PSC device on 2D domain (Tensor grid).
Simulating a three layer PSC device PCBM | MAPI | Pedot with mobile ions. The simulations are performed in 2D on a tensor grid, out of equilibrium and with abrupt interfaces.
module Ex201_PSC_tensorGrid
using ChargeTransport
using ExtendableGrids
using PyPlotyou can also use other Plotters, if you add them to the example file
function main(;n = 3, Plotter = PyPlot, plotting = false, verbose = false, test = false,
parameter_file = "../parameter_files/Params_PSC_PCBM_MAPI_Pedot.jl", # choose the parameter file)
)
################################################################################
if test == false
println("Define physical parameters and model")
end
################################################################################
include(parameter_file) # include the parameter file we specified
bregionNoFlux = 3
height = 5.00e-6 * cm
# contact voltage
voltageAcceptor = 1.2 * V
# primary data for I-V scan protocol
scanrate = 0.4 * V/s
number_tsteps = 31
endVoltage = voltageAcceptor # bias goes until the given voltage at acceptor boundary
# with fixed timestep sizes we can calculate the times a priori
tend = endVoltage/scanrate
tvalues = range(0, stop = tend, length = number_tsteps)
if test == false
println("*** done\n")
end
################################################################################
if test == false
println("Set up grid and regions")
end
################################################################################
δ = 4*n # the larger, the finer the mesh
t = 0.5*(cm)/δ # tolerance for geomspace and glue (with factor 10)
k = 1.5 # the closer to 1, the closer to the boundary geomspace
coord_n_u = collect(range(0.0, h_ndoping/2, step=h_ndoping/(0.6*δ)))
coord_n_g = geomspace(h_ndoping/2, h_ndoping,
h_ndoping/(0.7*δ), h_ndoping/(1.1*δ),
tol=t)
coord_i_g1 = geomspace(h_ndoping, h_ndoping+h_intrinsic/k,
h_intrinsic/(5.1*δ), h_intrinsic/(1.0*δ),
tol=t)
coord_i_g2 = geomspace(h_ndoping+h_intrinsic/k, h_ndoping+h_intrinsic,
h_intrinsic/(1.0*δ), h_intrinsic/(5.1*δ),
tol=t)
coord_p_g = geomspace(h_ndoping+h_intrinsic, h_ndoping+h_intrinsic+h_pdoping/2,
h_pdoping/(1.3*δ), h_pdoping/(0.3*δ),
tol=t)
coord_p_u = collect(range(h_ndoping+h_intrinsic+h_pdoping/2, h_ndoping+h_intrinsic+h_pdoping, step=h_pdoping/(0.6*δ)))
coord = glue(coord_n_u, coord_n_g, tol=10*t)
coord = glue(coord, coord_i_g1, tol=10*t)
coord = glue(coord, coord_i_g2, tol=10*t)
coord = glue(coord, coord_p_g, tol=10*t)
coord_length = glue(coord, coord_p_u, tol=10*t)
height_L = geomspace(0.0, height/2, height/(0.4*δ), height/(0.4*δ))
height_R = geomspace(height/2, height, height/(0.4*δ), height/(0.4*δ))
coord_height = glue(height_L, height_R, tol = 10*t)
grid = simplexgrid(coord_length, coord_height)
# specify inner regions
cellmask!(grid, [0.0, 0.0], [h_ndoping, height], regionDonor, tol = 1.0e-18)
cellmask!(grid, [h_pdoping, 0.0], [h_ndoping + h_intrinsic, height], regionIntrinsic, tol = 1.0e-18)
cellmask!(grid, [h_ndoping + h_intrinsic, 0.0], [h_total, height], regionAcceptor, tol = 1.0e-18)
# specifiy outer regions
# metal interfaces
bfacemask!(grid, [0.0, 0.0], [0.0, height], bregionDonor) # BregionNumber = 1
bfacemask!(grid, [h_total, 0.0], [h_total, height], bregionAcceptor) # BregionNumber = 2
# no flux interfaces [xmin, ymin], [xmax, ymax]
bfacemask!(grid, [0.0, 0.0], [h_total, 0.0], bregionNoFlux) # BregionNumber = 3
bfacemask!(grid, [0.0, height], [h_total, height], bregionNoFlux) # BregionNumber = 3
if plotting
gridplot(grid, Plotter= Plotter, resolution=(600,400),linewidth=0.5, legend=:lt)
Plotter.title("Grid")
end
if test == false
println("*** done\n")
end
################################################################################
if test == false
println("Define System and fill in information about model")
end
################################################################################
# Initialize Data instance and fill in data
data = Data(grid, numberOfCarriers)
# Possible choices: Stationary, Transient
data.modelType = Transient
# Possible choices: Boltzmann, FermiDiracOneHalfBednarczyk, FermiDiracOneHalfTeSCA,
# FermiDiracMinusOne, Blakemore
data.F = [FermiDiracOneHalfTeSCA, FermiDiracOneHalfTeSCA, FermiDiracMinusOne]
data.bulkRecombination = set_bulk_recombination(;iphin = iphin, iphip = iphip,
bulk_recomb_Auger = false,
bulk_recomb_radiative = true,
bulk_recomb_SRH = true)
