I have generated the band structure of my material using Wien2k software ,
Please could you explain me how we can calculate the effective mass of electron and hole for perovskite materials ?
Thanks ,
Thank you Mundher,
And welocme Yassine,
Since the electrons will occupy normally the bottom levels in the band the the most suitable range is at the minimum of the E-k diagram. Then you have to fit the bottom region with a parabola similar to that has been done in the Figure but shift the red parabola down ward to make it coincide with the simulated curve.
Best wishes
Having the E-k curve in the conduction band and valence band then you can calculate the effective mass by assuming that the free electron model holds at the bottom of the conduction band and the top of the valence band.
The free electron relation between the energy and the momentum isd as follows:
E-Ec= P^2/2me where P is the the electron momentum and me is the effective electron mass.
From the de Broglie relation we have
P=h/lambda= (h/2pi) k= h^- k with h^- = h/2pi
where k is the wave vector
Then it follows that
E-Ec= h^- ^2 k^2/ 2me,
Differentiating the above relation twice one can get an expression for the effective mass me such that
me= h^- ^2/ d2(E-Ec)/ d k^2
That is the effective mass is = the reduced h^2/ the second derivative of E versus K.
The same holds for the mp in the valence band.
I would like that you get more information from the book: Book Electronic Devices
Thanks Dear Abdelhalim abdelnaby Zekry Means , we can use the electronic band structure to plot the polynimial fit to get d^2E/dK^2 ( attached fig ) ? . but it is still a bit confusing which point should choose to make the calculations ?
Thank you Mundher,
And welocme Yassine,
Since the electrons will occupy normally the bottom levels in the band the the most suitable range is at the minimum of the E-k diagram. Then you have to fit the bottom region with a parabola similar to that has been done in the Figure but shift the red parabola down ward to make it coincide with the simulated curve.
Best wishes
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