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extractor.py
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extractor.py
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# import
import warnings
warnings.filterwarnings("ignore")
import pandas as pd
import matplotlib.pyplot as plt
import scipy
import numpy as np
from sklearn.linear_model import LinearRegression
from shapely.geometry import LineString, Point
def autoextract(data, savepath, ev_range=[1.4, 1.65], smoothing=20, intensity_scale=10000, verbose=False):
'''
===================================
== AUTOMATIC BAND GAP EXTRACTOR ==
===================================
Inputs:
data: An (n x m) pandas array with n reflectance data points and (m - 1) measured spectra, where m = 0 is the wavelength
savepath: Local file path to save Tauc plot images and band gap csv
ev_range: List of eVs to run band gap extractor between: [lower, upper]. The tighter the range, the more accurate the band gap calculation
smoothing: The degree to smooth the Tauc plots to remove noise that may impact band gap calculation
intensity_scale: The value to divide the raw reflectance intensity by to output a decimal E [0,1]
For the Resonon PikaL, intensity_scale = 10000
verbose: If True, plots the fitted band gap line and Tauc plot inline
Outputs:
EG: An (e x (m-1)) array with e band gaps per spectra if more than one band gap is observed, where (m - 1) are the number of measured spectra
'''
# calcualte (F*E)^2 Tauc from reflectivity
tauc = data.iloc[:, 1:]
wl = data.iloc[:, 0]
R = tauc / intensity_scale # convert from 10,000 percentage points to decimal reflectivity
k = (1. - R) ** 2 # k=(1-R)^2
s = 2 * R # s = 2*R
F = k / s # absorpotion coefficient
ev = 1240. / wl # calcualte eV from wavelength
ev.name = 'eV' # rename column
tauc = F.mul(ev, axis=0) ** 2 # calculate tauc
tauc = pd.concat([ev, tauc], axis=1) # add ev column back to data
tauc_ev = tauc[(ev >= ev_range[0]) & (ev <= ev_range[1])] # bound ev range
tauc_smooth_raw = tauc_ev.copy()
smooth = scipy.signal.savgol_filter(tauc_ev.iloc[:, 1:], window_length=smoothing, polyorder=3,
axis=0) # savitsky-golay smoothing
# upsample the number of datapoints from ~100 to 1000
upsample = 1000 # number of points to upsample to
f = scipy.interpolate.interp1d(tauc_smooth_raw.iloc[:, 0], smooth, axis=0)
ev_upsample = np.linspace(np.max(tauc_smooth_raw.iloc[:, 0]), np.min(tauc_smooth_raw.iloc[:, 0]), upsample)
tauc_smooth_1 = pd.DataFrame(np.hstack([ev_upsample.reshape(upsample, 1), f(ev_upsample)]),
columns=tauc_smooth_raw.columns.values)
tauc_smooth = tauc_smooth_1.iloc[::-1].reset_index(drop=True) # sort ascending eV
############################################################################################
###################### Recursive Segmentation of Spectra #######################
############################################################################################
np.random.seed(0)
bandgaps = [] # list of bandgaps for all spectra
for i in range(tauc_smooth.shape[1] - 1):
bandgaps_per_tauc = []
current_tauc = tauc_smooth.iloc[:, i + 1].name # name of current tauc spectra
TAUC_X = np.array(tauc_smooth.iloc[:, 0]).reshape(-1, 1)
TAUC_Y = np.array(tauc_smooth.iloc[:, i + 1]).reshape(-1, 1)
X0 = [TAUC_X] # initialize X values
Y0 = [TAUC_Y] # initialize Y values
target_len = len(X0[0]) # target length to stop recursion
R_tol = 0.990 # R^2 linear regression fit tolerance for line segments
X_tol = [] # X segments above R_tol
Y_tol = [] # Y segments above R_tol
m = [] # list of slopes
current_len = 0
# run recursive segmentation
while current_len < target_len:
X = []
Y = []
for segX, segY in zip(X0, Y0):
mid = len(segX) // 2
# left segments
X_L = segX[:mid + 1] # left segment
Y_L = segY[:mid + 1] # left segment
model_L = LinearRegression().fit(X_L, Y_L)
if model_L.score(X_L, Y_L) >= R_tol:
X_tol.append(X_L)
Y_tol.append(Y_L)
m.append(model_L.coef_.item())
else:
X.append(X_L)
Y.append(Y_L)
# right segments
X_R = segX[mid:] # right segment
Y_R = segY[mid:] # right segment
model_R = LinearRegression().fit(X_R, Y_R)
if model_R.score(X_R, Y_R) >= R_tol:
X_tol.append(X_R)
Y_tol.append(Y_R)
m.append(model_R.coef_.item())
else:
X.append(X_R)
Y.append(Y_R)
