Integrated χ(2) devices are a widespread tool for the generation and manipulation of light fields, since they exhibit high efficiency, a small footprint and the ability to interface them with fibre networks. Surprisingly, some commonly used material substrates are not yet fully understood, in particular potassium titanyl phosphate (KTP). A thorough understanding of the fabrication process of waveguides in this material and analysis of their properties is crucial for the realization and the engineering of high efficiency devices for quantum applications. In this paper we present our studies on rubidium-exchanged waveguides fabricated in KTP. Employing energy dispersive X-ray spectroscopy (EDX), we analysed a set of waveguides fabricated with different production parameters in terms of time and temperature. We find that the waveguide depth is dependent on their widths by reconstructing the waveguide depth profiles. Narrower waveguides are deeper, contrary to the theoretical model usually employed. Moreover, we found that the variation of the penetration depth with the waveguide width is stronger at higher temperatures and times. We attribute this behaviour to stress-induced variation in the diffusion process.