their molecular sizes. Hence, the chemical shrink process is modeled by the set of reaction-diffusion equations: o½PC ¼ k C ½P½C½HA; ot o½HA m ¼ r ðDH r½HAÞ k a ½HA a ; ot
ð3Þ ð4Þ
where [P], [C], [HA], and [PC] are the concentrations of the water-soluble polymers, the cross-linkers, the photoacids, and the cross-linked sites of the polymers, respectively. Eq. (3) models the catalytic cross-linking reaction (1). kC is the reaction constant. Its temperature dependence is given by the Arrhenius relation, k C ¼ ACL eECL =kT ;
ð5Þ
where ACL and ECL are the prefactor and the activation energy of the cross-linking reaction, respectively. Eq. (4) models the diffusion and the inactivation of photoacids. The first term on the right hand side of Eq. (4) models the diffusion. The model of the diffusivity DH of the photoacids is expressed by the product of a temperature-dependent part and a polymerization-dependent factor, DH ¼ ADIFF eEDIFF =kT eag =ð1 þ bgÞ;
ð6Þ
where g = ([P]0 [PC])/[P]0 is the degree of unpolymerization which ranges between 0 and 1, [P]0 is the initial concentration of the water-soluble polymers. a and b are empirical parameters. The photoacid trapping reaction (2) is modeled by the second term of Eq. (4), which is a photoacids loss term in the equation. The reaction constant is given by k a ¼ AT eET =kT ; and the reaction order is denoted by ma.
ð7Þ
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T.-L. Li, J.-H. Ting / Chemical Physics Letters 414 (2005) 292–295
This model for the chemical shrink process is employed to investigate the effects of reaction-diffusion mechanisms on the process, using the polymer activation energies as the main parameters characterizing the mechanisms involved in the process. The three polymer activation energies of the model are for the photoacids diffusion (EDIFF), the photoacids trapping (ET), and the cross-linking reaction (ECL). If only one of these three activation energies is varied, the trends of the shrinkage change can be qualitatively predicted. The qualitative predictions are summarized in Table 1. The shrinkage is the difference between the initial contact hole size and the final critical dimension. On one hand, increasing the photoacids diffusion activation energy or increasing the cross-linking reaction activation energy will alleviate the catalytic cross-linking reaction, and thus the amount of shrinkage decreases. On the other hand, increasing the photoacids trapping activation energy will lessen the rate of photoacids trapping during the diffusion process, and thus the shrinkage increases. The competitive effects between any two of the three activation energies cannot be inferred from these qualitative arguments, and have to be studied by numerical calculations. The initial photoacids distributions for the chemical shrink process simulation are obtained from other simulation codes [11–13]. The initial distributions of the watersoluble polymers, [P]0 and the cross-linkers, [C]0 in the chemical shrink are assumed to be uniform before the mixing bake process starts. Vanishing Neumann boundary conditions are imposed on the four sides of the simulation domain in Fig. 1c. This chemical shrink model is solved in two-dimension by extending the alternating direction implicit method [14] applied to the simulation of chemically amplified resists [11]. The model parameters for the reaction-diffusion mechanisms of the chemical shrink process were obtained by comparing the simulation with the experimental data obtained by the electron beam lithography [7]. It was shown that, within the statistical deviations of the experimental data, the simulation agree well with the experiment [15]. 3. Results and discussions A typical cross-linked polymer concentration profile after the chemical shrink process is shown in Fig. 2. A sharp gradient of the cross-linked polymers is observed. The thickness of the cross-linked polymers is calculated by assuming that, at the water rinsing step, only the cross-linked polymers with the concentrations larger that a critical value such as 25 · 106/lm3 remain; while all other
Table 1 Qualitative trend of shrinkage Activation energy change
Shrinkage change
Photoacids diffusion EDIFF increases Photoacids trapping ET increases Cross-linking reaction ECL increases
Decrease Increase Decrease
Fig. 2. A typical cross-linked polymer concentration profile after the mixing bake. The unit of the concentration is in 106/lm3. The thickness of the cross-linked polymers on the sidewall is 56.22 nm.
