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??座右銘：行百里者，半于九十。

??????本文目錄如下：??????

目錄

??1 概述

??2 運(yùn)行結(jié)果

??3?參考文獻(xiàn)

??4 Matlab代碼及文獻(xiàn)

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??1 概述

文獻(xiàn)來源：

改進(jìn)了著名的Scharfetter-Gummmel（SG）方案，用于半導(dǎo)體和氣體放電等離子體的對(duì)流主導(dǎo)問題。考慮了一維對(duì)流-擴(kuò)散方程。結(jié)果表明，如果兩個(gè)相鄰節(jié)點(diǎn)之間的電位降遠(yuǎn)小于電子溫度，則原始SG方案是準(zhǔn)確的。為了滿足此條件，在相鄰節(jié)點(diǎn)之間插入了一對(duì)附加節(jié)點(diǎn)。這些“虛擬”節(jié)點(diǎn)之間的距離可以選擇得足夠小，以高精度獲得細(xì)胞結(jié)合處的通量。虛擬節(jié)點(diǎn)上的數(shù)字密度是通過插值法找到的。測(cè)試表明，該方案的精度與FCT技術(shù)相當(dāng)，但相比之下，它不會(huì)對(duì)快速變化的功能產(chǎn)生“樓梯”干擾。

原文摘要：

A well-known Scharfetter-Gummel (SG) scheme for convection-dominated problems of semiconductor and gas discharge plasmas is improved. A one-dimensional convection-diffusion equation is considered. It is shown that the original SG scheme is accurate if the potential drop between two adjacent nodes is much less than the electron temperature. To satisfy this condition a pair of additional nodes between adjacent nodes are inserted. The distance between these "virtual" nodes can be choosen small enough to obtain flux at the cell bound with the high accuracy. The number densities at virtual nodes are found by interpolation. Tests have shown that the accuracy of this scheme is comparable to the FCT technique, but in contrast it does not produce a "staircase" disturbance on rapidly changing functions.

??2 運(yùn)行結(jié)果

【漂移-擴(kuò)散通量重建 FV 方案】用于半導(dǎo)體和氣體放電模擬的電子傳輸?shù)母鼫?zhǔn)確的 Sharfetter-Gummel 算法(Matlab代碼實(shí)現(xiàn)）_嗶哩嗶哩_bilibili

?部分代碼：

% Constants from original paper
mue = 1.0; De = 1.0; A = 1.0e+4; epsilon = 0.01;
% Linear field
E = A*x;

h(1:N-1) = x(2:N)-x(1:(N-1)); h(N) = h(N-1); h(N+1) = h(N);

for k=1:(N-1)
? ? % Distance between virtual nodes h_v (see (21))
? ? h_v = sqrt(2.0*epsilon*De*h(k)/mue/abs(E(k+1)-E(k)));
? ? % If h_v>=h then use SG scheme
? ? if (h_v >= h(k)) ? ? ? ?
? ? ? ? if 0.5*abs(E(k+1)+E(k))> eps
? ? ? ? ? ? alpha = mue*h(k)/De*0.5*(E(k+1)+E(k));
? ? ? ? ? ? I0 = ( exp(alpha) - 1.0 )/alpha;
? ? ? ? ? ? j(k+1) = De/h(k)*(u(k) - exp(alpha)*u(k+1))/I0;
? ? ? ? else

??3?參考文獻(xiàn)

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??4 Matlab代碼及文獻(xiàn)

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