Source code for solcore.absorption_calculator.transfer_matrix

""" This module serves as interface between solcore structures (junctions, layers, materials...) and the
transfer matrix package developed by Steven Byrnes and included in the PyPi repository.

"""
import numpy as np
import solcore
import tmm as old_tmm
from solcore.interpolate import interp1d
from solcore.structure import ToStructure
from solcore.absorption_calculator import tmm_core_vec as tmm

degree = np.pi / 180


[docs]class OptiStack(object): """ Class that contains an optical structure: a sequence of layers with a thickness and a complex refractive index. It serves as an intermediate step between solcore layers and materials and the stack of thicknesses and and n and k values necessary to run calculations involving TMM. When creating an OptiStack object, the thicknesses of all the layers forming the Solcore structure and the optical data of the materials of the layers are extracted and arranged in such a way they can be easily and fastly read by the TMM functions. In addition to a solcore structure with Layers, it can also take a list where each element represent a layer written as a list and contains the layer thickness and the dielectrical model, the raw n and k data as a function of wavelengths, or a whole Device structure as the type used in the PDD model. In summary, this class acepts: - A solcore structure with layers - A list where each element is [thickness, DielectricModel] - A list where each element is [thickness, wavelength, n, k] - A list mixing the above: [ [thickness, DielectricModel], [thickness, wavelength, n, k], solcore.Layer, solcore.Layer ] This allows for maximum flexibility when creating the optical model, allowing to construct the stack with experimental data, modelled data and known material properties from the database. Yet anther way of defining the layers mixes experimental data with a DielectricModel within the same layer but in spectrally distinct regions. The syntaxis for the layer is: layer = [thickness, wavelength, n, k, DielectricModel, mixing] where mixing is a list containing three elements: [the mixing point (nm), the mixing width (nm), zero or one] depending if the mixing function should be increasing with the wavelength or decreasing. If increasing (zero), the Dielectric model will be used at long wavelengths and the experimental data at short wavelengths. If decreasing (one) the oposite is done. The mixing point and mixing width control how smooth is the transition between one and the other type of data. Extra layers such as he semi-infinite, air-like first and last medium, and a back highly absorbing layer are included at runtime to fulfill the requirements of the TMM solver or to solve some of its limitations. """ def __init__(self, structure=(), no_back_reflexion=False, substrate=None): """ Class constructor. It takes a Solcore structure and extract the thickness and optical data from the Layers and the materials. Option is given to indicate if the reflexion from the back of the structure must be supressed, usefull for ellipsometry calculations. This is done by creating an artificial highly absorbing but not reflecting layer just at the back. Alternativelly, it can take simply a list of [thickness, DielectricModel] or [thickness, wavelength, n, k] for each layer accounting for the refractive index of the layers. The three options can be mixed for maximum flexibility. :param structure: A list with one or more layers. :param no_back_reflexion: If reflexion from the back must be suppressed. Default=False. :param substrate: a semi-infinite transmission medium. Note that if no_back_reflexion is set to True, adding a substrate won't make any difference. """ self.widths = [] self.n_data = [] self.k_data = [] self.models = [] self.layers = [] self.substrate = substrate self.num_layers = 0 self.add_layers(structure) self.no_back_reflexion = no_back_reflexion
