Extensive theoretical and experimental investigation of the chlorine and argon chemically assisted ion beam etching process for the fabrication of vertical, ultrahigh quality facets in GaAs are reported. The dependence of etch rate and verticality of the etched profile on chlorine flow and ion flux have been studied and analytical expressions for the etch rate are presented. The analytical expressions are based on previously suggested surface-reaction models as well as on a new model where the reactions are stimulated by the incident argon ions. Using this new surface-reaction model together with ion trajectory simulations. computer programs were developed for the etch rate and etch profile which allow us to study the dependence on chlorine flow, argon ion current density. and argon ion energy. The dependence of the etch rate and the etch profile on the chlorine flow is explained by the combined effect of a saturation of the chlorine surface coverage and increased scattering of the high-energetic argon ions with increasing chlorine flow. Furthermore, the importance of the etch-mask profile as well as adequate heat sinking, for the verticality of the etched facets is demonstrated.