Resistor (3D) - Quasi Fermi Method
Jump to navigation
Jump to search
################################################################### # 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 / $q] set Emob 350.0 set Hmob 150.0 set small 1.0e-10 ################################################################### # Define the Grid # ################################################################### set MeshSpac 0.10 set Side 2.0 line x loc=0.0 spac=$MeshSpac tag=Top line x loc=$Side spac=$MeshSpac tag=Bottom line y loc=0.0 spac=$MeshSpac tag=Lside line y loc=$Side spac=$MeshSpac tag=Rside line z loc=0.0 spac=$MeshSpac tag=Zlo line z loc=1.0 spac=$MeshSpac*2 tag=Zhi mater add name=Silicon region Silicon xlo=Top xhi=Bottom ylo=Lside yhi=Rside zlo=Zlo zhi=Zhi init ################################################################### # Contacts and Doping # ################################################################### # place the contacts on the corners of the square set Contact 0.2 set buf [ expr $MeshSpac/2] contact name=GND Silicon xlo=$MeshSpac-$buf xhi=$Contact+$buf ylo=$MeshSpac-$buf yhi=$Contact+$buf zlo=-$buf zhi=$buf add contact name=VSS Silicon xlo=$Side-$Contact-$buf xhi=$Side+$buf-$MeshSpac ylo=$Side-$Contact-$buf yhi=$Side+$buf-$MeshSpac zlo=-$buf zhi=$buf add sel z=1.0e20 name=Nd sel z=1.0e17 name=Na sel z=(Nd-Na) name=Doping #Plot the doping concentration sel z=log10(abs(Doping+1.0)) window xwin col=2 plot2d zvalue=0.2 levels=05 graph= Doping\ Concentration\ at\ z=0.2 ################################################################### # Equations # ################################################################### solution add name=DevPsi pde solve negative damp solution add name=Elec pde solve !negative solution add name=Hole pde solve !negative solution add name=Circuit solve negative damp circuit const val=0.0 set eqnP "$eps * grad( DevPsi ) + Doping - Elec + Hole" set eqnE "ddt(Elec) - ($Emob) * $Vt * sgrad(Elec, DevPsi/$Vt)" set eqnH "ddt(Hole) - ($Hmob) * $Vt * sgrad(Hole, -DevPsi/$Vt)" pdbSetString Silicon DevPsi Equation $eqnP pdbSetString Silicon Elec Equation $eqnE pdbSetString Silicon Hole Equation $eqnH 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 OhmicContact {Contact} { global Vt ni pdbSetBoolean $Contact Elec Flux 1 pdbSetBoolean $Contact Hole Flux 1 pdbSetBoolean $Contact DevPsi Flux 1 pdbSetBoolean $Contact Elec Fixed 1 pdbSetBoolean $Contact Hole Fixed 1 pdbSetBoolean $Contact DevPsi Fixed 1 pdbSetDouble $Contact Elec Flux.Scale 1.619e-19 pdbSetDouble $Contact Hole Flux.Scale 1.619e-19 pdbSetString $Contact DevPsi Equation "Nd - Na - Elec + Hole" pdbSetString $Contact Elec Equation "DevPsi - $Vt*log((Elec)/$ni) -$Contact" pdbSetString $Contact Hole Equation "DevPsi + $Vt*log((Hole)/$ni) -$Contact" } OhmicContact VSS OhmicContact GND #Bias contacts contact name=VSS voltage supply=0.0 contact name=GND voltage supply=0.0 ################################################################### # Solve # ################################################################### #Initial Guess sel z= {(Doping>0.0) ? (0.025*log( (Doping + 1e-10) / 1.1e10)) : (-0.025*log(-(Doping + 1e-10) / 1.1e10))} name = DevPsi sel z=$ni*exp(DevPsi/$Vt) name=Elec sel z=$ni*exp(-DevPsi/$Vt) name=Hole #First DC solve at Equilibrium (0V) device puts "Electron Flux [contact name=VSS sol=Elec flux]" puts "Hole Flux [contact name=VSS sol=Hole flux]" #initialize an array, bias (Vb) and counter (i), and create and new graph window array set curr {} set i 1 #Ramp from 0.0-1.2V and Plot for {set bias 0.0} {$bias < 1.2} {set bias [expr $bias+0.05]} { contact name=VSS supply=$bias device init set curr($i) [expr ([contact name=VSS sol=Elec flux] - [contact name=VSS sol=Hole flux])] chart graph=IV curve=IV xval=$bias yval=$curr($i) incr i }