[docs] def get_indices(self, wl): """ Returns the complex refractive index of the stack. :param wl: Wavelength of the light in nm. :return: A list with the complex refractive index of each layer, including the semi-infinite front and back layers and, opionally, the back absorbing layer used to suppress back surface relfexion. """ out = [] wl_m = solcore.si(wl, 'nm') if hasattr(self, 'n_sub'): n1 = self.n_sub(wl_m) + self.k_sub(wl_m)*1.0j else: if hasattr(wl, 'size'): n1 = np.ones_like(wl, dtype=complex) else: n1 = 1 if hasattr(wl, 'size'): n0 = np.ones_like(wl, dtype=complex) else: n0 = 1 for i in range(self.num_layers): out.append(self.n_data[i](wl_m) + self.k_data[i](wl_m) * 1.0j) # substrate irrelevant if no_back_reflexion = True if self.no_back_reflexion: return [n0] + out + [self.n_data[-1](wl_m) + self._k_absorbing(wl_m) * 1.0j, n1] # look at last entry in stack, # make high;y absorbing layer based on it. else: return [n0] + out + [n1]
[docs] def get_widths(self): """ Returns the widths of the layers of the stack. :return: A list with the widths each layer, including the semi-infinite front and back layers and, opionally, the back absorbing layer used to suppress back surface relfexion, defined as 1 mm thick. """ if self.no_back_reflexion: return [np.inf] + self.widths + [1e6, np.inf] else: return [np.inf] + self.widths + [np.inf]
def _k_absorbing(self, wl): """ k value of the back highly absorbing layer. It is the maximum between the bottom layer of the stack or a finite, small value that will absorb all light within the absorbing layer thickness. :param wl: Wavelength of the light in nm. :return: The k value at each wavelength. """ return np.maximum(wl / 1e-3, self.k_data[-1](wl)) @staticmethod def _k_dummy(wl): """ Dummy k value to be used with the dielectric model, which produces the refractive index as a complex number. :param wl: Wavelength of the light in nm. :return: The k value at each wavelength... set to zero. """ return 0.
[docs] def add_layers(self, layers): """ Generic function to add layers to the OptiStack. Internally, it calls add_solcore_layer, add_modelled_layer or add_raw_nk_layer. :param layers: A list with the layers to add (even if it is just one layer) It can be one or more and it can mixed, Solcore-based and modelled layers. :return: None """ try: # If the input is a whole device structure, we get just the layers information if type(layers) is dict: layers = ToStructure(layers) if self.substrate is not None: self.n_sub = self.substrate.n self.k_sub = self.substrate.k for layer in layers: self.layers.append(layer) if 'Layer' in str(type(layer)): self._add_solcore_layer(layer) elif 'DielectricConstantModel' in str(type(layer[1])): self._add_modelled_layer(layer) else: self._add_raw_nk_layer(layer) self.num_layers += 1 except Exception as err: print('Error when adding a new layer to the OptiStack. {}'.format(err))
[docs] def remove_layer(self, idx): """ Removes layer with index idx from the OptiStack :param idx: Index of the layer to remove :return: None """ if idx >= self.num_layers: print('Error when removing layers. idx must be: 0 <= idx <= {}.'.format(self.num_layers - 1)) return self.widths.pop(idx) self.models.pop(idx) self.n_data.pop(idx) self.k_data.pop(idx) self.num_layers -= 1
[docs] def swap_layers(self, idx1, idx2): """ Swaps two layers in the OptiStack. :param idx1: The index of one of the layers. :param idx2: The index of the other. :return: None """ if idx1 >= self.num_layers or idx2 >= self.num_layers: print('Error when removing layers. idx must be: 0 <= idx1, idx2 <= {}.'.format(self.num_layers - 1)) return self.widths[idx1], self.widths[idx2] = self.widths[idx2], self.widths[idx1] self.models[idx1], self.models[idx2] = self.models[idx2], self.models[idx1] self.n_data[idx1], self.n_data[idx2] = self.n_data[idx2], self.n_data[idx1] self.k_data[idx1], self.k_data[idx2] = self.k_data[idx2], self.k_data[idx1]
