Diff of QDD Model - OdanakaHP

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*Numerical Analysis of QDD Equation [#h3d44c35]
The quantum hydrodynamic(QHD) model, which is available for modeling of carrier transport in semiconductors at the room temperature, is derived from a Chapman-Enskog expansion of the Wigner-Boltzmann equation adding a collision term. The quantum drift-diffusion(QDD) and quantum energy transport(QET) models are further derived by the diffusion scaling of the OHD models and hence the QDD model is viewed as one of the hierarchy of QHD models as a generalization of the classical drift-diffusion(DD) model. The numerical methods for the QDD and QET equations are a major concern to realize advanced device models in [[TCAD]](Technology Computer-Aided Design).~
We develop numerical schemes and iterative solution methods, studying numerical approximation and existence of solutions to semiconductor transport equations and numerically motivated solution maps of the equation system. The numerical methods developed in our work include high-accuracy nonlinear schemes, a high-resolution method for quantum confinement transport, a positivity-preserving iterative method, and adaptive time discretization for a transient QDD model. These numerical schemes are also applied to develop numerical methods for quantum energy transport(QET)models.
**High-Accuracy Nonlinear Scheme [#i33ce880]
**High-Accuracy Conservative Scheme [#i33ce880]
+S.Odanaka, "Multidimensional discretization of the stationary quantum drift-diffusion model for ultrasmall MOSFET structures," IEEE Trans., on CAD of ICAS, vol.23, pp.837-842, 2004. &ref(Oda04.pdf);
+S.Odanaka, "A high-resolution method for quantum confinement transport simulation in MOSFETs," IEEE Trans., on CAD of ICAS, vol.26, pp.80-85, 2007.&ref(Oda07.pdf);

**High-Resolution Method [#ac1b5456]
+S.Odanaka, "A high-resolution method for quantum confinement transport simulation in MOSFETs," IEEE Trans., on CAD of ICAS, vol.26, pp.80-85, 2007.&ref(Oda07.pdf);
**Existence and Numerical Approximation of Solutions [#h3872a46]
+S.Odanaka, "A numerical scheme for quantum hydrodynamics in a semiconductor," Surikaisekikenkyusho Kokyuroku, No.1495(2006)51-59.&ref(Oda06.pdf);

**Positivity-Preserving Iterative Method [#fd459350]
+S.Odanaka, "Multidimensional discretization of the stationary quantum drift-diffusion model for ultrasmall MOSFET structures," IEEE Trans., on CAD of ICAS, vol.23, pp.837-842, 2004.&ref(Oda04.pdf);
//+S.Odanaka, "A numerical scheme for quantum hydrodynamics in a semiconductor," Surikaisekikenkyusho Kokyuroku, No.1495(2006)51-59.&ref(Oda06.pdf);
**Adaptive Time Discretization [#eb083da7]
+T.Shimada and S.Odanaka, "Adaptive time discretization for a transient quantum drift-diffusion model," Proc. of SISPAD Vol.12, Edited by T.Grasser and S.Selberherr, pp.337-340, 2007.&ref(SO07.pdf);
+T.Shimada and S.Odanaka, "A numerical method for a transient quantum drift-diffusion model arising in semiconductor devices," Journal of Computational Electronics, vol.7, no.4, pp.485-493, 2008.&ref(SO08.pdf);
**Quantum Energy Transport Model [#rfa06d55]
+S.Sho and S.Odanaka, "Numerical methods for a quantum energy transport model 
arising in scaled MOSFETs," Proc. of SISPAD, pp.303-306, 2011.&ref(ShO11.pdf);
+S.Sho and S.Odanaka, "A quantum energy transport model for semiconductor device simulation," Journal of Computational Physics, vol.235, pp.486-496, 2013.&ref(ShO13.pdf);
+S.Sho, S.Odanaka and A.Hiroki,“Analysis of carrier transport in Si and Ge MOSFETs including quantum confinement and hot carrier effects”, Proc. of 16th International Workshop on Computational Electronics, pp.160-161, Nara, 2013.