Iterative scheme for MFIS simulation does not converge when applied voltage is high

[prkkumar]

For problems containing ferroelectric, dielectric, and semiconductor layers we compute self-consistent rho and phi using an iterative scheme to achieve true first or second order accuracy. Without this scheme rho computation is done using phi at the previous time step which reduces the overall order of accuracy.

When the Dirichlet BC for Poisson solve is set to Phi_BC_lo = 0.0 and Phi_BC_hi = 1.2 to get an applied voltage of 1.2V across the MFIS stack, the iterative scheme does not converge. The error oscillates between two values rather than going down below a user specified tolerance which is set to be 1.0e-5.

The issue can be reproduced using the following script.

n_cell = 64 64 32

max_grid_size = 32

prob_type = 2

P_BC_flag_lo = 0 # Polarization BC at FE-DE interface
P_BC_flag_hi = 1 # Polarization BC at FE-Metal interface

Phi_Bc_lo = 0.0  # Dirichlet BC for Poisson solve at bottom metal contact
Phi_Bc_hi = 1.2   # Dirichlet BC for Poisson solve at top metal contact

TimeIntegratorOrder = 1

nsteps = 1
plot_int = 1

dt = 2.0e-13

prob_lo = -16.e-9 -16.e-9 0.e-9
prob_hi =  16.e-9  16.e-9 16.e-9

epsilon_0 = 8.85e-12
epsilonX_fe = 24.0
epsilonZ_fe = 24.0
epsilon_de = 3.9
epsilon_si = 11.7
alpha = -2.5e9
beta = 6.0e10
gamma = 1.5e11
BigGamma = 100
g11 = 1.0e-9
g44 = 1.0e-9

SC_lo = 0.0
SC_hi = 10.0e-9
DE_lo = 10.0e-9
DE_hi = 11.0e-9
FE_lo = 11.0e-9
FE_hi = 16.0e-9

lambda = 3.0e-9