Solubility Prediction of Organic Ionic Compounds with ...

Solubility Prediction of Organic Ionic Compounds with Computational Methods for Photoresist

Application

Eui-Hyun Ryua*, Myung-Yeol Kima, You-Jung Yoona, Kwang-Hwyi Ima, Hae-Mi Jeonga, Hyun Jeona, Hankyul Leeb, and Hyungjun Kimb*

aDow Electronic Materials, 20, Samsung 1-Ro 5-Gil, Hwaseong, Gyeonggi-Do, 445-170, South Korea

bGraduate School of EEWS, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon 305-701 South Korea

Solubility prediction of organic ionic compounds in both aqueous and organic solvents is important for understanding and optimizing lithographic performances. In this study, we proposed computational methods to predict solubility of organic ionic compounds. To compare the predicted solubility with the experimental one, we applied a multiple linear regression model by changing a set of explanatory variables. We conclude that the variables of solvation free energies of cation-anion pair, cation and anion, which are ��○ , ��○ and ��○ respectively, will be sufficient to describe the relationship between the predicted and experimental solubility values. We expect that the more accurate empirical model for quantitative prediction of solubility of organic ionic compounds by expanding these regression models and further optimizing the parameters based on larger set of experimental values will be reserved. Keywords: solubility prediction, organic ionic compound, computational method

1. IntroductionIn chemically amplified resist (CAR) system,

catalytic acids, which are generated after UV irradiation, react with leaving groups of photoresist polymers to differentiate the solubility of UV exposed area out of UV unexposed areas in developing solvents. As a result, well-defined lithographic patterns can be obtained. During this process, various organic ionic compounds, such as photo-acid generators for catalytic reaction and photo-decomposable quenchers for catalytic reactivity control, are utilized. Therefore the basic understanding of physical and chemical properties of organic ionic compounds is mostly important for optimizing the lithographic performances, such as pattern profiles, I/D bias, DoF margin and so on [1]. For more efficient and effective optimization of lithographic performances and development of new materials without involving direct synthesis and analysis, it is mostly useful to develop new simulation and

computational methods predicting the properties of organic ionic compounds.

In lithography, solubility is one of the most important properties of organic ionic compounds out of other physical and chemical properties such as photo-efficiency, diffusion length and so on. However lower solubility of some organic ionic compounds in relatively non-polar solvents environments, which is induced by their polar ionic characters, may be limited in potential use in lithographic application. Additionally ion exchange of mixed organic ionic compounds in formulation solution can produce unexpected fairs of organic ionic compounds and may induce shelf-life issues by precipitation during storage and defect issues by partial aggregation during lithographic process [2]. In order to minimize the potential problems induced by solubility of organic ionic compounds, practical solubility prediction methods are required.

For several decades, researchers have tried to

Journal of Photopolymer Science and Technology

Volume 29, Number 5 (2016) － Ⓒ 2016SPST731 736

April 2, 2016May 9, 2016

Received Accepted　

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predict solubility parameters by applying artificial neural networks (ANNs) [3-6], genetic algorithms (GAs) [6], multiple linear regressions [7], partial least squares (PLSs) [8, 9], support vector machines (SVMs) [10, 11], random forest (RF) models [12] and so on. However, there are not many previous works to directly compute solubility parameters from solvation free energy that is the fundamental physical variable determining the solvation process.

Previous approaches to predict solubility were limited by shortcomings in that classical MD simulations cannot accurately handle ionic solutes where strong polarization effect occurs that should be described using quantum mechanics (QM). Moreover, the newly determined “MD computed Hansen solubility parameters” cannot be directly commensurate with the “already empirically optimized Hansen solubility parameter database”. Aside from limitations from predicting solubility parameters, it was also somewhat problematic to compute solvation free energies in that explicit solvation methods require much computational cost with state-of-the-art level of simulation techniques.

In this study, we will propose the computational method combining with experimental results for predicting solubility of organic ionic compounds.