part of the polymers are etched away. For example, the thickness of the cross-linked polymers on the sidewall of the profile given in Fig. 2 is 56.22 nm. The effects of the reaction-diffusion mechanisms on the chemical shrink process are explored with the calibrated models. The activation energies of the water-soluble polymers are used as the main parameters characterizing the reaction-diffusion mechanisms involved in the process. The effectiveness of the reaction-diffusion mechanism on the process is measured by the change of activation energy that is required to induce a certain amount of deviation on shrinkage. The larger the change of activation energy is, the smaller the effectiveness of the mechanism associated with the energy is. The activation energies for the photoacids diffusion (EDIFF), the photoacids trapping (ET), and the cross-linking reaction (ECL) are varied around the central values of 1.1411, 0.7555, and 1.4453 eV, respectively. Then, the shrinkages are calculated with one of the three activation energies held constant. The shrinkages deviated from the central value of 112.43 nm are plotted in Fig. 3 as contours over the deviations of any two of the three activation energies concerned. Positive shrinkage deviation implies that the actual shrinkage is greater than the central value, while negative shrinkage deviation means otherwise. It is observed that the shrinkage deviations on the third, the fourth, and the second quadrants of subplots of Fig. 3a–c, respectively, are all positive, and that the shrinkage deviations on the opposite quadrant of each subplot are all negative. These are consistent with the qualitative results given in Table 1. The effectiveness of the activation energies on the contact holes shrinkage is extracted using Fig. 3. Approximately, every 15–60 meV change in the polymer activation energy can cause the shrinkage change of 20 nm, the cross-linking reaction being closer to the 60 meV side; while the other two mechanisms being closer to the 15 meV side. Comparison between subplots of Fig. 3a–c shows that the effectiveness of the activation energies for the photoacids diffusion and the photoacids
T.-L. Li, J.-H. Ting / Chemical Physics Letters 414 (2005) 292–295
a
b
295
c
Fig. 3. Contours of the shrinkage deviations over the deviations of any pair of the three activation energies of the chemical shrink model. The three activation energies are for the photoacids diffusion (EDIFF), the photoacids trapping (ET), and the cross-linking reaction (ECL). The shrinkages and the activation energies deviations are measured relative to the central values noted in the plot.
trapping is about the same, and is about four times as strong as the activation energy of the cross-linking reaction. Therefore, it is concluded that, although the crosslinking reaction is the indispensable mechanism for the chemical shrink process, its effectiveness on the shrinkage amount, that is, on the chemical shrink process is minor when compared with the photoacids diffusion and trapping mechanisms. Using the reaction-diffusion models of this work, similar analyses and calculations may be performed for other materials systems of the chemical shrink process for application to chemical shrink material design and to manufacturing process integration. 