Asymptotic expansions of the solutions of the Cauchy problem for nonlinear parabolic equations

Let $u$ be a solution of the Cauchy problem for the nonlinear parabolic equation $$\partial_t u=\Delta u+F(x,t,u,\nabla u) \quad in \quad{\bf R}^N\times(0,\infty), \quad u(x,0)=\varphi(x)\quad in \quad{\bf R}^N,$$ and assume that the solution $u$ behaves like the Gauss kernel as $t\to\infty$. In this paper, under suitable assumptions of the reaction term $F$ and the initial function $\varphi$, we establish the method of obtaining higher order asymptotic expansions of the solution $u$ as $t\to\infty$. This paper is a generalization of our previous paper, and our arguments are applicable to the large class of nonlinear parabolic equations

Metal Inserted Poly-Si with High Temperature Annealing for Achieving EOT of 0.62nm in La-silicate MOSFET

Abstract-This paper reports device process approach for further EOT scaling with small interface state density based on controlling La-silicate/Si interface. The interface state density of 1.6 x 10 11 cm -2 eV -1 can be achieved by annealing at 800 o C for 30min in forming gas while significant increase in EOT has been also observed. EOT increase caused by high temperature annealing has been drastically inhibited with MIPS stacks accompanied by high quality interface. The effective electron mobility of 155 cm 2 /Vsec at 1MV/cm with an EOT of 0.62 nm has been obtained in direct contact La-silicate/Si structure by combination of MIPS stacks with high temperature annealing

Advantage of TiN Schottky Gate over Conventional Ni for Improved Electrical Characteristics in

Abstract-Metal induced effects on electrical characteristics in AlGaN/GaN Schottky HEMT are reported. Focus is given to the collapse of drain current attributed to Schottky metal. Of particular interest for discussion is that TiN gate can suppresses the collapse of drain current compared with conventional Ni gate. Nitrogen concentrations in TiN gate are found to be correlated to the current collapse, indicating that the nitrogen vacancy is responsible for the traps in AlGaN/GaN HEMT. The reduction in a concentration gradient of nitrogen should be accomplished for preventing the formation of the traps. Because of the metal dependent collapse of the drain current, the traps are considered to be formed under the gate edge on the drain side in AlGaN layer