TITLE 'paticals in two dimensions'
 
select
modes=1
spectral_colors errlim=1e-5
 
variables
Phi,V,D
 
definitions
p0=8.85e-12     {the permittivity constat of free space}
pr=11.7            {relative permittivity}
 
mt=1
m0=9.109e-31
h=1.055e-34
 
q=1.602e-19      {one charge}
k=1.38e-23       {the Boltzmann constant}
T=300               {temperature}
md=1
Ef=1.602e-20      {fermi level}
 
Lx=3e-9
Ly=3e-9
 
equations
Phi:(h^2/(2*m0*mt))*div(grad(Phi))+V*Phi= Lambda*Phi
V: div(grad(V))=-D/(p0*pr)
D: D=-q*abs(Phi^2)*k*T*log10(1+exp((Ef-lambda)/(k*T)))*(md*m0/(PI*h^2))
 
boundaries
region 'box'  START(0,0)
value(V)=0
line to(Lx,0) to (Lx,Ly) to (0,Ly) to finish
 
value(Phi)=0  LINE TO (Lx,0)
value(Phi)=0  LINE TO (Lx,Ly)
value(Phi)=0  LINE TO (0,Ly)
value(Phi)=0  LINE TO FINISH
 
plots
contour(Phi)
surface(abs(Phi^2))
surface(D)
surface(V)
 
SUMMARY
      REPORT LAMBDA {report the list of eigen-value}
END