pySIMsalabim.aux_funcs package

Submodules

pySIMsalabim.aux_funcs.DRT module

Find System Lifetimes using Distribution of Relaxation Times (DRT) Fitting in the Time Domain

class pySIMsalabim.aux_funcs.DRT.DRT_Fit_Result(time, tau, U, y_inf, y=None, MSE=None, R_2=None)

Bases: object

A class that bundles together all results from fitting a predict_y_model curve to data

U

Fitted coefficients [U_1, U_2, …, U_m]

Type:

numpy.ndarray, shape (m,)

tau

Fitted lifetimes [tau_1, tau_2, …, tau_m]

Type:

numpy.ndarray, shape (m,)

y_inf

y_inf of the steady state of the fitted signal from 0

Type:

float

m

Number of lifetimes/coefficients used in predict_y_model, given by the length of U/tau

Type:

int

y_model

Model given by

y_model = U_1*exp(-t/tau_1) + U_2*exp(-t/tau_2)… + U_m*exp(-t/tau_m) + y_inf

Type:

{None, numpy.ndarray}

U_norm

Fitted coefficients normalised by np.sum(self.U)

Type:

{None, numpy.ndarray with shape (m,)}

MSE

Mean square error between the model (self.y) and the fitted signal

Type:

float

R_2

R^2 error between the model (self.y) and the fitted signal

Type:

float

plot_U(normalised=False, tau_analytic=None, U_analytic=None, xaxis_label='$\\tau$ [s]', yaxis_label='Auto', U_model_label='Model', U_label='Analytic', plot_title='DRT', return_ax=False)

Plot the fitted DRT against an optional analytic DRT

Parameters:

• normalised (bool (optional)) – Determines whether self.U (False) or self.U_norm (Ture) is plotted. Default (False)

• tau_analytic ({None, numpy.ndarray shape (l,)} (optional)) – Array of tau values use to generate the analytic curve, if known. This is mostly for comparision if fitting to a known DRT for testing purposes. Default None.

• U_analytic ({None, numpy.ndarray shape (l,)} (optional)) – Array of U values used in the analytic curve, if known. This is mostly for comparision if fitting to a known DRT for testing purposes. Default None.

• xaxis_label (str (optional)) – Label for the x axis of the output plot. ‘$tau$ [s]’ by default.

• yaxis_label (str (optional)) – Label for the y axis of the output plot. ‘U’ by default.

• U_model_label (str (optional)) – Label for the curve U_model in the output plot legend. ‘Model’ by default.

• U_label (str (optional)) – Label for the U_analytic curve in the output plot legend. ‘Analytic’ by default.

• plot_title (str (optional)) – Title of the output plot. ‘DRT’ by default.

• return_ax (bool (optional)) – Determines whether the matplotlib.axes.Axes object is returned (True) or plotted (False). Default False.

Returns:

ax – Returned axes object if return_ax is True.

Return type:

matplotlib.axes.Axes (optional)

plot_cumulative_U(normalised=False, tau_analytic=None, U_analytic=None, xaxis_label='$\\tau$ [s]', yaxis_label='Auto', U_model_label='Model', U_label='Analytic', plot_title='Cumulative DRT', return_ax=False)

Plot the cumulative sum of self.U or self.U_norm, optionally against a known analytical form.

Parameters:

• normalised (bool (optional)) – Determines whether self.U (False) or self.U_norm (Ture) is plotted. Default (False)

• tau_analytic ({None, numpy.ndarray shape (l,)} (optional)) – Array of tau values use to generate the analytic curve, if known. This is mostly for comparision if fitting to a known DRT for testing purposes. Default None.

• U_analytic ({None, numpy.ndarray shape (l,)} (optional)) – Array of U values used in the analytic curve, if known. This is mostly for comparision if fitting to a known DRT for testing purposes. Default None.

• xaxis_label (str (optional)) – Label for the x axis of the output plot. ‘$tau$ [s]’ by default.

• yaxis_label (str (optional)) – Label for the y axis of the output plot. ‘Cumulative U’ by default.

• U_model_label (str (optional)) – Label for the curve U_model in the output plot legend. ‘Model’ by default.

• U_label (str (optional)) – Label for the U_analytic curve in the output plot legend. ‘Analytic’ by default.

• plot_title (str (optional)) – Title of the output plot. ‘Cumulative DRT’ by default.

• return_ax (bool (optional)) – Determines whether the matplotlib.axes.Axes object is returned (True) or plotted (False). Default False.

Returns:

ax – Returned axes object if return_ax is True.

Return type:

matplotlib.axes.Axes (optional)

plot_y_model(time, y_data=None, xaxis_label='Time [s]', yaxis_label='y(t)', y_data_plot_label='Data', y_model_plot_label='Model', plot_title='DRT Fit', return_ax=False)

Plot the fitted model agains the data

Parameters:

• time (numpy.ndarray, shape (n,)) – The time values over which the simulated experiment took place

• y_data ({None, numpy.ndarray shape (n,)} (optional)) – The data the model was fitted to. Either y_model or y must not be None. y is None by default.

• xaxis_label (str (optional)) – Label for the x axis of the output plot. ‘Time [s]’ by default.

• yaxis_label (str (optional)) – Label for the y axis of the output plot. ‘y(t)’ by default.

• y_data_plot_label (str (optional)) – Label for the curve y in the output plot legend. ‘Data’ by default.

