Como evaluar la masa efectiva electrónica usando el método de ajuste de curvas?

R. Puedes hacerlo de dos formas:

1. Para bandas parabólicas graficas E vs k2 y el inverso de la pendiente es la masa efectiva.

2. Para bandas no parabólicas evalúas la energía en una dirección de k, desarrollas la energía en un polinomio de k en esa dirección y el coeficiente del término de segundo orden se relaciona con la masa efectiva. En este caso el valor obtenido es un elemento del tensor masa efectiva.

How to evaluate electronic effective mass using the curve fitting method?

A. You can do it in two ways:

1. For parabolic bands you draws E vs k2 and the inverse of the slope is the effective mass.

2. For non-parabolic bands you evaluate the energy in a direction of k, you develop the energy in a polynomial of k in that direction and the coefficient of the second-order term is related to the effective mass. In this case, the value obtained is an element of the effective mass tensor.

There are programs such as QuantumATK that has very useful tools to get the effective mass.

https://docs.quantumwise.com/tutorials/effective_mass/effective_mass.html

Regards

Denoting the effective mass as m*,

the wave vector as k,

the band energy, (which depends on k) as E(k)

and the Planck constant as h,

T effective mass of electrons (holes) in a band is given by,

m* = (h/2*Pi)^2 {d^2 E(k)/d k^2}^(-1)

In the fitting approach, a few E(k) points near to the VBM/CBM are calculated for the band of interest. These points are fit to a Taylor series, (often just three points near the VBM/CBM are fit to a parabola) and the second derivative is taken to obtain the quantity in {} above. As Luiggi points out, this yields an element of the effective mass tensor.

Some electronic structure codes contain an option to calculate the effective mass so no such manual fitting of points is needed.

fit the band gap vs temperature curve to the experimentally observed one