Initial Guess

Procedures

Initial guess assumes charge neutrality

For Scharfetter-Gummel (Elec Hole DevPsi) solution

proc InitialGuess {Doping} { 
	sel z= {(Doping>0.0) 
		?  ( 0.025*log( (Doping+1.0e10) / 1.0e10))
		:  (-0.025*log(-(Doping+1.0e10) / 1.0e10))} name = DevPsi
	sel z=1.0e10*exp(DevPsi/0.025) name=Elec
	sel z=1.0e10*exp(-DevPsi/0.025) name=Hole
	sel z=0.0 name=Qfn
	sel z=0.0 name=Qfp
} 

For Quasi-Fermi Solution (Qfn Qfp DevPsi) solution

proc InitialGuessQF {Doping} {
	sel z= {(Doping>0.0) 
		?  ( 0.025*log( (Doping+1.0e10) / 1.0e10))
		:  (-0.025*log(-(Doping+1.0e10) / 1.0e10))} name = DevPsi store
	sel z=1.0e10*exp((DevPsi)/0.025) name=Elec store
	sel z=1.0e10*exp((-DevPsi)/0.025) name=Hole store
	sel z=0.0 name=Qfn store
	sel z=0.0 name=Qfp store
}

For Slotboom (SBn SBp DevPsi) solution

proc InitialGuessSB {Doping} {
	sel z= {(Doping>0.0) 
		?  ( 0.025*log( (Doping+1.0e10) / 1.0e10))
		:  (-0.025*log(-(Doping+1.0e10) / 1.0e10))} name = DevPsi store
	sel z=1.0e10*exp((DevPsi)/0.025) name=Elec 
	sel z=1.0e10*exp((-DevPsi)/0.025) name=Hole 
	sel z=1.0 name=SBn store
	sel z=1.0 name=SBp store
}

Poisson-Only Solve as Initial Guess First

Sometimes it is very hard to get convergence on your first try. For example, when Elec and Hole concentrations are very low. In this case, you can improve your initial guess by doing a Poisson-Only solve first (a DevPsi only solve). Then you can use your improved DevPsi solution as an initial guess to your full solve:

#===================================ponly===========================================#
# Solution Variables
solution add name=DevPsi pde   solve negative damp;#electrostatic potential (Device Psi)
solution add name=Elec   const solve val = "(Elec0)";# electron concentration /cm^3
solution add name=Hole   const solve val = "(Hole0)";# hole concentration /cm^3
pdbSetBoolean PoissonOnly 1;#this flag controls if statements in supporting procedures

# Bulk Equations
AddPoisson 	Oxide
AddPoisson	Silicon
BandTerms Oxide     Semiconductor;# sets Ec, Ev, nQFL, pQFL, Elec0, Hole0
BandTerms Silicon   Semiconductor
SetDoping 

#Poisson only - no cont. eqns - just add charge to Poisson in Mats that have charge
AddCharge Oxide   "-Elec+Hole"
AddCharge Silicon "-Elec+Hole" 

# Boundary Conditions
solution name=DevPsi continuous 

# Contact Equations
MetalContact top Aluminum
OhmicContact bot Silicon Ntype 

# Initial Conditions - bias the Contacts to 0 
contact name=top voltage supply=0.0 
contact name=bot voltage supply=0.0

#Initial guess
puts "You are Guessing"
sel z=-(4.8) name=DevPsi;#this value may be different depending on where your "0" is

# Poisson-Only Solution (Finally we SS Solve)
device init 

# Plots
PlotBands x.v=0 y.v=0
PlotConc ponly 
 
#end of Poisson only
pdbSetBoolean PoissonOnly 0;#turn off ponly flag
 	
#========================zerobias================================#
# Solution Variables - change all to pde
solution name=DevPsi    pde   solve negative damp;#electrostatic potential (Device Psi)
solution name=Elec	 pde   solve !negative;# electron concentration /cm^3
solution name=Hole	 pde   solve !negative;# hole concentration /cm^3 

# Bulk Equations
AddPoisson 	Oxide
AddPoisson	Silicon
BandTerms Oxide     Semiconductor;# sets Ec, Ev, nQFL, pQFL
BandTerms Silicon   Semiconductor
SetDoping 

AddSpecies	Hole		Oxide		MOB	1.0e-5	+
AddSpecies	Elec		Oxide		MOB	20.0	-
AddSpecies	Hole		Silicon		MOB	150.0	+
AddSpecies	Elec		Silicon		MOB	300.0	- 

# Boundary Conditions
solution name=DevPsi continuous 

# Contact Equations
MetalContact top Aluminum 
OhmicContact bot Silicon Ntype

#Initial Guess 
    #use DevPsi from ponly solve above
    sel z=Elec0 name=Elec;#is a fcn of DevPsi
    sel z=Hole0 name=Hole;#is a fcn of DevPsi
pdbSetDouble Math iterLimit 50;#give SS a chance
device

#PlotBands x.v=0 y.v=0
#PlotConc zerobias

struct outf=init.str

supporting procedures

• see Poisson's_Equation#A_More_General_Approach for AddPoisson and AddCharge
• see Defining_Your_Band_Terms#A_More_General_Method for BandTerms
• see Adding_Ionized_Dopants#support_procedures for SetDoping
• see General_Equation_Builder for AddSpecies
• see Device_Models#Contact_Physics for MetalContact and OhmicContact
• see Plotting_Examples_-_new_short_version for PlotBands and PlotConc