• y_model_plot_label (str (optional)) – Label for the y_model curve in the output plot legend. ‘Model’ by default.

• plot_title (str (optional)) – Title of the output plot. ‘DRT Fit’ by default.

• return_ax (bool (optional)) – Determines whether the matplotlib.axes.Axes object is returned (True) or plotted (False). Default False.

Returns:

ax – Returned axes object if return_ax is True.

Return type:

matplotlib.axes.Axes (optional)

set_U_norm()

Set self.U_norm equal to self.U/np.sum(self.U)

set_y_model(t)

Sets self.predict_y_model = predict_y_model(t) using the objects attributes

Parameters:

• t (float or list/numpy.ndarray, shape (n,)) – Time values to calculate the predict_y_model curve

• backend ({'numpy', 'torch'} (optional)) – Determines whether matrix operations are done with numpy or pytorch. Default numpy.

• device (torch.device (optional)) – Determines what device is used for matrix ops if backend=’torch’.

Return type:

None

exception pySIMsalabim.aux_funcs.DRT.FitError

Bases: Exception

Custom fit error

pySIMsalabim.aux_funcs.DRT.calculate_tau(time)

Generate a range of tau values for DRT fitting based off an observation window over time values ‘time’

Parameters:

time (arraylike, shape (n,)) – Time values data is observed over

Returns:

tau_values

Return type:

arraylike, shape (m,)

pySIMsalabim.aux_funcs.DRT.checkerboard_fit(time, y_data, tau='Auto', y_inf='Auto', checkerboard_iters=50, fit_scaling=True)

Performs a ‘checkerboard’ DRT fit by iteratively fitting capacitive and inductive effects in supplied data (y)

Parameters:

• time (arraylike, shape (n,)) – Time values over which the simulated experiment took place

• y_data (arraylike, shape (n,)) – Data for model fitting

• tau ({'Auto', tuple(tau_min, tau_max, m), array_like of shape (m,)} (optional)) –

  The tau values used in the model

  y_model = U_1*exp(-t/tau_1) + U_2*exp(-t/tau_2)… + U_m*exp(-t/tau_m) + y_inf

  ’Auto’ will use the ‘calculate_tau’ method to determine lifetimes for fitting. Passing a tuple in the form (tau_min, tau_max, m) will generate a logarithmic array of m values between tau_min and tau_max. Any passed array_like that isn’t a tuple of length 3 will be used for all tau values. Default ‘Auto’.

• y_inf ({'Auto', float} (optional)) – Amplitude of steady state signal, assumed to be at y(infinity) when set to ‘Auto’. (Default ‘Auto’)

• checkerboard_iters (int, optional) – The number of iterations to perform using the checkerboard fitting method. (Default 50)

• fit_scaling (bool, optional) – Determines whether minmax scaling is used during each call of the ‘linear_fit’ method. Can impact the smoothness of the MSE and R^2 over many iterations. Default True.

Returns:

fits – An array of fit objects corresponding to each iteration of the checkerboard procedure.

Return type:

arraylike(DRT_Fit_Results), shape (checkerboard_iters,)

Raises:

• FitError – Invalid input: input time and input data (y_data) have mismatch lengths

• FitError – Invalid input: ‘tau’ must be either ‘Auto’, a tuple of length 3, or an array-like of length n

• FitError – Invalid input: ‘y_inf’ must be either ‘Auto’ or a float

pySIMsalabim.aux_funcs.DRT.linear_fit(time, y_data, tau='Auto', y_inf='Auto', bounds=None, scaling=True)

Performs a linear fit of

y_model = U_1*exp(-t/tau_1) + U_2*exp(-t/tau_2)… + U_m*exp(-t/tau_m) + y_inf

to the data (y_data)

Converts the linear fit problem to a convex quadratic program and minimises using the Operator Splitting Quadratic Program (OSQP) package solver [2]. Using a QP solver was inspired by the pyDRTtools package [3].

Parameters:

• time (numpy.ndarray, shape (n,)) – Time values over which the simulated experiment took place

• y_data (numpy.ndarray, shape (n,)) – Data for model fitting

• tau ({'Auto', (tau_min, tau_max, m), array_like of shape (m,)} (optional)) –

  The tau values used in the model

  y_model = U_1*exp(-t/tau_1) + U_2*exp(-t/tau_2)… + U_m*exp(-t/tau_m) + y_inf

  ’Auto’ will use the ‘calculate_tau’ method to determine lifetimes for fitting. Passing a tuple in the form (tau_min, tau_max, m) will generate a logarithmic array of m values between tau_min and tau_max. Any passed array_like that isn’t a tuple of length 3 will be used for all tau values. Default ‘Auto’.

• bounds ({None, (lower, upper)} (optional)) – Sets the bounds for the fitted coeffs. U. Use np.inf for unbounded limit. Default None.

• scaling (bool (optional)) – Determines whether minmax scaling is applied to the data before fitting (the data is scaled back post fit). Would recomend leaving at default value. Default True.

• Results

• -------

• fit (DRT_Fit_Result) – Fit object containing fit data.

pySIMsalabim.aux_funcs.DRT.main(argv=None)

Script entry point for running a checkerboard fit.

