Rutherford Backscattering Spectroscopy was used to analyze and quantify the out-diffusion of Cs and Rb from silicon during solid-phase epitaxial regrowth under N2 atmosphere. Out-diffused amounts of about 60% Rb and 30% Cs were determined. The transient out-diffusion behavior of the alkali atoms in ultra-high vacuum was monitored during recrystallization by secondary neutral mass spectroscopy. The analysis showed that the alkali atoms diffuse out without forming chemical bonds which are critical for the proposed application. With our results it could be estimated that this filling method has a potential to replace other methods for producing atomic vapor cells