def _add_solcore_layer(self, layer): """ Adds a Solcore layer to the end (bottom) of the stack, extracting its thickness and n and k data. :param layer: The Solcore layer :return: None """ self.widths.append(solcore.asUnit(layer.width, 'nm')) self.models.append([]) self.n_data.append(layer.material.n) self.k_data.append(layer.material.k) def _add_modelled_layer(self, layer): """ Adds a layer to the end (bottom) of the stack. The layer must be defined as a list containing the layer thickness in nm and a dielectric model. :param layer: The new layer to add as [thickness, DielectricModel] :return: None """ self.widths.append(layer[0]) self.models.append(layer[1]) self.n_data.append(self.models[-1].n_and_k) self.k_data.append(self._k_dummy) def _add_raw_nk_layer(self, layer): """ Adds a layer to the end (bottom) of the stack. The layer must be defined as a list containing the layer thickness in nm, the wavelength, the n and the k data as array-like objects. :param layer: The new layer to add as [thickness, wavelength, n, k] :return: None """ # We make sure that the wavelengths are increasing, revering the arrays otherwise. if layer[1][0] > layer[1][-1]: layer[1] = layer[1][::-1] layer[2] = layer[2][::-1] layer[3] = layer[3][::-1] self.widths.append(layer[0]) if len(layer) >= 5: self.models.append(layer[4]) c = solcore.si(layer[5][0], 'nm') w = solcore.si(layer[5][1], 'nm') d = layer[5][2] # = 0 for increasing, =1 for decreasing def mix(x): out = 1 + np.exp(-(x - c) / w) out = d + (-1) ** d * 1 / out return out n_data = lambda x: self.models[-1].n_and_k(x) * mix(x) + (1 - mix(x)) * interp1d( x=solcore.si(layer[1], 'nm'), y=layer[2], fill_value=layer[2][-1])(x) k_data = lambda x: interp1d(x=solcore.si(layer[1], 'nm'), y=layer[3], fill_value=layer[3][-1])(x) self.n_data.append(n_data) self.k_data.append(k_data) else: self.models.append([]) self.n_data.append(interp1d(x=solcore.si(layer[1], 'nm'), y=layer[2], fill_value=layer[2][-1])) self.k_data.append(interp1d(x=solcore.si(layer[1], 'nm'), y=layer[3], fill_value=layer[3][-1]))
[docs]def calculate_rat(structure, wavelength, angle=0, pol='u', coherent=True, coherency_list=None, no_back_reflexion=True): """ Calculates the reflected, absorbed and transmitted intensity of the structure for the wavelengths and angles defined. :param structure: A solcore Structure object with layers and materials or a OptiStack object. :param wavelength: Wavelengths (in nm) in which calculate the data. An array. :param angle: Angle (in degrees) of the incident light. Default: 0 (normal incidence). :param pol: Polarisation of the light: 's', 'p' or 'u'. Default: 'u' (unpolarised). :param coherent: If the light is coherent or not. If not, a coherency list must be added. :param coherency_list: A list indicating in which layers light should be treated as coeherent ('c') and in which incoherent ('i'). It needs as many elements as layers in the structure. :param no_back_reflexion: If reflexion from the back must be supressed. Default=True. :return: A dictionary with the R, A and T at the specified wavelengths and angle. """ num_wl = len(wavelength) if 'OptiStack' in str(type(structure)): stack = structure stack.no_back_reflexion = no_back_reflexion else: stack = OptiStack(structure, no_back_reflexion=no_back_reflexion) if not coherent: if coherency_list is not None: assert len(coherency_list) == stack.num_layers, \ 'Error: The coherency list must have as many elements (now {}) as the ' \ 'number of layers (now {}).'