Loading AUTHORS.md +0 −1 Original line number Diff line number Diff line Loading @@ -73,4 +73,3 @@ The following authors, in alphabetical order, have developed or contributed to A * Morag Williams, University of Glasgow, [williamm](https://gitlab.cern.ch/williamm) * Koen Wolters, [kwolters](https://gitlab.cern.ch/kwolters) * Samuel Wood, University of Oxford, [sam-sw](https://github.com/sam-sw) * Jixing Ye, University of Trento, [jiye](https://gitlab.cern.ch/jiye) doc/usermanual/06_models/04_trapping.md +50 −116 Original line number Diff line number Diff line Loading @@ -23,24 +23,15 @@ Please refer to the corresponding reference publications for further details. The trapping probability is calculated as an exponential decay as a function of the simulation timestep as ```math p_{e, h} = \left(1 - \exp^{ 1 \frac{\delta t} { \tau_ { e, h } }}\right) p_{e, h} = \left(1 - \exp^{1 \frac{\delta t}{\tau_{e, h}}}\right) ``` where $`\delta t`$ is the simulation timestep and $`\tau{ e, h } `$ the effective lifetime of electrons and holes, respectively.At the same time, a total time spent in the trap is calculated if a detrapping model is selected.Here, the time until the charge carrier is de - trapped is calculated as where $`\delta t`$ is the simulation timestep and $`\tau{e,h}`$ the effective lifetime of electrons and holes, respectively. At the same time, a total time spent in the trap is calculated if a detrapping model is selected. Here, the time until the charge carrier is de-trapped is calculated as ```math \delta t = - \tau_ { e.h } \ln { 1 - p } \delta t = - \tau_{e.h} \ln{1-p} ``` where $`p`$ is a probability randomly chosen from a uniform distribution between 0 and 1. Loading @@ -54,37 +45,27 @@ The following models for trapping of charge carriers can be selected: In the Ljubljana (sometimes referred to as *Kramberger*) model \[[@kramberger]\], the trapping time follows the relation ```math \tau^{ -1}(T) = \beta(T)\Phi_{eq} , \tau^{-1}(T) = \beta(T)\Phi_{eq} , ``` where the temperature scaling of $`\beta`$ is given as ```math \beta(T) = \beta(T_0)\left(\frac{T}{ T_0}\right)^{ \kappa} , \beta(T) = \beta(T_0)\left(\frac{T}{T_0}\right)^{\kappa} , ``` extracted at the reference temperature of $`T_0 = -10 \,\text{ °C } `$. extracted at the reference temperature of $`T_0 = -10 \,\text{°C}`$. The parameters used in Allpix Squared are ```math \begin { aligned } \begin{aligned} \beta_{e}(T_0) &= 5.6\times 10^{-16} \,\text{cm}^2\,\text{ns}^{-1} \\ \kappa_{e} &= -0.86 \\ \\ \beta_{h}(T_0) &= 7.7\times 10^{-16} \,\text{cm}^2\,\text{ns}^{-1} \\ \kappa_{h} &= -1.52 \end { aligned } \end{aligned} ``` for electrons and holes, respectively. Loading @@ -93,21 +74,13 @@ While \[[@kramberger]\] quotes different values for $`\beta`$ for irradiation wi for protons have been applied here. The parameters arise from measurements of the were obtained evaluating current signals of irradiated sensors via light injection at fluences up to $`\Phi_{eq} = 2\times 10^{ 14} \ n_{ eq } \,\text{cm} ^ 2`$. injection at fluences up to $`\Phi_{eq} = 2\times 10^{14} \ n_{eq}\,\text{cm}^2`$. This model can be selected in the configuration file via the parameter `trapping_model = "ljubljana"`. This model can be selected in the configuration file via the parameter `trapping_model = "ljubljana"`. ### Dortmund The Dortmund(sometimes referred to as * Krasel*) model \[[@dortmundTrapping]\], describes the effective trapping times as The Dortmund (sometimes referred to as *Krasel*) model \[[@dortmundTrapping]\], describes the effective trapping times as ```math \tau^{-1} = \gamma\Phi_{eq} , Loading @@ -116,24 +89,16 @@ injection at fluences up to $`\Phi_{eq} = 2\times 10^{ with the parameters ```math \begin { aligned } \begin{aligned} \gamma_{e} &= 5.13\times 10^{-16} \,\text{cm}^2\,\text{ns}^{-1} \\ \gamma_{h} &= 5.04\times 10^{-16} \,\text{cm}^2\,\text{ns}^{-1} \end { aligned } \end{aligned} ``` for electrons and holes, respectively. The values have been extracted evaluating current signals of irradiated sensors via light injection at fluences up to $`\Phi_{eq} = 8.9 \times 10^{ 14}\ n_{ eq } \,\text{cm} ^ 2`$, at a temperature of $`T = 0\,\text {°C }`$. No temperature scaling is $`\Phi_{eq} = 8.9 \times 10^{14}\ n_{eq}\,\text{cm}^2`$, at a temperature of $`T = 0\,\text{°C}`$. No temperature scaling is provided. Values for neutron and proton irradiation have been evaluated in \[[@dortmundTrapping]\], Allpix Squared makes use of the values for proton irradiation. Loading @@ -142,34 +107,25 @@ This model can be selected in the configuration file via the parameter `trapping ### CMS Tracker This effective trapping model has been developed by the CMS Tracker Group. It follows the results of \[[@CMSTrackerTrapping]\], with measurements at fluences of up to $`\Phi_{eq} = 3 \times 10^{ 15} \ n_{ eq } \,\text{cm} ^ 2`$, at a temperature of $`T = -20 \,\text {°C } `$ and an irradiation with protons. \[[@CMSTrackerTrapping]\], with measurements at fluences of up to $`\Phi_{eq} = 3 \times 10^{15} \ n_{eq}\,\text{cm}^2`$, at a temperature of $`T = -20 \,\text{°C}`$ and an irradiation with protons. The interpolation of the results follows the relation ```math \tau ^ { -1 } = {\beta\Phi_{eq}} + \tau_0 ^ { -1 } \tau^{-1} = {\beta\Phi_{eq}} + \tau_0^{-1} ``` with the parameters ```math \begin { aligned } \begin{aligned} \beta_{e}(T_0) &= 1.71\times 10^{-16} \,\text{cm}^2\,\text{ns}^{-1} \\ \tau_{0,e}^{-1} &= -0.114 \,\text{ns}^{-1} \\ \\ \beta_{h}(T_0) &= 2.79\times 10^{-16} \,\text{cm}^2\,\text{ns}^{-1} \\ \tau_{0,h}^{-1} &= -0.093 \,\text{ns}^{-1} \end{ aligned } \end{aligned} ``` for electrons and holes, respectively. Loading @@ -181,12 +137,7 @@ This model can be selected in the configuration file via the parameter `trapping ### Mandic The Mandić model \[[@Mandic]\] is an empirical model developed from measurements with high fluences ranging from $`\Phi_{eq} = 5\times 10^{ 15} \ n_{ eq } \,\text{cm} ^ 2`$ to $`\Phi_{eq} = 1\times 10 ^ { 17 } \ n_ { eq } \,\text{cm}^2`$ and describes $`\Phi_{eq} = 5\times 10^{15} \ n_{eq}\,\text{cm}^2`$ to $`\Phi_{eq} = 1\times 10^{17} \ n_{eq}\,\text{cm}^2`$ and describes the lifetime via ```math Loading @@ -197,31 +148,18 @@ with the parameters ```math \begin{aligned} c_e &= 0.54 \,\text{ ns } \,\text{cm} ^ { -2 } \\ c_e &= 0.054 \,\text{ns}\,\text{cm}^{-2} \\ \kappa_e &= -0.62 \\ \ c_h &= 0.0427 \,\text { ns } \,\text{cm} ^ { -2 } \\ \\ c_h &= 0.0427 \,\text{ns}\,\text{cm}^{-2} \\ \kappa_h &= -0.62 \end { aligned } \end{aligned} ``` for electrons and holes, respectively. The parameters for electrons are taken from \[[@Mandic]\], for measurements at a temperature of $`T = -20 \,\text{ °C } `$, and the results extrapolated to $`T = -30 \,\text {°C }`$. See \[[@MandicErratum]\] for updated power function fitting parameters. A scaling from electrons to holes was performed based on the default The parameters for electrons are taken from \[[@Mandic]\], for measurements at a temperature of $`T = -20 \,\text{°C}`$, and the results extrapolated to $`T = -30 \,\text{°C}`$. A scaling from electrons to holes was performed based on the default values in Weightfield2 \[[@weightfield2]\]. This model can be