GaAs diode: transient with traps (1D).
Simulating transient charge transport in a GaAs p-i-n diode with an electron trap.
module Ex109_Traps
using ChargeTransport
using ExtendableGrids
using PyPlot
# function to initialize the grid for a possble extension to other p-i-n devices.
function initialize_pin_grid(refinementfactor, h_ndoping, h_intrinsic, h_pdoping)
coord_ndoping = collect(range(0.0, stop = h_ndoping, length = 3 * refinementfactor))
coord_intrinsic = collect(range(h_ndoping, stop = (h_ndoping + h_intrinsic), length = 3 * refinementfactor))
coord_pdoping = collect(range((h_ndoping + h_intrinsic),
stop = (h_ndoping + h_intrinsic + h_pdoping),
length = 3 * refinementfactor))
coord = glue(coord_ndoping, coord_intrinsic)
coord = glue(coord, coord_pdoping)
return coord
endyou 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, unknown_storage=:sparse)
if plotting
Plotter.close("all")
end
################################################################################
if test == false
println("Set up grid and regions")
end
################################################################################
# region numbers
regionAcceptor = 1 # p doped region
regionIntrinsic = 2 # intrinsic region
regionDonor = 3 # n doped region
regions = [regionAcceptor, regionIntrinsic, regionDonor]
numberOfRegions = length(regions)
# boundary region numbers
bregionAcceptor = 1
bregionDonor = 2
bregionJunction1 = 3
bregionJunction2 = 4
# grid
refinementfactor = 2^(n-1)
h_pdoping = 2.0 * μm
h_intrinsic = 2.0 * μm
h_ndoping = 2.0 * μm
h_total = h_pdoping + h_intrinsic + h_ndoping
w_device = 0.5 * μm # width of device
z_device = 1.0e-4 * cm # depth of device
coord = initialize_pin_grid(refinementfactor,
h_pdoping,
h_intrinsic,
h_ndoping)
grid = simplexgrid(coord)
# set different regions in grid
cellmask!(grid, [0.0 * μm], [h_pdoping], regionAcceptor) # p-doped
cellmask!(grid, [h_pdoping], [h_pdoping + h_intrinsic], regionIntrinsic) # intrinsic
cellmask!(grid, [h_pdoping + h_intrinsic], [h_total], regionDonor) # n-doped
bfacemask!(grid, [h_pdoping], [h_pdoping], bregionJunction1, tol = 1.0e-18)
bfacemask!(grid, [h_pdoping + h_intrinsic], [h_pdoping + h_intrinsic], bregionJunction2, tol = 1.0e-18)
if plotting
gridplot(grid, Plotter = Plotter, legend=:lt)
Plotter.title("Grid")
end
if test == false
println("*** done\n")
end
################################################################################
if test == false
println("Define physical parameters and model")
end
################################################################################
iphin = 1 # index electron quasi Fermi potential
iphip = 2 # index hole quasi Fermi potential
iphit = 3 # index trap quasi Fermi potential
numberOfCarriers = 3 # electrons, holes and traps
# physical data
Ec = 1.424 * eV
Ev = 0.0 * eV
Et = 0.6 * eV
Nc = 4.351959895879690e17 / (cm^3)
Nv = 9.139615903601645e18 / (cm^3)
Nt = 1e16 / (cm^3)
mun = 8500.0 * (cm^2) / (V * s)
mup = 400.0 * (cm^2) / (V * s)
mut = 0.0 * (cm^2) / (V * s) # such that there is no flux
εr = 12.9 * 1.0 # relative dielectric permittivity of GAs
T = 300.0 * K
# recombination parameters
ni = sqrt(Nc * Nv) * exp(-(Ec - Ev) / (2 * kB * T)) # intrinsic concentration
n0 = Nc * Boltzmann( (Et-Ec) / (kB*T) ) # Boltzmann equilibrium concentration
p0 = ni^2 / n0 # Boltzmann equilibrium concentration
Auger = 1.0e-29 * cm^6 / s # 1.0e-41
SRH_LifeTime = 1.0e-3 * ns
Radiative = 1.0e-10 * cm^3 / s # 1.0e-16
G = 1.0e25 / (cm^3 * s)
# doping -- trap doping will not be set and thus automatically zero
dopingFactorNd = 1.0
dopingFactorNa = 0.46
Nd = dopingFactorNd * Nc
Na = dopingFactorNa * Nv
# contact voltage
voltageAcceptor = 1.5 * V
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 = true,
bulk_recomb_radiative = true,
bulk_recomb_SRH = true)
# Here, we enable the traps and parse the respective index and the regions where the trap is defined.
enable_trap_carrier!(;data = data, trapCarrier = iphit, regions = regions)
