Several active areas of research in novel energy storage technologies, including three-dimensional solid state batteries and passivation coatings for reactive battery electrode components, require conformal solid state electrolytes. We describe an atomic layer deposition (ALD) process for a member of the lithium phosphorus oxynitride (LiPON) family, which is employed as a thin film lithium-conducting solid electrolyte. The reaction between lithium tert-butoxide (LiO$^t$Bu) and diethyl phosphoramidate (DEPA) produces conformal, ionically conductive thin films with a stoichiometry close to Li$_2$PO$_2$N between 250 and 300$^circ$C. The P/N ratio of the films is always 1, indicative of a particular polymorph of LiPON which closely resembles a polyphosphazene. Films grown at 300$^circ$C have an ionic conductivity of $6.51:(pm0.36)times10^{-7}$ S/cm at 35$^circ$C, and are functionally electrochemically stable in the window from 0 to 5.3V vs. Li/Li$^+$. We demonstrate the viability of the ALD-grown electrolyte by integrating it into full solid state batteries, including thin film devices using LiCoO$_2$ as the cathode and Si as the anode operating at up to 1 mA/cm$^2$. The high quality of the ALD growth process allows pinhole-free deposition even on rough crystalline surfaces, and we demonstrate the fabrication and operation of thin film batteries with the thinnest (<100nm) solid state electrolytes yet reported. Finally, we show an additional application of the moderate-temperature ALD process by demonstrating a flexible solid state battery fabricated on a polymer substrate.