Monte Carlo simulation of GaN quantum dot formation in plasma-enhanced deposition with continuum modelling

Abstract This study introduces a hybrid computational framework combining Monte Carlo simulations with partial differential equations (PDEs) to model gallium nitride (GaN) quantum dot (QD) formation during plasma-enhanced chemical vapor deposition (PECVD). The Monte Carlo approach captures stochastic particle deposition and nucleation on a 100 × 100 nm 2 grid, incorporating energy-dependent sticking probabilities, electrostatic repulsion, and a log-normal QD size distribution (mean 4 nm, σ = 0.2). The PDE model describes surface diffusion and nucleation dynamics, linking stochastic outcomes to deterministic physical mechanisms. Experimental parameters include a deposition rate of 0.05 particles/(s·nm 2 ), substrate temperature of 700 K, plasma pressure of 0.2–1.0 Torr, particle energy of 30 eV, and plasma temperature of 30,000 K. The simulations generate spatial distribution maps and size histograms, achieving QD densities of 3.0 × 10 10 to 1.2 × 10 11 cm −2 , validated against experimental data for LED applications. Results show that increasing plasma pressure enhances QD density but reduces spatial uniformity due to faster nucleation outpacing diffusion, with implications for optimizing optoelectronic device performance. This framework provides a robust tool for tailoring deposition conditions to achieve high-density, uniform GaN QD arrays for advanced optoelectronic applications.