# Which energy should I consider while trying to analyse the variation in transport coefficients with temperature?

I am using the BolzTraP code [I'm completely new to this code] to calculate the Thermo-electric coefficients as per this tutorial. And the output file obtained from BoltzTraP is given below. The column labels and what they stand for are given below :

• Ef[Ry] : Fermi Energy level

• T [K] : Temperature

• N: Number of Carriers

• DOS(Ef) : Density of States

• S: Seebeck Coefficient

• s/t : conductivity/ electron relaxation time

• R_H: Hall Coefficient

• kappa0: Thermal Conductivity

• c: Electronic Specific Heat

• chi: Pauli Magnetic Susceptibility

  Ef[Ry]     T [K]            N         DOS(Ef)           S             s/t               R_H        kappa0         c                 chi
0.39136    1.0000     14.59160339  0.27749010E+04  0.00000000E+00  0.15404697E+22 -0.16852985E-11 -0.00000000E+00  0.00000000E+00  0.41426895E-07
0.39136    2.0000     14.59160339  0.13874505E+04 -0.12814074E-20  0.77023484E+21 -0.33705969E-11  0.10277212E+01  0.65901673E-14  0.20713447E-07
0.39136    3.0000     14.59160339  0.92496701E+03 -0.44231269E-15  0.51348989E+21 -0.50558954E-11  0.23649732E+06  0.15165172E-08  0.13808965E-07
0.39136    4.0000     14.59160339  0.69372528E+03 -0.23870272E-12  0.38511743E+21 -0.67411938E-11  0.95722814E+08  0.61381369E-06  0.10356724E-07
0.39136    5.0000     14.59160340  0.55498083E+03 -0.98897905E-11  0.30809428E+21 -0.84264870E-11  0.31727480E+10  0.20344954E-04  0.82853882E-08
0.39136    6.0000     14.59160341  0.46249068E+03 -0.11450615E-09  0.25674891E+21 -0.10111701E-10  0.30612680E+11  0.19630110E-03  0.69045896E-08
0.39136    7.0000     14.59160348  0.39645474E+03 -0.64293135E-09  0.22008938E+21 -0.11796403E-10  0.14734045E+12  0.94481076E-03  0.59187295E-08
0.39136    8.0000     14.59160376  0.34700703E+03 -0.23031393E-08  0.19263855E+21 -0.13479177E-10  0.46195667E+12  0.29623023E-02  0.51805175E-08
0.39136    9.0000     14.59160447  0.30870652E+03 -0.61253650E-08  0.17137573E+21 -0.15156879E-10  0.10928617E+13  0.70082134E-02  0.46087238E-08


Here you can see that the coefficients from column 4 to 10 vary with temperature, for a given Ef or N.

I've got the BoltzTraP user guide but it doesn't mention as to which energy I should study the variation at. Should it be analysed at the Fermi Level which is obtained during the SCF calculation? or at the experimentally determined carrier concentration?

• Isn't the Fermi energy dependent of the carrier concentration? – Camps Jan 11 at 11:41
• @Camps Yes, it does! The Ef term indicates the Fermi energy [I've made the correction] actually hence it remains constant for the given number of carriers as given in the data [columns 1 and 3]. I'm not sure at which concentration I should look at the variation S vs T. – Anoop A Nair Jan 11 at 12:09