# Why the mobilities of holes and electrons are not identical in an intrinsic material?

In an intrinsic material, the lifetime $\tau$ of electrons and holes is the same, so in the equation for mobility, $$\mu = \frac{e\tau}{m^*}$$ the only difference between mobility of electrons an holes is their effective mass, $m^*$. But why would this mass be different if it represents the same phenomena?

Even in an intrinsic material, $\tau$ is different for electrons and holes. This is because in the equation for $\mu$, the value of $\tau$ is not lifetime but rather the average time between scattering events. Since holes aren’t an actual particle, the movement of holes is really the movement of electrons in the valence band. Because there are many more electrons in the valence band than in the conduction band, electrons in the valence band scatter much with other electrons than electrons in the conduction band do. Therefore, $\tau$ for holes is smaller than tau for electrons, making the mobility of holes less than that of electrons in most (if not all) semiconductors.