How to compute a capacitance-voltage curve

[JunwenDiao]

I was simulating the Capacitance vs Voltage curve for a HPGe detector with depletion_handling = true for calculate_electric_potential! and observed a strange behavior of the plot: it is being basically constant before depletion and starting to increase after the depletion voltage, while keeping the variation very small.

The problem is probably due to the ϵ_r for the undepleted region not being set to the scaling_factor_for_permittivity_in_undepleted_region but the same as the depleted ϵ_r (which is 16 for HPGe I believe)

the ϵ_r is not changing with the depletion:
0V:

Partially depleted:

Fully depleted:

So that above the depletion voltage the depleted region goes into the contact, turning the ϵ_r from 1.0 to 16.0, thus increasing the value of the capacitance in the calculation:

[fhagemann]

So, we do not scale up ϵ_r in the plot but in code, so the plots you are showing make perfect sense.

See for example these lines, where this is applied in-code:

SolidStateDetectors.jl/src/PotentialCalculation/PotentialCalculationSetup/PotentialCalculationSetupCartesian3D.jl

Lines 183 to 197 in bb477d9

	if depletion_handling
	for iz in axes(ϵ, 3)
	for iy in axes(ϵ, 2)
	for ix in axes(ϵ, 1)
	pt::CartesianPoint{T} = CartesianPoint{T}(mpx[ix], mpy[iy], mpz[iz])
	ig = find_closest_gridpoint(pt, point_types.grid)
	if is_undepleted_point_type(point_types.data[ig...])
	ϵ[ix, iy, iz] *= scaling_factor_for_permittivity_in_undepleted_region(det.semiconductor) * (1 - imp_scale[ig...])
	elseif is_fixed_point_type(point_types.data[ig...])
	ϵ[ix, iy, iz] *= scaling_factor_for_permittivity_in_undepleted_region(det.semiconductor)
	end
	end
	end
	end
	end

The formula you are quoting depend on the WEIGHITNG POTENTIALS, not the electric potential. In order to calculate the capacitance, you would then also need to calculate the weighting potential with depletion_handling = true. Is that what you are doing right now?

[fhagemann]

The variations you are seeing right now are just based on the different grid spacings resulting from simulations at different bias voltages.

[JunwenDiao]

Hi,
thank you very much for your reply!
I think that is real source of the problem. I made a stupid mistake when testing depletion_handling = true for calculate_weighting_potential which made we think that I can not do that! Now it is giving me the right plot