optimpv.RateEqfits package

Submodules

optimpv.RateEqfits.Pumps module

Pump pulse generation for transient experiments

optimpv.RateEqfits.Pumps.gaussian_pulse_norm(t, tpulse, width)[source]

Returns a gaussian pulse

Parameters:

  • t (1-D sequence of floats) – t time axis (unit: s)

  • tpulse (float) – tpulse center of the pulse (unit: s)

  • width (float) – width of the pulse (unit: s)

Returns:

Vector containing the gaussian pulse

Return type:

1-D sequence of floats

optimpv.RateEqfits.Pumps.gaussian_pump(t, fpu, pulse_width, P, t0, background=0, G_frac=1)[source]

Gaussian pump pulse

Parameters:

  • t (ndarray of shape (n,)) – array of time values in seconds

  • fpu (float) – pump frequency in Hz

  • pulse_width (float) – width of the pump pulse in seconds

  • P (float) – total volume density of generated photons m^-3

  • t0 (float) – center of the pulse in seconds

  • background (float, optional) – background volume density of generated photons, by default 0

  • G_frac (float, optional) – scaling for the power of the pulse, by default 1

Returns:

density of generated photons m^-3 at each time point

Return type:

ndarray of shape (n,)

optimpv.RateEqfits.Pumps.get_flux_density(Power, wavelength, fpu, Area, alpha)[source]

From the measured power, repetition rate and area, get photons/m2 and approximate photons/m3 per pulse

Parameters:

  • Power (float) – total CW power of pulse in W

  • wavelength (float) – excitation wavelength in m

  • fpu (float) – repetition rate in Hz

  • Area (float) – effective pump area in m^-2

  • alpha (float) – penetration depth in m

Returns:

  • flux (float) – flux in photons m^-2

  • density (float) – average volume density in photons m^-3

optimpv.RateEqfits.Pumps.initial_carrier_density(t, fpu, N0, background=0, G_frac=1)[source]

Initial carrier density

Parameters:

  • t (ndarray of shape (n,)) – array of time values in seconds

  • fpu (float) – pump frequency in Hz

  • N0 (float) – initial carrier density in m^-3

  • background (float, optional) – background carrier density, by default 0

  • G_frac (float, optional) – scaling for the power of the pulse, by default 1

Returns:

initial carrier density in m^-3

Return type:

ndarray of shape (n,)

optimpv.RateEqfits.Pumps.square_pump(t, fpu, pulse_width, P, t0=0, background=0, G_frac=1)[source]

Square pump pulse

Parameters:

  • t (ndarray of shape (n,)) – array of time values in seconds

  • fpu (float) – pump frequency in Hz

  • pulse_width (float) – width of the pump pulse in seconds

  • P (float) – total volume density of generated photons m^-3

  • t0 (float, optional) – time shift of the pump pulse, by default 0

  • background (float, optional) – background volume density of generated photons, by default 0

  • G_frac (float, optional) – scaling for the power of the pulse, by default 1

Returns:

density of generated photons m^-3 at each time point

Return type:

ndarray of shape (n,)

optimpv.RateEqfits.RateEqAgent module

Provides general functionality for Agent objects for Rate Equation simulations

class optimpv.RateEqfits.RateEqAgent.RateEqAgent(params, X, y, model=<function BT_model>, pump_model=<function initial_carrier_density>, pump_args={}, exp_format='trPL', fixed_model_args={}, metric='mse', loss='linear', threshold=100, minimize=True, yerr=None, weight=None, tracking_metric=None, tracking_loss=None, tracking_exp_format=None, tracking_X=None, tracking_y=None, tracking_weight=None, name='RateEq', equilibrate=True, detection_limit=None, **kwargs)[source]

Bases: BaseAgent

Agent object for fitting rate equation models. Available models are:

  • Bimolecular-Trapping (BT)

  • Bimolecular-Trapping-detrapping (BTD)

see optimpv.RateEqfits.RateEqModel.py for more details about the available models

Parameters:

  • params (list of Fitparam() objects) – List of Fitparam() objects.

  • X (array-like) – 1-D or 2-D array containing the voltage (1st column) and if specified the Gfrac (2nd column) values.

  • y (array-like) – 1-D array containing the current values.

  • pump_model (function, optional) – Function to get the generated carrier density profile, by default initial_carrier_density.

  • pump_args (dict, optional) – Arguments for the pump_model function, by default {}.

  • exp_format (str or list of str, optional) – Format of the experimental data, cane be [‘trPL’,’TAS’,’trMC’], by default ‘trPL’.

  • exp_format_agrs (dict, optional) – Arguments dependent on the exp_format function, by default {}.

