Appl Math

Applied mathematics and computational science related to semiconductor transport †

The purpose of applied mathematics is to create mathematical and computational models related to natural and social science, and engineering in industry. Solving "real" problems has motivated the development of numerical and applied mathematics. We can see the recent progress of computational theory and applied mathematics in the field of semiconductor modeling and simulations. Here computational theory and applied mathematics have played an important role in the development of mathematical and computational models for semiconductor transport and large-scale scientific computing for semiconductor simulations. It was possible to realize computer-aided design of semiconductor integrated circuits processes and devices, as well as understanding of physical phenomena, in semiconductor industry.

Invited Talk †

• 2005 The Institute of Mathematical Science, The Chinese University of Hong Kong, Hong Kong
  • A numerical scheme for quantum hydrodynamics in semiconductor
• 2006 Institute of Mathematics, Academia Sinica, Taiwan
  • Numerical simulation in semiconductor industry
  • Physics of semiconductor transport: Quantum hydrodynamics in a semiconductor
  • Mathematical analysis of quantum hydrodynamics in a semiconductor
  • Numerical scheme for quantum hydrodynamics in a semiconductor

Journal Articles(Computational theory and applied mathematics) †

1. S.Odanaka and T.Nogi, "Massivelly parallel computation using a splitting up operator method for three-dimensional device simulation," IEEE Trans. Computer Aided Design of ICAS, vol.14, pp.824-832, 1995.
2. S.Odanaka, Multidimensional discretization of the stationary quantum drift-diffusion model for ultrasmall MOSFET structures, IEEE Trans., on CAD of ICAS, 23(2004)837-842. Oda04.pdf
3. S.Odanaka, A numerical scheme for quantum hydrodynamics in a semiconductor, Surikaisekikenkyusho Kokyuroku, No.1495(2006)51-59.Oda06.pdf
4. S.Odanaka, A high-resolution method for quantum confinement transport simulation in MOSFETs, IEEE Trans., on CAD of ICAS, 26(2007)80-85.Oda07.pdf
5. T.Shimada and S.Odanaka, "A numerical method for a transient quantum drift-diffusion model arising in semiconductor devices," Journal of Computational Electronics, 7(2008)485-493.
6. S.Odanaka, Mathematical modeling and simulation of quantum hydrodynamics in semiconductors, Sugaku, 61(2009)83-93(in Japanese).Oda09.pdf
7. F.Huang, H.Li, A.Matsumura, S.Odanaka, Well-posedness and stability of quantum hydrodynamics for semiconductors in R^3, Ser.Contemp. Appl.Math.CAM, 15(2010)131-160.
8. S.Sho and S.Odanaka, "A quantum energy transport model for semiconductor device simulation," Journal of Computational Physics, 235(2013)486-496.ShO13.pdf
9. S.Sho, S.Odanaka, and A.Hiroki, "A Fermi-Dirac Statistics Based Quantum Energy Transport Model for High Mobility MOSFETs," Journal of Advanced Simulation in Science and Engineering, Vol.2(2015)153-170.