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Generally the electron and hole effective masses are calculated by fitting the region around the band minimum or maximum to a parabola. Does this also work for a non-Gamma point? My system is a direct band gap material with minimum at the Y-point. Lets say I calculated the G(0,0,0)-Y(0,1/2,0)-A(-1/2,1/2,0) segment of the band structure. By fitting GY and YA lines to a parabola would I then get the m_y and m_x components of the effective mass tensor? I suspect the parabolic approximation only works for small k near the Gamma-point. But then is there a good way to define the effective mass for a non-Gamma material in the above sense?

Raul Laasner

Duke University, MEMS Department

Duke University, MEMS Department

- raul_l
**Posts:**74**Joined:**Sun Jan 08, 2012 8:45 pm

You can always define and calculate the band mass, for any band at any k-point from the inverse of the second k- derivatives of the band energy (see classic solid state texts for this - Kittel or Ashcroft+Mermin).

Normal "effective mass" theory is often used for Si, for example, where the CBM is not at Gamma.

You can happily fit a parabola to the bands around Y to get the different masses in different directions. Just be careful with the units on the k-axis when you do the fit (reduced k has to be changed to absolute k distance from Y, in cartesian coordinates = bohr^-1), to get the correct mass in m_e.

Matthieu

Normal "effective mass" theory is often used for Si, for example, where the CBM is not at Gamma.

You can happily fit a parabola to the bands around Y to get the different masses in different directions. Just be careful with the units on the k-axis when you do the fit (reduced k has to be changed to absolute k distance from Y, in cartesian coordinates = bohr^-1), to get the correct mass in m_e.

Matthieu

Matthieu Verstraete

University of Liege, Belgium

University of Liege, Belgium

- mverstra
**Posts:**618**Joined:**Wed Aug 19, 2009 12:01 pm

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