Source code for solcore.quantum_mechanics.high_level_kp_QW

from solcore.quantum_mechanics.kp_QW import solve_bandstructure_QW
from solcore.quantum_mechanics.heterostructure_alignment import VBO_align
from solcore.quantum_mechanics.structure_utilities import structure_to_potentials
from solcore.quantum_mechanics.potential_utilities import potentials_to_wavefunctions_energies
from solcore.quantum_mechanics import graphics
from solcore.absorption_calculator.absorption_QW import calc_alpha
from solcore.interpolate import interp1d
from solcore.constants import q, vacuum_permittivity
import numpy as np

[docs]def schrodinger(structure, plot_bands=False, kpoints=40, krange=1e9, num_eigenvalues=10, symmetric=True, quasiconfined=0.0, return_qw_boolean_for_layer=False, Efield=0, blur=False, blurmode="even", mode='kp8x8_bulk', step_size=None, minimum_step_size=0, smallest_feature_steps=20, filter_strength=0, periodic=False, offset=0, graphtype=[], calculate_absorption=False, alpha_params=None, **kwargs): """ Solves the Schrodinger equation of a 1 dimensional structure. Depending on the inputs, the method for solving the problem is more or less sophisticated. In all cases, the output includes the band structure and effective masses around k=0 as a function of the position, the energy levels of the QW (electrons and holes) and the wavefunctions, although for the kp4x4 and kp6x6 modes, this is provided as a function of the k value, and therefore there is much more information. :param structure: The strucutre to solve :param plot_bands: (False) If the bands should be plotted :param kpoints: (30) The number of points in the k space :param krange: (1e-9) The range in the k space :param num_eigenvalues: (10) Maximum number of eigenvalues to calculate :param symmetric: (True) If the structure is symmetric, in which case the calculation can be speed up :param quasiconfined: (0.0 eV) Energy above the band edges that an energy level can have before rejecting it :param return_qw_boolean_for_layer: (False) Return an boolean array indicating which positions are inside the QW :param Efield: (0) Electric field. :param blur: (False) If the potentials and effective masses have to be blurred :param blurmode: ('even') Other values are 'right' and 'left' :param mode: ('kp4x4') The mode of calculating the bands and effective masses. See 'structure_utilities.structure_to_potentials' :param step_size: (None) The discretization step of the structure. If none, it is estimated based on the smallest feature. :param minimum_step_size: (0) The minimum step size. :param smallest_feature_steps: (20) The number of steps in the smallest feature :param filter_strength: (0) If > 0, defines the fraction of the wavefunction that has to be inside the QW in order to consider it 'confined' :param periodic: (False) If the structure is periodic. Affects the boundary conditions. :param offset: (0) Energy offset used in the calculation of the energy levels in the case of the 'bulk' solvers :param graphtype: [] If 'potential', the band profile and wavefunctions are ploted :return: A dictionary containing the band structure and wavefunctions as a function of the position and k """ if Efield != 0: symmetric = False aligned_structure = VBO_align(structure) potentials = structure_to_potentials(aligned_structure, return_qw_boolean_for_layer=return_qw_boolean_for_layer, Efield=Efield, blur=blur, blurmode=blurmode, mode=mode, step_size=step_size, minimum_step_size=minimum_step_size, smallest_feature_steps=smallest_feature_steps) # Now that we have the potential and effective masses ready, we solve