.format(len(coherency_list), stack.num_layers) if stack.no_back_reflexion: coherency_list = ['i'] + coherency_list + ['i', 'i'] else: coherency_list = ['i'] + coherency_list + ['i'] else: raise Exception('Error: For incoherent or partly incoherent calculations you must supply the ' 'coherency_list parameter with as many elements as the number of layers in the ' 'structure') output = {'R': np.zeros(num_wl), 'A': np.zeros(num_wl), 'T': np.zeros(num_wl), 'all_p': [], 'all_s': []} if pol in 'sp': if coherent: out = tmm.coh_tmm(pol, stack.get_indices(wavelength), stack.get_widths(), angle * degree, wavelength) A_per_layer = tmm.absorp_in_each_layer(out) output['R'] = out['R'] output['A'] = 1 - out['R'] - out['T'] output['T'] = out['T'] output['A_per_layer'] = A_per_layer else: out = tmm.inc_tmm(pol, stack.get_indices(wavelength), stack.get_widths(), coherency_list, angle * degree, wavelength) A_per_layer = np.array(tmm.inc_absorp_in_each_layer(out)) output['R'] = out['R'] output['A'] = 1 - out['R'] - out['T'] output['T'] = out['T'] output['A_per_layer'] = A_per_layer else: if coherent: out_p = tmm.coh_tmm('p', stack.get_indices(wavelength), stack.get_widths(), angle * degree, wavelength) out_s = tmm.coh_tmm('s', stack.get_indices(wavelength), stack.get_widths(), angle * degree, wavelength) A_per_layer_p = tmm.absorp_in_each_layer(out_p) A_per_layer_s = tmm.absorp_in_each_layer(out_s) output['R'] = 0.5 * (out_p['R'] + out_s['R']) output['T'] = 0.5 * (out_p['T'] + out_s['T']) output['A'] = 1 - output['R'] - output['T'] output['A_per_layer'] = 0.5*(A_per_layer_p + A_per_layer_s) else: out_p = tmm.inc_tmm('p', stack.get_indices(wavelength), stack.get_widths(), coherency_list, angle * degree, wavelength) out_s = tmm.inc_tmm('s', stack.get_indices(wavelength), stack.get_widths(), coherency_list, angle * degree, wavelength) A_per_layer_p = np.array(tmm.inc_absorp_in_each_layer(out_p)) A_per_layer_s = np.array(tmm.inc_absorp_in_each_layer(out_s)) output['R'] = 0.5 * (out_p['R'] + out_s['R']) output['T'] = 0.5 * (out_p['T'] + out_s['T']) output['A'] = 1 - output['R'] - output['T'] output['all_p'] = out_p['power_entering_list'] output['all_s'] = out_s['power_entering_list'] output['A_per_layer'] = 0.5*(A_per_layer_p + A_per_layer_s) return output
[docs]def calculate_ellipsometry(structure, wavelength, angle, no_back_reflexion=True): """ Calculates the ellipsometric parameters psi and delta. It can only deal with coherent light and the whole stack (including back surface) is considered, so caution must be taken when comparing the simulated results with experiments where the back surface is rough or layers are thick and coherent light propagation makes no sense. The optional argument no_back_reflexion can be included to add an extra layer on the back absorbing all light that reaches that position without any reflexion, to remove the reflexion from the back surface. :param structure: A solcore structure with layers and materials. :param wavelength: Wavelengths (in nm) in which calculate the data. An array. :param angle: A tupple or list with the angles (in degrees) in which to calculate the data. :param no_back_reflexion: If reflexion from the back must be suppressed. Default=True. :return: A dictionary with psi and delta at the specified wavelengths and angles (2D arrays). """ num_wl = len(wavelength) num_ang = len(angle) if 'OptiStack' in str(type(structure)): stack = structure stack.no_back_reflexion = no_back_reflexion else: if hasattr(structure, 'substrate'): substrate = structure.substrate else: substrate = None stack = OptiStack(structure, no_back_reflexion=no_back_reflexion, substrate=substrate) output = {'psi': np.zeros((num_wl, num_ang)), 'Delta': np.zeros((num_wl, num_ang))} for i, ang in enumerate(angle): out = tmm.ellips(stack.get_indices(wavelength), stack.get_widths(), ang * degree, wavelength) output['psi'][:, i] = out['psi'] / degree # We revere the sign of Delta in order to use Woollam sign convention output['Delta'][:, i] = -out['Delta'] / degree output['Delta'][:, i] = np.where(output['Delta'][:, i] > 0, -output['Delta'][:, i], output['Delta'][:, i]) output['Delta'][:, i] = np.where(output['Delta'][:, i] < 180, 180 - output['Delta'][:, i], output['Delta'][:, i]) return output