4. Conclusions The effectiveness of the reaction-diffusion mechanisms on the chemical shrink process is studied by a two-dimensional simulator. The mechanisms included with the simulator are the cross-linking reaction, the photoacids diffusion, and the photoacids trapping. The model parameters are obtained by comparing the simulation with the electron beam lithography experiment data. For the particular chemical shrink materials systems, it is shown that approximately every 15–60 meV change in the polymers activation energy can induce the shrinkage change of 20 nm. It is found that the effectiveness of the photoacids diffusion and trapping activation energies on the chemical shrink process is about the same, and is about four times as strong as the activation energy of the cross-linking reaction. This fact demonstrates that, though indispensable for the chemical shrink process, the cross-linking reaction is
relatively ineffective to the formation of the nanoscale polymer films at chemical shrink sidewalls when compared with the photoacids diffusion and trapping mechanisms. References [1] E. Kawaguchi, K. Watanabe, E. Kurose, T. Furukawa, T. Itani, Jpn. J. Appl. Phys. 43 (6B) (2004) 3668. [2] T.Y. Lee, C.Y. Yu, M.Y. Hsui, R. Hayashi, T. Hirayama, T. Iwai, H. Komano, J.C. Shih, D.C. Owe-Yang, B.C. Ho, J. Photopolym. Sci. Technol. 17 (4) (2004) 541. [3] J.H. Han, J.-Y. Yoon, M. Hata, S.W. Kim, H.-W. Kim, S.-G. Woo, H.-K. Cho, W.-S. Han, J.-T. Moon, B.-I. Ryu, Jpn. J. Appl. Phys. 43 (6B) (2004) 3663. [4] C. Wallace, J. Schacht, I.H. Huang, R.H. Hsu, Proc. SPIE 5376 (2004) 238. [5] T. Ishibashi, T. Toyoshima, N. Yasuda, T. Kanda, H. Tanaka, Y. Kinoshita, N. Watase, R. Eakin, Jpn. J. Appl. Phys. Part 1 40 (1) (2001) 419. [6] T. Ishibashi, T. Toyoshima, T. Kanda, N. Yasuda, K. Katayama, M. Tanaka, H. Tanaka, Jpn. J. Appl. Phys. Part 1 40 (12) (2001) 7156. [7] H.-L. Chen, F.-H. Ko, L.-S. Li, C.-K. Hsu, B.-C. Chen, T.-C. Chu, Jpn. J. Appl. Phys. Part 1 41 (6B) (2002) 4163. [8] M. Terai, T. Toyoshima, T. Ishibashi, S. Tarutani, K. Takahashi, Y. Takano, H. Tanaka, J. Photopolym. Sci. Technol. 16 (4) (2003) 507. [9] M. Padmanaban, T. Kudo, G. Lin, S. Hong, T. Nishibe, Y. Takano, J. Photopolym. Sci. Technol. 17 (4) (2004) 489. [10] S. Hong, T. Nishibe, T. Okayasu, K. Takahashi, Y. Takano, W. Kang, H. Tanaka, Proc. SPIE 5376 (2004) 285. [11] T.L. Li, J. Comput. Phys. 173 (1) (2001) 348. [12] T.L. Li, J.H. Ting, Jpn. J. Appl. Phys. Part 1 41 (1) (2002) 79. [13] T.L. Li, J.H. Ting, Jpn. J. Appl. Phys. Part 2 40 (3B) (2001) L259. [14] A. Iserles, A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, Cambridge, 1996. [15] T.L. Li, J.H. Ting, Temporal saturation effects of nanoscale contact holes fabricated by chemical shrink techniques, Jpn. J. Appl. Phys. Part 1 44 (8) (2005) 6327.
Reaction-diffusion mechanisms for the chemical shrink process of nanofabrication Tsung-Lung Li
a,*,1
, Jyh-Hua Ting
b
a
b
Department of Applied Physics, National Chia-Yi University, 300 Hsueh-Fu Road, Chiayi 60004, Taiwan National Nano Device Laboratories, 26 Prosperity Road I, Science-Based Industrial Park, Hsinchu 30078, Taiwan Received 15 May 2005; in final form 5 August 2005 Available online 9 September 2005
Abstract The effectiveness of reaction-diffusion mechanisms on the formation of nanoscale polymer films in the chemical shrink process is investigated by a two-dimensional model. The model includes three mechanisms: the catalytic cross-linking reaction of water-soluble polymers and cross-linkers, the diffusion of photoacids, and the trapping of photoacids by the cross-linked polymers. It is found that, although the cross-linking reaction is the vital mechanism for the chemical shrink process, it is much less effective on the formation of nanoscale polymer films than the photoacids diffusion and trapping mechanisms. 2005 Elsevier B.V. All rights reserved.
