The variation of diffusion with charge

Dear developer,
In the process of simulating different charge particle, we have observed some differences between the diffusion of charges in silicon and actual data. This difference may arise from the initial distribution of charge carriers deposited during the primary deposition.
In the article titled ‘Design considerations to overcome cross talk in a photon counting silicon strip detector for computed tomography,’ doi:10.1016/j.nima.2010.04.071. In Section 3.2, an empirical formula is provided that varies with the deposition energy. I would like to inquire about how the initial diffusion is configured in the software and whether there are methods available for modification.

Your help in this matter is greatly appreciated.

Dear @c_7I

it is indeed an interesting topic you are raising here. Currently there is no initial charge could simulated at the point of deposition. This has several reasons:

  • Historically most of the simulations performed with APSQ were done with MIPs, and a point-like deposition is a relatively good description there. This of course should not serve as an argument to keep it this way!
  • In the simulation, one of the speed-ups we can achieve is to group charge carriers and to only move groups of e.g. 10e/h at the same time. This, however, works only as long as they originate from the same point, which would not be the case anymore when simulating an initial cloud. This means, we would likely make this optional and add a WARNING output when enabled together with charge groups larger than one.
  • The matter overall is quite tricky. When we have large localized current or charge carrier densities in the sensor, there are additional effects such as self-shielding or plasma effects that play a role and alter the diffusion behavior.

There have been several attempts in the past of describing this behavior in a simplified model suitable for MC simulations, but we have not yet found one that works nicely and across large charge carrier densities. The model you reference has the relation

\sigma_1 [\mu m] = 0.0044 (E [keV])^1.75

where I am a little concerned about the units. Also, in reference [15] I cannot find a mention of this approximate model.

If you would like to play with the initial charge cloud yourself, the appropriate place in the code to distribute charge carriers is at their creation. If you would like to alter the diffusion constant overall during the charge carrier propagation, have a look at this code instead.

Should you find a model that works well with your data, please let is know, we’d be more than happy to discuss an inclusion into the main simulation code repository.

Best regards,

Dear Simon,

Thank you for your detailed response! we are experimenting with the distribution of charge carriers at their creation point and considering the potential impact on diffusion behavior.

If we achieve positive results and identify a model that works well with our data, we will certainly inform you. Once again, thank you for your guidance and insights.

Best regards,
Yu-Xin Cui

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Dear Yu-Xin,

I had a quick look at your nice paper concerning the simulations. Maybe your recent simulations are a bit different, but one thing that we have found has a big impact on the charge carrier diffusion is the combination of mobility model and doping concentration.
As I understand the paper, you do not include a doping concentration in the simulation, but doing that can have a significant effect on exactly the diffusion of charge carriers. It is recommended that you then also use the masetti_canali mobility model in the propagation, in order to take both high and low doping concentrations into account.

Kind regards,

Dear Håkan,

Indeed, the previous simulations did not take into account the doping concentration, as the diffusion effects for protons and helium are very weak. It is a very good suggestion to incorporate the mobility model and doping concentration. I will attempt simulations following your advice to observe the results. Thank you for your suggestions again!

Best regards,
Yu-Xin Cui