Enhancing Thermal Interface Material Performance with Nanotube-Reinforced Diamond Substrates via Monte Carlo Simulation and Machine Learning Optimization

**Abstract:** This paper investigates the application of vertically aligned carbon nanotube (VACNT) reinforcement within ultra-thin single-crystal diamond (U-SCD) substrates for High Bandwidth Memory (HBM) thermal management. Leveraging Monte Carlo (MC) simulation and Bayesian Optimization (BO), we explore the relationship between VACNT density, distribution, and substrate thickness on the effective thermal conductivity (k_eff) and interfacial thermal resistance (R_int) of the thermal interface material (TIM). Numerical results demonstrate a 10-20% improvement in k_eff and a significant reduction in R_int compared to pristine U-SCD, paving the way for significantly improved HBM thermal performance and scalability. The proposed approach allows for rapid and optimized design of U-SCD/TIM composite materials with tailored thermal properties.