selected in the configuration file via the parameter `trapping_model = "mandic"`. Loading Loading @@ -261,13 +199,10 @@ as arrays via the `trapping_parameters_electrons` and `trapping_parameters_holes are denoted with squared brackets and a parameter number, for example `[0]` for the first parameter provided. Parameters specified separately from the formula can contain units which will be interpreted automatically. { { % alert title = "Note" color = "info" % } } Both fluence and temperature are not inherently available in the custom trapping model, but need to be provided as additional parameters as described above.{ { % / alert % } } {{% alert title="Note" color="info" %}} Both fluence and temperature are not inherently available in the custom trapping model, but need to be provided as additional parameters as described above. {{% /alert %}} The following configuration parameters replicate the [Ljubljana model](#ljubljana) using a custom trapping model. Loading Loading @@ -324,5 +259,4 @@ detrapping_time_hole = 10ns [@dortmundTrapping]: https://doi.org/10.1109/TNS.2004.839096 [@CMSTrackerTrapping]: https://doi.org/10.1088/1748-0221/11/04/p04023 [@Mandic]: https://doi.org/10.1088/1748-0221/15/11/p11018 [@MandicErratum]: https://doi.org/10.1088/1748-0221/16/03/E03001 [@weightfield2]: http://personalpages.to.infn.it/~cartigli/Weightfield2/index.html src/physics/Trapping.hpp +1 −1 Original line number Diff line number Diff line Loading @@ -136,7 +136,7 @@ namespace allpix { class Mandic : virtual public TrappingModel { public: explicit Mandic(double fluence) { tau_eff_electron_ = 0.54 * pow(fluence / Units::get(1e16, "/cm/cm"), -0.62); tau_eff_electron_ = 0.054 * pow(fluence / Units::get(1e16, "/cm/cm"), -0.62); tau_eff_hole_ = tau_eff_electron_ * (4.9 / 6.2); } }; Loading Loading
AUTHORS.md +0 −1 Original line number Diff line number Diff line Loading @@ -73,4 +73,3 @@ The following authors, in alphabetical order, have developed or contributed to A * Morag Williams, University of Glasgow, [williamm](https://gitlab.cern.ch/williamm) * Koen Wolters, [kwolters](https://gitlab.cern.ch/kwolters) * Samuel Wood, University of Oxford, [sam-sw](https://github.com/sam-sw) * Jixing Ye, University of Trento, [jiye](https://gitlab.cern.ch/jiye)
doc/usermanual/06_models/04_trapping.md +50 −116 Original line number Diff line number Diff line Loading @@ -23,24 +23,15 @@ Please refer to the corresponding reference publications for further details. The trapping probability is calculated as an exponential decay as a function of the simulation timestep as ```math p_{e, h} = \left(1 - \exp^{ 1 \frac{\delta t} { \tau_ { e, h } }}\right) p_{e, h} = \left(1 - \exp^{1 \frac{\delta t}{\tau_{e, h}}}\right) ``` where $`\delta t`$ is the simulation timestep and $`\tau{ e, h } `$ the effective lifetime of electrons and holes, respectively.At the same time, a total time spent in the trap is calculated if a detrapping model is selected.Here, the time until the charge carrier is de - trapped is calculated as where $`\delta t`$ is the simulation timestep and $`\tau{e,h}`$ the effective lifetime of electrons and holes, respectively. At the same time, a total time spent in the trap is calculated if a detrapping model is selected. Here, the time until the charge carrier is de-trapped is calculated as ```math \delta t = - \tau_ { e.h } \ln { 1 - p } \delta t = - \tau_{e.h} \ln{1-p} ``` where $`p`$ is a probability randomly chosen from a uniform distribution between 0 and 1. Loading @@ -54,37 +45,27 @@ The following models for trapping of charge carriers can be selected: In the