Characterization of CaF$_{2}$ surfaces using Adsorption-Desorption Isotherms and Atomic Force Microscopy

We are interested in using rough CaF$_{2}$ films to study the superfluid transition in two-dimensional helium systems. These experiments require quantitative information regarding the topography of the CaF$_{2}$ surfaces. The surface roughness of CaF$_{2}$ films is known to increase with film thickness as has been shown with previous atomic force microscopy (AFM) measurements [1]. We have fabricated a series of CaF$_{2 }$samples of different film thicknesses and thus different surface roughnesses. These surfaces were studied using AFM and adsorption-desorption isotherm measurements with liquid nitrogen at T=77 K. The isotherm measurements allow us to determine the pore size distribution of each CaF$_{2 }$film thickness. We find the emergence of hysteretic capillary condensation due to deep pores in the CaF$_{2}$ as the film thickness increases. The development of these deep pores is also seen in our AFM measurements. Our combined results provide a detailed description of CaF$_{2}$ surface roughness which can be utilized in the planned superfluid experiment. [1] D.R. Luhman and R.B. Hallock, Phys Rev. E \textbf{70}, 051606 (2004).