2. Experimental section 2.1. General methods

All reagents and solvents were of A.C.S certified grade or higher, and were used as received from commercial suppliers. All glassware and syringes were dried in an oven at least overnight prior to use.

2.2. Experimental solubility measurement

Solubility of organic ionic compounds was measured by using the thermal-gravimetric analysis (TGA) method. TGA instrument of TGA Q50 from TA instrument was used. In order to measure solubility, saturated solution of organic ionic compounds in n-butyl acetate (nBA) or propylene glycol monomethyl ether (PGMEA) were prepared. Two drops of saturated solution was loaded on the platinum pan and the prepared pan was transferred to TGA chamber automatically. It was equilibrated at 35°C for 1.0min and then heated up to 100°C with 20 °C/min rates and maintained at that temperature for 30min under nitrogen

environment. Data was collected and analyzed by using Thermal Analysis V.2.0 software and Universal Analysis 2000 Version 4.5A from TA instrument.

2.3. Calculation methods With the aid of density functional theory (DFT) calculations combined with the Poisson- Boltzmann (PB) implicit solvation [13] solver as implemented in Jaguar 8.9 software [14], the solvation free energies and cation-anion interaction energies were theoretically calculated for the given set of target compounds. Such DFT calculations were performed with Perdue-Burke- Ernzerhof (PBE) exchange-correlation functional [15] and LACVP** basis sets. 2.4. Litho-performance

Samples for Resist and BARC coatings, baking and development were performed with Lithius-i Clean Track from TEL for 300mm wafers. Silicon wafers were spin-coated with the dual bottom-antireflective coating (BARC) materials and a target film thickness was that BARC A as bottom layer was 800 Å and BARC B as upper layer was 400 Å. A photoresist was coated on the BARC coated wafer and a target film thickness was 1200 Å. Post application bake was performed at 110oC for 60s. Exposure was carried out with ASML 1900i 193nm scanner with binary mask with 50nm 1:1 line and space. Illumination condition was 1.20NA and Dipole-35Y with 0.90 outer and 0.75 inner sigma and X-polarization. Post exposure bake was done at 95oC for 60s. Development was done by using 2.38% TMAH solution. Defect inspection was performed with KLA2380 defect inspection tool from KLA Tenchor Co. 3. Results and discussion 3.1. Solubility measurements

In order to measure the solubility of organic ionic compounds, a series of PAGs, which is commonly used in photo-lithography, were selected. PAG A and B are composed of triphenylsulfonium (TPS) and triplate (Tf) or nonaflate (Nf). PAG C has a more flexible functional group in a cation part with Nf anion. PAG D has a more rigid functionality than other PAGs in a cation part. (see, Figure 1).

For solubility measurement, saturated solution of every PAG was prepared by adding excess amounts of solute in nBA or PGMEA. Two drops

J. Photopolym. Sci. Technol., Vol. 29, No. 5, 2016

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predict solubility parameters by applying artificial neural networks (ANNs) [3-6], genetic algorithms (GAs) [6], multiple linear regressions [7], partial least squares (PLSs) [8, 9], support vector machines (SVMs) [10, 11], random forest (RF) models [12] and so on. However, there are not many previous works to directly compute solubility parameters from solvation free energy that is the fundamental physical variable determining the solvation process.

Previous approaches to predict solubility were limited by shortcomings in that classical MD simulations cannot accurately handle ionic solutes where strong polarization effect occurs that should be described using quantum mechanics (QM). Moreover, the newly determined “MD computed Hansen solubility parameters” cannot be directly commensurate with the “already empirically optimized Hansen solubility parameter database”. Aside from limitations from predicting solubility parameters, it was also somewhat problematic to compute solvation free energies in that explicit solvation methods require much computational cost with state-of-the-art level of simulation techniques.

In this study, we will propose the computational method combining with experimental results for predicting solubility of organic ionic compounds.

