Resistor (2D) - Quasi Fermi Method
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################################################################### # 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 / $q] set Emob 350.0 set Hmob 150.0 set small 1.0e-10 ################################################################### # Define the Grid # ################################################################### line x loc=0.0 spac=0.05 tag=Top line x loc=0.5 spac=0.1 line x loc=1.0 spac=0.1 tag=Bottom line y loc=-2.0 spac=0.05 tag=Lside line y loc=2.0 spac=0.05 tag=Rside mater add name=Silicon region Silicon xlo=Top xhi=Bottom ylo=Lside yhi=Rside init ################################################################### # Contacts and Doping # ################################################################### contact name=GND Silicon xlo=-0.05 xhi=0.05 ylo=-1.25 yhi=-1.00 add contact name=VSS Silicon xlo=-0.05 xhi=0.05 ylo=1.00 yhi=1.25 add window col=2 row=1 plot2d grid graph= Grid plot2d contact=GND graph= Grid plot2d contact=VSS graph= Grid sel z=1.0e20 name=Nd sel z=1.0e17 name=Na sel z=(Nd-Na) name=Doping ################################################################### # Equations # ################################################################### # Bulk Equations DevicePackage solution name=Potential nosolve solution add name=DevPsi solve negative damp solution add name=Qfn solve negative solution add name=Qfp solve negative solution add name=Elec const solve val= "1.0e10*exp((DevPsi-Qfn)/0.025)" solution add name=Hole const solve val= "1.0e10*exp((Qfp-DevPsi)/0.025)" set eqnP "$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 $Contact Equation "1.619e-19 * (Flux_Hole - Flux_Elec)" } ohmic.contact VSS ohmic.contact GND #Bias contacts contact name=VSS voltage supply=0.0 contact name=GND voltage supply=0.0 ################################################################### # Solve # ################################################################### #Initial Guess sel z= {(Doping>0.0) ? (0.025*log( (Doping + 1e-10) / 1.1e10)) : (-0.025*log(-(Doping + 1e-10) / 1.1e10))} name = DevPsi sel z=$ni*exp(DevPsi/$Vt) name=Elec sel z=$ni*exp(-DevPsi/$Vt) name=Hole #First DC solve at Equilibrium (0V) device puts "Electron Flux [contact name=VSS sol=Qfn flux]" puts "Hole Flux [contact name=VSS sol=Qfp flux]" #initialize an array, bias (Vb) and counter (i), and create and new graph window array set curr {} set i 1 #Ramp from 0.0-1.2V and Plot for {set bias 0.0} {$bias < 1.2} {set bias [expr $bias+0.05]} { contact name=VSS supply=$bias device init set curr($i) [expr ([contact name=VSS sol=Qfn flux] - [contact name=VSS sol=Qfp flux])] chart graph=IV curve=IV xval=$bias yval=$curr($i) incr i }