Parameters:

argv ([str] (optional)) – List of strings containing command line args and flags. Default None

Returns:

EXIT_CODE – 0 on a success 1 on a failure 2 on a failure due to a usage error

Return type:

int

pySIMsalabim.aux_funcs.DRT.parse_arguments(argv=None)

Parses command line arguments into an ArgumentParser object

Parameters:

argv ({[str] or Dict[str, str]} (optional)) – List or dictrionary of strings containing command line args and flags. If list, must be in the format [dataFile_path, ‘-flag1’, argument1, ‘-flag2’, argument2, …]. If dict, must be in the format {‘dataFile’ : dataFile_path, ‘flag1’ : argument1, …} If none, parses sys.argv[1:] instead.

Returns:

args

Return type:

argparse.ArgumentParser

Example

# Parses sys.argv[1:] args1 = parse_arguments()

# Parses a list args2 = parse_arguments([‘dataFile.txt’, ‘-timeCol’, ‘time’, ‘-iters’, ‘20’])

# Parses a dictionary args3 = parse_arguments([‘dataFile’ : ‘dataFile.txt’, ‘timeCol’ : ‘time’, ‘iters’ : ‘20’])

pySIMsalabim.aux_funcs.DRT.plot_MSE(error_array, xaxis_label='Iteration', yaxis_label='MSE', plot_title='MSE per Fit Iteration', return_ax=False)

Plots the mean square error. Useful for checking how the MSE varies with iteration during checkerboard fit.

Parameters:

• error_array ({array_like(DRT_Fit_Result) of shape (i,), arraylike(float)}) – An iterable conatining EITHER DRT_Fit_Result objects from which the MSE values are taken OR float values which are considered to be the MSE values

• xaxis_label (str (optional)) – Label for the x axis of the output plot. ‘Iteration’ by default.

• yaxis_label (str (optional)) – Label for the y axis of the ouput plot. ‘MSE’ by default.

• plot_title (str (optional)) – Title for the output plot. ‘MSE per Fit Iteration’ by default.

• return_ax (bool (optional)) – Determines whether the matplotlib.axes.Axes object is returned (True) or plotted (False). Default False.

Returns:

ax – Returned axes object if return_ax is True.

Return type:

matplotlib.axes.Axes (optional)

pySIMsalabim.aux_funcs.DRT.plot_R_2(error_array, ylim=(0, 1.1), xaxis_label='Iteration', yaxis_label='$R^2$', plot_title='$R^2$ per fit Iteration', return_ax=False)

Plots the R^2 error. Useful for checking how R^2 varies with iteration during checkerboard fit.

Parameters:

• fit_array (array_like(DRT_Fit_Result), shape (i,)) – An iterable conatining DRT_Fit_Result objects from which the R^2 values are taken

• ylim (tuple, (2,) (optional)) – Set the ylimits of the plot. ylim[0] gives the lower bound, y[1] the upper. Default (0, 1.1)

• xaxis_label (str (optional)) – Label for the x axis of the output plot. ‘Iteration’ by default.

• yaxis_label (str (optional)) – Label for the y axis of the ouput plot. ‘$R^2$’ by default.

• plot_title (str (optional)) – Title for the output plot. ‘$R^2$ per fit Iteration’.

• return_ax (bool (optional)) – Determines whether the matplotlib.axes.Axes object is returned (True) or plotted (False). Default False.

Returns:

ax – Returned axes object if return_ax is True.

Return type:

matplotlib.axes.Axes (optional)

pySIMsalabim.aux_funcs.DRT.plot_U(tau_model, U_model, tau_analytic=None, U_analytic=None, xaxis_label='$\\tau$ [s]', yaxis_label='U', U_model_label='Model', U_label='Analytic', plot_title='DRT', return_ax=False)

Plot the fitted DRT against an optional analytic DRT

Parameters:

• tau_model (numpy.ndarray, shape (m,)) – The tau values used in the model

• U_model (numpy.ndarray shape (m,)) –

  The coeffs from the DRT fit, given by U in

  y_model = U_1*exp(-t/tau_1) + U_2*exp(-t/tau_2)… + U_m*exp(-t/tau_m) + y_inf

• tau_analytic ({None, numpy.ndarray shape (l,)} (optional)) – Array of tau values use to generate the analytic curve, if known. This is mostly for comparision if fitting to a known DRT for testing purposes. Default None.

• U_analytic ({None, numpy.ndarray shape (l,)} (optional)) – Array of U values used in the analytic curve, if known. This is mostly for comparision if fitting to a known DRT for testing purposes. Default None.

• xaxis_label (str (optional)) – Label for the x axis of the output plot. ‘$tau$ [s]’ by default.

• yaxis_label (str (optional)) – Label for the y axis of the output plot. ‘U’ by default.

• U_model_label (str (optional)) – Label for the curve U_model in the output plot legend. ‘Model’ by default.

• U_label (str (optional)) – Label for the U_analytic curve in the output plot legend. ‘Analytic’ by default.

• plot_title (str (optional)) – Title of the output plot. ‘DRT’ by default.

• return_ax (bool (optional)) – Determines whether the matplotlib.axes.Axes object is returned (True) or plotted (False). Default False.

Returns:

ax – Returned axes object if return_ax is True.