2. Experimental section 2.1. General methods

All reagents and solvents were of A.C.S certified grade or higher, and were used as received from commercial suppliers. All glassware and syringes were dried in an oven at least overnight prior to use.

2.2. Experimental solubility measurement

Solubility of organic ionic compounds was measured by using the thermal-gravimetric analysis (TGA) method. TGA instrument of TGA Q50 from TA instrument was used. In order to measure solubility, saturated solution of organic ionic compounds in n-butyl acetate (nBA) or propylene glycol monomethyl ether (PGMEA) were prepared. Two drops of saturated solution was loaded on the platinum pan and the prepared pan was transferred to TGA chamber automatically. It was equilibrated at 35°C for 1.0min and then heated up to 100°C with 20 °C/min rates and maintained at that temperature for 30min under nitrogen

environment. Data was collected and analyzed by using Thermal Analysis V.2.0 software and Universal Analysis 2000 Version 4.5A from TA instrument.

2.3. Calculation methods With the aid of density functional theory (DFT) calculations combined with the Poisson- Boltzmann (PB) implicit solvation [13] solver as implemented in Jaguar 8.9 software [14], the solvation free energies and cation-anion interaction energies were theoretically calculated for the given set of target compounds. Such DFT calculations were performed with Perdue-Burke- Ernzerhof (PBE) exchange-correlation functional [15] and LACVP** basis sets. 2.4. Litho-performance

Samples for Resist and BARC coatings, baking and development were performed with Lithius-i Clean Track from TEL for 300mm wafers. Silicon wafers were spin-coated with the dual bottom-antireflective coating (BARC) materials and a target film thickness was that BARC A as bottom layer was 800 Å and BARC B as upper layer was 400 Å. A photoresist was coated on the BARC coated wafer and a target film thickness was 1200 Å. Post application bake was performed at 110oC for 60s. Exposure was carried out with ASML 1900i 193nm scanner with binary mask with 50nm 1:1 line and space. Illumination condition was 1.20NA and Dipole-35Y with 0.90 outer and 0.75 inner sigma and X-polarization. Post exposure bake was done at 95oC for 60s. Development was done by using 2.38% TMAH solution. Defect inspection was performed with KLA2380 defect inspection tool from KLA Tenchor Co. 3. Results and discussion 3.1. Solubility measurements

In order to measure the solubility of organic ionic compounds, a series of PAGs, which is commonly used in photo-lithography, were selected. PAG A and B are composed of triphenylsulfonium (TPS) and triplate (Tf) or nonaflate (Nf). PAG C has a more flexible functional group in a cation part with Nf anion. PAG D has a more rigid functionality than other PAGs in a cation part. (see, Figure 1).

For solubility measurement, saturated solution of every PAG was prepared by adding excess amounts of solute in nBA or PGMEA. Two drops

Fig. 1. Examples of organic ionic compounds; PAG A, B, C and D. of prepared solution were loaded on the platinum pan and transferred to TGA chamber. TGA analysis was performed without delaying time. After all solvents were evaporated, solid content was directly measured from the weight loss of total solution. Finally weight percentage of solute was transformed to molar concentration of every saturated solution. (see, Table 1) Table 1. Solubility of the organic ionic compounds, PAG A, B, C and D in nBA (gray) and PGMEA (white).

S (unit: M) Log S

PAG A 0.0013 -2.89 0.0281 -1.55

PAG B 0.0308 -1.51 1.8283 0.26

PAG C 0.0434 -1.36 0.2225 -0.65

PAG D 0.0090 -2.05 0.1501 -0.82

3.2. Solvation free energy

The solvation free energy between the target compound and the solvent of interest can be estimated by PB implicit solver where solvent part is treated as a dielectric continuum field. Such a continuum solvation model requires to specify two parameters – dielectric constant �ε� and probe radius �� – in order to determine electrostatic interactions between solute and solvent and the solvent accessible surface area, respectively. Table 2 indicates all ε and �� values for nBA and PGMEA solvents. The value of probe radius can be estimated by the following formula:

�� 10�� (1)

where Δ is a packing density (nearly 0.5) and ρ is

a density �� at 20 deg. C. We used the PB implicit solvation method

(Section 2.2) to calculate the solvation free energies and binding energies for given ionic solutes. The overall results are tabulated as shown in Table 3 and 4. With regard to calculated binding energies for cation-anion pairs, there is not much differences among �� values in the unit of kcal/mol. Table 2. Parameters of organic solvents; nBA and PGMEA.

