# Illustration Band structure (energy dispersion) and effective mass

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Exemplarily drawn dispersion relation $$W(k)$$ (energy as a function of wavenumber) with completely filled valence band and partially filled conduction band separated by a band gap $$\Delta W$$.

The effective mass $$m^*$$ of an electron in the conduction band or the effective mass of a hole (missing electron) in the valence band depends reciprocally on the magnitude of the band curvature $$\frac{\partial^2 W}{\partial k^2}$$.

• At the conduction band minimum (blue dot), the band curvature is large (and positive), that is, the effective electron mass is small.
• At the valence band maximum (red dot), the band curvature is large (and negative), that is, the effective hole mass is small.
• At an inflection point (green), the band curvature is small, that is, the effective mass is large.