# def calculate_absorption_profile(structure, wavelength, z_limit=None, steps_size=2, dist=None, # no_back_reflexion=True): # """ It calculates the absorbed energy density within the material. From the documentation: # # 'In principle this has units of [power]/[volume], but we can express it as a multiple of incoming light power # density on the material, which has units [power]/[area], so that absorbed energy density has units of 1/[length].' # # Integrating this absorption profile in the whole stack gives the same result that the absorption obtained with # calculate_rat as long as the spacial mesh (controlled by steps_thinest_layer) is fine enough. If the structure is # very thick and the mesh not thin enough, the calculation might diverege at short wavelengths. # # For now, it only works for normal incident, coherent light. # # :param structure: A solcore structure with layers and materials. # :param wavelength: Wavelengths in which calculate the data (in nm). An array-like object. # :param z_limit: Maximum value in the z direction # :return: A dictionary containing the positions (in nm) and a 2D array with the absorption in the structure as a # function of the position and the wavelength. # """ # # num_wl = len(wavelength) # # if 'OptiStack' in str(type(structure)): # stack = structure # stack.no_back_reflexion = no_back_reflexion # else: # stack = OptiStack(structure, no_back_reflexion=no_back_reflexion) # # if dist is None: # if z_limit is None: # z_limit = np.sum(np.array(stack.widths)) # dist = np.arange(0, z_limit, steps_size) # # output = {'position': dist, 'absorption': np.zeros((num_wl, len(dist)))} # # for i, wl in enumerate(wavelength): # out = tmm.coh_tmm('p', stack.get_indices(wl), stack.get_widths(), 0, wl) # for j, d in enumerate(dist): # layer, d_in_layer = tmm.find_in_structure_with_inf(stack.get_widths(), d) # data = tmm.position_resolved(layer, d_in_layer, out) # output['absorption'][i, j] = data['absor'] # # return output
[docs]def calculate_absorption_profile(structure, wavelength, z_limit=None, steps_size=2, dist=None, no_back_reflexion=True, angle=0, pol = 'u', coherent=True, coherency_list=None): """ It calculates the absorbed energy density within the material. From the documentation: 'In principle this has units of [power]/[volume], but we can express it as a multiple of incoming light power density on the material, which has units [power]/[area], so that absorbed energy density has units of 1/[length].' Integrating this absorption profile in the whole stack gives the same result that the absorption obtained with calculate_rat as long as the spacial mesh (controlled by steps_thinest_layer) is fine enough. If the structure is very thick and the mesh not thin enough, the calculation might diverge at short wavelengths. :param structure: A solcore structure with layers and materials. :param wavelength: Wavelengths in which calculate the data (in nm). An array :param z_limit: Maximum value in the z direction :param steps_size: if the dist is not specified, the step size in nm to use in the depth-dependent calculation :param dist: the positions (in nm) at which to calculate depth-dependent absorption :param no_back_reflexion: whether to suppress reflections from the back interface (True) or not (False) :param angle: incidence angle in degrees :param pol: polarization of incident light: 's', 'p' or 'u' (unpolarized) :param coherent: True if all the layers are to be treated coherently, False otherwise :param coherency_list: if coherent is False, a list of 'c' (coherent) or 'i' (incoherent) for each layer :return: A dictionary containing the positions (in nm) and a 2D array with the absorption in the structure as a function of the position and the wavelength. """ num_wl = len(wavelength) if 'OptiStack' in str(type(structure)): stack = structure stack.no_back_reflexion = no_back_reflexion else: stack = OptiStack(structure, no_back_reflexion=no_back_reflexion) if dist is None: if z_limit is None: z_limit = np.sum(np.array(stack.widths)) dist = np.arange(0, z_limit, steps_size) if not coherent: if coherency_list is not None: if stack.no_back_reflexion: coherency_list = ['i'] + coherency_list + ['i', 'i'] else: coherency_list = ['i'] + coherency_list + ['i'] else: raise Exception('Error: For incoherent or partly incoherent calculations you must supply the ' 'coherency_list parameter with as many elements as the number of layers in the ' 'structure') output = {'position': dist, 'absorption': np.zeros((num_wl, len(dist)))} if pol in 'sp': # print(stack.get_indices(wavelength).shape) if coherent: out = tmm.coh_tmm(pol, stack.get_indices(wavelength), stack.get_widths(), angle*degree, wavelength) layer, d_in_layer = tmm.find_in_structure_with_inf(stack.get_widths(), dist) data = tmm.position_resolved(layer, d_in_layer, out) output['absorption'] = data['absor'] else: out = tmm.inc_tmm(pol, stack.get_indices(wavelength), stack.get_widths(), coherency_list, angle * degree, wavelength) layer, d_in_layer = tmm.find_in_structure_with_inf(stack.get_widths(), dist) data = tmm.inc_position_resolved(layer, d_in_layer, out, coherency_list, 4*np.pi*np.imag(stack.get_indices(wavelength))/wavelength) output['absorption'] = data else: if coherent: out1 = tmm.coh_tmm('s', stack.get_indices(wavelength), stack.get_widths(), angle * degree, wavelength) out2 = tmm.coh_tmm('p', stack.get_indices(wavelength), stack.get_widths(), angle * degree, wavelength) layer, d_in_layer = tmm.find_in_structure_with_inf(stack.get_widths(), dist) data_s = tmm.position_resolved(layer, d_in_layer, out1) data_p = tmm.position_resolved(layer, d_in_layer, out2) output['absorption'] = 0.5*(data_s['absor'] + data_p['absor']) else: out1 = tmm.inc_tmm('s', stack.get_indices(wavelength), stack.get_widths(), coherency_list, angle * degree, wavelength) out2 = tmm.inc_tmm('p', stack.get_indices(wavelength), stack.get_widths(), coherency_list, angle * degree, wavelength) layer, d_in_layer = tmm.find_in_structure_with_inf(stack.get_widths(), dist) data_s = tmm.inc_position_resolved(layer, d_in_layer, out1, coherency_list, 4*np.pi*np.imag(stack.get_indices(wavelength))/wavelength) data_p = tmm.inc_position_resolved(layer, d_in_layer, out2, coherency_list, 4*np.pi*np.imag(stack.get_indices(wavelength))/wavelength) output['absorption'] = 0.5*(data_s + data_p) return output
if __name__ == '__main__': import matplotlib.pyplot as plt from solcore import material, si from solcore.structure import Layer, Structure GaAs = material('GaAs')(T=300) InGaAs = material('InGaAs')(T=300, In=0.1) my_structure = Structure([ Layer(si(3000, 'nm'), material=InGaAs), Layer(si(30, 'um'), material=GaAs), ]) wavelength = np.linspace(450, 1100, 300) out = calculate_rat(my_structure, wavelength, coherent=True, no_back_reflexion=False) # # # plt.plot(wavelength, out['R'], 'b', label='Reflexion') # plt.plot(wavelength, out['A'], 'r', label='Absorption') # plt.plot(wavelength, out['T'], 'g', label='Transmission') # plt.legend() # plt.show() angles = [60, 65, 70] out = calculate_ellipsometry(my_structure, wavelength, angle=angles) # plt.plot(wavelength, out['psi'][:, 0], 'b', label='psi') plt.plot(wavelength, out['Delta'][:, 0], 'r', label='Delta') for i in range(1, len(angles)): plt.plot(wavelength, out['psi'][:, i], 'b') plt.plot(wavelength, out['Delta'][:, i], 'r') # # plt.legend() # out = calculate_absorption_profile_2(my_structure, wavelength, z_limit=3000) # # print(tuple(out['absorption'][0])) # # plt.plot(out['position'], out['absorption'][0]) # A = np.zeros_like(wavelength) # # # for i, absorption in enumerate(out['absorption'][:]): # A[i] = np.trapz(absorption, out['position']) # # # plt.plot(wavelength, A, 'k', label='Integrated Abs') # # plt.contourf(out['position'], wavelength, out['absorption'], 200) plt.legend() plt.show()