# Possible choices: OhmicContact, SchottkyContact (outer boundary) and InterfaceNone,
# InterfaceRecombination (inner boundary).
data.boundaryType[bregionAcceptor] = OhmicContact
data.boundaryType[bregionDonor] = OhmicContact
# Present ionic vacancies in perovskite layer
enable_ionic_carrier!(data, ionicCarrier = iphia, regions = [regionIntrinsic])
# Choose flux discretization scheme: ScharfetterGummel, ScharfetterGummelGraded,
# ExcessChemicalPotential, ExcessChemicalPotentialGraded, DiffusionEnhanced, GeneralizedSG
data.fluxApproximation .= ExcessChemicalPotential
if test == false
println("*** done\n")
end
################################################################################
if test == false
println("Define Params and fill in physical parameters")
end
################################################################################
params = Params(grid, numberOfCarriers)
params.temperature = T
params.UT = (kB * params.temperature) / q
params.chargeNumbers[iphin] = zn
params.chargeNumbers[iphip] = zp
params.chargeNumbers[iphia] = za
for ireg in 1:numberOfRegions # region data
params.dielectricConstant[ireg] = ε[ireg] * ε0
# effective DOS, band edge energy and mobilities
params.densityOfStates[iphin, ireg] = Nn[ireg]
params.densityOfStates[iphip, ireg] = Np[ireg]
params.densityOfStates[iphia, ireg] = Na[ireg]
params.bandEdgeEnergy[iphin, ireg] = En[ireg]
params.bandEdgeEnergy[iphip, ireg] = Ep[ireg]
params.bandEdgeEnergy[iphia, ireg] = Ea[ireg]
params.mobility[iphin, ireg] = μn[ireg]
params.mobility[iphip, ireg] = μp[ireg]
params.mobility[iphia, ireg] = μa[ireg]
# recombination parameters
params.recombinationRadiative[ireg] = r0[ireg]
params.recombinationSRHLifetime[iphin, ireg] = τn[ireg]
params.recombinationSRHLifetime[iphip, ireg] = τp[ireg]
params.recombinationSRHTrapDensity[iphin, ireg] = trap_density!(iphin, ireg, params, EI[ireg])
params.recombinationSRHTrapDensity[iphip, ireg] = trap_density!(iphip, ireg, params, EI[ireg])
end
# interior doping
params.doping[iphin, regionDonor] = Cn
params.doping[iphia, regionIntrinsic] = Ca
params.doping[iphip, regionAcceptor] = Cp
data.params = params
ctsys = System(grid, data, unknown_storage=:sparse)
if test == false
show_params(ctsys)
println("*** done\n")
end
################################################################################
if test == false
println("Define control parameters for Solver")
end
################################################################################
control = SolverControl()
control.verbose = verbose
control.maxiters = 300
control.max_round = 5
control.damp_initial = 0.1
control.damp_growth = 1.21 # >= 1
if test == false
println("*** done\n")
end
################################################################################
if test == false
println("Compute solution in thermodynamic equilibrium for Boltzmann")
end
################################################################################
solution = equilibrium_solve!(ctsys, control = control)
inival = solution
if plotting # currently, plotting the solution was only tested with PyPlot.
ipsi = data.index_psi
X = grid[Coordinates][1,:]
Y = grid[Coordinates][2,:]
Plotter.figure()
Plotter.surf(X[:], Y[:], solution[ipsi, :])
Plotter.title("Electrostatic potential \$ \\psi \$ (Equilibrium)")
Plotter.xlabel("length [m]")
Plotter.ylabel("height [m]")
Plotter.zlabel("potential [V]")
Plotter.tight_layout()
################
Plotter.figure()
Plotter.surf(X[:], Y[:], solution[iphin,:] )
Plotter.title("quasi Fermi potential \$ \\varphi_n \$ (Equilibrium)")
Plotter.xlabel("length [m]")
Plotter.ylabel("height [m]")
Plotter.zlabel("potential [V]")
Plotter.tight_layout()
end
if test == false
println("*** done\n")
end
################################################################################
if test == false
println("I-V Measurement Loop")
end
################################################################################
# for saving I-V data
IV = zeros(0) # for IV values
biasValues = zeros(0) # for bias values
for istep = 2:number_tsteps
t = tvalues[istep] # Actual time
Δu = t * scanrate # Applied voltage
Δt = t - tvalues[istep-1] # Time step size
# Apply new voltage; set non equilibrium boundary conditions
set_contact!(ctsys, bregionAcceptor, Δu = Δu)
if test == false
println("time value: t = $(t) s")
end
solution = solve(ctsys, inival = inival, control = control, tstep = Δt)
# get I-V data
current = get_current_val(ctsys, solution, inival, Δt)
push!(IV, current)
push!(biasValues, Δu)
inival = solution
end # time loop
if plotting
Plotter.figure()
Plotter.surf(X[:], Y[:], solution[ipsi, :])
Plotter.title("Electrostatic potential \$ \\psi \$ at end time")
Plotter.xlabel("length [m]")
Plotter.ylabel("height [m]")
Plotter.zlabel("potential [V]")
################
Plotter.figure()
Plotter.surf(X[:], Y[:], solution[iphin,:] )
Plotter.title("quasi Fermi potential \$ \\varphi_n \$ at end time")
Plotter.xlabel("length [m]")
Plotter.ylabel("height [m]")
Plotter.zlabel("potential [V]")
################
Plotter.figure()
Plotter.plot(biasValues, IV.*(cm)^2/height, label = "", linewidth= 3, marker = "o")
Plotter.grid()
Plotter.ylabel("total current [A]") #
Plotter.xlabel("Applied Voltage [V]")
end
if test == false
println("*** done\n")
end
testval = sum(filter(!isnan, solution))/length(solution) # when using sparse storage, we get NaN values in solution
return testval
end # main
function test()
testval = -0.5818799192233242
main(test = true) ≈ testval
end
if test == false
println("This message should show when this module is successfully recompiled.")
end
end # moduleThis page was generated using Literate.jl.