# Poisson Equation System for Electronic Devices in Equilibrium # # Solution Variables/Equations: # # psi: div (eps grad psi) + q*(holes - electrons + netdope) = 0 # # Interface Constraints: # # psi: continuous across all internal interfaces # # Boundary Conditions: # # psi: default_dirichlet at any ohmic contact # # Functions: # # electrons = ni * exp[( psi)/kTq] (psi2np_qf) # holes = ni * exp[(-psi)/kTq] (psi2np_qf) # # Notes: # # 1. Define netdope before using this system. # 2. box_div computes the negative divergence, -div. # 3. "potflux" computes the negative of the second term in the PDE. # 4. "psi2np_qf" computes the equilibrium electrons/holes. # 5. This system can be used to initialize an equilibrium solution of # more complex electronic device models, such as newton2 or qfermi. system name=poisson + sysvars=psi + nterm=4 + term0=box_div.lapflux(psi|psi)@{silicon,oxide,poly} + term1=nodal.potflux(electrons,holes,netdope|psi)@{silicon,poly} + term2=constraint.continuity(psi|psi)@{silicon/oxide,oxide/poly,silicon/poly} + term3=dirichlet.device_dirichlet(netdope|psi)@{silicon/anode,silicon/cathode,silicon/emitter,silicon/base,silicon/collector,silicon/back,silicon/source,silicon/drain,poly/gate,silicon/gate,oxide/gate} + tmpvars=electrons,holes + nfunc=1 + func0=psi2np_qf(psi|electrons,holes)@{silicon,poly}