Return type:

matplotlib.axes.Axes (optional)

pySIMsalabim.aux_funcs.DRT.plot_cumulative_U(tau_model, U_model, tau_analytic=None, U_analytic=None, xaxis_label='$\\tau$ [s]', yaxis_label='Cumulative U', U_model_label='Model', U_label='Analytic', plot_title='Cumulative DRT', return_ax=False)

Plot the fitted DRT against an optional analytic DRT

Parameters:

• tau_model (numpy.ndarray, shape (m,)) – The tau values used in the model

• U_model (numpy.ndarray shape (m,)) –

  The coeffs from the DRT fit, given by U in

  y_model = U_1*exp(-t/tau_1) + U_2*exp(-t/tau_2)… + U_m*exp(-t/tau_m) + y_inf

• tau_analytic ({None, numpy.ndarray shape (l,)} (optional)) – Array of tau values use to generate the analytic curve, if known. This is mostly for comparision if fitting to a known DRT for testing purposes. Default None.

• U_analytic ({None, numpy.ndarray shape (l,)} (optional)) – Array of U values used in the analytic curve, if known. This is mostly for comparision if fitting to a known DRT for testing purposes. Default None.

• xaxis_label (str (optional)) – Label for the x axis of the output plot. ‘$tau$ [s]’ by default.

• yaxis_label (str (optional)) – Label for the y axis of the output plot. ‘Cumulative U’ by default.

• U_model_label (str (optional)) – Label for the curve U_model in the output plot legend. ‘Model’ by default.

• U_label (str (optional)) – Label for the U_analytic curve in the output plot legend. ‘Analytic’ by default.

• plot_title (str (optional)) – Title of the output plot. ‘Cumulative DRT’ by default.

• return_ax (bool (optional)) – Determines whether the matplotlib.axes.Axes object is returned (True) or plotted (False). Default False.

Returns:

ax – Returned axes object if return_ax is True.

Return type:

matplotlib.axes.Axes (optional)

pySIMsalabim.aux_funcs.DRT.plot_y(time, y_model=None, y_data=None, xaxis_label='Time [s]', yaxis_label='y(t)', y_data_plot_label='Data', y_model_plot_label='Model', plot_title='DRT Fit', return_ax=False)

Plot the fitted model agains the data

Parameters:

• time (numpy.ndarray, shape (n,)) – The time values over which the simulated experiment took place

• y_model ({None, numpy.ndarray shape (n,)} (optional)) – The model predicted curve. Either y_model or y must not be None. y_model is None by default.

• y_data ({None, numpy.ndarray shape (n,)} (optional)) – The data the model was fitted to. Either y_model or y must not be None. y is None by default.

• xaxis_label (str (optional)) – Label for the x axis of the output plot. ‘Time [s]’ by default.

• yaxis_label (str (optional)) – Label for the y axis of the output plot. ‘y(t)’ by default.

• y_plot_label (str (optional)) – Label for the curve y in the output plot legend. ‘Data’ by default.

• y_model_plot_label (str (optional)) – Label for the y_model curve in the output plot legend. ‘Model’ by default.

• plot_title (str (optional)) – Title of the output plot. ‘DRT Fit’ by default.

• return_ax (bool (optional)) – Determines whether the matplotlib.axes.Axes object is returned (True) or plotted (False). Default False.

Returns:

ax – Returned axes object if return_ax is True.

Return type:

matplotlib.axes.Axes (optional)

pySIMsalabim.aux_funcs.DRT.predict_y_model(time, U, tau, y_inf=0)

Calculate the function

predict_y_model(t) = U_1*exp(-t/tau_1) + U_2*exp(-t/tau_2) + … + U_m*exp(-t/tau_m) + y_inf

Parameters:

• time (numpy.ndarray, shape (n,)) – The time values over which the simulated impedance-adjacent experiment takes place

• U (numpy.ndarray with shape (m,)) – Coefficients for the exponential decay functions such that U[i] is the coefficient of exp(-t/tau[i])

• tau (numpy.ndarray with shape (m,)) – The relaxation times used in the model as above.

• y_inf (float (optional)) – The amplitude of the steady state signal in y_data i.e. y(infinity)

Returns:

y_model – predict y_model at all time values in t

Return type:

numpy.ndarray with shape (n,)

pySIMsalabim.aux_funcs.DRT.save_model_errors_to_txt(path, fits, float_format='%.5e')

Save the MSE and R_2 values from a collection of DRT_Fit_Result objects to a txt file.

Parameters:

• path (str) – File path of save file

• fits (arraylike(DRT_Fit_Result)) – Array like object of fit results

• float_format (str (optional)) – Controls how float values are save to file

Return type:

None

pySIMsalabim.aux_funcs.DRT.save_model_predictions_to_txt(path, fits, float_format='%.5e')

Save the y_model values from a collection of DRT_Fit_Result objects to a txt file.

Parameters:

• path (str) – File path of save file

• fits (arraylike(DRT_Fit_Result)) – Array like object of fit results

• time (numpy.ndarray) – Time values over which each fit was made

• float_format (str (optional)) – Controls how float values are save to file

Return type:

None

pySIMsalabim.aux_funcs.DRT.save_models_to_txt(path, fits, float_format='%.5e')

Save the tau and U values from a collection of DRT_Fit_Result objects to a txt file. Stores y_inf as a # comment in the first line of the file.

Parameters:

• path (str) – File path of save file

• fits (arraylike(DRT_Fit_Result)) – Array like object of fit results

• float_format (str (optional)) – Controls how float values are save to file

Return type:

None

pySIMsalabim.aux_funcs.DRT.save_to_json(directory_path, fits)

Saves array of models to .json file in the passed directory

Parameters:

• directory_path (String) – Directory path for save data

• fits (array-like[DRT_Fit_Result])

Return type:

None

pySIMsalabim.aux_funcs.DRT.save_to_txt(directory_path, fits, float_format='%.5e')

Save tau, U, y, MSE, and R_2 values from a collection of fit objects to text files.