1. Introduction Modern manufacturing technology of advanced semiconductor devices involves the fabrication of patterns with sub-100 nm feature size. Different resolution enhancement techniques integrated with the conventional lithographic procedures have been developed, including the thermal flow process [1,2], the shrink assist film for enhanced resolution (SAFIER) process [3,4], and the resolution enhancement of lithography assisted by chemical shrink (RELACS) process [1,5]. To shrink patterns down to sub-100 nm regions, the RELACS process makes use of the nanoscale polymer films formed by the reaction-diffusion mechanisms occurring at the materials interfaces. As illustrated in Fig. 1, the RELACS process is a pattern shrinking process applied after the conventional lithographic process [1,5]. The RELACS process is also called the chemical shrink process. The material used for the process is called the chemical shrink. The chemical shrink process involves spin coating, mixing *
Corresponding author. Fax: +886 5 2717909. E-mail address: [email protected] (T.-L. Li). 1 This work is supported by National Science Council of Taiwan through Grant No. NSC93-2112-M-415-002. 0009-2614/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.08.078
bake, and rinsing steps. The chemical shrink film formed at the spin coating step is composed of water-soluble polymers and cross-linkers. In the mixing bake step, the residual photoacids around the edge of the pre-defined resist pattern diffuse to the chemical shrink film, and catalyze the cross-linking reaction of the water-soluble polymers and the cross-linkers. The cross-linked polymers become insoluble. Shrunken patterns are attained after the rinsing step. The chemical shrink process had been applied to the i-line [6], the 248 nm [5], the 193 nm [3], the 157 nm [1], and the electron-beam [7] lithography. Assisted by the chemical shrink process, the last three of the lithographic technologies mentioned above were demonstrated to shrink the contact holes down to sub-100 nm regions. Recently, the chemical shrink materials were optimized for various sub-100 nm manufacturing technologies [8,9]. Theoretical studies of the reaction-diffusion phenomena at the interface of resist and chemical shrink are important for material design and process integration [10], but are still lacking. In this work, a two-dimensional chemical shrink process simulator is developed to investigate the reaction-diffusion phenomena at the interface of the resist and chemical shrink. The three mechanisms built with the model are the catalytic cross-linking reaction, the photoacids diffusion, and the
T.-L. Li, J.-H. Ting / Chemical Physics Letters 414 (2005) 292–295
293
RESIST PATTER N
CHEMICAL SHRINK COATIN G
MIXING BAKE
WATER RINSE
a
b
c
d CA RESIST
CHEMICAL SHRINK
SUBSTRATE
Fig. 1. The chemical shrink process steps.
photoacids trapping by the cross-linked polymers. The catalytic cross-linking reaction is the vital mechanism for the formation of nanoscale polymer films at the interface. The photoacids diffusion and trapping mechanisms affect the supplies of the catalysts, the photoacids, to the cross-linking reaction. Each of the above three mechanisms is characterized by its corresponding activation energy and other parameters. To the extent that these modeling parameters are the approximate representation of the chemical shrink material properties, investigating the effects of the polymer activation energies on the chemical shrink process is equivalent to studying the effects of the reaction-diffusion mechanisms on the process. This will contribute to better understanding and application of the reaction-diffusion phenomena at the interface of the resist and chemical shrink. 2. Reaction-diffusion models As sketched in subplots of Fig. 1b,c, there are two types of materials on the substrate in the mixing bake step: the chemically amplified (CA) resist film and the chemical shrink film. These two films have different chemical compositions. The CA resist film contains residual photoacids resulted from the process steps prior to the chemical shrink process. The chemical shrink film mainly contains watersoluble polymers and cross-linkers. At the elevated temperatures of the mixing bake step, the residual photoacids in the CA resist diffuse to the chemical shrink materials and catalyze the cross-linking reaction of the water-soluble polymers and the cross-linkers, P þ C þ HA ! PC þ HA
ð1Þ
where P, C, HA, and PC denote the water-soluble polymers, the cross-linkers, the photoacids, and the crosslinked polymers, respectively. In the process of diffusion, some of the photoacids may be trapped by the cross-linked polymers and can no longer move to the proper sites for the next catalytic reaction. These trapped photoacids are considered to be inactivated. This photoacids trapping process is modeled by the reaction,
