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get_effective_mass.py
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get_effective_mass.py
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import re
import pandas as pd
import numpy as np
from scipy.optimize import curve_fit
from scipy.constants import physical_constants
eV_to_hartree = physical_constants['electron volt-hartree relationship'][0]
bohr_to_m = physical_constants['Bohr radius'][0]
angstrom_to_bohr = bohr_to_m / 1e-10
pd.options.display.max_columns = None
pd.options.display.max_rows = None
# 能带的每一条路径 K 点数目
# 比如 KPOINTS 长这样的话要向下面这么设置：
"""
K-Path Generated by VASPKIT.
80
Line-Mode
Reciprocal
0.0000000000 0.0000000000 0.0000000000 G
0.5000000000 0.0000000000 0.0000000000 M
0.5000000000 0.0000000000 0.0000000000 M
0.3333333333 0.3333333333 0.0000000000 K
0.3333333333 0.3333333333 0.0000000000 K
0.0000000000 0.0000000000 0.0000000000 G
"""
K_lists = [80, 80, 80, ]
class EffectiveMass:
def __init__(self, num_sample_points=6):
# 能带数据文件夹名字
self.file_name = "BAND.dat"
# K 点数目，能带条数
self.K_number, self.bands_number = self.get_K_number_and_bands_number()
if sum(K_lists) == self.K_number:
# 能带的所有数据
self.datas = pd.read_csv(self.file_name, comment="#", sep="\s+" , names=['K', 'bands'])
# 每一条能带的数据 (DataFrame 对象列表)
self.Bands = self.get_Bands()
# 最低导带的下标，最高价带的下标
self.CBM_index, self.VBM_index = self.get_VBM_CBM_index()["CBM"], self.get_VBM_CBM_index()["VBM"]
# ：每一段路径的最高价带的能带数据
# ： VBM 的 K 点，
# ： VBM 的能带数据
self.VBM_list_bands, self.VBM_kpoints, self.VBM_bands = self.split_bands_by_K_lists(self.Bands[self.VBM_index], K_lists)
self.get_fitting_effective_mass_of_every_path(self.VBM_kpoints, self.VBM_bands, band_type="VBM", num_sample_points=num_sample_points)
# ：每一段路径的最高价带的能带数据
# ： CBM 的 K 点，
# ： CBM 的能带数据
self.CBM_list_bands, self.CBM_kpoints, self.CBM_bands = self.split_bands_by_K_lists(self.Bands[self.CBM_index], K_lists)
self.get_fitting_effective_mass_of_every_path(self.CBM_kpoints, self.CBM_bands, band_type="CBM", num_sample_points=num_sample_points)
else:
print("输入的 K 点数目 和 能带数据文件不符合, 请检查 K_lists 的设置")
def get_K_number_and_bands_number(self):
nums = []
with open(self.file_name, 'r') as f:
next(f)
nums = re.findall(r"\d+\.?\d*", f.readline())
return (int(nums[0]), int(nums[1]))
def get_Bands(self):
Bands = []
for i in range(self.bands_number):
X = []
Y = []
for j in range(self.K_number):
index = i * self.K_number + j
X.append(self.datas.K[index])
Y.append(self.datas.bands[index])
# 创建 DF 对象
temp = pd.DataFrame(np.array([X, Y]).T, columns=["K", "bands"])
Bands.append(temp)
return Bands
def get_VBM_CBM_index(self):
for i in range(self.bands_number - 1):
