A Second-Order Stabilized Control Volume Finite Element Method for Self-Heating Effects Simulation of Semiconductor Devices based on Triangular Elements
Keywords:CVFEM-MS, self-heating effects, semiconductor devices, triangular element
A second-order control volume finite element method combined with the multiscale flux approximation (CVFEM-MS) based on triangular elements is proposed to numerically investigate the selfheating effects of semiconductor devices. The multiscale fluxes are combined with a selected set of second-order vector basis functions to stabilize the discretization of carrier continuity equations with respect to triangular elements. Numerical results reveal that the proposed method is robust and accurate, even on the mesh of low-quality, where the detrimental impacts caused by the severe self-heating on the terminal currents can be obviously observed for a bipolar transistor model.
M. Braccioli, G. Curatola, Y. Yang, E. Sangiorgi, and C. Fiegna, “Simulation of self-heating effects in different SOI MOS architectures,” Solid-State Electron., vol. 53, no. 4, pp. 445-451, Apr. 2009.
F. Nasri, F. Echouchene, M. F. B. Aissa, I. Graur, and H. Belmabrouk, “Investigation of self-heating effects in a 10-nm SOI-MOSFET with an insulator region using electrothermal modeling,” IEEE Trans. on Electron Devices, vol. 62, no. 8, pp. 2410-2415, Aug. 2015.
G. Zhu, W. Chen, D. Wang, H. Xie, Z. Zhao, P. Gao, J. Schutt-Aine, and W. Yin, “Study on high-density integration resistive random access memory array from multiphysics perspective by parallel computing,” IEEE Trans. on Electron Devices, vol. 66, no. 4, pp. 1747-1753, Apr. 2019.
N. Bushyager, B. McGarvey, and E. M. Tentzeris, “Introduction of an adaptive modeling technique for the simulation of RF structures requiring the coupling of Maxwell's, mechanical, and solid-state equations,” Applied Computational Electromagn. Soc. J., vol. 17, no. 1, pp. 104-111, Mar. 2002.
A. Amerasekera, M. Chang, J. A. Seitchik, A. Chatterjee, K. Mayaram, and J. Chern, “Selfheating effects in basic semiconductor structures,” IEEE Trans. on Electron Devices, vol. 40, no. 10, pp. 1836-1844, Oct. 1993.
R. E. Bank, D. J. Rose, and W. Fichtner, “Numerical methods for semi-conductor device simulation,” IEEE Trans. Electron Devices, vol. 30, no. 9, pp. 1031-1041, Sept. 1983.
P. Bochev and K. Peterson, “A parameter-free stabilized finite element method for scalar advection-diffusion problems,” Cent. Eur. J. Math., vol. 11, no. 8, pp. 1458-1477, May 2013.
P. Bochev, K. Peterson, and X. Gao, “A new control volume finite element method for the stable and accurate solution of the drift-diffusion equations on general unstructured grids,” Comput. Methods Appl. Mech. Engrg., vol. 254, pp. 126- 145, Feb. 2013.
A. N. Brooks and T. J. R. Hughes, “Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations,” Comput. Methods Appl. Mech. Engrg., vol. 32, no. 1, pp. 199-259, Sept. 1982.
H. Bao, D. Ding, J. Bi, W. Gu, and R. Chen, “An efficient spectral element method for semiconductor transient simulation,” Applied Computational Electromagn. Soc. J., vol. 31, no. 11, pp. 1337- 1342, Nov. 2016.
F. Li, Q. H. Liu, and D. P. Klemer, “Numerical Simulation of high electron mobility transistors based on the spectral element Method,” Applied Computational Electromagn. Soc. J., vol. 31, no. 10, pp. 1144-1150, Oct. 2016.
A. Cheng, S. Chen, H. Zeng, D. Ding, and R. Chen, “Transient analysis for electrothermal properties in nanoscale transistors,” IEEE Trans. Electron Devices, vol. 65, no. 9, pp. 3930-3935, Sept. 2018.
Y. Liu and C.-W. Shu, “Analysis of the local discontinuous Galerkin method for the driftdiffusion model of semiconductor devices,” Sci. China Math., vol. 59, no. 1, pp. 115-140, Jan. 2016.
P. Bochev, K. Peterson, and M. Perego, “A multiscale control volume finite element method for advection-diffusion equations,” Int. J. Numer. Methods Fluids, vol. 77, no. 11, pp. 641-667, Jan. 2015.
R. D. Graglia, D. R. Wilton, and A. F. Peterson, “Higher order interpolatory vector bases for computational electromagnetics,” IEEE Trans. Antennas Propag., vol. 45, no. 3, pp. 329-342, Mar. 1997.
A. Ahagon and T. Kashimoto, “Three-dimensional electromagnetic wave analysis using high order edge elements,” IEEE Trans. Magn., vol. 31, no. 3, pp. 1753-1756, May 1995.
P. R. Amestoy, I. S. Duff, J. Koster, and J.-Y. L’Excellent, “A fully asynchronous multifrontal solver using distributed dynamic scheduling,” SIAM J. Matrix Anal. Appl., vol. 23, no. 1, pp. 15- 41, April 2001.
N. D. Arora, J. R. Hauser, and D. J. Roulston, “Electron and hole mobilities in silicon as a function of concentration and temperature,” IEEE Trans. Electron Devices, vol. 29, no. 2, pp. 292- 295, Feb. 1982.
COMSOL Multiphysics Reference Manual, pp. 628-634, COMSOL Multiphysics® ver. 5.5. COMSOL AB, Stockholm, Sweden, 2019.