The study of chemical segregation at interfaces, and in particular the ability to predict the thickness of segregated layers via analytical expressions or computational modeling, is a fundamentally challenging topic in the design of novel heterostructured materials. This issue is particularly relevant for the phase-field (PF) methodology, which has become a prominent tool for describing phase transitions. These models rely on phenomenological parameters that pertain to the interfacial energy and thickness, quantities that cannot be experimentally measured. Instead of back-calculating these parameters from experimental data, here we combine a set of analytical expressions based on the Cahn-Hilliard approach with ab initio calculations to compute the gradient energy parameter κ and the thickness λ of the segregated Li layer at the Li_{x}Si-Cu interface. With this bottom-up approach we calculate the thickness λ of the Li diffuse interface to be on the order of a few nm, in agreement with prior experimental secondary ion mass spectrometry observations. Our analysis indicates that Li segregation is primarily driven by solution thermodynamics, while the strain contribution in this system is relatively small. This combined scheme provides an essential first step in the systematic evaluation of the thermodynamic parameters of the PF methodology, and we believe that it can serve as a framework for the development of quantitative interface models in the field of Li-ion batteries.