Parameters:

• directory_path (str) – All save files are saved to this directory

• fits (arraylike(DRT_Fit_Result)) – Array like object of fit results

• time (numpy.ndarray) – Time values over which each fit was made

• float_format (str (optional)) – Controls how float values are save to file

Return type:

None

pySIMsalabim.aux_funcs.JV_funcs module

Useful helper functions for pySIMsalabim

pySIMsalabim.aux_funcs.JV_funcs.Find_Solar_Cell_Parameters(Volt, Curr, max_interpolation_order=3, threshold_err=0.05)

Finds Jsc, Voc, MPP (and thus FF) by interpolating the V-J data points

Parameters:

• Volt (1D numpy array) – Array of voltage values.

• Curr (1D numpy array) – Array of current values corresponding to Volt.

• max_interpolation_order (int, optional) – Maximum order of the interpolation polynomial, by default 3

• threshold_err (float, optional) – Maximum allowable error for interpolation, by default 0.05

Returns:

Dictionary containing the extracted solar cell parameters.

Return type:

dict

pySIMsalabim.aux_funcs.JV_funcs.Fit_Parabola(x1, x2, x3, y1, y2, y3)

Fits a parabola through [(x1, y1), (x2, y2), (x3,y3)], y = ax^2 + bx + c

Parameters:

• x1 (float) – X-coordinates of the three points.

• x2 (float) – X-coordinates of the three points.

• x3 (float) – X-coordinates of the three points.

• y1 (float) – Y-coordinates of the three points.

• y2 (float) – Y-coordinates of the three points.

• y3 (float) – Y-coordinates of the three points.

Returns:

• a (float) – Quadratic coefficient.

• b (float) – Linear coefficient.

• c (float) – Constant term.

pySIMsalabim.aux_funcs.JV_funcs.InterExtraPolation(x, y, x0, order, extra_index=0)

Interpolation / extrapolation routine. This is a wrapper for Neville’s algorithm.

Parameters:

• x (1D numpy array) – Array of x values (ascending or descending).

• y (1D numpy array) – Array of y values corresponding to x.

• x0 (float) – Target value to interpolate or extrapolate.

• order (int) – Order of the interpolation polynomial.

• extra_index (int, optional) –

  Extrapolation control:

  0 -> no extrapolation allowed 1 -> limited extrapolation 2 -> full extrapolation

  ,by default 0

Returns:

success (bool), y_estimate (float), err_estimate (float)

Return type:

tuple

Raises:

ValueError – If the interpolation order is invalid.

pySIMsalabim.aux_funcs.JV_funcs.Locate(x, x0, imin, imax)

Simple, slow, (hopefully) robust routine to an index within

row x (from imin to imax). x0 is some target we’re looking for. The resulting index is such that x0 sits between x[i] and x[i+1] if x0 is outside the interval determined by x[imin], x[imax] then it returns imin-1 or imax+1.

Parameters:

• x (1D numpy array) – Array of x values (ascending or descending).

• x0 (float) – Target value to locate within x.

• imin (int) – Minimum index to consider.

• imax (int) – Maximum index to consider.

Returns:

Index i such that x0 sits between x[i] and x[i+1], or imin-1 or imax+1 if x0 is outside the interval.

Return type:

int

pySIMsalabim.aux_funcs.JV_funcs.Neville(x0, x, y, n=None)

Neville interpolation.

Parameters:

• x0 (float) – x0: x of desired point

• x (1D numpy array) – Array of x values (ascending or descending).

• y (1D numpy array) – Array of y values corresponding to x.

• n (int, optional) – Number of points to use (Defaults to len(x)).

Returns:

• float – Interpolated y value at x0.

• float – Estimated error of the interpolation.

pySIMsalabim.aux_funcs.JV_funcs.get_FF(Volt, Curr)

Get the fill factor (FF) from solar cell JV-curve by calculating the maximum power point

Parameters:

• Volt (1-D sequence of floats) – Array containing the voltages.

• Curr (1-D sequence of floats) – Array containing the current-densities.

Returns:

FF – Fill factor value

Return type:

float

pySIMsalabim.aux_funcs.JV_funcs.get_FF_SIMsalabim(Volt, Curr, max_interpolation_order=3, threshold_err=0.05)

SIMsalabim-style FF extraction (standalone).

Parameters:

• Volt (1D numpy array) – Array of voltage values.

• Curr (1D numpy array) – Array of current values corresponding to Volt.

• max_interpolation_order (int, optional) – Maximum order of the interpolation polynomial, by default 3

• threshold_err (float, optional) – Maximum allowable error for interpolation, by default 0.05

Returns:

Extracted fill factor (FF) value.

Return type:

float

pySIMsalabim.aux_funcs.JV_funcs.get_Jsc(Volt, Curr)

Get the short-circuit current (Jsc) from solar cell JV-curve by interpolating the current at 0 V

Parameters:

• Volt (1-D sequence of floats) – Array containing the voltages.

• Curr (1-D sequence of floats) – Array containing the current-densities.

