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{ 2D_FINITE_POTENTIAL_WELL.PDE
Submitted by Ali Reza Ghaffari, 07/22/2016.
This script solves the Schrodinger equation for a two dimensional finite potential well.
This script finds energies and wave functions of a wire with rectangle cross section.
The wire is made up of GA As which is placed in a AlGalAs medum.
}
TITLE 'infinitely deep rectangular wires'
COORDINATES cartesian2
VARIABLES Phi {the wavefunction}
SELECT
modes=4
NGRID=13
ERRLIM=1e-3
painted { show colour-filled contours }
thermal_colors = on { red is minimum }
DEFINITIONS
mass{default value}
volt { in eV}
hbar=1.05457e-34
m0=9.11e-31
e0=1.6e-19
xx=200e-10
yy=200e-10
x1=50e-10
y1=50e-10
x2=150e-10
y2=150e-10
v0=.228
mass_shell=0.067*m0 {mhh}!0.067 {GaAs}
mass_core=0.1*m0! {Al0.5Ga0.5As}
N=integral(phi^2)
EQUATIONS
Phi: ((-1)* hbar^2/(2*mass*e0))*div(grad(Phi))+volt*Phi-LAMBDA*Phi =0
BOUNDARIES
Region 1
mass= mass_shell, volt=v0
start(0,0)
point value (phi)=0 line to (xx,0)
value (phi)=0 line to (xx,yy)
value (phi)=0 line to (0,yy)
to close
Region 2
mass= mass_core, volt=0
start(x1,y1)
line to (x2,y1) to (x2,y2) to (x1,y2)
to close
!MONITORS
! no monitors since problem solves so fast
PLOTS
CONTOUR(Phi^2/sqrt(N))
SUMMARY
REPORT(LAMBDA*1000) as "Energy Level (meV)" !in milielectron volt
END