Ljubljana (sometimes referred to as *Kramberger*) model \[[@kramberger]\], the trapping time follows the relation ```math \tau^{ -1}(T) = \beta(T)\Phi_{eq} , \tau^{-1}(T) = \beta(T)\Phi_{eq} , ``` where the temperature scaling of $`\beta`$ is given as ```math \beta(T) = \beta(T_0)\left(\frac{T}{ T_0}\right)^{ \kappa} , \beta(T) = \beta(T_0)\left(\frac{T}{T_0}\right)^{\kappa} , ``` extracted at the reference temperature of $`T_0 = -10 \,\text{ °C } `$. extracted at the reference temperature of $`T_0 = -10 \,\text{°C}`$. The parameters used in Allpix Squared are ```math \begin { aligned } \begin{aligned} \beta_{e}(T_0) &= 5.6\times 10^{-16} \,\text{cm}^2\,\text{ns}^{-1} \\ \kappa_{e} &= -0.86 \\ \\ \beta_{h}(T_0) &= 7.7\times 10^{-16} \,\text{cm}^2\,\text{ns}^{-1} \\ \kappa_{h} &= -1.52 \end { aligned } \end{aligned} ``` for electrons and holes, respectively. Loading @@ -93,21 +74,13 @@ While \[[@kramberger]\] quotes different values for $`\beta`$ for irradiation wi for protons have been applied here. The parameters arise from measurements of the were obtained evaluating current signals of irradiated sensors via light injection at fluences up to $`\Phi_{eq} = 2\times 10^{ 14} \ n_{ eq } \,\text{cm} ^ 2`$. injection at fluences up to $`\Phi_{eq} = 2\times 10^{14} \ n_{eq}\,\text{cm}^2`$. This model can be selected in the configuration file via the parameter `trapping_model = "ljubljana"`. This model can be selected in the configuration file via the parameter `trapping_model = "ljubljana"`. ### Dortmund The Dortmund(sometimes referred to as * Krasel*) model \[[@dortmundTrapping]\], describes the effective trapping times as The Dortmund (sometimes referred to as *Krasel*) model \[[@dortmundTrapping]\], describes the effective trapping times as ```math \tau^{-1} = \gamma\Phi_{eq} , Loading @@ -116,24 +89,16 @@ injection at fluences up to $`\Phi_{eq} = 2\times 10^{ with the parameters ```math \begin { aligned } \begin{aligned} \gamma_{e} &= 5.13\times 10^{-16} \,\text{cm}^2\,\text{ns}^{-1} \\ \gamma_{h} &= 5.04\times 10^{-16} \,\text{cm}^2\,\text{ns}^{-1} \end { aligned } \end{aligned} ``` for electrons and holes, respectively. The values have been extracted evaluating current signals of irradiated sensors via light injection at fluences up to $`\Phi_{eq} = 8.9 \times 10^{ 14}\ n_{ eq } \,\text{cm} ^ 2`$, at a temperature of $`T = 0\,\text {°C }`$. No temperature scaling is $`\Phi_{eq} = 8.9 \times 10^{14}\ n_{eq}\,\text{cm}^2`$, at a temperature of $`T = 0\,\text{°C}`$. No temperature scaling is provided. Values for neutron and proton irradiation have been evaluated in \[[@dortmundTrapping]\], Allpix Squared makes use of the values for proton irradiation. Loading @@ -142,34 +107,25 @@ This model can be selected in the configuration file via the parameter `trapping ### CMS Tracker This effective trapping model has been developed by the CMS Tracker Group. It follows the results of \[[@CMSTrackerTrapping]\], with measurements at fluences of up to $`\Phi_{eq} = 3 \times 10^{ 15} \ n_{ eq } \,\text{cm} ^ 2`$, at a temperature of $`T = -20 \,\text {°C } `$ and an irradiation with protons. \[[@CMSTrackerTrapping]\], with measurements at fluences of up to $`\Phi_{eq} = 3 \times 10^{15} \ n_{eq}\,\text{cm}^2`$, at a temperature of $`T = -20 \,\text{°C}`$ and an irradiation with protons. The interpolation of the results follows the relation ```math \tau ^ { -1 } = {\beta\Phi_{eq}} + \tau_0 ^ { -1 } \tau^{-1} = {\beta\Phi_{eq}} + \tau_0^{-1} ``` with the parameters ```math \begin { aligned } \begin{aligned} \beta_{e}(T_0) &= 1.71\times 