Returns:

Jsc – Short-circuit current value

Return type:

float

pySIMsalabim.aux_funcs.JV_funcs.get_Jsc_SIMsalabim(Volt, Curr, max_interpolation_order=3, threshold_err=0.05)

SIMsalabim-style Jsc extraction (standalone).

Parameters:

• Volt (1D numpy array) – Array of voltage values.

• Curr (1D numpy array) – Array of current values corresponding to Volt.

• max_interpolation_order (int, optional) – Maximum order of the interpolation polynomial, by default 3

• threshold_err (float, optional) – Maximum allowable error for interpolation, by default 0.05

Returns:

Extracted short-circuit current (Jsc) value.

Return type:

float

pySIMsalabim.aux_funcs.JV_funcs.get_PCE(Volt, Curr, suns=1)

Get the power conversion efficiency (PCE) from solar cell JV-curve

Parameters:

• Volt (1-D sequence of floats) – Array containing the voltages.

• Curr (1-D sequence of floats) – Array containing the current-densities.

Returns:

PCE – Power conversion efficiency value.

Return type:

float

pySIMsalabim.aux_funcs.JV_funcs.get_PCE_SIMsalabim(Volt, Curr, suns=1, max_interpolation_order=3, threshold_err=0.05)

SIMsalabim-style PCE extraction (standalone).

Parameters:

• Volt (1D numpy array) – Array of voltage values.

• Curr (1D numpy array) – Array of current values corresponding to Volt.

• suns (int, optional) – Number of suns for illumination, by default 1

• max_interpolation_order (int, optional) – Maximum order of the interpolation polynomial, by default 3

• threshold_err (float, optional) – Maximum allowable error for interpolation, by default 0.05

Returns:

Extracted power conversion efficiency (PCE) value.

Return type:

float

pySIMsalabim.aux_funcs.JV_funcs.get_Vmpp_SIMsalabim(Volt, Curr)

SIMsalabim-style Vmpp extraction (standalone).

Parameters:

• Volt (1D numpy array) – Array of voltage values.

• Curr (1D numpy array) – Array of current values corresponding to Volt.

Returns:

Extracted voltage at maximum power point (Vmpp) value.

Return type:

float

pySIMsalabim.aux_funcs.JV_funcs.get_Voc(Volt, Curr)

Get the Open-circuit voltage (Voc) from solar cell JV-curve by interpolating the Voltage when the current is 0

Parameters:

• Volt (1-D sequence of floats) – Array containing the voltages.

• Curr (1-D sequence of floats) – Array containing the current-densities.

Returns:

Voc – Open-circuit voltage value

Return type:

float

pySIMsalabim.aux_funcs.JV_funcs.get_Voc_SIMsalabim(Volt, Curr, max_interpolation_order=3, threshold_err=0.05)

SIMsalabim-style Voc extraction (standalone).

Parameters:

• Volt (1D numpy array) – Array of voltage values.

• Curr (1D numpy array) – Array of current values corresponding to Volt.

• max_interpolation_order (int, optional) – Maximum order of the interpolation polynomial, by default 3

• threshold_err (float, optional) – Maximum allowable error for interpolation, by default 0.05

Returns:

Extracted open-circuit voltage (Voc) value.

Return type:

float

pySIMsalabim.aux_funcs.JV_funcs.get_ideality_factor(suns, Vocs, T=295)

Returns ideality factor from suns-Voc data linear fit of Voc = (nIF/Vt)*log(suns) + intercept

Parameters:

• suns (1-D sequence of floats) – Array containing the intensity in sun.

• Vocs (1-D sequence of floats) – Array containing the open-circuit voltages.

• T (float optional) – Temperature in Kelvin (Default = 295 K).

Returns:

• nIF (float) – Ideality factor value.

• intercept (float) – Intercept of the regression line.

• rvalue (float) – Correlation coefficient.

• pvalue (float) – Two-sided p-value for a hypothesis test whose null hypothesis is that the slope is zero, using Wald Test with t-distribution of the test statistic.

• stderr (float) – Standard error of the estimated gradient.

pySIMsalabim.aux_funcs.JV_funcs.get_mpp_SIMsalabim(Volt, Curr)

SIMsalabim-style MPP extraction (standalone).

Parameters:

• Volt (1D numpy array) – Array of voltage values.

• Curr (1D numpy array) – Array of current values corresponding to Volt.

Returns:

Extracted maximum power point (MPP) value.

Return type:

float

pySIMsalabim.aux_funcs.PathChecksWin module

Check and convert Windows paths to long path format if necessary.

pySIMsalabim.aux_funcs.PathChecksWin.convert_to_long_path(tempPath)

Convert a path to a Windows long path by adding the \?prefix

Parameters:

tempPath (string) – Path to be converted

Returns:

Converted Path object with long path prefix

Return type:

Path

pySIMsalabim.aux_funcs.SCLC_funcs module

pySIMsalabim.aux_funcs.SCLC_funcs.Make_SCLC_plot(ax, data_JV, x='Vext', y=['Jext'], show_tangent=[1, 2, 3], xlimits=[], ylimits=[], plot_type=0, labels='', colors='b', line_type=['-'], mark='', legend=True, plot_jvexp=False, data_JVexp=Empty DataFrame Columns: [] Index: [], save_yes=False, pic_save_name='JV.jpg')

Make typical plot for SCLC measurement analysis for SIMsalabim

Parameters:

• num_fig (int) – number of the fig to plot JV

• data_JV (DataFrame) – Panda DataFrame containing JV_file

• x (str, optional) – xaxis data (default = ‘Vext’), by default ‘Vext’

• y (list of str, optional) – yaxis data can be multiple like [‘Jext’,’Jbimo’] (default = [‘Jext’]), by default [‘Jext’]

• show_tangent (list of int, optional) – show tangent line at V1,Vinf,V2 (default = [1,2,3]), by default [1,2,3]

• xlimits (list, optional) – x axis limits if = [] it lets python chose limits, by default []

• ylimits (list, optional) – y axis limits if = [] it lets python chose limits, by default []

• plot_type (int, optional) – type of plot 1 = logx, 2 = logy, 3 = loglog else linlin (default = linlin), by default 0

• labels (str, optional) – label of the JV, by default ‘’

• colors (str, optional) – color for the JV line, by default ‘b’

• line_type (list, optional) – type of line for simulated data plot size line_type need to be = size(y), by default [‘-‘]

• mark (str, optional) – type of Marker for the JV, by default ‘’

• legend (bool, optional) – Display legend or not, by default True

• plot_jvexp (bool, optional) – plot an experimental JV or not, by default False

• data_JVexp ([type], optional) – Panda DataFrame containing experimental JV_file with ‘V’ the voltage and ‘J’ the current, by default pd.DataFrame()

• save_yes (bool, optional) – If True, save JV as an image with the file name defined by “pic_save_name”, by default False

• pic_save_name (str, optional) – name of the file where the figure is saved, by default ‘JV.jpg’

Returns:

• Vslopef (list) – list of of the Voltage values after filtering

• Jslopef (list) – list of of the current values after filtering

• slopesf (list) – list of logarithmic slopes of the JV after filtering

• get_tangentf (bool) – True if tangents are calculated i.e. if max(slopef) > 2, False if not

• idx_maxf (int) – index of the max slope of the JV after filtering

• max_slopesf (float) – max slope of the JV after filtering

• tang_val_V1f (list) – list of the tangent values of the JV after filtering for the first tangent point. Typically crossing between the ohmic and Trap filled limited regime.

• tang_val_V2f (list) – list of the tangent values of the JV after filtering for the second tangent point (here the inflexion point)

• tang_val_V3f (list) – list of the tangent values of the JV after filtering for the third tangent point. Typically crossing between the Trap filled limited regime and the Mott-Gurney regime.

• V1f (float) – Voltage value of the first crossing point

• J1f (float) – current value of the first crossing point

• V2f (float) – Voltage value of the second crossing point

• J2f (float) – current value of the second crossing point

• Vinf (float) – Voltage value of the inflexion point

• Jinf (float) – current value of the inflexion point

pySIMsalabim.aux_funcs.SCLC_funcs.MottGurney(V, mu, eps_r, Vbi, L)

Mott-Gurney equation typically used to fit single carrier devices JVs to get the mobility.

J = (9/8)*eps_0*eps_r*mu*((V-Vbi)**2)/(L**3)

Refs: Mott N F and Gurney R W 1940 Electronic Processes in Ionic Crystals (Oxford: Oxford University Press) Nice paper to read on MG ==> J. Phys.: Condens. Matter 30 (2018) 105901

Parameters:

• V (1-D sequence of floats) – Array containing the voltages (V)

• mu (float) – Mobility (m^2/(Vs))

• eps_r (float) – Relative dielectric constant

• Vbi (float) – Built-in voltage (V)

• L (float) – Thickness (m)

Returns:

Array containing the current-density (A m^-2)

Return type:

1-D sequence of floats

pySIMsalabim.aux_funcs.SCLC_funcs.SCLC_get_data_plot(volt, curr)

Get the data for the SCLC plot

Parameters:

• volt (1-D sequence of floats) – Voltage data

• curr (1-D sequence of floats) – Current data

Returns:

• V_slopef (1-D sequence of floats) – Voltage data after filtering

• J_slopef (1-D sequence of floats) – Current data after filtering

• slopesf (1-D sequence of floats) – logarithmic slopes of the JV after filtering

• get_tangentf (bool) – True if tangents are calculated i.e. if max(slopef) > 2, False if not

• idx_maxf (int) – index of the max slope of the JV after filtering

• max_slopesf (float) – max slope of the JV after filtering

• tang_val_V1f (1-D sequence of floats) – tangent values of the JV after filtering for the first tangent point. Typically crossing between the ohmic and Trap filled limited regime.

• tang_val_V2f (1-D sequence of floats) – tangent values of the JV after filtering for the second tangent point (here the inflexion point)

• tang_val_V3f (1-D sequence of floats) – tangent values of the JV after filtering for the third tangent point. Typically crossing between the Trap filled limited regime and the Mott-Gurney regime.