Solvent Dielectric constant (ε)

Probe radius (��, Å)

nBA 5.07 2.97 PGMEA 8.30 3.00

Table 3. The calculated cation-anion binding energies of each target compound in gas phases.

PAG A PAG B PAG C PAG D�� -81.49 -78.51 -83.44 -80.73

(unit: kcal/mol) Table 4. The calculated solvation free energies of cation, anion and cation-anion pair for target compounds in nBA (gray) and PGMEA (white) solvents via PB implicit models.

Cation-anion (��○ �

Cation (��○�

Anion (��○�

PAG A -16.02 -33.73 -49.08 -18.23 -37.06 -54.03

PAG B -14.94 -33.73 -45.27 -17.40 -37.06 -50.03

PAG C -18.21 -37.74 -45.27 -20.91 -41.53 -50.03

PAG D -15.77 -34.42 -45.27 -18.04 -37.88 -50.03

(unit: kcal/mol) Given a specific ionic compound, by

controlling two parameters ε and �� , we figured out that the dielectric constant is more sensitive than the probe radius to determine the implicit solvation energies. Since, moreover, the probe radii of nBA and PGMEA solvents are almost same, PB implicit solvation free energies in these solvents can be determined by only dielectric constant. The dielectric constant of PGMEA is larger than that of nBA and thus such solute-solvent electrostatic interaction results in stabilizing solvation processes. 3.3. Solvation vs solubility

Solubility (�, mol/L) can be converted into the


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formula for the mole fraction (��) of organic ion compounds of interest, namely, AB where A and B are a cation and an anion, respectively. The relationship of � and �� is as follows:

��

��

(2)

where �� and �� are the molecular weight and density of the solvent, respectively. �� of the target compound can be related to

the free energy changes during solvation process of the salt (��○ ) as the following formula [16]:

�� ○ � (3)

Then, by considering the thermodynamic cycle shown in Figure 2, ��○ can be defined as: ��○ � �� ○ � ��○ � ��○ ��○ � � ��○ (4)

where ��○ , ��○ , and ��○ are the standard-state aqueous free energy of solvation of cation-anion dimer, cation, and anion, respectively. � denotes the dissociation constant, ��○ is the binding free energy, ��○ is the free energy change associated for the sublimation of gaseous AB dimer from the solid-phase of salt.

If one can determine all the free energy quantities in an accurate manner, theoretical calculation of the solubility can be possible in principle. However, considering the exponential dependence of �� and ��○ , and intrinsic error range of PB and DFT calculations, accurate estimation of the solubility is hardly available.

Thus, to estimate the solubility from the calculated solvation free energies, our model was developed in an empirical manner, by using a multiple linear regression to find out the relationship between the logarithm of mole fraction (��) of the target solute and a set of solute-based descriptors: PB implicit solvation energy of the cation-anion pair (��○ ), isolated cation and anion solvation energies (��○ and ��○ ) and the gas-phase cation-anion binding energy (�� ) (instead of the free energy quantity). The remaining term of ��○ , which is associated with the thermodynamic process from a crystalline solid to a gas phase, sublimation, needs to be taken into account.

Fig. 2. Thermodynamic cycle for the decomposition of ��○ .

