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Mesoscale simulation of molecular resists: The effect of PAG distribution homogeneity on LER
Microelectronic Engineering 86 (2009) 741–744
Contents lists available at ScienceDirect
Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
Mesoscale simulation of molecular resists: The effect of PAG distribution homogeneity on LER Richard A. Lawson, Clifford L. Henderson * School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, 311 Ferst Drive NW, Atlanta, GA 30332-0100, United States
a r t i c l e
i n f o
Article history: Received 1 October 2008 Received in revised form 25 November 2008 Accepted 15 December 2008 Available online 25 December 2008 Keywords: Molecular resists Line edge roughness Mesoscale simulation Kinetic Monte Carlo PAG aggregation
a b s t r a c t In order to better understand the effects of PAG distribution homogeneity on LER, a mesoscale kinetic Monte Carlo simulation of molecular resists was developed. PAG distribution was controlled by creating random aggregates of PAGs with different sizes. Many common experimentally found defects were recreated in the model simply by increasing the amount of PAG aggregation. LER increases with increasing PAG aggregation for resists with short photoacid diffusion lengths. Increasing the diffusion length helps to smooth out the initial PAG distribution inhomogeneity, but still induces LER through the effect of random diffusion of photoacid outside of the patterned region. PAG aggregation was found to play an important role in LER formation, and affirms that efforts to reduce PAG aggregation and increase PAG distribution homogeneity will likely be critical to meet edge roughness requirements for future ITRS roadmap patterning nodes. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction Line edge roughness (LER) is an increasing concern for the continued reduction in critical feature sizes for integrated circuits and other microelectronic devices because the size scale of LER is rapidly becoming a significant portion of the total feature size [1]. While there has been much effort to model chemically amplified resist (CAR) physics that may induce LER such as shot noise effects [2] and photoacid diffusion and reaction [3], little work has been done to model material homogeneity effects that may contribute to LER, especially photoacid generator (PAG) homogeneity. While PAGs are essential to the proper function of modern CARs, it has been observed that the most commonly used ionic types of these small molecule additives tend to aggregate and phase separate from the resist resin, regardless of whether the resin is a molecular glass or polymer [4,5]. This segregation creates a number of problems that ultimately can induce LER [6]. Since typical PAGs can behave as dissolution inhibitors, if they aggregate, they can prevent dissolution at their random cluster locations. Similarly, an aggregate of irradiated PAGs can cause random locations of higher photoacid concentration that can lead to regions of higher resist dissolution rate. Beyond LER, PAG aggregation can even have significant effects on resolution and sensitivity for many smaller features as feature sizes begin to approach that of potential PAG aggregate sizes. * Corresponding author. Tel.: +1 404 385 0525; fax: +1 404 894 2866. E-mail address: [email protected] (C.L. Henderson). 0167-9317/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2008.12.042
Continuum based models have long been used to simulate photoresist behavior, and this approach allows for fast simulation of resist performance and can model global inhomogeneities such as concentration gradients due to exposure effects, e.g. standing wave, absorption, etc. Unfortunately, the utility of continuum models is limited for modeling LER, localized material homogeneity effects such as PAG aggregation, and the stochastic behavior of individual events like PAG decomposition and acid diffusion. The length scales of interest are rapidly approaching the size of individual molecules, and thus the resist behavior becomes strongly influenced by stochastic effects. A full kinetic Monte Carlo mesoscale simulation of molecular resists has been developed to probe the effect of resist composition, processing parameters, and PAG aggregation on the resolution, sensitivity, and LER of CARs. 2. Model description A complete description of the mesoscale model can be found elsewhere [7], but a short description is provided here. The model this work is based on uses a two dimensional lattice with 1 nm by 1 nm cells, with a total simulation space of 150 by 150 cells. Inside each cell is placed a resist molecule which contains three protecting groups. Each cell may also contain a PAG, but the number of protecting groups required to be removed for that cell is the same as a cell containing no PAG. This is a reasonable assumption for low PAG loadings, and still would apply at very high PAG loadings since the PAG would likely require some resist functionality in order to properly pattern at such high loadings [8], similar to PAGs
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R.A. Lawson, C.L. Henderson / Microelectronic Engineering 86 (2009) 741–744
Fig. 1. Graphical representation of resolved patterns obtained for low D with an aggregate size of 1 (a), 10 (b), 25 (c), and 50 (d).