# 减去费米能级的能带数据，价带小于 0 ，导带大于 0.
# 判断第 i 条带所有能带值小于 0 且 第 i + 1 条带大于 0
if ((self.Bands[i].bands < 0).all()) and (self.Bands[i+1].bands > 0).all():
CBM_index = i+1
VBM_index = i
break
try:
with open("./VBM", "w+") as f:
print(self.Bands[VBM_index], file=f)
with open("./CBM", "w+") as f:
print(self.Bands[CBM_index], file=f)
return {"CBM": CBM_index, "VBM": VBM_index}
except:
print("检查最高价带和最低导带是否重叠了，或者最高价带和最低导带越过了费米面")
def fit_effective_mass(self, kpoints, energies, parabolic=True):
if parabolic:
fit = np.polyfit(kpoints, energies, 2)
c = 2 * fit[0] # curvature therefore 2 * the exponent on the ^2 term
else:
# Use non parabolic description of the bands
# 使用非抛物线拟合
def f(x, alpha, d):
top = np.sqrt(4 * alpha * d * x**2 + 1) - 1
bot = 2 * alpha
return top / bot
# set boundaries for curve fitting: alpha > 1e-8
# as alpha = 0 causes an error
bounds = ((1e-8, -np.inf), (np.inf, np.inf))
popt, _ = curve_fit(f, kpoints, energies, p0=[1., 1.],
bounds=bounds)
c = 2 * popt[1]
eff_mass = (angstrom_to_bohr**2 / eV_to_hartree) / c
# print("系数： {}".format((angstrom_to_bohr**2 / eV_to_hartree)))
return eff_mass
"""
sons_band:
K，bands 的 dataframe 对象
kpoints:
K 点的 list 对象
energies:
能带数值的 list 对象
"""
# 按路径划分能带
def split_bands_by_K_lists(self, band, K_lists):
path_number = len(K_lists)
sons_band = []
kpoints = []
energies = []
start = 0
last = 0
for i in range(path_number):
last = last + K_lists[i]
temp = band[start: last]
sons_band.append(temp)
kpoints.append(temp["K"].tolist())
energies.append(temp["bands"].tolist())
start = last + 1
return sons_band, kpoints, energies
def get_fitting_effective_mass_of_every_path(self, kpoints, bands, band_type=None, num_sample_points=3):
if band_type==None:
print("Please set VBM or CBM")
return
len_bands = len(bands)
if band_type=="VBM":
for i in range(len_bands):
temp_energy = bands[i]
temp_kpoint = kpoints[i]
len_temp_energy = len(temp_energy)
max_temp_energy = max(temp_energy)
# 最大值下标
max_index = temp_energy.index(max_temp_energy)
# 将能量和坐标移至 0 的位置
temp_energy = (np.array(temp_energy) - max_temp_energy)
temp_kpoint = (np.array(temp_kpoint) - temp_kpoint[max_index])
# 收集数据
if max_index - num_sample_points >= 0:
start_id = max_index - num_sample_points
end_id = max_index + 1
energy_datas = temp_energy[start_id: end_id]
kpoint_datas = temp_kpoint[start_id: end_id]
energy_datas = np.concatenate([ energy_datas[:-1], energy_datas[::-1] ])
kpoint_datas = np.concatenate([ kpoint_datas[:-1], -kpoint_datas[::-1] ])
elif max_index + num_sample_points <= len_temp_energy:
start_id = max_index
end_id = max_index + num_sample_points + 1
energy_datas = temp_energy[start_id: end_id]
kpoint_datas = temp_kpoint[start_id: end_id]
energy_datas = np.concatenate([ energy_datas[::-1], energy_datas[1:] ])
kpoint_datas = np.concatenate([ -kpoint_datas[::-1], kpoint_datas[1:] ])
mass = self.fit_effective_mass(kpoint_datas, energy_datas)
print("第 {ith_path} 条路径的 VBM 的有效质量： {mass: 6.5f} m0".format(ith_path=i+1, mass=mass))
elif band_type=="CBM":
for i in range(len_bands):
temp_energy = bands[i]
temp_kpoint = kpoints[i]
len_temp_energy = len(temp_energy)
min_temp_energy = min(temp_energy)
# 最大值下标
min_index = temp_energy.index(min_temp_energy)
# 将能量和坐标移至 0 的位置
temp_energy = (np.array(temp_energy) - min_temp_energy)
temp_kpoint = (np.array(temp_kpoint) - temp_kpoint[min_index])
# 收集数据
if min_index - num_sample_points >= 0:
start_id = min_index - num_sample_points
end_id = min_index + 1
energy_datas = temp_energy[start_id: end_id]
kpoint_datas = temp_kpoint[start_id: end_id]
energy_datas = np.concatenate([ energy_datas[:-1], energy_datas[::-1] ])
kpoint_datas = np.concatenate([ kpoint_datas[:-1], -kpoint_datas[::-1] ])
elif min_index + num_sample_points <= len_temp_energy:
start_id = min_index
end_id = min_index + num_sample_points + 1
energy_datas = temp_energy[start_id: end_id]
kpoint_datas = temp_kpoint[start_id: end_id]
energy_datas = np.concatenate([ energy_datas[::-1], energy_datas[1:] ])
kpoint_datas = np.concatenate([ -kpoint_datas[::-1], kpoint_datas[1:] ])
mass = self.fit_effective_mass(kpoint_datas, energy_datas)
print("第 {ith_path} 条路径的 CBM 的有效质量： {mass: 6.5f} m0".format(ith_path=i+1, mass=mass))
def __del__(self):
print("......")
if __name__ == "__main__":
Exa_1 = EffectiveMass()