Inactive layer simulation: True coaxial detector
Set the physical models for the inactive layer (dead layer) simulation with YAML
- using drift model for the inactive layer
- using constant lifetime trapping model
- using mobility-tied diffusion model (by calling the
calculate_mobilityfunction with the drift model)
using Plots
using Unitful
using SolidStateDetectors
T = Float64;the geometry parameters of the model for following display
det_rin = 1u"mm"
det_z = det_r = 10u"mm"
z_draw = det_z/2
pn_r = 8.957282u"mm" # this one was calculated by searching the zero impurity point (displayed in the following section)
sim = Simulation{T}(SSD_examples[:TrueCoaxial])
cfn = SSD_examples[:TrueCoaxial]
print(open(f -> read(f, String), cfn))
plot(sim.detector, xunit = u"mm", yunit = u"mm", zunit = u"mm")name: TrueCoaxial
units:
length: mm
angle: deg
potential: V
temperature: K
grid:
coordinates: cylindrical
axes:
r:
to: 10.01
boundaries: inf
phi:
from: 0
to: 0
boundaries:
left: periodic
right: periodic
z:
from: -0.01
to: 10.01
boundaries:
left: inf
right: inf
medium: vacuum
detectors:
- semiconductor:
material: HPGe
temperature: 90
impurity_density:
name: PtypePNjunction
lithium_annealing_temperature: 623K
lithium_annealing_time: 18minute
doped_contact_id: 2
bulk_impurity_density:
name: constant
value: -1e10cm^-3
charge_drift_model:
model: InactiveLayerChargeDriftModel
temperature: 90K
neutral_impurity_density:
name: constant
value: 5.6769e15cm^-3
# # Uncomment the following lines if you want to use different bulk and surface impurity densities in the charge_drift_model section
# bulk_impurity_density:
# name: constant
# value: -1e10cm^-3
# surface_impurity_density:
# name: li_diffusion
# lithium_annealing_temperature: 623K
# lithium_annealing_time: 18minute
# doped_contact_id: 2
charge_trapping_model:
model: ConstantLifetime
parameters:
τh: 1ms
τe: 1ms
model_inactive: ConstantLifetime
parameters_inactive:
τh: 1μs
τe: 1μs
inactive_layer_geometry:
tube:
r:
from: 8.957282 # set to the depth of the pn junction boundary when lithium diffusion temperature is 623 K, time is 18 minutes
to: 10.0
h: 10.0
origin:
z: 5.0
geometry:
tube:
r:
from: 1.0
to: 10.0
h: 10.0
origin:
z: 5.0
contacts:
- name: "P⁺"
id: 1
material: HPGe
potential: -500
geometry:
tube:
r:
from: 1.0
to: 1.0
h: 10.0
origin:
z: 5.0
- name: "N⁺"
id: 2
material: HPGe
potential: 0
geometry:
tube:
r:
from: 10.0
to: 10.0
h: 10.0
origin:
z: 5.0
In the configuration file shown above, the position of the PN junction boundary
pn_rwas calculated as the position where the density is zero.
Display the impurity profile defined
r_list = 0u"mm":0.01u"mm":det_r
imp_list = map(r -> let pt::CylindricalPoint{T} = CylindricalPoint(r, 0u"°", z_draw)
SolidStateDetectors.get_impurity_density(sim.detector.semiconductor.impurity_density_model, pt) * 1e-6u"cm^-3"
end, r_list)
plot(r_list, imp_list, xlabel = "r / mm", ylabel = "Impurity density / cm\$^{-3}\$", unitformat = :nounit, label = "",
color = :darkblue, lw = 2, grid = :on, xlims = (0, 10), ylims = (-2e10, 1e11))
vline!([pn_r], lw = 2, ls = :dash, color = :darkred, label = "PN junction boundary")
Display the mobility curve
using SolidStateDetectors: Electron, Hole
cdm = sim.detector.semiconductor.charge_drift_model
depth_list = 0u"mm":0.01u"mm":(det_r-pn_r)
mobility_list = map(depth -> let pt::CartesianPoint{T} = CartesianPoint(det_r - depth, 0, z_draw)
(µe = SolidStateDetectors.calculate_mobility(cdm, pt, Hole) * 10000u"cm^2/(V*s)",
µh = SolidStateDetectors.calculate_mobility(cdm, pt, Electron) * 10000u"cm^2/(V*s)")
end, depth_list)
plot(depth_list, getfield.(mobility_list, :µh), label = "Hole", lw = 4)
plot!(depth_list, getfield.(mobility_list, :µe), label = "Electron", lw = 4)
plot!(xlabel = "Depth to surface / mm", ylabel = "Mobility / cm\$^2\$/Vs", unitformat = :nounit, legend = :topleft, xlims = (0u"mm", det_r-pn_r))
Calculate the electric field
To simulate the inactive layer, we need to calculate the electric field on a very fine grid.