X0 = X # reinit
Y0 = Y # reinit
# count num of element in X_tol. When X_tol == target_len, end recrusion.
current_len = 0
medians = [] # get list of all medians to sort list of lists later
for l in X_tol:
current_len += len(l)
medians.append(np.median(l))
# sort lists of lists based on X_tol order
sort_mask = np.argsort(medians)
X_tol_sort = np.array(X_tol, dtype=object)[sort_mask]
Y_tol_sort = np.array(Y_tol, dtype=object)[sort_mask]
thetas = np.rad2deg(
np.arctan(np.array(m)[sort_mask])) # calcualte inclination angles between segment slopes and x-axis
# second smooth of tauc plot just to get clear signal for peaks
peaks = scipy.signal.find_peaks(tauc_smooth.iloc[:, i + 1], height=200,
width=(0, 999999)) # only find peaks with height TPs>20
peak_height_idx = np.argsort(peaks[1]['peak_heights'])[::-1] # sort from highest to lowest peak
working_e = [] # list of all e-values that work to produce a line that intersects x=0 axis
rmse_list = [] # list of all rmse
for p_idx in peak_height_idx:
for e in range(len(X_tol_sort)):
try:
model = LinearRegression().fit(np.vstack([X_tol_sort[-1 - e], X_tol_sort[-2 - e]]), np.vstack(
[Y_tol_sort[-1 - e],
Y_tol_sort[-2 - e]])) # take foruth last and fifth last segment to run regression
y_fit = model.predict(TAUC_X)
tngt = LineString([(np.min(TAUC_X), np.min(y_fit)), (np.max(TAUC_X), np.max(y_fit))])
xax = LineString([(np.min(TAUC_X), 0.), (np.max(TAUC_X), 0.)])
int_pt = tngt.intersection(xax)
Eg = int_pt.x # bandgap, if no x-intercept, will throw an error
upper = int(
peaks[0][p_idx] - peaks[1]['widths'][p_idx] / 2) # index location of peak minus half peak width
lower = int(np.abs(y_fit - 0).argmin()) # where y_fit intersects with x-axis
if len(peak_height_idx) > 1 and lower < peaks[0][p_idx - 1] and peaks[0][p_idx] > peaks[0][
p_idx - 1]: # if there are multiple peaks
lower = int(peaks[0][p_idx - 1] - peaks[1]['widths'][p_idx - 1] / 2)
if model.coef_ > 0 and upper > lower: # positive slope and lower < upper bound
rmse = np.sqrt(np.mean(
(TAUC_Y[lower:upper] - y_fit[lower:upper]) ** 2)) # find RMSE of fit and true tauc curve
rmse_list.append(rmse)
working_e.append(e)
except:
pass # keep looping if unsuccessful
# only save band gap and tangent line where rmse is lowest
try:
best_e = working_e[np.array(rmse_list).argmin()]
model = LinearRegression().fit(np.vstack([X_tol_sort[-1 - best_e], X_tol_sort[-2 - best_e]]), np.vstack(
[Y_tol_sort[-1 - best_e],
Y_tol_sort[-2 - best_e]])) # take fourth last and fifth last segment to run regression
y_fit = model.predict(TAUC_X)
tngt = LineString([(np.min(TAUC_X), np.min(y_fit)), (np.max(TAUC_X), np.max(y_fit))])
xax = LineString([(np.min(TAUC_X), 0.), (np.max(TAUC_X), 0.)])
int_pt = tngt.intersection(xax)
Eg = np.round(int_pt.x, 3) # bandgap
bandgaps_per_tauc.append(Eg) # append bandgap
fig, ax = plt.subplots(figsize=(3, 2))
for n in range(len(X_tol_sort)):
ax.scatter(X_tol_sort[n][0], Y_tol_sort[n][0], marker='o', c='#040357', s=30, zorder=15)
ax.scatter(X_tol_sort[n][-1], Y_tol_sort[n][-1], marker='o', c='#040357', s=30, zorder=15)
plt.plot(TAUC_X, TAUC_Y, c='#040357', lw=2.5, zorder=15)
plt.plot(TAUC_X, y_fit, c='r', lw=3, alpha=0.75, zorder=20)
plt.axvline(Eg, c='#e00000', ls='--', lw=1.5, zorder=5)
plt.ylim([0, np.max(TAUC_Y)])
plt.title(f'Material Deposit {current_tauc}')
t = plt.text(Eg, np.max(TAUC_Y) * 0.95, f'E$_g$={Eg}eV', c='#e00000', ha='center', va='top',
weight='bold', zorder=10)
t.set_bbox(dict(facecolor='w', alpha=0.9, lw=0))
plt.xlabel(r'$hv$ (eV)')
plt.ylabel(r'$(F(R)*hv)^2$ (a.u.)')
ax.minorticks_on()
ax.grid(which='minor', color='gray', linestyle='--', alpha=0.35)
ax.grid(which='major', color='gray', linestyle='--', alpha=0.35)
plt.tick_params(axis='both', labelleft=False)
if len(bandgaps_per_tauc) > 1 and bandgaps_per_tauc[-1] != bandgaps_per_tauc[-2]:
plt.savefig(f'{savepath}\\{current_tauc}_bandgap{len(bandgaps_per_tauc)}.png', dpi=300,
bbox_inches='tight')
else:
plt.savefig(f'{savepath}\\{current_tauc}.png', dpi=300, bbox_inches='tight')
if verbose: # plot
plt.show()
except: # if the tangent line does not intersect with x-axis => no band gap
bandgaps_per_tauc.append(np.nan)
bandgaps.append(np.array(bandgaps_per_tauc))
for b in range(len(bandgaps)):
bandgaps[b] = bandgaps[b][np.sort(np.unique(bandgaps[b], return_index=True)[1])] # remove duplicates
EG = pd.DataFrame(bandgaps).T.set_axis(tauc_smooth.columns.values[1:], axis=1)
EG = EG.set_index(f'bandgap{n}' for n in range(EG.shape[0]))
EG.to_csv(f'{savepath}\\Extracted_Band_Gaps.csv')
return EG