Analysis of Immittance Spectra: Finding Unambiguous Electrical Equivalent Circuits to Represent the Underlying Physics

An alternate approach of analyzing immittance spectra with electrical equivalent circuits, which not only eliminates circuit ambiguity but also directly extracts the system-specific parameters of the selected physical models, is proposed. To understand the underlying mechanisms, a fundamental electrical equivalent circuit, representing Maxwell's equations, is derived. Allowing nonlinear characteristics for the elements in the circuit results in a universal immittance that is neither limited to the fundamental frequency nor to linear response functions. Process-specific physical models with their intrinsic, potentially nonlinear, dependencies on external parameters are introduced as components of the circuit. This allows the extraction of the system-specific parameters of the models instead of single values for idealized components like resistors and capacitors. The resulting electrical equivalent circuits are unambiguous and can be fitted to measured immittance data for a whole set of varied external parameters instead of the frequency of the applied stimulus only. Furthermore, the different dependencies of the physical models on external parameters automatically weight the regions of their dominance. Exemplarily, for a well-known system, the impedance of a depletion layer in silicon is calculated by using models for the resistance and capacitance that are both dependent on the external parameters voltage and temperature. In addition to a detailed comparison with conventional electrical equivalent circuits, differences between the presented approach and analytical Poisson-Nernst-Planck models are discussed.