  Stability and precision of atomic devices are closely tied to the quality and
stability of the internal atmosphere of the atomic vapor cells on which they
rely. Such atmosphere can be stabilized by building the cell with low
permeation materials such as sapphire, or aluminosilicate glass in
microfabricated devices. Recently, we showed that permeation barriers made of
Al$_{2}$O$_{3}$ thin-film coatings deposited on standard borosilicate glass
could be an alternative for buffer gas pressure stabilization. In this study,
we hence investigate how helium permeation is influenced by the thickness,
ranging from 5 to 40 nm, of such Al$_{2}$O$_{3}$ thin-films coated by atomic
layer deposition. Permeation rates are derived from long-term measurements of
the pressure-shifted transition frequency of a coherent population trapping
(CPT) atomic clock. From thicknesses of 20 nm onward, a significant enhancement
of the cell hermeticity is experienced, corresponding to two orders of
magnitude lower helium permeation rate. In addition, we test cesium vapor cells
filled with neon as a buffer gas and whose windows are coated with 20 nm of
Al$_{2}$O$_{3}$. As for helium, the permeation rate of neon is significantly
reduced thanks to alumina coatings, leading to a fractional frequency stability
of 4x10$^{-12}$ at 1 day when the cell is used in a CPT clock. These features
outperform the typical performances of uncoated Cs-Ne borosilicate cells and
highlight the significance of Al$_{2}$O$_{3}$ coatings for buffer gas pressure
stabilization.
