A power metal-oxide-semiconductor field-effect transistor(MOSFET) with dielectric trench is investigated to enhance the reversed blocking capability. The dielectric trench with a low permittivity to reduce the electri...A power metal-oxide-semiconductor field-effect transistor(MOSFET) with dielectric trench is investigated to enhance the reversed blocking capability. The dielectric trench with a low permittivity to reduce the electric field at reversed blocking state has been studied. To analyze the electric field, the drift region is segmented into four regions, where the conformal mapping method based on Schwarz–Christoffel transformation has been applied. According to the analysis, the improvement in the electric field for using the low permittivity trench is mainly due to the two electric field peaks generated in the drift region around this dielectric trench. The analytical results of the electric field and the potential models are in good agreement with the simulation results.展开更多
Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the add...Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the additive Schwarz method for the biharmonic equation in this paper. We prove the convergence of the Schwarz methods from a new point of view, and provide detailed information about the convergence speeds and their dependence on the overlapping size of subdomains. The obtained results are independent of any unknown constant and discretization method, showing that the Schwarz alternating method converges twice as quickly as the additive Schwarz method.展开更多
In this paper we study the function , for z∈C. We derive a functional equation that relates G(z) and G(1−z) for all z∈C, and we prove: 1) that G and the Riemann zeta function ζ have exactly the same zeros in the cr...In this paper we study the function , for z∈C. We derive a functional equation that relates G(z) and G(1−z) for all z∈C, and we prove: 1) that G and the Riemann zeta function ζ have exactly the same zeros in the critical region D:= {z∈C:ℜz∈(0,1)};2) the Riemann hypothesis, i.e., that all of the zeros of G in D are located on the critical line := {z∈D:ℜz =1/2};and that 3) all the zeros of the Riemann zeta function located on the critical line are simple.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.61404110)the National Higher-education Institution General Research and Development Project,China(Grant No.2682014CX097)
文摘A power metal-oxide-semiconductor field-effect transistor(MOSFET) with dielectric trench is investigated to enhance the reversed blocking capability. The dielectric trench with a low permittivity to reduce the electric field at reversed blocking state has been studied. To analyze the electric field, the drift region is segmented into four regions, where the conformal mapping method based on Schwarz–Christoffel transformation has been applied. According to the analysis, the improvement in the electric field for using the low permittivity trench is mainly due to the two electric field peaks generated in the drift region around this dielectric trench. The analytical results of the electric field and the potential models are in good agreement with the simulation results.
基金supported by the National Natural Science Foundation of China (No. 10671154)the Na-tional Basic Research Program (No. 2005CB321703)the Science and Technology Foundation of Guizhou Province of China (No. [2008]2123)
文摘Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the additive Schwarz method for the biharmonic equation in this paper. We prove the convergence of the Schwarz methods from a new point of view, and provide detailed information about the convergence speeds and their dependence on the overlapping size of subdomains. The obtained results are independent of any unknown constant and discretization method, showing that the Schwarz alternating method converges twice as quickly as the additive Schwarz method.
文摘In this paper we study the function , for z∈C. We derive a functional equation that relates G(z) and G(1−z) for all z∈C, and we prove: 1) that G and the Riemann zeta function ζ have exactly the same zeros in the critical region D:= {z∈C:ℜz∈(0,1)};2) the Riemann hypothesis, i.e., that all of the zeros of G in D are located on the critical line := {z∈D:ℜz =1/2};and that 3) all the zeros of the Riemann zeta function located on the critical line are simple.