a2 D¼ 2ds
ð1Þ
The kinetic Monte Carlo aspect of the model is captured by considering the relative rates of acid diffusion and deprotection reaction. The rate of deprotection is the deprotection rate constant, k, times
the number of protecting groups at the lattice site where an acid resides. The rate of photoacid diffusion is proportional to the acid diffusion coefficient D. The total summation of rates for the system, RN, is the summation of the diffusion rate and deprotection rate of every acid in the lattice. A uniform random number is multiplied by RN, to determine which event occurs and which acid carries out that event. Simulation time each turn is updated by the same method as Gillespie [10] until it reaches 60 s. PAG aggregation is discussed in this work using a quantity called aggregate size. To simulate PAG aggregation, the PAG loading and aggregate size was specified for each simulation. The PAG loading is divided by the aggregate size to calculate the number of PAG clusters, and the proper number of lattice sites for this number of PAG clusters are randomly seeded with PAGs. The PAG aggregates are then created by selecting a cluster and adding a PAG in a cell directly adjacent to either the ‘‘seed PAG” or growing
31 29
LER at Esize (nm)
described elsewhere [9]. Ideal aerial image profiles consisting of a step function have been used to study the pure material response. Photoacid generation is controlled using Dill C kinetics with a C parameter of 0.03, implying that 95% of all PAGs are converted to acids at a dose of 100 mJ/cm2. Individual photoacids random walk around the lattice to simulate mesoscale diffusion processes. The calculated deprotection level map is converted to a final imaged feature by using a simple threshold removal of molecules. Since the model is a two dimensional representation of three dimensional physics, certain differences arise that must be accounted for. Because diffusion into the third dimension is ignored, the average time for an acid jump during diffusion must be modified such that the mean squared displacement for an acid is the same as it would be in three dimensions; i.e. the effective deprotection circle of the acid should be equivalent to the two dimensional projection of the deprotection sphere that would occur in a three dimensional lattice. The relation between diffusion coefficient D, the lattice spacing a (1 nm in this case), the time step for each acid diffusion jump s and the lattice dimensionality d (2 in this case) is given by Eq. (1). Likewise, since LER is normally determined using a top–down SEM image, the LER that is commonly considered is actually the edge roughness of the projected line edge. Since the model is a two dimensional model, the reported LER values should be similar to the roughness of a single slice normal to the substrate through the resist feature. If a series of the two dimensional edge profiles resulting from the 2D lattice model presented in this work are overlayed and the resulting projection of the line edge used in a manner anagous to a top–down CD-SEM view, the LER value determined is commensurate with experimental LER values.
27 25 23
k=1.8
21
k=4.8
19
k=18
17
k=100
15
0
5
10
15
20
25
PAG Aggregate Size (# PAGs) Fig. 2. LER at Esize vs. PAG aggregate size for a low D (D = 0.18 nm2/s) and four different values for the reaction rate constant k.
R.A. Lawson, C.L. Henderson / Microelectronic Engineering 86 (2009) 741–744
PAG cluster cells until the number of PAGs included in the clusters is equivalent to the PAG loading. In this way, the average number of PAGs is constant for any amount of aggregation for a given PAG loading. The PAG loading used in all simulations was 0.05 or 5%, the average amount used in most standard CARs. 3. Results and discussion The effect of aggregation can be easily studied by examining patterned features for different amounts of aggregation. Fig. 1 shows the resolved patterns obtained for a low photoacid diffusion (i.e. low D) case with average aggregate sizes of 1 (1a), 10 (1b), 25 (1c), and 50 (1d) PAGs per cluster. Although these patterns are obtained only from a single simulation each, they are good repre55
LER at Esize (nm)
50 45 40 35 30
k=1.8
25
k=4.8 k=18
20 15
k=100 0
5
10
15
PAG Aggregate Size (# PAGs)
20
25
Fig. 3. LER at Esize vs. PAG aggregate size for a high D (D = 1.8 nm2/s) and four different values for the reaction rate constant k.
