Molecular Dynamics Simulation of Calculation of Adhesion Energies
Authors: Tabe Hirofumi , Seki Ryuichi , Fujiwara Naozumi , Sato Masanobu 
Published: December 2024

Evaluations of adhesion energies between materials in contact have been important topics for wet-cleaning process developments. For instance, the balance of adhesion energies among polymers, particles, and a substrate was investigated to elucidate a particle removal mechanism for a polymer-based cleaning process [1] for the purpose of optimizing polymer solution formulations and so on. However, it would be difficult to experimentally evaluate only a targeted adhesion energy when multiple materials interact with each other. We thought using numerical simulation methods would be effective to calculate adhesion energies between targeted materials. The molecular dynamics (MD) simulation is one of the most powerful tools because it enables to easily calculate the intermolecular interactions between arbitrary materials under various conditions. Thus, we conducted MD simulations to calculate adhesion energies between materials related to the wet-cleaning process in semiconductor production.
To calculate adhesion energies in MD simulations, we used a thermodynamic integration (TI) method [2]. Although this method is originally used to calculate the free energy difference between two equilibrium states, it also enables us to calculate properties regarding an adhesion energy between materials such as a work of adhesion between a liquid film and a solid substrate [3].
In the TI method, two equilibrium states have to be quasi-statically transitioned for the calculation of the free energy difference between those two states. In particular, to calculate an adhesion energy from the free energy difference, the two equilibrium states are desired. One is a state where materials are in contact and the other is a state where they are separated, as shown in States 1 and 2 in Fig. 1a. Thus, as the method to quasi-statically transition between those states, a phantom wall such that only repulsive interaction works with an arbitrary material is often introduced in the TI method [3, 4].
When the phantom wall interacts only with Material B shown in Fig. 1a, State 1 can be transitioned to State 2 by gradually raising the position of the phantom wall. Figure 1b shows the force exerted on Material B by the phantom wall at each wall position. By numerically integrating this result, the free energy difference between the two states and the corresponding adhesion energy can be calculated [3, 5]. As a verification of the TI method implemented in our MD calculation systems, we calculated the work of adhesion between the water film and the solid substrate using the TI method with the phantom wall, and we obtained values of the work of adhesion comparable to those reported in the previous MD study [3].
From the above, we conclude that the properties regarding adhesion energies between materials in contact with can be calculated using the TI method with the phantom wall in our MD calculation systems. In the presentation at the conference, we will present detailed results of MD analysis on adhesion energies between materials used in wet-cleaning processes, such as H-terminated Si, OH-terminated SiO2, PTFE, and so on.
References
[1] Yu, Seong Hoon, et al., Chemical Engineering Journal 470 (2023): 144102.
[2] Leroy, Frédéric, et al., Macromolecular rapid communications 30.9‐10 (2009): 864-870.
[3] Bistafa, Carlos, et al., The Journal of Chemical Physics 155.6 (2021).
[4] Leroy, Frédéric, and Florian Müller-Plathe, The Journal of chemical physics 133.4 (2010).
[5] Yamaguchi, Yasutaka, et al., ECS Transactions 108.4 (2022): 93.
Figure 1: (a) State 1 in which Materials A and B are in contact and State 2 in which they are separated. Material B can be pulled away from Material A by raising the position of the phantom wall. (b) The force exerted on Material B by the phantom wall at each wall position.

Figure 1