Semiconductor Dielectric Function Modeling Using the Tanguy Analytical Expression for the Hulthen Exciton

Tanguy\textsc{\char13}s analytical expression\footnote{C. Tanguy, \textbf{Phy. Rev. B} 60, 10660 (1999).} for the complex dielectric function associated with a Hulthen exciton in a semiconductor is used to obtain second derivatives that can be used for fast fits of spectroscopic ellipsometry data. Since the Hulthen potential provides an excellent description of a screened exciton, the expressions obtained are ideally suited to investigate the possible excitonic origin of the \textit{ad hoc} phase factors that are often needed to match dielectric function theory with ellipsometry data. A detailed analysis is presented with applications to elemental semiconductors such as Ge.