Influence of the ``second gap'' on the optical absorption of transparent conducting oxides

Transparent conducting oxides (TCOs) are critical to many technologies (e.g., thin-film solar cells, flat-panel displays or organic light-emitting diodes). TCOs are heavily doped (\emph{n} or \emph{p}-type) oxides that satisfy many design criteria such as high transparency to visible light (i.e., a band gap $>$ 3 eV), high concentration and mobility of carriers (leading to high conductivity), ... In such (highly doped) systems, optical transitions from the conduction band minimum to higher energy bands in \emph{n}-type or from lower energy bands to the valence band maximum in \emph{p}-type are possible and can degrade transparency. In fact, it has been claimed that a high energy ($>$ 3eV) for any of these transitions made possible by doping, commonly referred as a high ``second gap'', is a necessary design criterion for high performance TCOs. Here, we study the influence of this second gap on the transparency of doped TCOs by using \emph{ab initio} calculations within the random phase approximation (RPA) for several well-known \emph{p}-type and \emph{n}-type TCOs. Our work highlights how the second gap affects the transparency of doped TCOs, shining light on more accurate design criteria for high performance TCOs.