# 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}