calculate_electric_potential!(sim, max_n_iterations = 10, grid = Grid(sim), verbose = false, depletion_handling = true)
g = sim.electric_potential.grid
ax1, ax2, ax3 = g.axes
bulk_tick_dis = 0.05u"mm"
dl_tick_dis = 0.01u"mm"
user_additional_ticks_ax1 = sort(vcat(ax1.interval.left*u"m":bulk_tick_dis:pn_r, pn_r:dl_tick_dis:ax1.interval.right*u"m"))
user_ax1 = typeof(ax1)(ax1.interval, SolidStateDetectors.to_internal_units.(user_additional_ticks_ax1))
user_g = typeof(g)((user_ax1, ax2, ax3))
calculate_electric_potential!(sim, refinement_limits = 0.1, grid = user_g, depletion_handling = true)
calculate_electric_field!(sim)
calculate_weighting_potential!(sim, 1, depletion_handling = true)
calculate_weighting_potential!(sim, 2, depletion_handling = true);
plot(
begin
imp = plot(sim.imp_scale, φ = 0, xunit = u"mm", yunit = u"mm", title = "impurity scale")
vline!([pn_r], lw = 2, ls = :dash, color = :darkred, label = "PN junction boundary", legendfontsize = 6)
end,
begin
plot(sim.point_types, φ = 0, xunit = u"mm", yunit = u"mm", title = "point types")
vline!([pn_r], lw = 2, ls = :dash, color = :darkred, label = "PN junction boundary", legendfontsize = 6)
end,
begin
plot(sim.electric_potential, xunit = u"mm", yunit = u"mm", title = "electric potential")
vline!([pn_r], lw = 2, ls = :dash, color = :darkred, label = "PN junction boundary", legendfontsize = 6)
end,
begin
plot(sim.electric_field, xunit = u"mm", yunit = u"mm", title = "electric field", clims = (0, 100*2000))
vline!([pn_r], lw = 2, ls = :dash, color = :darkred, label = "PN junction boundary", legendfontsize = 6)
end,
size = (800, 600), layout = (2, 2),
)Simulation: TrueCoaxial
Electric Potential Calculation
Bias voltage: 500.0 V
φ symmetry: Detector is φ-symmetric -> 2D computation.
Precision: Float64
Device: CPU
Max. CPU Threads: 4
Coordinate system: Cylindrical
N Refinements: -> 1
Convergence limit: 1.0e-7 => 5.0e-5 V
Initial grid size: (286, 1, 16)
Grid size: (286, 1, 16) - using 4 threads now
┌ Info: In electric field calculation: Keyword `n_points_in_φ` not set.
└ Default is `n_points_in_φ = 36`. 2D field will be extended to 36 points in φ.
Simulation: TrueCoaxial
Weighting Potential Calculation - ID: 1
φ symmetry: Detector is φ-symmetric -> 2D computation.
Precision: Float64
Device: CPU
Max. CPU Threads: 4
Coordinate system: Cylindrical
N Refinements: -> 3
Convergence limit: 1.0e-7
Initial grid size: (12, 1, 16)
Grid size: (16, 1, 16) - using 4 threads now
Grid size: (24, 1, 16) - using 4 threads now
Grid size: (38, 1, 16) - using 4 threads now
Simulation: TrueCoaxial
Weighting Potential Calculation - ID: 2
φ symmetry: Detector is φ-symmetric -> 2D computation.
Precision: Float64
Device: CPU
Max. CPU Threads: 4
Coordinate system: Cylindrical
N Refinements: -> 3
Convergence limit: 1.0e-7
Initial grid size: (12, 1, 16)
Grid size: (16, 1, 16) - using 4 threads now
Grid size: (24, 1, 16) - using 4 threads now
Grid size: (38, 1, 16) - using 4 threads now
Pulse shape and CCE simulation
depth_list = 0.1u"mm":0.1u"mm":(det_r-pn_r)
totTime = 5u"µs"
totEnergy = 1u"keV" # --> simulating ~339 carrier pairs
N = Int(totEnergy÷2.95u"eV")
pulse_plot = plot()
eff_list = map(depth -> begin
r = det_r-depth
energy_depos = fill(2.95u"eV", N)
starting_positions = repeat([CartesianPoint(r, 0, z_draw)], N)
evt = Event(starting_positions, energy_depos)
simulate!(evt, sim, Δt = 1u"ns", max_nsteps = round(Int, totTime / 1u"ns"), diffusion = true, end_drift_when_no_field = false, self_repulsion = false)
pulse = evt.waveforms[1]
plot!(pulse_plot, pulse, label = "Depth: $(round(typeof(depth), depth, digits = 1))", lw = 2, yunit = u"eV/V")
maximum(pulse.signal)/N
end, depth_list)
plot!(pulse_plot, legend = :topright, xlabel = "Time / ns", ylabel = "Amplitude / e", unitformat = :nounit)
cce_plot = plot(depth_list, eff_list, xlabel = "Depth to surface / mm", ylabel = "Charge collection efficiency", lw = 2, color = :black, label = "", unitformat = :nounit)
plot(pulse_plot, cce_plot, layout = (1, 2), size = (1000, 400), margin = 5Plots.mm)
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