  • metric (str or list of str, optional) – Metric to evaluate the model, see optimpv.general.calc_metric for options, by default ‘mse’.

  • loss (str or list of str, optional) – Loss function to use, see optimpv.general.loss_function for options, by default ‘linear’.

  • threshold (int or list of int, optional) – Threshold value for the loss function used when doing multi-objective optimization, by default 100.

  • minimize (bool or list of bool, optional) – If True then minimize the loss function, if False then maximize the loss function (note that if running a fit minize should be True), by default True.

  • yerr (array-like or list of array-like, optional) – Errors in the current values, by default None.

  • weight (array-like or list of array-like, optional) – Weights used for fitting if weight is None and yerr is not None, then weight = 1/yerr**2, by default None.

  • tracking_metric (str or list of str, optional) – Additional metrics to track and report in run_Ax output, by default None.

  • tracking_loss (str or list of str, optional) – Loss functions to apply to tracking metrics, by default None.

  • tracking_exp_format (str or list of str, optional) – Experimental formats for tracking metrics, by default None.

  • tracking_X (array-like or list of array-like, optional) – X values for tracking metrics, by default None.

  • tracking_y (array-like or list of array-like, optional) – y values for tracking metrics, by default None.

  • tracking_weight (array-like or list of array-like, optional) – Weights for tracking metrics, by default None.

  • name (str, optional) – Name of the agent, by default ‘RateEq’.

  • **kwargs (dict) – Additional keyword arguments.

reformat_data(df, X, parameters, exp_format='trPL')[source]

Reformat the data to the experimental format

Parameters:

  • df (DataFrame) – DataFrame containing the simulation results.

  • X (array-like) – 1-D or 2-D array containing the voltage (1st column) and if specified the Gfrac (2nd column) values.

  • parameters (dict) – Dictionary of parameter names and values.

  • exp_format (str, optional) – Format of the experimental data, cane be [‘trPL’,’TAS’,’trMC’], by default ‘trPL’.

Returns:

DataFrame containing the simulation results in the experimental format.

Return type:

DataFrame

run(parameters, X=None, exp_format='trPL')[source]

Run the diode model and calculate the loss function

Parameters:

parameters (dict) – Dictionary of parameter names and values.

Returns:

Array containing the current values.

Return type:

array-like

run_Ax(parameters)[source]

Run the diode model and calculate the loss function

Parameters:

parameters (dict) – Dictionary of parameter names and values.

Returns:

Loss function value.

Return type:

float

run_RateEq(parameters)[source]

Run the diode model and calculate the loss function

Parameters:

parameters (dict) – Dictionary of parameter names and values.

Returns:

Loss function value.

Return type:

float

optimpv.RateEqfits.RateEqModel module

Rate equation models for charge carrier dynamics in semiconductors

optimpv.RateEqfits.RateEqModel.BTD_model(parameters, t, Gpulse, t_span, N0=0, G_frac=1, equilibrate=True, eq_limit=0.01, maxcount=1000.0, solver_func='odeint', output_trap_dens=False, **kwargs)[source]

Solve the bimolecular trapping and detrapping equation :

dn/dt = G - k_trap * n * (N_t_bulk - n_t) - k_direct * n * (p + N_A) dn_t/dt = k_trap * n * (N_t_bulk - n_t) - k_detrap * n_t * (p + N_A) dp/dt = G - k_detrap * n_t * (p + N_A) - k_direct * n * (p + N_A)

Based on the beautiful work of:

Péan, Emmanuel V. and Dimitrov, Stoichko and De Castro, Catherine S. and Davies, Matthew L., Phys. Chem. Chem. Phys., 2020,22, 28345-28358, http://dx.doi.org/10.1039/D0CP04950F

Parameters:

  • parameters (dict) –

    dictionary containing the parameters of the model it must contain ‘k_trap’, ‘k_direct’, ‘k_detrap’, ‘N_t_bulk’ and ‘N_A’.

    k_trapfloat

    Trapping rate constant in m^3 s^-1

    k_directfloat

    Bimolecular/direct recombination rate constant in m^3 s^-1

    k_detrapfloat

    Detrapping rate constant in m^3 s^-1

    N_t_bulkfloat

    Bulk trap density in m^-3

    N_Afloat

    Ionized p-doping concentration in m^-3

  • t (ndarray of shape (n,)) – time values in s

  • Gpulse (ndarray of shape (n,)) – array of values of the charge carrier generation rate m^-3 s^-1

  • t_span (ndarray of shape (n,), optional) – time values for the pulse time step in case it is different from t, by default None

  • N0 (float, optional) – initial values of the electron, trapped electron and hole concentrations in m^-3, by default 0

  • G_frac (float, optional) – fraction of the generation rate that is absorbed, by default 1