743
sentations of the typical features and defects that might be encountered as PAGs begin to aggregate within a film. For low levels of aggregation, the patterns form with good continuity inside the feature and exhibit moderate LER. As the aggregate size increases (1b), the patterns still are well resolved, but small defects begin to appear near the edges of the features. Larger aggregates (1c) begin to show major line defects. The line will likely resolve in most places, but there will be significant defects such as socalled ‘‘mouse bite” defects along the line edge. The largest level of aggregation (1d) can lead to near catastrophic patterning failure. Large amounts of the pattern fail to resolve, and parts of the line that do resolve exhibit large bridging defects. More quantitative simulation results were obtained by choosing a specific combination of k and D and varying dose from 0.5 mJ/cm2 to 100 mJ/cm2 (1.5–95% of all PAGs generate acid) and examining the resulting critical dimension (CD) and LER response curves. The procedure was repeated for multiple different values of D, k, and aggregate size. To further reduce that data, the minimum dose was found (dose-to-size, Esize) that produced exactly the desired CD (i.e. in this case 50 nm) and the LER was calculated at that point (LER at Esize). Fig. 2 shows LER at Esize vs. PAG aggregate size curves for a low D in this system (D = 0.18 nm2/s) and four different values for the deprotection reaction rate constant k. LER increases linearly as aggregate size increases. For the case of low D, the photoacids diffuse away from one another, but the diffusion length is not great enough to effectively smooth out the inhomogeneity of the initial PAG placement. As aggregate size increases, the average distance between each aggregate cluster increases; this leads to an increase in inhomogeneity which leads to an increase in LER. The aggregation is the dominant factor in LER for this case. Values of k above 4.8 show little difference in performance because in all those cases the rate of deprotection is so much faster than the rate of diffusion
Fig. 4. Graphical representation of the smoothing effect of photoacid diffusion, (a) PAG distribution for an aggregate size of 25, (b) the final photoacid distribution of (a) after diffusion for low D = 0.18 nm2/s, (c) different PAG distribution for an aggregate size of 25, (d) the final photoacid distribution (c) after diffusion for high D = 1.8 nm2/s.
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that the performance is mostly diffusion controlled. The lowest k (1.8) cannot resolve patterns for aggregate sizes greater than four PAGs and also shows slightly lower LER because the Esize was much higher for this case. Higher Esize means that there is more photoacid present which reduces the statistical variation in acid concentration along the line edge. This is a well-known relationship in CARs that increasing Esize typically reduces LER [11]. Fig. 3 shows LER at Esize vs. PAG aggregate size curves for a high D in this system (D = 1.8 nm2/s) and four different values for the deprotection reaction rate constant k. The LER response for high D shows little effect of aggregate size because the diffusion length of photoacids is now great enough to effectively smooth out the inhomogeneity of the initial PAG placement. Since the initial PAG inhomogeneity is smoothed out, the dominant controlling factor for LER under these conditions is the random diffusion of acids outside the line edge. Although higher D allows for smoothing out the initial PAG aggregates, there is a trade-off between the smoothing effect and the blurring of the feature; some aggregates require such a high D that the desired CD can never be patterned due to photoacid diffusion blur. The LER results for high D also show that lower k has a similar effect on LER as it does for the low D case. This is for the same reasons, i.e. a lower k results in a higher Esize. The effect of changing k is even greater for the high D case. Not only does k = 1.8 show LER improvement, but also k = 4.8, because a higher k is required for the resist to operate in a diffusion controlled regime. Fig. 4 graphically shows the smoothing effect of photoacid diffusion. Fig. 4a shows the initial PAG distribution for an aggregate size of 25, while Fig. 4b shows the final photoacid distribution after diffusion for low D = 0.18 nm2/s. Fig. 4c shows a different initial PAG distribution for an aggregate size of 25, while Fig. 4d shows the final photoacid distribution of that initial PAG after diffusion for high D = 1.8 nm2/s. It is clear that the low D case still has much of the inhomogeneity of initial PAG distribution, while each individual photoacid has spread apart. The high D case shows very little, if any, of the initial PAG distribution because diffusion has reduced the inhomogeneity. At the same time, it is also clear that photoacid has spread out far from the initial line edges at x = 50 and 100 nm; some acid has traveled almost to the edges of the simulation domain.
