Why Muons and Protons are Deep Donors in Si and Ge

The deep impurity character of interstitial positive muons or protons in Si and Ge is shown to result from the valley-orbit interaction of the six conduction-band minima along $\Delta$. This interaction, much stronger for interstitial than for substitutional point charges, leads to a breakdown of the effective-mass approximation and to the formation of a deep state. This is particularly striking in Ge, where the $\Delta$ minima are not the absolute ones.