Multi-Scale Simulations of Gas-Phase Particles Generated in Plasma Enhanced Atomic Layer Deposition Processes
Authors: Kosaki Yusuke , Uene Naoya , Mabuchi Takuya , Tokumasu Takashi 
Published: February 2024

Recently, Plasma Enhanced Atomic Layer Deposition (PEALD) has been investigated as an advanced semiconductor deposition method to expand the number and variety of materials other than those available in thermal ALD. The high reactivity of the plasma species at the deposition surface during PEALD has the advantage of increasing the degree of freedom of processing conditions and enabling a wider range of material properties. PEALD consists of four steps in the order of feed, 1st purge, reaction, and 2nd purge. In this reaction step, the secondary gas-phase reaction is important because the properties of the thin film vary greatly depending on the particles that arrive on the growing surface. Therefore, the particle distribution in the gas phase before arrival on the surface should be accurately predicted to estimate the film quality. Generally, the DSMC (Direct Simulation Monte Carlo) method is a commonly used method for analyzing particle distribution in the gas phase. The DSMC method requires reaction and scattering models that simulate the behavior between molecules. Variable Hard Sphere and Variable Soft Sphere are often used as the model in DSMC. These models are about molecular transport, such as molecular diffusion, and cannot deal with molecular reactions. The total collision energy model is determined for molecular reactions, but it may not accurately describe molecular reactions in non-equilibrium flow. The purpose of the study is to develop a new reaction-scattering model in non-equilibrium flow in the DSMC method for determining the particle distribution in the gas phase in the PEALD processes. Here, we focus on ammonia plasma used in the reaction step of boron nitride nanomaterial films, which are used in various applications, such as semiconductors and fine ceramics with two-dimensional and three-dimensional structures. This study focused on neutral and ionic molecules, NH3 and NH4
+, which can be the main collisional species in secondary gas-phase reactions.

A molecular dynamics simulation with a reactive force field (ReaxFF) was performed. The left figure shows the simulation system of NH3 and NH4
+ collisions. The periodic boundary conditions were applied to the simulation box for all directions in the size of 100 Å × 100 Å × 100 Å. Randomly oriented NH3 and NH4
+ were placed in a line at an initial distance of 15 Å. NH4
+ was given an electric charge of –0.22892 on N and 0.30723 on H. The initial translational energy of NH4
+ was set at 5-60 eV, and the difference in the vertical coordinate at 0.1-5.0 Å. The collisions were sampled 2000 times.

The right figure shows the calculated collision cross section, which determines whether a collision occurs or not. The collision coefficient bcoll
represents the difference in the maximum vertical coordinate at which the absolute value of the scattering angle is greater than 1 degree. The collision cross section decreases as the translational energy increases because the negligible attraction-force act on NH3 and NH4
+ at a long distance. When the translational energy exceeds 40 eV, the collisional cross-section no longer decreases and becomes asymptotic. The reason can be considered as follows. As the cross-section approaches 40 Å2, the collision cross section asymptotically approaches 40 Å2, regardless of the translational energy, because the attractive and repulsive forces are balanced. We compared our results with a reference model in grey color. In the reference model, Etr, 0
represents the minimum translational energy, σT,0
is the collision cross section at the minimum, Etr
is the translational energy, and ω is a fitting parameter. Here, ω was set at –3.1. The reference model shows a good agreement with our results. However, the collision cross section is asymptotic above 40 eV, which may affect the results when the DSMC simulations are performed. We will apply the reaction scattering model to the DSMC method and analyze the gas-phase reaction of PEALD, including a comparison of the results of existing models.

Figure 1