Confusion Regarding Semiconductor Material and Contacts Material

[rajxabc]

Hi Felix
why in all the Detectors construction , semiconductor and contacts have same material property ...Ex HPGe
in case we want to simulate Cu , Pt, Al etc. what should be the ϵ_r or other electrical properties to be defined in "MaterialProperties.jl"
??

[fhagemann]

So, in the simulation, the ϵ_r should not matter for objects that are set to a fixed potential, e.g. contacts. They become relatively important if they are not fixed to a potential.

For metals and conductors, you might wanna set it to a very high value (1e5 or higher) to mimic this behavior. For contacts, you can try but it shouldn’t make a big difference in the simulation results

[rajxabc]

Thanks
so it means ,
no matter what metal we opt for the contacts, results are going to be somewhat same/similar ?

[fhagemann]

With the current implementation they should be similar (maybe the Geant4 extension will give you slightly different results).

If you are thinking about some things to add to SSD simulations depending on the material of the contacts, I’d be happy to discuss

[rajxabc]

P.S. Missed your this comment ....
I tried , defining and using metal work function from this, but simulte! is kind of difficult to override and extend to "contacts"
and capacitance calculation is also going to be tricky . so gave up untill there is some inclusion of contacts and change in SSD
https://eng.libretexts.org/Bookshelves/Materials_Science/Supplemental_Modules_(Materials_Science)/Semiconductors/Metal-Semiconductors_Contacts

`# Schottky contact parameters structure
struct SchottkyContactParams{T}
barrier_height::T # eV
image_force_lowering::Bool
thermionic_emission::Bool
end

Extended contact information extraction

function extract_schottky_contacts(detector::SolidStateDetector{T}) where {T}
schottky_contacts = Dict{Int, SchottkyContactParams{T}}()

for contact in detector.contacts
    # Check if contact is Schottky (Al contacts in your case)
    if contact.material == "Al" || occursin("Al", contact.name)
        schottky_contacts[contact.id] = SchottkyContactParams{T}(
            0.8,  # Default barrier height for Al/p-CdTe (eV)
            true,  # Include image force lowering
            true   # Include thermionic emission
        )
    end
end
return schottky_contacts

end

Enhanced electric field calculation with Schottky effects

function get_electric_field_with_schottky(
pt::CartesianPoint{T},
sim::Simulation{T},
schottky_contacts::Dict{Int, SchottkyContactParams{T}}
)::SVector{3,T} where {T}
# Get base field from interpolation
ef = SolidStateDetectors.interpolated_vectorfield(sim.electric_field)
E = SolidStateDetectors.get_velocity_vector(ef, pt)

# Check if near any Schottky contact
for (contact_id, schottky_params) in schottky_contacts
    #contact = get_contact(sim.detector, contact_id)
    contact = sim.detector.contacts[contact_id]
    if is_near_contact(pt, contact, 10.0)  # Within 10μm
        # Image force lowering
        ϵ = 10.9 * 8.85e-14  # F/cm
        Δϕ = sqrt(norm(E) * 1.6e-19 / (4π * ϵ))  # Barrier lowering
        effective_barrier = max(0, schottky_params.barrier_height - Δϕ)
        
        # Modify field near Schottky contact
        if schottky_params.image_force_lowering
            E *= exp(-effective_barrier / (0.025 * 300/298))
        end
        break  # Assume only one nearby contact
    end
end
return E

end

Helper function to check if point is near a contact

function is_near_contact(pt::CartesianPoint{T}, contact, threshold::T) where {T}
# Simple distance check - implement based on your contact geometry
#if contact.geometry isa SolidStateDetectors.Box
if contact.geometry isa SolidStateDetectors.ConstructiveSolidGeometry.Box
box = contact.geometry
dx = abs(pt[1] - box.origin[1])
dy = abs(pt[2] - box.origin[2])
dz = abs(pt[3] - box.origin[3])
return dx < box.hX + threshold && dy < box.hY + threshold && dz < box.hZ + threshold
end
return false
end

Schottky capacitance model

struct SchottkyCapacitanceModel{T}
barrier_height::T
donor_density::T # Effective surface state density
dielectric_constant::T
area::T
end

function calculate_schottky_capacitance(model::SchottkyCapacitanceModel{T}, voltage::T) where {T}
q = 1.602e-19 # C
ϵ₀ = 8.854e-14 # F/cm
k_B = 8.617e-5 # eV/K

# Built-in potential
V_bi = model.barrier_height - (k_B * 300) * log(model.donor_density / 1e10)

# Depletion width
#W = sqrt(2 * model.dielectric_constant * ϵ₀ * (V_bi - voltage) / (q * model.donor_density))
W = sqrt(Complex(2 * model.dielectric_constant * ϵ₀ * (V_bi - voltage) / (q * model.donor_density)))

# Capacitance
C = model.dielectric_constant * ϵ₀ * model.area / W

return C

end

Calculate contact area

function calculate_contact_area(contact)
if contact.geometry isa SolidStateDetectors.ConstructiveSolidGeometry.Box
box = contact.geometry
return (2 * box.hX) * (2 * box.hY) * 1e-8 # Convert μm² to cm²
end
return 0.0
end

Enhanced trapping model with Schottky effects

#function SolidStateDetectors._calculate_signal(
function _calculate_signal(
model::SchottkyAwareTrappingModel{T},
path::Vector{CartesianPoint{T}},
timestamps::Vector{T},
charge::T,
wpot::Interpolations.Extrapolation{T,3},
::Type{Cartesian},
sim::Simulation{T},
schottky_contacts::Dict{Int, SchottkyContactParams{T}}
)::Vector{T} where {T <: Union{Float32,Float64}}
signal = zeros(T, length(timestamps))

for (i, (pt, t)) in enumerate(zip(path, timestamps))
    # Get field with Schottky effects
    E = get_electric_field_with_schottky(pt, sim, schottky_contacts)
    field_strength = norm(E)
    
    # Determine trapping time based on position
    z = pt[3]
    if z ≤ model.W
        # Depletion region: enhanced trapping
        τ_e = model.τ_dep_e * (1 + model.N_trap/1e12)
        τ_h = model.τ_dep_h
    else
        # Bulk region
        τ_e = model.τ_bulk_e
        τ_h = model.τ_bulk_h
    end
    
    # Hecht-like trapping
    λ_e = τ_e * 1000 * field_strength
    λ_h = τ_h * 110 * field_strength
    surviving_charge = charge * (λ_e/(2*model.W)*(1-exp(-2*model.W/λ_e)) + 
                      λ_h/(2*model.W)*(1-exp(-2*model.W/λ_h)))
    
    signal[i] = surviving_charge * wpot(pt[1], pt[2], pt[3])
end
return signal

end

Add this to your main code after setting up the simulation

schottky_contacts = extract_schottky_contacts(sim.detector)

Calculate Schottky capacitances

for (contact_id, schottky_params) in schottky_contacts
contact = sim.detector.contacts[contact_id]
area = calculate_contact_area(contact)

cap_model = SchottkyCapacitanceModel{T}(
    schottky_params.barrier_height,
    1e15,  # Default surface state density
    10.9,   # CdTe dielectric constant
    area
)

# Calculate capacitance at different bias voltages
for V in [0.0, 10.0, 50.0, 100.0]
    C = calculate_schottky_capacitance(cap_model, V)
    println("Contact $(contact.id) at $(V)V: C = $(C*1e12) pF")
end

end`