4. Conclusions A kinetic Monte Carlo mesoscale simulation of molecular resists was created to investigate the effect of PAG distribution homogeneity on LER. PAGs were distributed into random aggregates of different sizes and the resist performance for each case compared. The resolved images graphically show the effect of aggregation and replicate many of the same defects commonly found experimentally, including ‘‘mouse bites” and bridging. For cases where the photoacid diffusion length is low, aggregation has a strong effect on LER, increasing LER with increasing amount of aggregation. Higher photoacid diffusion lengths act to smooth out the initial PAG distribution inhomogeneity, but begin to induce lower spatial frequency LER through diffusion outside of the patterned area. Further detailed simulation studies are in progress to further elucidate this behavior and to produce scaling relationships that can be useful in discussing resist performance with respect to component inhomogeneity. Acknowledgement The authors gratefully acknowledge Intel Corporation for funding support of this research. References [1] M. Chandhok, Proc. SPIE 6519 (2007) 6519A. [2] Robert L. Brainard, P. Trefonas, J.H. Lammers, C.A. Cutler, J.F. Mackevich, A. Trefonas, S.A. Robertson, Proc. SPIE 5374 (2004) 74. [3] K.A. Lavery, V.M. Prabhu, E.K. Lin, W. Wu, S.K. Satija, K. Choi, M. Wormington, Appl. Phys. Lett. 92 (2008) 064106. [4] J.T. Woodward, J. Hwang, V.M. Prabhu, K. Choi, AIP Conf. Proc. 931 (2007) 413. [5] E.L. Jablonski, V.M. Prabhu, S. Sambasivan, D.A. Fischer, E.K. Lin, D.L. Goldfarb, M. Angelopoulos, H. Ito, Proc. SPIE 5376 (2004) 302. [6] T. Hirayama, D. Shiono, et al., Proc. SPIE 5753 (2005) 738. [7] R.A. Lawson, C.T. Lee, W. Yueh, L.M. Tolbert, C.L. Henderson, Proc. SPIE 6923 (2008) 69230Q. [8] E. Hassanein, C. Higgins, et al., Proc. SPIE 6921 (2008) 69211I. [9] R.A. Lawson, C.T. Lee, R. Whetsell, W. Yueh, J. Roberts, L.M. Tolbert, C.L. Henderson, Proc. SPIE 6519 (2007) 65191N. [10] D.T. Gillespie, J. Phys. Chem. 81 (1977) 2340. [11] R. Gronheid, F. Van Roey, D. Van Steenwinckel, J. Photopolym. Sci. Technol. 21 (2008) 429.
Contents lists available at ScienceDirect
Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
Mesoscale simulation of molecular resists: The effect of PAG distribution homogeneity on LER Richard A. Lawson, Clifford L. Henderson * School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, 311 Ferst Drive NW, Atlanta, GA 30332-0100, United States
a r t i c l e
i n f o
Article history: Received 1 October 2008 Received in revised form 25 November 2008 Accepted 15 December 2008 Available online 25 December 2008 Keywords: Molecular resists Line edge roughness Mesoscale simulation Kinetic Monte Carlo PAG aggregation
a b s t r a c t In order to better understand the effects of PAG distribution homogeneity on LER, a mesoscale kinetic Monte Carlo simulation of molecular resists was developed. PAG distribution was controlled by creating random aggregates of PAGs with different sizes. Many common experimentally found defects were recreated in the model simply by increasing the amount of PAG aggregation. LER increases with increasing PAG aggregation for resists with short photoacid diffusion lengths. Increasing the diffusion length helps to smooth out the initial PAG distribution inhomogeneity, but still induces LER through the effect of random diffusion of photoacid outside of the patterned region. PAG aggregation was found to play an important role in LER formation, and affirms that efforts to reduce PAG aggregation and increase PAG distribution homogeneity will likely be critical to meet edge roughness requirements for future ITRS roadmap patterning nodes. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction Line edge roughness (LER) is an increasing concern for the continued reduction in critical feature sizes for integrated circuits and other microelectronic devices because the size scale of LER is rapidly becoming a significant portion of the total feature size [1]. While there has been much effort to model chemically amplified resist (CAR) physics that may induce LER such as shot noise effects [2] and photoacid diffusion and reaction [3], little work has been done to model material homogeneity effects that may contribute to LER, especially photoacid generator (PAG) homogeneity. While PAGs are essential to the proper function of modern CARs, it has been observed that the most commonly used ionic types of these small molecule additives tend to aggregate and phase separate from the resist resin, regardless of whether the resin is a molecular glass or polymer [4,5]. This segregation creates a number of problems that ultimately can induce LER [6]. Since typical PAGs can behave as dissolution inhibitors, if they aggregate, they can prevent dissolution at their random cluster locations. Similarly, an aggregate of irradiated PAGs can cause random locations of higher photoacid concentration that can lead to regions of higher resist dissolution rate. Beyond LER, PAG aggregation can even have significant effects on resolution and sensitivity for many smaller features as feature sizes begin to approach that of potential PAG aggregate sizes. * Corresponding author. Tel.: +1 404 385 0525; fax: +1 404 894 2866. E-mail address: [email protected] (C.L. Henderson). 0167-9317/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2008.12.042
