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DBM_Dirac.py
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# -*- coding: utf-8 -*-
"""
Created on Wed Aug 16 11:11:30 2023
@author: viola
"""
# 2D DOUBLE-DIRAC-BAND MATERIALS #
# import necessary functions
from functions import F0c, F1c, F2c, F0v, F1v, F2v, Gic, Giv, func_Gi
# TE QUANTITIES - CONDUCTION BAND
def sigmac_DBMD(delta,
eta):
"""
function to calculate the electrical conductivity sigma for the conduction band
Parameters
----------
delta : TYPE float
DESCRIPTION energy gap value to be entered in the function
eta : TYPE float
DESCRIPTION chemical potential value to be entered in the function
Returns
-------
calculated function : TYPE float
DESCRIPTION calculated values for sigma of the conduction band
"""
return F0c(delta, eta) - Gic(func_Gi, 0, delta, eta)
def Sc_DBMD(delta,
eta):
"""
function to calculate the Seebeck coefficient S for the conduction band
Parameters
----------
delta : TYPE float
DESCRIPTION energy gap value to be entered in the function
eta : TYPE float
DESCRIPTION chemical potential value to be entered in the function
Returns
-------
calculated function : TYPE float
DESCRIPTION calculated values for S of the conduction band
"""
F_G_0 = F0c(delta, eta) - Gic(func_Gi, 0, delta, eta) # numerator (F0, G0 contribution)
F_G_1 = F1c(delta, eta) - Gic(func_Gi, 1, delta, eta) # denominator (F1, G1 contribution)
return -F_G_1/F_G_0
def kec_DBMD(delta,
eta):
"""
function to calculate the thermal electronic conductivity k_e sigma for the conduction band
Parameters
----------
delta : TYPE float
DESCRIPTION energy gap value to be entered in the function
eta : TYPE float
DESCRIPTION chemical potential value to be entered in the function
Returns
-------
calculated function : TYPE float
DESCRIPTION calculated values for k_e of the conduction band
"""
F_G_2 = F2c(delta, eta) - Gic(func_Gi, 2, delta, eta) # 1st term (F2, G2 contribution)
F_G_1 = (F1c(delta, eta) - Gic(func_Gi, 1, delta, eta))**2 # 2nd term numerator (F1, G1 contribution)
F_G_0 = F0c(delta, eta) - Gic(func_Gi, 0, delta, eta) # 2nd term denominator (F0, G0 contribution)
return F_G_2 - F_G_1/F_G_0
# TE QUANTITIES - VALENCE BAND
def sigmav_DBMD(delta,
eta):
"""
function to calculate the electrical conductivity sigma for the valence band
Parameters
----------
delta : TYPE float
DESCRIPTION energy gap value to be entered in the function
eta : TYPE float
DESCRIPTION chemical potential value to be entered in the function
Returns
-------
calculated function : TYPE float
DESCRIPTION calculated values for sigma of the valence band
"""
return F0v(delta, eta) - Giv(func_Gi, 0, delta, eta)
def Sv_DBMD(delta,
eta):
"""
function to calculate the Seebeck coefficient S for the valence band
Parameters
----------
delta : TYPE float
DESCRIPTION energy gap value to be entered in the function
eta : TYPE float
DESCRIPTION chemical potential value to be entered in the function
Returns
-------
calculated function : TYPE float
DESCRIPTION calculated values for S of the valence band
"""
F_G_1 = F1v(delta, eta) - Giv(func_Gi, 1, delta, eta) # numerator (F1, G1 contribution)
F_G_0 = F0v(delta, eta) - Giv(func_Gi, 0, delta, eta) # denominator (F0, G0 contribution)
return - F_G_1/F_G_0
def kev_DBMD(delta,
eta):
"""
function to calculate the thermal electronic conductivity k_e for the valence band
Parameters
----------
delta : TYPE float
DESCRIPTION energy gap value to be entered in the function
eta : TYPE float
DESCRIPTION chemical potential value to be entered in the function
Returns
-------
calculated function : TYPE float
DESCRIPTION calculated values for k_e of the valence band
"""
F_G_2 = F2v(delta, eta) - Giv(func_Gi, 2, delta, eta) # 1st term (F2, G2 contribution)
F_G_1 = (F1v(delta, eta) - Giv(func_Gi, 1, delta, eta))**2 # 2nd term numerator (F1, G1 contribution)
F_G_0 = F0v(delta, eta) - Giv(func_Gi, 0, delta, eta) # 2nd term denominator (F0, G0 contribution)
return F_G_2 - F_G_1/F_G_0
# TE QUANTITIES OF THE MATERIAL
def sigma_DBMD(delta,
eta):
"""
function to calculate the electrical conductivity sigma of the material
Parameters
----------
delta : TYPE float
DESCRIPTION energy gap value to be entered in the function
eta : TYPE float
DESCRIPTION chemical potential value to be entered in the function
Returns
-------
calculated function : TYPE float
DESCRIPTION calculated values for sigma of the material
"""
return sigmac_DBMD(delta, eta) + sigmav_DBMD(delta, eta)
def S_DBMD(delta,
eta):
"""
function to calculate the Sebeck coefficient S of the material
Parameters
----------
delta : TYPE float
DESCRIPTION energy gap value to be entered in the function
eta : TYPE float
DESCRIPTION chemical potential value to be entered in the function
Returns
-------
calculated function : TYPE float
DESCRIPTION calculated values for S of the material
"""
sigma_S_c = sigmac_DBMD(delta, eta)*Sc_DBMD(delta, eta) # 1st term of numerator (conduction band sigma and S contribution)
sigma_S_v = sigmav_DBMD(delta, eta)*Sv_DBMD(delta, eta) # 2nd term of numerator (valence band sigma and S contribution)
return (sigma_S_v + sigma_S_c)/sigma_DBMD(delta, eta)
def ke_DBMD(delta,
eta):
"""
function to calculate the themal electronic conductivity k_e of the material
Parameters
----------
delta : TYPE float
DESCRIPTION energy gap value to be entered in the function
eta : TYPE float
DESCRIPTION chemical potential value to be entered in the function
Returns
-------
calculated function : TYPE float
DESCRIPTION calculated values for k_e of the material
"""
sigma_cv = sigmac_DBMD(delta, eta)*sigmav_DBMD(delta, eta) # 1st factor of 1st term numerator (sigma contribution)
S_c_v = Sc_DBMD(delta, eta) - Sv_DBMD(delta, eta) # 2nd factor of 1st term numerator (S contribution)
ke_c_v = kec_DBMD(delta, eta) + kev_DBMD(delta, eta) # 2nd term (k_e contribution)
return (sigma_cv/sigma_DBMD(delta, eta))*(S_c_v)**2 + ke_c_v
def ZT_DBMD(delta,
eta,
rk):
"""
function to calculate the figure of merit ZT of the material
Parameters
----------
delta : TYPE float
DESCRIPTION energy gap value to be entered in the function
eta : TYPE float
DESCRIPTION chemical potential value to be entered in the function
rk : TYPE float
DESCRIPTION thermal lattice conductivity value to be entered in the function
Returns
-------
calculated function : TYPE float
DESCRIPTION calculated values for ZT of the material
"""
return ((S_DBMD(delta, eta)**2)*sigma_DBMD(delta, eta))/(ke_DBMD(delta,eta) + rk)