the problem. if mode in ['kp4x4', 'kp6x6']: bands = solve_bandstructure_QW(potentials, num=num_eigenvalues, kpoints=kpoints, krange=krange, symmetric=symmetric, quasiconfined=quasiconfined, plot_bands=plot_bands) result_band_edge = { "x": bands['x'], "potentials": {key: potentials[key] for key in potentials.keys() if key[0] in "Vx"}, "effective_masses": {key: potentials[key] for key in potentials.keys() if key[0] in "mx"}, "wavefunctions": {key: bands[key][:, 0] for key in bands.keys() if 'psi' in key}, "E": {key: bands[key][:, 0] for key in bands.keys() if key[0] in 'E'}, } else: bands = potentials_to_wavefunctions_energies(structure=structure, num_eigenvalues=num_eigenvalues, filter_strength=filter_strength, offset=offset, periodic=periodic, quasiconfined=quasiconfined, **potentials) result_band_edge = { "x": bands['x'], "potentials": {key: potentials[key] for key in potentials.keys() if key[0] in "Vx"}, "effective_masses": {key: potentials[key] for key in potentials.keys() if key[0] in "mx"}, "wavefunctions": {key: bands[key] for key in bands.keys() if 'psi' in key}, "E": {key: np.array(bands[key]) for key in bands.keys() if key[0] in "E"}, } if "potentials" is graphtype: schrodinger_plt = graphics.split_schrodinger_graph_potentials(result_band_edge, **kwargs) # schrodinger_plt.draw() if "potentialsLDOS" is graphtype: Ee, LDOSe, Eh, LDOSh = graphics.split_schrodinger_graph_LDOS(result_band_edge, **kwargs) result_band_edge["LDOS"] = {"x": bands['x'], 'Ee': Ee, 'LDOSe': LDOSe, 'Eh': Eh, 'LDOSh': LDOSh} if calculate_absorption: result_band_edge["alpha"] = calc_alpha(result_band_edge, **alpha_params) result_band_edge["alphaE"] = interp1d(x=result_band_edge["alpha"][0], y=result_band_edge["alpha"][1]) return result_band_edge, bands
if __name__ == "__main__": from solcore import si, material from solcore.structure import Layer, Structure import matplotlib.pyplot as plt import numpy as np bulk = material("GaAs")(T=293) barrier = material("GaAsP")(T=293, P=0.1) bulk.strained = False barrier.strained = True top_layer = Layer(width=si("30nm"), material=bulk) inter = Layer(width=si("3nm"), material=bulk) barrier_layer = Layer(width=si("15nm"), material=barrier) bottom_layer = top_layer E = np.linspace(1.15, 1.5, 300) * q alfas = np.zeros((len(E), 6)) alfas[:, 0] = E / q alpha_params = { "well_width": si("7.2nm"), "theta": 0, "eps": 12.9 * vacuum_permittivity, "espace": E, "hwhm": si("6meV"), "dimensionality": 0.16, "line_shape": "Gauss" } comp = [0.05, 0.10, 0.15, 0.20] colors =, 1, len(comp))) plt.figure(figsize=(6, 4.5)) for j, i in enumerate(comp): QW = material("InGaAs")(T=293, In=i) QW.strained = True well_layer = Layer(width=si("7.2nm"), material=QW) # test_structure = Structure([top_layer, barrier_layer, inter] + 1 * [well_layer, inter, barrier_layer, inter] + # [bottom_layer]) test_structure = Structure([barrier_layer, inter] + 1 * [well_layer, inter] + [barrier_layer]) # test_structure = Structure([top_layer, barrier_layer] + 10 * [well_layer, barrier_layer] + # [bottom_layer]) test_structure.substrate = bulk output = schrodinger(test_structure, quasiconfined=0, mode='kp4x4', plot_bands=False, num_eigenvalues=20, alpha_params=alpha_params, calculate_absorption=True) alfa = output[0]['alphaE'](E) plt.plot(1240 / (E / q), alfa / 100, label='{}%'.format(int(i * 100))) alfas[:, j + 1] = alfa / 100 plt.xlim(826, 1100) plt.ylim(0, 23000) plt.xlabel('Wavelength (nm)') plt.ylabel('$\\alpha$ cm$^{-1}$') plt.legend(loc='upper right', frameon=False) plt.tight_layout() import os root = os.path.expanduser('~') plt.savefig(root + '/Desktop/abs.pdf')