Continuum based models have long been used to simulate photoresist behavior, and this approach allows for fast simulation of resist performance and can model global inhomogeneities such as concentration gradients due to exposure effects, e.g. standing wave, absorption, etc. Unfortunately, the utility of continuum models is limited for modeling LER, localized material homogeneity effects such as PAG aggregation, and the stochastic behavior of individual events like PAG decomposition and acid diffusion. The length scales of interest are rapidly approaching the size of individual molecules, and thus the resist behavior becomes strongly influenced by stochastic effects. A full kinetic Monte Carlo mesoscale simulation of molecular resists has been developed to probe the effect of resist composition, processing parameters, and PAG aggregation on the resolution, sensitivity, and LER of CARs. 2. Model description A complete description of the mesoscale model can be found elsewhere [7], but a short description is provided here. The model this work is based on uses a two dimensional lattice with 1 nm by 1 nm cells, with a total simulation space of 150 by 150 cells. Inside each cell is placed a resist molecule which contains three protecting groups. Each cell may also contain a PAG, but the number of protecting groups required to be removed for that cell is the same as a cell containing no PAG. This is a reasonable assumption for low PAG loadings, and still would apply at very high PAG loadings since the PAG would likely require some resist functionality in order to properly pattern at such high loadings [8], similar to PAGs
742
R.A. Lawson, C.L. Henderson / Microelectronic Engineering 86 (2009) 741–744
Fig. 1. Graphical representation of resolved patterns obtained for low D with an aggregate size of 1 (a), 10 (b), 25 (c), and 50 (d).
a2 D¼ 2ds
ð1Þ
The kinetic Monte Carlo aspect of the model is captured by considering the relative rates of acid diffusion and deprotection reaction. The rate of deprotection is the deprotection rate constant, k, times
the number of protecting groups at the lattice site where an acid resides. The rate of photoacid diffusion is proportional to the acid diffusion coefficient D. The total summation of rates for the system, RN, is the summation of the diffusion rate and deprotection rate of every acid in the lattice. A uniform random number is multiplied by RN, to determine which event occurs and which acid carries out that event. Simulation time each turn is updated by the same method as Gillespie [10] until it reaches 60 s. PAG aggregation is discussed in this work using a quantity called aggregate size. To simulate PAG aggregation, the PAG loading and aggregate size was specified for each simulation. The PAG loading is divided by the aggregate size to calculate the number of PAG clusters, and the proper number of lattice sites for this number of PAG clusters are randomly seeded with PAGs. The PAG aggregates are then created by selecting a cluster and adding a PAG in a cell directly adjacent to either the ‘‘seed PAG” or growing
31 29
LER at Esize (nm)
described elsewhere [9]. Ideal aerial image profiles consisting of a step function have been used to study the pure material response. Photoacid generation is controlled using Dill C kinetics with a C parameter of 0.03, implying that 95% of all PAGs are converted to acids at a dose of 100 mJ/cm2. Individual photoacids random walk around the lattice to simulate mesoscale diffusion processes. The calculated deprotection level map is converted to a final imaged feature by using a simple threshold removal of molecules. Since the model is a two dimensional representation of three dimensional physics, certain differences arise that must be accounted for. Because diffusion into the third dimension is ignored, the average time for an acid jump during diffusion must be modified such that the mean squared displacement for an acid is the same as it would be in three dimensions; i.e. the effective deprotection circle of the acid should be equivalent to the two dimensional projection of the deprotection sphere that would occur in a three dimensional lattice. The relation between diffusion coefficient D, the lattice spacing a (1 nm in this case), the time step for each acid diffusion jump s and the lattice dimensionality d (2 in this case) is given by Eq. (1). Likewise, since LER is normally determined using a top–down SEM image, the LER that is commonly considered is actually the edge roughness of the projected line edge. Since the model is a two dimensional model, the reported LER values should be similar to the roughness of a single slice normal to the substrate through the resist feature. If a series of the two dimensional edge profiles resulting from the 2D lattice model presented in this work are overlayed and the resulting projection of the line edge used in a manner anagous to a top–down CD-SEM view, the LER value determined is commensurate with experimental LER values.
