How to calculate effective mass of elctron and hole in conduction and valence band?
Answers
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us discuss the effective mass concept in light of electrons and holes. We already know that the electrons in energy bands, behave differently to that of free-electrons. For general purpose, we can write the conduction and valance effective masses at their band minimum as for electrons and for hole.
The conduction band Energy in k space is , where Ec is the conduction band edge and similarly valance band energy.
Here one important thing : the conduction band effective mass is directly related to the band gap energy Eg. The smaller is the band gap, the smaller is the effective mass (Fig.2.20). Here you can observe some interesting points: for example see band gap is decreasing in the alloys CdS, CdSe and CdTe ( You know why?). Similarly AlAs, GaAs and InAs.
The band gaps of few semiconductors at the room temperature are given in the table. However, with the temperature the band gap substantially varies. This is shown graphically in fig 2.21. The empirical relation of band gap vs temperature is