  • equilibrate (bool, optional) – whether to equilibrate the system, by default True

  • eq_limit (float, optional) – limit for the relative change of the last time point to the previous one to consider the system in equilibrium, by default 1e-2

  • maxcount (int, optional) – maximum number of iterations to reach equilibrium, by default 1e3

  • solver_func (str, optional) – solver function to use can be [‘odeint’,’solve_ivp’], by default ‘odeint’

  • output_trap_dens (bool, optional) – whether to output the trapped electron concentration, by default False

  • kwargs (dict) –

    additional keyword arguments for the solver function

    ’method’str, optional

    method to use for the solver, by default ‘RK45’

    ’rtol’float, optional

    relative tolerance, by default 1e-3

Returns:

  • ndarray of shape (n,) – electron concentration in m^-3

  • ndarray of shape (n,) – hole concentration in m^-3

  • ndarray of shape (n,) – if output_trap_dens is True then we also output trapped electron concentration in m^-3

optimpv.RateEqfits.RateEqModel.BT_model(parameters, t, Gpulse, t_span, N0=0, G_frac=1, equilibrate=True, eq_limit=0.01, maxcount=1000.0, solver_func='solve_ivp', **kwargs)[source]

Solve the bimolecular trapping equation :

dn/dt = G - k_trap * n - k_direct * n^2

Based on the beautiful work of:

Péan, Emmanuel V. and Dimitrov, Stoichko and De Castro, Catherine S. and Davies, Matthew L., Phys. Chem. Chem. Phys., 2020,22, 28345-28358, http://dx.doi.org/10.1039/D0CP04950F

Parameters:

  • parameters (dict) –

    dictionary containing the parameters of the model it must contain ‘k_trap’ and ‘k_direct’.
    ’k_trap’float

    trapping rate constant in s^-1

    ’k_direct’float

    Bimolecular/direct recombination rate constant in m^-3 s^-1

  • t (ndarray of shape (n,)) – array of time values

  • G (ndarray of shape (n,)) – array of values of the charge carrier generation rate m^-3 s^-1

  • t_span (ndarray of shape (n,), optional) – array of time values for the pulse time step in case it is different from t, by default None

  • N0 (float, optional) – initial value of the charge carrier density, by default 0

  • G_frac (float, optional) – fraction of the generation rate that is absorbed, by default 1

  • equilibrate (bool, optional) – make sure equilibrium is reached?, by default True

  • eq_limit (float, optional) – relative change of the last time point to the previous one, by default 1e-2

  • maxcount (int, optional) – maximum number of iterations to reach equilibrium, by default 1e3

  • solver_func (str, optional) – solver function to use can be [‘odeint’,’solve_ivp’], by default ‘solve_ivp’

  • kwargs (dict) –

    additional keyword arguments for the solver function
    ’method’str, optional

    method to use for the solver, by default ‘RK45’

    ’rtol’float, optional

    relative tolerance, by default 1e-3

Returns:

array of values of the charge carrier density m^-3

Return type:

ndarray of shape (n,)

optimpv.RateEqfits.RateEqModel.DBTD_model(parameters, t, Gpulse, t_span, N0=0, G_frac=1, equilibrate=True, eq_limit=0.01, maxcount=1000.0, output_integrated_values=True, **kwargs)[source]

Solve the diffusion bimolecular trapping and detrapping model including diffusion.

The rate equation and model used here are based on the work by [Kober-Czerny et al. 2025](https://doi.org/10.1103/PRXEnergy.4.013001) see the [paper](https://doi.org/10.1103/PRXEnergy.4.013001) for more details or the [GitHub repository](https://github.com/manuelkoberczerny/assessing-TRPL-with-bayesian-inference_and-MCMC).

Parameters:

  • parameters (dict) –

    dictionary containing the parameters of the model it must contain ‘k_trap’, ‘k_direct’, ‘k_detrap’, ‘N_t_bulk’ and ‘N_A’.

    k_directfloat

    Bimolecular/direct recombination rate constant in m^3 s^-1

    k_deepfloat

    Deep trap rate constant in s^-1

    k_cfloat

    Capture rate constant in s^-1

    k_efloat

    Electron emission rate constant in s^-1

    S_frontfloat

    Front surface recombination velocity in m s^-1

    S_backfloat

    Back surface recombination velocity in m s^-1

    N_Afloat

    Acceptor doping density in m^-3

    Lfloat

    Length of the device in m

    alphafloat

    Absorption coefficient in m^-1

    mufloat

    Mobility in m^2 V^-1 s^-1

    Tfloat

    Temperature in K, by default 300

  • t (ndarray of shape (n,)) – time values in s

  • Gpulse (ndarray of shape (n,)) – array of values of the charge carrier generation rate m^-3 s^-1