10^{-16} \,\text{cm}^2\,\text{ns}^{-1} \\ \tau_{0,e}^{-1} &= -0.114 \,\text{ns}^{-1} \\ \\ \beta_{h}(T_0) &= 2.79\times 10^{-16} \,\text{cm}^2\,\text{ns}^{-1} \\ \tau_{0,h}^{-1} &= -0.093 \,\text{ns}^{-1} \end{ aligned } \end{aligned} ``` for electrons and holes, respectively. Loading @@ -181,12 +137,7 @@ This model can be selected in the configuration file via the parameter `trapping ### Mandic The Mandić model \[[@Mandic]\] is an empirical model developed from measurements with high fluences ranging from $`\Phi_{eq} = 5\times 10^{ 15} \ n_{ eq } \,\text{cm} ^ 2`$ to $`\Phi_{eq} = 1\times 10 ^ { 17 } \ n_ { eq } \,\text{cm}^2`$ and describes $`\Phi_{eq} = 5\times 10^{15} \ n_{eq}\,\text{cm}^2`$ to $`\Phi_{eq} = 1\times 10^{17} \ n_{eq}\,\text{cm}^2`$ and describes the lifetime via ```math Loading @@ -197,31 +148,18 @@ with the parameters ```math \begin{aligned} c_e &= 0.54 \,\text{ ns } \,\text{cm} ^ { -2 } \\ c_e &= 0.054 \,\text{ns}\,\text{cm}^{-2} \\ \kappa_e &= -0.62 \\ \ c_h &= 0.0427 \,\text { ns } \,\text{cm} ^ { -2 } \\ \\ c_h &= 0.0427 \,\text{ns}\,\text{cm}^{-2} \\ \kappa_h &= -0.62 \end { aligned } \end{aligned} ``` for electrons and holes, respectively. The parameters for electrons are taken from \[[@Mandic]\], for measurements at a temperature of $`T = -20 \,\text{ °C } `$, and the results extrapolated to $`T = -30 \,\text {°C }`$. See \[[@MandicErratum]\] for updated power function fitting parameters. A scaling from electrons to holes was performed based on the default The parameters for electrons are taken from \[[@Mandic]\], for measurements at a temperature of $`T = -20 \,\text{°C}`$, and the results extrapolated to $`T = -30 \,\text{°C}`$. A scaling from electrons to holes was performed based on the default values in Weightfield2 \[[@weightfield2]\]. This model can be selected in the configuration file via the parameter `trapping_model = "mandic"`. Loading Loading @@ -261,13 +199,10 @@ as arrays via the `trapping_parameters_electrons` and `trapping_parameters_holes are denoted with squared brackets and a parameter number, for example `[0]` for the first parameter provided. Parameters specified separately from the formula can contain units which will be interpreted automatically. { { % alert title = "Note" color = "info" % } } Both fluence and temperature are not inherently available in the custom trapping model, but need to be provided as additional parameters as described above.{ { % / alert % } } {{% alert title="Note" color="info" %}} Both fluence and temperature are not inherently available in the custom trapping model, but need to be provided as additional parameters as described above. {{% /alert %}} The following configuration parameters replicate the [Ljubljana model](#ljubljana) using a custom trapping model. Loading Loading @@ -324,5 +259,4 @@ detrapping_time_hole = 10ns [@dortmundTrapping]: https://doi.org/10.1109/TNS.2004.839096 [@CMSTrackerTrapping]: https://doi.org/10.1088/1748-0221/11/04/p04023 [@Mandic]: https://doi.org/10.1088/1748-0221/15/11/p11018 [@MandicErratum]: https://doi.org/10.1088/1748-0221/16/03/E03001 [@weightfield2]: http://personalpages.to.infn.it/~cartigli/Weightfield2/index.html
src/physics/Trapping.hpp +1 −1 Original line number Diff line number Diff line Loading @@ -136,7 +136,7 @@ namespace allpix { class Mandic : virtual public TrappingModel { public: explicit Mandic(double fluence) { tau_eff_electron_ = 0.54 * pow(fluence / Units::get(1e16, "/cm/cm"), -0.62); tau_eff_electron_ = 0.054 * pow(fluence / Units::get(1e16, "/cm/cm"), -0.62); tau_eff_hole_ = tau_eff_electron_ * (4.9 / 6.2); } }; Loading