27 25 23
k=1.8
21
k=4.8
19
k=18
17
k=100
15
0
5
10
15
20
25
PAG Aggregate Size (# PAGs) Fig. 2. LER at Esize vs. PAG aggregate size for a low D (D = 0.18 nm2/s) and four different values for the reaction rate constant k.
R.A. Lawson, C.L. Henderson / Microelectronic Engineering 86 (2009) 741–744
PAG cluster cells until the number of PAGs included in the clusters is equivalent to the PAG loading. In this way, the average number of PAGs is constant for any amount of aggregation for a given PAG loading. The PAG loading used in all simulations was 0.05 or 5%, the average amount used in most standard CARs. 3. Results and discussion The effect of aggregation can be easily studied by examining patterned features for different amounts of aggregation. Fig. 1 shows the resolved patterns obtained for a low photoacid diffusion (i.e. low D) case with average aggregate sizes of 1 (1a), 10 (1b), 25 (1c), and 50 (1d) PAGs per cluster. Although these patterns are obtained only from a single simulation each, they are good repre55
LER at Esize (nm)
50 45 40 35 30
k=1.8
25
k=4.8 k=18
20 15
k=100 0
5
10
15
PAG Aggregate Size (# PAGs)
20
25
Fig. 3. LER at Esize vs. PAG aggregate size for a high D (D = 1.8 nm2/s) and four different values for the reaction rate constant k.
743
sentations of the typical features and defects that might be encountered as PAGs begin to aggregate within a film. For low levels of aggregation, the patterns form with good continuity inside the feature and exhibit moderate LER. As the aggregate size increases (1b), the patterns still are well resolved, but small defects begin to appear near the edges of the features. Larger aggregates (1c) begin to show major line defects. The line will likely resolve in most places, but there will be significant defects such as socalled ‘‘mouse bite” defects along the line edge. The largest level of aggregation (1d) can lead to near catastrophic patterning failure. Large amounts of the pattern fail to resolve, and parts of the line that do resolve exhibit large bridging defects. More quantitative simulation results were obtained by choosing a specific combination of k and D and varying dose from 0.5 mJ/cm2 to 100 mJ/cm2 (1.5–95% of all PAGs generate acid) and examining the resulting critical dimension (CD) and LER response curves. The procedure was repeated for multiple different values of D, k, and aggregate size. To further reduce that data, the minimum dose was found (dose-to-size, Esize) that produced exactly the desired CD (i.e. in this case 50 nm) and the LER was calculated at that point (LER at Esize). Fig. 2 shows LER at Esize vs. PAG aggregate size curves for a low D in this system (D = 0.18 nm2/s) and four different values for the deprotection reaction rate constant k. LER increases linearly as aggregate size increases. For the case of low D, the photoacids diffuse away from one another, but the diffusion length is not great enough to effectively smooth out the inhomogeneity of the initial PAG placement. As aggregate size increases, the average distance between each aggregate cluster increases; this leads to an increase in inhomogeneity which leads to an increase in LER. The aggregation is the dominant factor in LER for this case. Values of k above 4.8 show little difference in performance because in all those cases the rate of deprotection is so much faster than the rate of diffusion
Fig. 4. Graphical representation of the smoothing effect of photoacid diffusion, (a) PAG distribution for an aggregate size of 25, (b) the final photoacid distribution of (a) after diffusion for low D = 0.18 nm2/s, (c) different PAG distribution for an aggregate size of 25, (d) the final photoacid distribution (c) after diffusion for high D = 1.8 nm2/s.