  • t_span (ndarray of shape (n,), optional) – time values for the pulse time step in case it is different from t, by default None

  • N0 (float, optional) – initial values of the electron, trapped electron and hole concentrations in m^-3, by default 0

  • G_frac (float, optional) – fraction of the generation rate that is absorbed, by default 1

  • equilibrate (bool, optional) – whether to equilibrate the system, by default True

  • eq_limit (float, optional) – limit for the relative change of the last time point to the previous one to consider the system in equilibrium, by default 1e-2

  • maxcount (int, optional) – maximum number of iterations to reach equilibrium, by default 1e3

  • output_integrated_values (bool, optional) – whether to output the integrated values, by default True

  • kwargs (dict) –

    additional keyword arguments for the solver function
    ’grid_size’int, optional

    size of the grid for the spatial discretization, by default 100

Returns:

  • list or ndarray – The integrated values of the electron density versus time and space. Each element of the list corresponds to a specific time point and contains the electron density values at different spatial positions.

  • list or ndarray – The integrated values of the hole density versus time and space. Each element of the list corresponds to a specific time point and contains the hole density values at different spatial positions.

Raises:

ValueError – If the parameters are not valid.

optimpv.RateEqfits.RateEqModel.DBTD_multi_trap(parameters, t, Gpulse, t_span, N0=0, G_frac=1, equilibrate=True, eq_limit=0.01, maxcount=1000.0, output_integrated_values=True, **kwargs)[source]

Solve the bimolecular, multi-trap trapping and detrapping model including diffusion. This implementation is based on the work by [M. Simmonds](https://github.com/MaximSimmonds-HZB/MAPI-FAPI-fitting).

Note: This needs to be tested further, I think there are some issues regarding the stability of the solver and whether the diffusion part was implemented properly.

Parameters:

  • parameters (dict) –

    dictionary containing the parameters of the model it must contain ‘k_trap’, ‘k_direct’, ‘k_detrap’, ‘N_t_bulk’ and ‘N_A’.

    k_directfloat

    Bimolecular/direct recombination rate constant in m^3 s^-1

    N_t_bulkfloat

    Bulk trap density (can be multiple) in m^-3

    C_nfloat

    Electron capture coefficient (can be multiple) in m^3 s^-1

    C_pfloat

    Hole capture coefficient (can be multiple) in m^3 s^-1

    E_t_bulkfloat

    Relative trap depth in the bandgap (can be multiple) in eV

    Lfloat

    Length of the device in m

    alphafloat

    Absorption coefficient in m^-1

    mu_nfloat

    Electron mobility in m^2 V^-1 s^-1

    mu_pfloat

    Hole mobility in m^2 V^-1 s^-1

    N_cfloat

    Effective density of states of the conduction band in m^-3

    N_vfloat

    Effective density of states of the valence band in m^-3

    Egfloat

    Bandgap energy in eV

    Tfloat

    Temperature in K

  • t (ndarray of shape (n,)) – time values in s

  • Gpulse (ndarray of shape (n,)) – array of values of the charge carrier generation rate m^-3 s^-1

  • t_span (ndarray of shape (n,), optional) – time values for the pulse time step in case it is different from t, by default None

  • N0 (float, optional) – initial values of the electron, trapped electron and hole concentrations in m^-3, by default 0

  • G_frac (float, optional) – fraction of the generation rate that is absorbed, by default 1

  • equilibrate (bool, optional) – whether to equilibrate the system, by default True

  • eq_limit (float, optional) – limit for the relative change of the last time point to the previous one to consider the system in equilibrium, by default 1e-2

  • maxcount (int, optional) – maximum number of iterations to reach equilibrium, by default 1e3

  • output_integrated_values (bool, optional) – whether to output the integrated values, by default True

  • kwargs (dict) –

    additional keyword arguments for the solver function

    ’method’str, optional

    method to use for the solver, by default ‘Radau’

    ’rtol’float, optional

    relative tolerance, by default 1e-3

    ’atol’float, optional

    absolute tolerance, by default 1e-6

    ’grid_size’int, optional

    size of the grid for the spatial discretization, by default 100

    ’dimensionless’bool, optional

    whether to use dimensionless variables, by default False

    ’timeout’float, optional

    maximum time to wait for the solver to finish, by default 120

Returns:

  • list or ndarray – The integrated values of the electron density versus time and space. Each element of the list corresponds to a specific time point and contains the electron density values at different spatial positions.

  • list or ndarray – The integrated values of the hole density versus time and space. Each element of the list corresponds to a specific time point and contains the hole density values at different spatial positions.

Raises:

ValueError – If the parameters are not valid.

Module contents