HA ! HAðtrappedÞ:
ð2Þ
During the mixing bake process, the water-soluble polymers, the cross-linkers, and the cross-linked polymers are assumed to be immobile, whereas the photoacids are diffusible due to their molecular sizes. Hence, the chemical shrink process is modeled by the set of reaction-diffusion equations: o½PC ¼ k C ½P½C½HA; ot o½HA m ¼ r ðDH r½HAÞ k a ½HA a ; ot
ð3Þ ð4Þ
where [P], [C], [HA], and [PC] are the concentrations of the water-soluble polymers, the cross-linkers, the photoacids, and the cross-linked sites of the polymers, respectively. Eq. (3) models the catalytic cross-linking reaction (1). kC is the reaction constant. Its temperature dependence is given by the Arrhenius relation, k C ¼ ACL eECL =kT ;
ð5Þ
where ACL and ECL are the prefactor and the activation energy of the cross-linking reaction, respectively. Eq. (4) models the diffusion and the inactivation of photoacids. The first term on the right hand side of Eq. (4) models the diffusion. The model of the diffusivity DH of the photoacids is expressed by the product of a temperature-dependent part and a polymerization-dependent factor, DH ¼ ADIFF eEDIFF =kT eag =ð1 þ bgÞ;
ð6Þ
where g = ([P]0 [PC])/[P]0 is the degree of unpolymerization which ranges between 0 and 1, [P]0 is the initial concentration of the water-soluble polymers. a and b are empirical parameters. The photoacid trapping reaction (2) is modeled by the second term of Eq. (4), which is a photoacids loss term in the equation. The reaction constant is given by k a ¼ AT eET =kT ; and the reaction order is denoted by ma.
ð7Þ
294
T.-L. Li, J.-H. Ting / Chemical Physics Letters 414 (2005) 292–295
This model for the chemical shrink process is employed to investigate the effects of reaction-diffusion mechanisms on the process, using the polymer activation energies as the main parameters characterizing the mechanisms involved in the process. The three polymer activation energies of the model are for the photoacids diffusion (EDIFF), the photoacids trapping (ET), and the cross-linking reaction (ECL). If only one of these three activation energies is varied, the trends of the shrinkage change can be qualitatively predicted. The qualitative predictions are summarized in Table 1. The shrinkage is the difference between the initial contact hole size and the final critical dimension. On one hand, increasing the photoacids diffusion activation energy or increasing the cross-linking reaction activation energy will alleviate the catalytic cross-linking reaction, and thus the amount of shrinkage decreases. On the other hand, increasing the photoacids trapping activation energy will lessen the rate of photoacids trapping during the diffusion process, and thus the shrinkage increases. The competitive effects between any two of the three activation energies cannot be inferred from these qualitative arguments, and have to be studied by numerical calculations. The initial photoacids distributions for the chemical shrink process simulation are obtained from other simulation codes [11–13]. The initial distributions of the watersoluble polymers, [P]0 and the cross-linkers, [C]0 in the chemical shrink are assumed to be uniform before the mixing bake process starts. Vanishing Neumann boundary conditions are imposed on the four sides of the simulation domain in Fig. 1c. This chemical shrink model is solved in two-dimension by extending the alternating direction implicit method [14] applied to the simulation of chemically amplified resists [11]. The model parameters for the reaction-diffusion mechanisms of the chemical shrink process were obtained by comparing the simulation with the experimental data obtained by the electron beam lithography [7]. It was shown that, within the statistical deviations of the experimental data, the simulation agree well with the experiment [15]. 3. Results and discussions A typical cross-linked polymer concentration profile after the chemical shrink process is shown in Fig. 2. A sharp gradient of the cross-linked polymers is observed. The thickness of the cross-linked polymers is calculated by assuming that, at the water rinsing step, only the cross-linked polymers with the concentrations larger that a critical value such as 25 · 106/lm3 remain; while all other
Table 1 Qualitative trend of shrinkage Activation energy change
Shrinkage change
Photoacids diffusion EDIFF increases Photoacids trapping ET increases Cross-linking reaction ECL increases
Decrease Increase Decrease
Fig. 2. A typical cross-linked polymer concentration profile after the mixing bake. The unit of the concentration is in 106/lm3. The thickness of the cross-linked polymers on the sidewall is 56.22 nm.
