在一些时候,我一个式子,既有x限制,也有y限制,我要怎么写。
代码如下
W = 30*10^-4;(*耗尽层宽度(um)*10^-4->cm*)
L = 3*10^-4;
Lk = 0.75*10^-4;
Nd = 5 10^15;
q = 1.6/10^19;(*电荷q:C*)
\[Epsilon]0 = 8.85*10^-14;(*真空介电常数:10^-12(F/m)*10^-2->(F/cm)*)
\[Epsilon]1 = 11.9*\[Epsilon]0;(*硅介电常数:F/cm*)
\[Epsilon]2 = 400*\[Epsilon]0;(*硅介电常数:F/cm*)
\[CapitalDelta]y = 1*10^-4;(*cm*)
M = W/\[CapitalDelta]y;
yn = m*\[CapitalDelta]y;
Kn = (n Pi)/\[CapitalDelta]y;
VR = 600;
Subscript[L, m] = L/2 - (W - (2 m - 1) \[CapitalDelta]y)/(2 W) Lk;
Nd1 = (1 - (2 W - (2 m - 1) \[CapitalDelta]y)/(2 W)*Lk/L) Nd;
Vd = ((\[CapitalDelta]y)^2*q*Nd1)/(2*\[Epsilon]1);
\[CapitalUpsilon] = Vd*4/(n*Pi)^3*((-1)^n - 1);
En = \[CapitalUpsilon]/(
Cosh[Kn*Subscript[L,
m]]*(1 - \[Epsilon]1/\[Epsilon]2*Tanh[Kn*Subscript[L, m]]*
Coth[Kn*(L - Subscript[L, m])]));
Dn = -\[CapitalUpsilon]/(
Cosh[Kn*(L - Subscript[L, m])]*(1 - \[Epsilon]2/\[Epsilon]1*
Tanh[Kn*(L - Subscript[L, m])]*Coth[Kn*Subscript[L, m]]));
Vu := -Vd*((y - yn)^2/(\[CapitalDelta]y)^2) +
Vd*(y - yn)/\[CapitalDelta]y + \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(n = 1\), \(200\)]\((En*Cosh[Kn*x]*
Sin[
\*FractionBox[\(\((n*Pi)\)*\((y -
yn)\)\), \(\[CapitalDelta]y\)]])\)\) /; x <= Subscript[L, m]
Vu := \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(n = 1\), \(200\)]\(Dn*
Cosh[Kn*\((x - L)\)]*Sin[Kn*\((y - yn)\)]\)\) /;
x > Subscript[L, m]
Vu1 := VR*y/W + \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(m = 0\), \(M - 1\)]Vu\) /;
m*\[CapitalDelta]y <= y < (m + 1)*\[CapitalDelta]y
Plot3D[Vu1, {x, 0, L}, {y, 0, W}]
就是说,其中Vu1是Vu的函数,所以它不止有x限制,还有y的限制,可是y限制只是随累加变量而变,所以我不知道怎么写,求助
代码如下
W = 30*10^-4;(*耗尽层宽度(um)*10^-4->cm*)
L = 3*10^-4;
Lk = 0.75*10^-4;
Nd = 5 10^15;
q = 1.6/10^19;(*电荷q:C*)
\[Epsilon]0 = 8.85*10^-14;(*真空介电常数:10^-12(F/m)*10^-2->(F/cm)*)
\[Epsilon]1 = 11.9*\[Epsilon]0;(*硅介电常数:F/cm*)
\[Epsilon]2 = 400*\[Epsilon]0;(*硅介电常数:F/cm*)
\[CapitalDelta]y = 1*10^-4;(*cm*)
M = W/\[CapitalDelta]y;
yn = m*\[CapitalDelta]y;
Kn = (n Pi)/\[CapitalDelta]y;
VR = 600;
Subscript[L, m] = L/2 - (W - (2 m - 1) \[CapitalDelta]y)/(2 W) Lk;
Nd1 = (1 - (2 W - (2 m - 1) \[CapitalDelta]y)/(2 W)*Lk/L) Nd;
Vd = ((\[CapitalDelta]y)^2*q*Nd1)/(2*\[Epsilon]1);
\[CapitalUpsilon] = Vd*4/(n*Pi)^3*((-1)^n - 1);
En = \[CapitalUpsilon]/(
Cosh[Kn*Subscript[L,
m]]*(1 - \[Epsilon]1/\[Epsilon]2*Tanh[Kn*Subscript[L, m]]*
Coth[Kn*(L - Subscript[L, m])]));
Dn = -\[CapitalUpsilon]/(
Cosh[Kn*(L - Subscript[L, m])]*(1 - \[Epsilon]2/\[Epsilon]1*
Tanh[Kn*(L - Subscript[L, m])]*Coth[Kn*Subscript[L, m]]));
Vu := -Vd*((y - yn)^2/(\[CapitalDelta]y)^2) +
Vd*(y - yn)/\[CapitalDelta]y + \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(n = 1\), \(200\)]\((En*Cosh[Kn*x]*
Sin[
\*FractionBox[\(\((n*Pi)\)*\((y -
yn)\)\), \(\[CapitalDelta]y\)]])\)\) /; x <= Subscript[L, m]
Vu := \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(n = 1\), \(200\)]\(Dn*
Cosh[Kn*\((x - L)\)]*Sin[Kn*\((y - yn)\)]\)\) /;
x > Subscript[L, m]
Vu1 := VR*y/W + \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(m = 0\), \(M - 1\)]Vu\) /;
m*\[CapitalDelta]y <= y < (m + 1)*\[CapitalDelta]y
Plot3D[Vu1, {x, 0, L}, {y, 0, W}]
就是说,其中Vu1是Vu的函数,所以它不止有x限制,还有y的限制,可是y限制只是随累加变量而变,所以我不知道怎么写,求助