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R.A. Lawson, C.L. Henderson / Microelectronic Engineering 86 (2009) 741–744
that the performance is mostly diffusion controlled. The lowest k (1.8) cannot resolve patterns for aggregate sizes greater than four PAGs and also shows slightly lower LER because the Esize was much higher for this case. Higher Esize means that there is more photoacid present which reduces the statistical variation in acid concentration along the line edge. This is a well-known relationship in CARs that increasing Esize typically reduces LER [11]. Fig. 3 shows LER at Esize vs. PAG aggregate size curves for a high D in this system (D = 1.8 nm2/s) and four different values for the deprotection reaction rate constant k. The LER response for high D shows little effect of aggregate size because the diffusion length of photoacids is now great enough to effectively smooth out the inhomogeneity of the initial PAG placement. Since the initial PAG inhomogeneity is smoothed out, the dominant controlling factor for LER under these conditions is the random diffusion of acids outside the line edge. Although higher D allows for smoothing out the initial PAG aggregates, there is a trade-off between the smoothing effect and the blurring of the feature; some aggregates require such a high D that the desired CD can never be patterned due to photoacid diffusion blur. The LER results for high D also show that lower k has a similar effect on LER as it does for the low D case. This is for the same reasons, i.e. a lower k results in a higher Esize. The effect of changing k is even greater for the high D case. Not only does k = 1.8 show LER improvement, but also k = 4.8, because a higher k is required for the resist to operate in a diffusion controlled regime. Fig. 4 graphically shows the smoothing effect of photoacid diffusion. Fig. 4a shows the initial PAG distribution for an aggregate size of 25, while Fig. 4b shows the final photoacid distribution after diffusion for low D = 0.18 nm2/s. Fig. 4c shows a different initial PAG distribution for an aggregate size of 25, while Fig. 4d shows the final photoacid distribution of that initial PAG after diffusion for high D = 1.8 nm2/s. It is clear that the low D case still has much of the inhomogeneity of initial PAG distribution, while each individual photoacid has spread apart. The high D case shows very little, if any, of the initial PAG distribution because diffusion has reduced the inhomogeneity. At the same time, it is also clear that photoacid has spread out far from the initial line edges at x = 50 and 100 nm; some acid has traveled almost to the edges of the simulation domain.
4. Conclusions A kinetic Monte Carlo mesoscale simulation of molecular resists was created to investigate the effect of PAG distribution homogeneity on LER. PAGs were distributed into random aggregates of different sizes and the resist performance for each case compared. The resolved images graphically show the effect of aggregation and replicate many of the same defects commonly found experimentally, including ‘‘mouse bites” and bridging. For cases where the photoacid diffusion length is low, aggregation has a strong effect on LER, increasing LER with increasing amount of aggregation. Higher photoacid diffusion lengths act to smooth out the initial PAG distribution inhomogeneity, but begin to induce lower spatial frequency LER through diffusion outside of the patterned area. Further detailed simulation studies are in progress to further elucidate this behavior and to produce scaling relationships that can be useful in discussing resist performance with respect to component inhomogeneity. Acknowledgement The authors gratefully acknowledge Intel Corporation for funding support of this research. References [1] M. Chandhok, Proc. SPIE 6519 (2007) 6519A. [2] Robert L. Brainard, P. Trefonas, J.H. Lammers, C.A. Cutler, J.F. Mackevich, A. Trefonas, S.A. Robertson, Proc. SPIE 5374 (2004) 74. [3] K.A. Lavery, V.M. Prabhu, E.K. Lin, W. Wu, S.K. Satija, K. Choi, M. Wormington, Appl. Phys. Lett. 92 (2008) 064106. [4] J.T. Woodward, J. Hwang, V.M. Prabhu, K. Choi, AIP Conf. Proc. 931 (2007) 413. [5] E.L. Jablonski, V.M. Prabhu, S. Sambasivan, D.A. Fischer, E.K. Lin, D.L. Goldfarb, M. Angelopoulos, H. Ito, Proc. SPIE 5376 (2004) 302. [6] T. Hirayama, D. Shiono, et al., Proc. SPIE 5753 (2005) 738. [7] R.A. Lawson, C.T. Lee, W. Yueh, L.M. Tolbert, C.L. Henderson, Proc. SPIE 6923 (2008) 69230Q. [8] E. Hassanein, C. Higgins, et al., Proc. SPIE 6921 (2008) 69211I. [9] R.A. Lawson, C.T. Lee, R. Whetsell, W. Yueh, J. Roberts, L.M. Tolbert, C.L. Henderson, Proc. SPIE 6519 (2007) 65191N. [10] D.T. Gillespie, J. Phys. Chem. 81 (1977) 2340. [11] R. Gronheid, F. Van Roey, D. Van Steenwinckel, J. Photopolym. Sci. Technol. 21 (2008) 429.