# Possible choices: GenerationNone, GenerationUniform
data.generationModel = GenerationUniform
# Possible choices: OhmicContact, SchottkyContact (outer boundary) and InterfaceNone,
# InterfaceRecombination (inner boundary).
data.boundaryType[bregionAcceptor] = OhmicContact
data.boundaryType[bregionDonor] = OhmicContact
data.ohmicContactModel = OhmicContactRobin
# 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] = -1
params.chargeNumbers[iphip] = 1
params.chargeNumbers[iphit] = -1 # trap charge number determines whether hole or electron trap is used
for ireg in 1:numberOfRegions # region data
params.dielectricConstant[ireg] = εr * ε0
# effective DOS, band-edge energy and mobilities
params.densityOfStates[iphin, ireg] = Nc
params.densityOfStates[iphip, ireg] = Nv
params.densityOfStates[iphit, ireg] = Nt
params.bandEdgeEnergy[iphin, ireg] = Ec
params.bandEdgeEnergy[iphip, ireg] = Ev
params.bandEdgeEnergy[iphit, ireg] = Et
params.mobility[iphin, ireg] = mun
params.mobility[iphip, ireg] = mup
params.mobility[iphit, ireg] = mut
# recombination parameters
params.recombinationRadiative[ireg] = Radiative
params.recombinationSRHLifetime[iphin, ireg] = SRH_LifeTime
params.recombinationSRHLifetime[iphip, ireg] = SRH_LifeTime
params.recombinationSRHTrapDensity[iphin, ireg] = n0
params.recombinationSRHTrapDensity[iphip, ireg] = p0
params.recombinationAuger[iphin, ireg] = Auger
params.recombinationAuger[iphip, ireg] = Auger
params.generationUniform[ireg] = G
end
# doping
params.doping[iphin, regionDonor] = Nd
params.doping[iphin, regionIntrinsic] = ni
params.doping[iphip, regionIntrinsic] = 0.0
params.doping[iphip, regionAcceptor] = Na
data.params = params
ctsys = System(grid, data, unknown_storage=unknown_storage)
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.tol_round = 1.0e-4
control.damp_initial = 0.5
control.damp_growth = 1.61
control.max_round = 3
if test == false
println("*** done\n")
end
################################################################################
if test == false
println("Compute solution in thermodynamic equilibrium")
end
################################################################################
# solve thermodynamic equilibrium and update initial guess
solution = equilibrium_solve!(ctsys, control = control)
inival = solution
if test == false
println("*** done\n")
end
if plotting
label_solution, label_density, label_energy = set_plotting_labels(data)
# add labels for traps
label_energy[1, iphit] = "\$E_{\\tau}-q\\psi\$"; label_energy[2, iphit] = "\$ - q \\varphi_{\\tau}\$"
label_density[iphit] = "\$n_{\\tau}\$"; label_solution[iphit] = "\$ \\varphi_{\\tau}\$"
Plotter.figure()
plot_energies(Plotter, ctsys, solution, "Equilibrium", label_energy)
Plotter.figure()
plot_densities(Plotter, ctsys, solution,"Equilibrium", label_density)
Plotter.figure()
plot_solution(Plotter, ctsys, solution, "Equilibrium", label_solution)
end
################################################################################
if test == false
println("Loop for putting generation on")
end
################################################################################
# Scan rate and time steps
scanrate = 1.0 * V/s
number_tsteps = 25
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(0.0, stop = tend, length = number_tsteps)
Δt = tvalues[2] - tvalues[1]these values are needed for putting the generation slightly on
I = collect(20:-1:0.0)
LAMBDA = 10 .^ (-I)
IV = zeros(0) # for IV values
biasValues = zeros(0) # for bias values
for istep = 1:length(I)-1
# turn slowly generation on
data.λ2 = LAMBDA[istep + 1]
if test == false
println("increase generation with λ2 = $(data.λ2)")
end
solution = solve(ctsys, inival = inival, control = control)
inival = solution
end # generation loop
if test == false
println("*** done\n")
end
################################################################################
if test == false
println("IV Measurement loop")
end
################################################################################
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, w_device * z_device * current)
push!(biasValues, Δu)
inival = solution
end # bias loop
if test == false
println("*** done\n")
end
# plot solution and IV curve
if plotting
Plotter.figure()
plot_energies(Plotter, ctsys, solution, "bias \$\\Delta u\$ = $(endVoltage), \$ t=$(tvalues[number_tsteps])\$", label_energy)
Plotter.figure()
plot_densities(Plotter, ctsys, solution,"bias \$\\Delta u\$ = $(endVoltage), \$ t=$(tvalues[number_tsteps])\$", label_density)
Plotter.figure()
plot_solution(Plotter, ctsys, solution, "bias \$\\Delta u\$ = $(endVoltage), \$ t=$(tvalues[number_tsteps])\$", label_solution)
Plotter.figure()
plot_IV(Plotter, biasValues,IV, "bias \$\\Delta u\$ = $(biasValues[end])", plotGridpoints = true)
end
testval = sum(filter(!isnan, solution))/length(solution) # when using sparse storage, we get NaN values in solution
return testval
if test == false
println("*** done\n")
end
end # main
function test()
testval = 0.9699245385329192
main(test = true, unknown_storage=:dense) ≈ testval && main(test = true, unknown_storage=:sparse) ≈ testval
end
if test == false
println("This message should show when the PIN module has successfully recompiled.")
end
end # moduleThis page was generated using Literate.jl.