• V1f (float) – Voltage value of the first crossing point

• J1f (float) – current value of the first crossing point

• V2f (float) – Voltage value of the second crossing point

• J2f (float) – current value of the second crossing point

• Vinf (float) – Voltage value of the inflexion point

• Jinf (float) – current value of the inflexion point

pySIMsalabim.aux_funcs.SCLC_funcs.calc_Vnet_with_ions(ions, traps, L, eps_r)

Calculate Vnet for SCLC measurement in the presence of Ions as defined in equation (4) in ACS Energy Lett. 2021, 6, 3, 1087–1094 https://doi.org/10.1021/acsenergylett.0c02599

Vnet = q * n_net * L**2 /( 2 * eps_0 * eps_r) = q * (traps-ions) * L**2 /( 2 * eps_0 * eps_r)

Parameters:

• ions (float) – Ion density (m^-3)

• traps (float) – Trap density (m^-3)

• L (float) – Thickness (m)

• eps_r (float) – Relative dielectric constant

Returns:

returns vnet as defined in

Return type:

float

pySIMsalabim.aux_funcs.SCLC_funcs.calc_Vsat(L, Nc, phi, eps_r, T)

Calculate Vsat for SCLC measurement as defined in equation (15) in https://doi.org/10.1021/acsenergylett.0c02599

Vsat = (8/9) * ((q*Nc*L**2)/(eps_0*eps_r))*exp(-q*phi/k*T)

Parameters:

• L (float) – Thickness (m)

• Nc (float) – Effective density of states (m^-3)

• phi (float) – Injection barrier (V)

• eps_r (float) – Relative dielectric constant

• T (float) – Temperature (K)

Returns:

returns Vsat as defined in

Return type:

float

pySIMsalabim.aux_funcs.SCLC_funcs.calc_Vtfl(traps, L, eps_r)

Calculate VTFL for SCLC measurement as defined in equation (2) in ACS Energy Lett. 2021, 6, 3, 1087–1094 https://doi.org/10.1021/acsenergylett.0c02599

Vnet = q * n_traps * L**2 /( 2 * eps_0 * eps_r)

Parameters:

• traps (float) – Trap density (m^-3)

• L (float) – Thickness (m)

• eps_r (float) – Relative dielectric constant

Returns:

returns vnet as defined in

Return type:

float

pySIMsalabim.aux_funcs.SCLC_funcs.calc_net_charge(Vnet, L, eps_r)

Calculate the net charge for SCLC measurement as defined in equation (4) in ACS Energy Lett. 2021, 6, 3, 1087–1094 https://doi.org/10.1021/acsenergylett.0c02599

Vnet = q * n_net * L**2 /( 2 * eps_0 * eps_r)

Note that if there are not ions or dopant n_net = traps

Parameters:

• Vnet (float) – Vnet see ref

• L (float) – Thickness (m)

• eps_r (float) – Relative dielectric constant

Returns:

net-charge in the bulk

Return type:

float

pySIMsalabim.aux_funcs.SCLC_funcs.calc_nt_min(L, eps_r, T)

Calculate the minimum appearant trap density for SCLC measurement as defined in equation (3) in ACS Energy Lett. 2021, 6, 3, 1087–1094 https://doi.org/10.1021/acsenergylett.0c02599

Ntmin = 4*np.Pi()**2*((k*T)/(q**2))*((eps_0*eps_r)/(L**2))

Parameters:

• L (float) – Thickness (m)

• eps_r (float) – Relative dielectric constant

• T (float) – Temperature (K)

Returns:

minimum appearant trap density

Return type:

float

pySIMsalabim.aux_funcs.SCLC_funcs.calc_trap_charge(Vnet, L, eps_r)

Calculate the trap charges for SCLC measurement as defined in equation (2) in ACS Energy Lett. 2021, 6, 3, 1087–1094 https://doi.org/10.1021/acsenergylett.0c02599

Vnet = q * n_trap * L**2 /( 2 * eps_0 * eps_r)

Note that if there are not ions or dopant n_net = traps

Parameters:

• Vtfl (float) – Vtfl see ref

• L (float) – Thickness (m)

• eps_r (float) – Relative dielectric constant

Returns:

trapped charges in the bulk

Return type:

float

pySIMsalabim.aux_funcs.SCLC_funcs.deriv(x, y)

Get the derivative of input data dy/dx

Parameters:

• x (1-D sequence of floats) – x-axis data

• y (1-D sequence of floats) – y-axis data

Returns:

dy/dx

Return type:

1-D sequence of floats

pySIMsalabim.aux_funcs.SCLC_funcs.fit_MottGurney(V, J, mu, eps_r, Vbi, L, var2fit=['mu'])

Fit the Mott-Gurney equation to the data

Parameters:

• V (1-D sequence of floats) – Array containing the voltages (V)

• J (1-D sequence of floats) – Array containing the current-density (A m^-2)

• mu (float) – Mobility (m^2/(Vs))

• eps_r (float) – Relative dielectric constant

• Vbi (float) – Built-in voltage (V)

• L (float) – Thickness (m)

• var2fit (list, optional) – Chose variable to fit (can be multiple), by default [‘mu’]

Returns:

list of the fitted values in the same order than var2fit

Return type:

list

pySIMsalabim.aux_funcs.SCLC_funcs.log_slope(x, y)

Get the slope of the logarithmic data

Parameters:

• x (1-D sequence of floats) – x-axis data

• y (1-D sequence of floats) – y-axis data

Returns:

slope of the logarithmic data

Return type:

1-D sequence of floats

pySIMsalabim.aux_funcs.addons module

Useful helper functions for pySIMsalabim

pySIMsalabim.aux_funcs.addons.sci_notation(number, sig_fig=2)

Make proper scientific notation for graphs

Parameters:

• number (float) – Number to put in scientific notation.

• sig_fig (int, optional) – Number of significant digits (Defaults = 2).

Returns:

output – String containing the number in scientific notation

Return type:

str

Module contents