The University of Michigan-Shanghai Jiao Tong University Joint Institute (UM-SJTU JI, JI hereafter) Associate Professor Hua Bao’s research team has developed an ultra-efficient and parameter-free phonon Boltzmann transport equation (BTE) solver capable of obtaining accurate temperature distribution in 3D transistors (with 13 million degrees of freedom in the numerical simulation), marking by far the most efficient non-Fourier thermal simulation solver that has been reported in the literature. The research article entitled “Ultra-efficient and parameter-free computation of submicron thermal transport with phonon Boltzmann transport equation” was recently published in Fundamental Research, a journal sponsored by the National Natural Science Foundation of China.

During the operation of transistors, electrons scatter with the lattice and generate a large amount of heat. The “thermal bottleneck” is actually the most important limiting factor for the further development of microprocessors. At the transistor level, how heat is generated in the transistors and then conducted to the substrate is largely unknown. Because of the extremely small size of transistors, the traditional heat diffusion equation that governs macroscopic heat conduction cannot be applied to obtain the temperature distribution and the phonon BTE must be solved. However, the efficient numerical solution of phonon BTE has long been challenging owing to the complexity of the equation. In the literature, the numerical solution of phonon BTE was only carried out for relatively simple 1D and 2D systems. For real 3D full-scale transistors with many degrees of freedom, the computational cost is formidable.

To address this challenge, Professor Bao’s team has developed an efficient phonon BTE solver by integrating a suitable ensemble of advanced numerical algorithms, which can reduce the computational time by thousands of times compared with the current peer solvers. The developed solver can be used on a single personal computer to complete the thermal simulation of a 3D full-scale transistor within two hours. Such simulation was prohibitive even on supercomputers. In addition, it can be generally applied to perform thermal simulations for any crystalline material without fitting parameters. The research work enables accurately resolving the temperature profiles at the transistor level, which helps better the understanding of the self-heating effect of electronics.

Hua Bao is the corresponding author of the paper. JI doctoral student Yue Hu is the first author. JI Associate Professor Yongxing Shen participated in the research. The research also obtained support from Minhua Wen’s team of Shanghai Jiao Tong University Center for High-performance Computing in programming and parallelization. Professor Bao’s team is expected to work with the SJTU center to further improve the current in-house code in the future.

Personal Profile

Hua Bao is an associate professor at the UM-SJTU Joint Institute, Shanghai Jiao Tong University. He received his B.S. degree from the Department of Physics of Tsinghua University in 2006 and his Ph.D. from Purdue University in 2012. Professor Bao’s current research interests include micro/nanoscale thermal energy transport and applications for thermal management. He has published more than 80 papers in international journals, including Nature Communications, Physical Review B, and the International Journal of Heat and Mass Transfer.