#--------------------
# Create 1D structure
#--------------------
#Grid
line x loc=0.0 spac=0.1 tag=Top
line x loc=0.5 spac=0.01
line x loc=1.0 spac=0.1 tag=Bottom
mater add name=Silicon
region Silicon xlo=Top xhi=Bottom
init
#Contacts
contact name=GND Silicon xlo=-0.1 xhi=0.1 add
contact name=VSS Silicon xlo=0.9 xhi=1.1 add
#-----------------------------
# Declare solution variables
#-----------------------------
DevicePackage
solution name=Potential nosolve
solution add name=DevPsi solve negative damp
solution add name=Qfn solve negative
solution add name=Qfp solve negative
solution add name=Elec const solve val= "1.0e10*exp((DevPsi-Qfn)/0.025)"
solution add name=Hole const solve val= "1.0e10*exp((Qfp-DevPsi)/0.025)"
#-----------------------------
# Define constants
#-----------------------------
set T 300.0
set k 1.38066e-23
set q 1.619e-19
set Vt [expr {$k*$T/$q}]
set ni 1.1e10
set esi [expr 11.8 * 8.85418e-14]
set eps [expr $esi / $q]
set Emob 350.0
set Hmob 150.0
set small 1.0e-10
#-----------------------------
# Ionized dopant profile
#-----------------------------
sel z=1.0e20 name=Nd
sel z=1.0e17 name=Na
sel z=(Nd-Na) name=Doping
#-----------------------------
# Bulk Equations
#-----------------------------
set eqnP "$eps * grad(DevPsi) + Doping - Elec + Hole"
set eqnQfn "ddt(Elec) - $Emob * Elec * grad(Qfn)"
set eqnQfp "ddt(Hole) - $Hmob * Hole * grad(Qfp)"
pdbSetString Silicon DevPsi Equation $eqnP
pdbSetString Silicon Qfn Equation $eqnQfn
pdbSetString Silicon Qfp Equation $eqnQfp
pdbSetDouble Silicon DevPsi DampValue $Vt
pdbSetDouble Silicon DevPsi Abs.Error 1.0e-9
pdbSetDouble Silicon Elec Abs.Error 1.0e-5
pdbSetDouble Silicon Hole Abs.Error 1.0e-5
#-----------------------------
# Contact Equations
#-----------------------------
proc ohmic.contact {Contact} {
set vt 0.02558357
set ni 1.1e10
pdbSetBoolean $Contact Qfn Flux 1
pdbSetBoolean $Contact Qfp Flux 1
pdbSetBoolean $Contact DevPsi Flux 1
pdbSetBoolean $Contact Qfn Fixed 1
pdbSetBoolean $Contact Qfp Fixed 1
pdbSetBoolean $Contact DevPsi Fixed 1
pdbSetDouble $Contact Qfn Flux.Scale 1.619e-19
pdbSetDouble $Contact Qfp Flux.Scale 1.619e-19
pdbSetString $Contact Qfn Equation "Qfn-$Contact"
pdbSetString $Contact Qfp Equation "Qfp-$Contact"
pdbSetString $Contact DevPsi Equation "Doping - $ni*exp((DevPsi-Qfn)/$vt) + $ni*exp((Qfp-DevPsi)/$vt)"
pdbSetString $Contact Equation "1.619e-19 * (Flux_Hole - Flux_Elec)"
}
ohmic.contact VSS
ohmic.contact GND
#-----------------------------
# Initial Conditions
#-----------------------------
#Bias contacts
contact name=VSS voltage supply=0.0
contact name=GND voltage supply=0.0
#Initial Guess
sel z= {
(Doping>0.0)
? (0.025*log( (Doping + 1e-10) / 1.1e10))
: (-0.025*log(-(Doping + 1e-10) / 1.1e10))} name = DevPsi
sel z=$ni*exp(DevPsi/$Vt) name=Elec
sel z=$ni*exp(-DevPsi/$Vt) name=Hole
#-----------------------------------
# 1st DC Solve at Equilibrium (0V)
#-----------------------------------
device
puts "Electron Flux [contact name=VSS sol=Qfn flux]"
puts "Hole Flux [contact name=VSS sol=Qfp flux]"
window row=1 col=3
#Plot the equilibrium concentration profiles
foreach var {Doping Elec Hole} {
sel z=log10(abs($var+1.0))
plot1d graph=Doping
}
#--------------------------------------
# Ramp the DC Bias to make I-V plot
#--------------------------------------
#initialize an array, bias (Vb) and counter (i), and create and new graph window
array set curr {}
set i 1
#Ramp from 0.0-1.2V and Plot
for {set bias 0.0} {$bias < 1.2} {set bias [expr $bias+0.05]} {
set Vbias($i) $bias
incr i
contact name=VSS supply=$bias
device init
set curr($i) [expr ([contact name=VSS sol=Qfn flux] - [contact name=VSS sol=Qfp flux])]
sel z=log10(abs(Hole)+1.0)
plot1d graph=HoleConc
chart graph=IV curve=IV xval=$bias yval=$curr($i)
}
set winRefresh 1
if {$winRefresh} {
plot1d graph=Doping clear
plot1d graph=HoleConc clear
chart graph=IV curve=IV clear
}