We have conducted Auger depth profiling analyses of InP/GaInAsP multilayer specimens, in which the surface roughness was caused by the argon ion sputtering. We have, then, carried out the quantitative evaluation of the surface roughness using the distribution of the each pixel height taken by an atomic force microscope. The obtained histograms of surface roughness were used to calculate the resolution function together with the functions of electron escape depth and atomic mixing (Hofmann's MRI model). We also compared the resulting resolution function with the one obtained by the depth profiles measured. In this convolution calculation, we have assumed that the atomic mixing layer thickness was 2 nm and the information depth was 0.75 nm. The resulting resolution function was in excellent agreement with the one obtained from Auger depth profile. Therefore, we conclude that the distribution of the height of each pixel taken by AFM corresponds to the functions of surface roughness of the depth resolution function on the AES depth profile with sample cooling method.