However, it is challenging to calculate lattice energies for most organic ionic compounds. Assuming that sublimation free energies are not much different to some extent, in the case of isovalent ion pairs, the coefficient �� would be enough to represent the term for a lattice energy. Then, the corresponding equation is as follows:

�� ○ � � ��○� � ��○�

� �� where ��’s are coefficients from a multiple linear regression (Table 5). Table 5. The optimal coefficients from the results of a multiple linear regression. The variable �� was excluded from the model due to statistical insignificance. ��

-70.70 +4.53 -3.52 -0.32 -

To compare the predicted solubility with the experimental one (Figure 3), we applied a multiple linear regression model by changing a set of explanatory variables. Among several types of models, we found that two of them give us a satisfactory accuracy:

[model 1] ��○ , ��○ and ��○ [model 2] ��○ , ��○, ��○, and ��.

Obviously, [model 1] with more explanatory variables had more mean unsigned error (MUE) than [model 2], 0.24 and 0.20, respectively. However, in the results of statistical tests, no variables of [model 2] had a significance level less than 0.05, whereas all of them in [model 1] achieved a significance level of 0.05. Thus, we can conclude that the variables ��○ , ��○ and ��○ would be sufficient to describe the relationship between the predicted and experimental solubility values. By expanding these regression models and further optimizing the parameters based on larger set of


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formula for the mole fraction (��) of organic ion compounds of interest, namely, AB where A and B are a cation and an anion, respectively. The relationship of � and �� is as follows:

��

��

(2)

where �� and �� are the molecular weight and density of the solvent, respectively. �� of the target compound can be related to

the free energy changes during solvation process of the salt (��○ ) as the following formula [16]:

�� ○ � (3)

Then, by considering the thermodynamic cycle shown in Figure 2, ��○ can be defined as: ��○ � �� ○ � ��○ � ��○ ��○ � � ��○ (4)

where ��○ , ��○ , and ��○ are the standard-state aqueous free energy of solvation of cation-anion dimer, cation, and anion, respectively. � denotes the dissociation constant, ��○ is the binding free energy, ��○ is the free energy change associated for the sublimation of gaseous AB dimer from the solid-phase of salt.

If one can determine all the free energy quantities in an accurate manner, theoretical calculation of the solubility can be possible in principle. However, considering the exponential dependence of �� and ��○ , and intrinsic error range of PB and DFT calculations, accurate estimation of the solubility is hardly available.

Thus, to estimate the solubility from the calculated solvation free energies, our model was developed in an empirical manner, by using a multiple linear regression to find out the relationship between the logarithm of mole fraction (��) of the target solute and a set of solute-based descriptors: PB implicit solvation energy of the cation-anion pair (��○ ), isolated cation and anion solvation energies (��○ and ��○ ) and the gas-phase cation-anion binding energy (�� ) (instead of the free energy quantity). The remaining term of ��○ , which is associated with the thermodynamic process from a crystalline solid to a gas phase, sublimation, needs to be taken into account.

Fig. 2. Thermodynamic cycle for the decomposition of ��○ .

However, it is challenging to calculate lattice energies for most organic ionic compounds. Assuming that sublimation free energies are not much different to some extent, in the case of isovalent ion pairs, the coefficient �� would be enough to represent the term for a lattice energy. Then, the corresponding equation is as follows:

�� ○ � � ��○� � ��○�

� �� where ��’s are coefficients from a multiple linear regression (Table 5). Table 5. The optimal coefficients from the results of a multiple linear regression. The variable �� was excluded from the model due to statistical insignificance. ��

-70.70 +4.53 -3.52 -0.32 -

To compare the predicted solubility with the experimental one (Figure 3), we applied a multiple linear regression model by changing a set of explanatory variables. Among several types of models, we found that two of them give us a satisfactory accuracy:

[model 1] ��○ , ��○ and ��○ [model 2] ��○ , ��○, ��○, and ��.