part of the polymers are etched away. For example, the thickness of the cross-linked polymers on the sidewall of the profile given in Fig. 2 is 56.22 nm. The effects of the reaction-diffusion mechanisms on the chemical shrink process are explored with the calibrated models. The activation energies of the water-soluble polymers are used as the main parameters characterizing the reaction-diffusion mechanisms involved in the process. The effectiveness of the reaction-diffusion mechanism on the process is measured by the change of activation energy that is required to induce a certain amount of deviation on shrinkage. The larger the change of activation energy is, the smaller the effectiveness of the mechanism associated with the energy is. The activation energies for the photoacids diffusion (EDIFF), the photoacids trapping (ET), and the cross-linking reaction (ECL) are varied around the central values of 1.1411, 0.7555, and 1.4453 eV, respectively. Then, the shrinkages are calculated with one of the three activation energies held constant. The shrinkages deviated from the central value of 112.43 nm are plotted in Fig. 3 as contours over the deviations of any two of the three activation energies concerned. Positive shrinkage deviation implies that the actual shrinkage is greater than the central value, while negative shrinkage deviation means otherwise. It is observed that the shrinkage deviations on the third, the fourth, and the second quadrants of subplots of Fig. 3a–c, respectively, are all positive, and that the shrinkage deviations on the opposite quadrant of each subplot are all negative. These are consistent with the qualitative results given in Table 1. The effectiveness of the activation energies on the contact holes shrinkage is extracted using Fig. 3. Approximately, every 15–60 meV change in the polymer activation energy can cause the shrinkage change of 20 nm, the cross-linking reaction being closer to the 60 meV side; while the other two mechanisms being closer to the 15 meV side. Comparison between subplots of Fig. 3a–c shows that the effectiveness of the activation energies for the photoacids diffusion and the photoacids
T.-L. Li, J.-H. Ting / Chemical Physics Letters 414 (2005) 292–295
a
b
295
c
Fig. 3. Contours of the shrinkage deviations over the deviations of any pair of the three activation energies of the chemical shrink model. The three activation energies are for the photoacids diffusion (EDIFF), the photoacids trapping (ET), and the cross-linking reaction (ECL). The shrinkages and the activation energies deviations are measured relative to the central values noted in the plot.
trapping is about the same, and is about four times as strong as the activation energy of the cross-linking reaction. Therefore, it is concluded that, although the crosslinking reaction is the indispensable mechanism for the chemical shrink process, its effectiveness on the shrinkage amount, that is, on the chemical shrink process is minor when compared with the photoacids diffusion and trapping mechanisms. Using the reaction-diffusion models of this work, similar analyses and calculations may be performed for other materials systems of the chemical shrink process for application to chemical shrink material design and to manufacturing process integration. 4. Conclusions The effectiveness of the reaction-diffusion mechanisms on the chemical shrink process is studied by a two-dimensional simulator. The mechanisms included with the simulator are the cross-linking reaction, the photoacids diffusion, and the photoacids trapping. The model parameters are obtained by comparing the simulation with the electron beam lithography experiment data. For the particular chemical shrink materials systems, it is shown that approximately every 15–60 meV change in the polymers activation energy can induce the shrinkage change of 20 nm. It is found that the effectiveness of the photoacids diffusion and trapping activation energies on the chemical shrink process is about the same, and is about four times as strong as the activation energy of the cross-linking reaction. This fact demonstrates that, though indispensable for the chemical shrink process, the cross-linking reaction is
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