  In this article, we derive and discuss a physics-based model for impedance
spectroscopy of lithium batteries. Our model for electrochemical cells with
planar electrodes takes into account the solid-electrolyte interphase (SEI) as
porous surface film. We present two improvements over standard impedance
models. Firstly, our model is based on a consistent description of lithium
transport through electrolyte and SEI. We use well-defined transport
parameters, e.g., transference numbers, and consider convection of the
center-of-mass. Secondly, we solve our model equations analytically and state
the full transport parameter dependence of the impedance signals. Our
consistent model results in an analytic expression for the cell impedance
including bulk and surface processes. The impedance signals due to
concentration polarizations highlight the importance of electrolyte convection
in concentrated electrolytes. We simplify our expression for the complex
impedance and compare it to common equivalent circuit models. Such simplified
models are good approximations in concise parameter ranges. Finally, we compare
our model with experiments of lithium metal electrodes and find large
transference numbers for lithium ions. This analysis reveals that lithium-ion
transport through the SEI has solid electrolyte character.
