Atomistic calculations of the precursor molecular diffusivity at rarefaction: Understanding gas transport in semiconductor fabrication lines

Accurate knowledge of gas-phase diffusion properties of metal-containing precursors is essential for optimizing semiconductor manufacturing processes such as chemical vapour deposition (CVD) and atomic layer deposition (ALD). In this study, we employ classical molecular dynamics (MD) simulations to estimate the self- and mixture diffusivities of key molybdenum oxychloride precursors MoOCl, MoOCl 2 , and MoO 2 Cl 2 under a range of process-relevant conditions. We have performed high fidelity molecular computations for long duration, up to the microsecond levels (contrary to nanoseconds) at rarefied conditions, to effectively capture the molecular collisions, establishing the Brownian dynamics. Transition from ballistic to diffusive motion was characterized via mean square displacement analysis to ensure accurate extraction of transport coefficients. In line with kinetic theory, the mixture diffusivity of MoO2Cl2 is estimated as a function of the mole fraction ( c ), temperature (T) and pressure (P), valid in the range of 2-15% concentration, D i j ( c m 2 / s ) = 0.094 [ T 3 ( 1 M w , i + 1 M w , j ) ] ( 1 2 ) P σ i j 2 Ω D ( 1 1 + 2 c ) A comparative analysis of the three precursors reveals that diffusivity decreases with increasing molecular weight and complexity, with MoOCl exhibiting the highest and MoO 2 Cl 2 the lowest mobility. At 200 torr, the diffusivity of MoOCl ranges from (0.18-0.26) cm2/s, for MoOCl2: (0.13-0.19) cm2/s and for MoO2Cl2: (0.06-0.11) cm2/s, across the temperature range of 300-360 K. In mixtures with argon and nitrogen, the precursor diffusivity lies between the self-diffusivities of the carrier and precursor species, while increased precursor concentration reduces mixture diffusivity due to enhanced momentum resistance. The work addresses a longstanding challenge in accurately predicting precursor mobility under non-continuum flow regimes, especially relevant in CVD/ALD systems.