Transport tutorial
In this section, we describe how to use Perturbopy to process a Perturbo transport calculation. The possible calculation modes are: 'trans', 'trans-rta', 'trans-ita', 'trans-mag-rta', 'trans-mag-ita', and 'trans-pp'. Any of these calculation modes can be processed with the Trans object described below.
The transport calculation modes solve the Boltzmann transport equation (BTE) to compute the electrical conductivity, carrier mobility tensors as well as the Seebeck coefficient and thermal conductivity. We first run the Perturbo calculation following the instructions on the Perturbo website (running trans-rta as an example) and obtain the YAML file, ‘si_trans_rta.yml’. For more information, please refer to the Perturbo website.
Next, we create the Trans object using the YAML file as an input. This object contains all of the information from the YAML file.
import perturbopy.postproc as ppy
# Example using the trans-rta calculation mode
si_trans_rta = ppy.Trans.from_yaml('si_trans-rta.yml')
# Examples for the other calculation modes
si_trans_ita = ppy.Trans.from_yaml('si_trans-ita.yml')
si_trans_mag_rta = ppy.Trans.from_yaml('si_trans-mag-rta.yml')
si_trans_mag_ita = ppy.Trans.from_yaml('si_trans-mag-ita.yml')
si_trans_pp = ppy.Trans.from_yaml('si_trans-pp.yml')
Accessing the data
The main results of the results are categorized below:
Configuration information (temperature, chemical potential, carrier concentration, and potentially magnetic field)
Computed transport properties for each configuration (electrical conductivity, carrier mobility tensors, and potentially Seebeck coefficient and thermal conductivity. If running an ITA calculation, there will also be conductivity results for each iteration.)
See Exporting data to learn how to access data from si_phdisp that is general for all calculation modes, such as input parameters and the material’s crystal structure.
Configuration data
Transport calculations are run for various system configurations, i.e. the temperature, chemical potential, and carrier concentration. Information about the configuration(s), are stored in the following attributes:
Trans.temperTrans.chem_potTrans.concTrans.bfield(if applicable)
All of these attributes are UnitsDict objects, which are Python dictionaries with an additional attribute that stores the units. The keys of the dictionary represent the configuration number. The values are floats representing the temperature, chemical potential, or carrier concentration of that configuration. If running a magnetic field calculation, there will also be an attribute for the magnetic field of each configuration.
For example, let’s look at the temperatures.
# Keys are configuration number, values are temperatures
si_trans_rta.temper
>> {1: 150.0, 2: 200.0, 3: 250.0, 4: 300.0, 5: 350.0}
# Units are in Kelvin
si_trans_rta.temper.units
>> 'K'
If we use the magnetic field calculation, we can also access the magnetic field,
# We have one configuration and one B field
si_trans_mag_rta.bfield
>> {1: array([0.1, 0. , 0. ])}
# Units are in Tesla
si_trans_mag_rta.bfield.units
>> 'T'
Please see the section Physical quantities for details on working with UnitsDict objects.
Transport results
The following transport results are stored:
Trans.cond: electrical conductivityTrans.mob: carrier mobilityTrans.seebeck: Seebeck coefficientTrans.therm_cond: thermal conductivity
All of these attributes are also UnitsDict objects. The keys of the dictionary represent the configuration number. The values are 3x3 numpy arrays, which represent the computed tensors for conductivity, mobility, seebeck coefficient, and thermal conductivity.
For example, let’s look at the mobilities.
# Get the mobility tensor for the 4th configuration
si_trans_rta.mob[4]
>> array([[ 1.5574091e+03, -6.3873187e-03, -4.9675237e-03],
[-6.3873187e-03, 1.5574506e+03, 2.4670994e-03],
[-4.9675237e-03, 2.4670994e-03, 1.5574129e+03]])
# Get the units
si_trans_rta.mob.units
>> 'cm2/V/s'
If a quantity is empty, it means it was not computed. This is sometimes the case for the Seebeck coefficient and thermal conductivity.
Please see the section Physical quantities for details on working with UnitsDict objects.
Iteration data
If we run calc_mode = trans-ita or trans-mag-ita, we are solving the BTE iteratively. In this case, we can obtain information on the convergence of the conductivity over the iterations. The data is stored in Trans.cond_iter, which is a dictionary of dictionaries. The top level keys give the configuration number, and the second level keys give the iteration number.
# Get the conductivity tensors for the 1st configuration, at each of the four iterations
si_trans_ita.cond_iter[2]
>> {1: {1: [[24817.3, -0.10178186, -0.079157444],
[-0.10178186, 24817.96, 0.039313206],
[-0.079157444, 0.039313206, 24817.36]],
2: [[25288.733, -0.025526387, -0.12887813],
[-0.025526387, 25289.902, 0.058570355],
[-0.12887813, 0.058570355, 25288.974]],
3: [[25401.491, -0.034944053, -0.20791663],
[-0.034944053, 25402.694, 0.059040028],
[-0.20791663, 0.059040028, 25401.714]],
4: [[25389.272, -0.031056698, -0.20778462],
[-0.031056698, 25390.489, 0.059898721],
[-0.20778462, 0.059898721, 25389.5]]}}
# Get the units
si_trans_ita.cond_iter.units
Plotting the data
Below is an example for plotting the ‘xx’ component of mobility as a function of temperature.
import perturbopy.postproc as ppy
import matplotlib.pyplot as plt
import numpy as np
fig, ax = plt.subplots()
# Optional
plt.rcParams.update(ppy.plot_tools.plotparams)
temperatures = np.array(list(si_trans_rta.temper.values()))
# Get xx components of mobilities
mobilities = np.array(list(si_trans_rta.mob.values()))[:, 0, 0]
ax.plot(temperatures, mobilities)
ax.set_xlabel(f"Temperature ({si_trans_rta.temper.units})")
ax.set_ylabel(f"Mobility ({si_trans_rta.mob.units})")
plt.show()
It is straightforward to modify the above code to plot a different configuration property on the x-axis (such as magnetic field or carrier concentration) or a different computed transport property on the y-axis (such as conductivity).