Obviously, [model 1] with more explanatory variables had more mean unsigned error (MUE) than [model 2], 0.24 and 0.20, respectively. However, in the results of statistical tests, no variables of [model 2] had a significance level less than 0.05, whereas all of them in [model 1] achieved a significance level of 0.05. Thus, we can conclude that the variables ��○ , ��○ and ��○ would be sufficient to describe the relationship between the predicted and experimental solubility values. By expanding these regression models and further optimizing the parameters based on larger set of

experimental values, we expect to reserve the more accurate empirical model for quantitative prediction of solubility solely based on some physical variables computed using quantum mechanics.

Fig. 3. Comparison of the experimental solubility (x-axis) and the predicted solubility (y-axis). MUE indicates the mean unsigned error. 3.4. Defects in lithographic performances Solubility of the organic ionic compounds in organic solvent is important in the preparation of formulated solutions and in better lithographic performances. Simultaneously, solubility of organic ionic compounds in an aqueous developing solvent is also critical in lithographic performances. If organic ionic compounds are poorly soluble in an aqueous developing solvent, unexpected problems may be generated during a developing process.

In order to understand the relationship between lithographic performances and solubility of organic ionic compounds in an aqueous developing solvent, two photoresist solutions, such as exp #1 and exp #2, were prepared. Both solutions contain the same photoresist polymer and the different photo-acid generators, PAG E or PAG F (see, Figure 4). PAG E in exp #1 has a non-polar functionality with a large volume in an anion part and it shows bad solubility in an aqueous developing solvent in PTD process. Otherwise, PAG F in exp #2 has relatively polar functionality with small volume. It shows better solubility than PAG E in an aqueous developing solvent.

PAG E

S+ -O3SE

PAG F

S+ -O3S FFE

2. PAG E and F

Fig. 4. Structures of a binder polymer, PAG E, and PAG F.

In order to check the solubility effect of photoresist from two different PAGs, both prepared solutions were spin-coated selectively on the BARC materials with 1200 Å in film thickness and baked at 110 oC for 60 s. UV exposure of 193nm was carried out with binary mask of 50nm 1:1 line and space, and post exposure bake was done at 95 oC for 60s. After development was done by using 2.38% of TMAH solution, the defects of lithographic patterns were inspected.

In both experiments, blob defects were observed. Interestingly, almost 100 of blob defects were detected at unexposed area in exp #2 however the number of blob defects in exp #2 was increased almost 10 times higher than ones in exp #1 (see, Table 6 and Figure 5). Table 6. Number of defects in exp #1 and exp #2.

Experiment PAG # of blob defects

#1 E ~1000 #2 F ~100

Out of various ingredients in both

formulations, major difference is in photo-acid generators. PAG E in exp #1 is more non-polar and less soluble in an aqueous developing solvent than PAG F In exp #2. According to this result, we may propose that the blob defect is induced by the aggregation of poorly soluble PAG E in an aqueous solvent on the surface of coated photoresist film at unexposed areas during developing process. These results also say that it is important to understand the solubility of organic ionic compounds in both an aqueous solvent and organic solvent in order to optimize and improve lithographic performances.


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Fig. 5. Image of blob defect (A) and defect maps of exp #1 (B) and exp #2 (C). 4. Conclusions

Solubility of organic ionic compounds in aqueous or organic solvents is important properties in lithographic performances. If the organic ionic compounds are less soluble in formulation solvents or developing solvents, potential use will be limited. Therefore the development of solubility prediction methods are required for new materials development and quality managements.

As a result, we proposed new computational method to predict solubility of organic ionic compounds. Initially solvation free energy of organic ionic compounds in nBA or PGMEA was calculated. To compare the predicted solubility with the experimental one, we applied a multiple linear regression model by changing a set of explanatory variables. Finally we conclude that the variables ��○ , ��○ and ��○ would be sufficient to describe the relationship between the predicted and experimental solubility values.

In the future, we expect to reserve the more accurate empirical model for quantitative prediction of solubility of organic ionic compounds by expanding these regression models and further optimizing the parameters based on larger set of experimental values. References 1. L. F. Thompson, C. G. willson and M. J.

Bowden, Introduction to Microlithography second edition, 1994, p.269.

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