A novel approach of immittance-spectra analysis and how it resolves a decade-old deviation of the Frenkel-Poole model

Immittance (i.e. a generalisation of all quantities containing identical information as e.g. the impedance) spectroscopy is a well-established and versatile method with a broad range of applications in a wide variety of different fields and subjects. Although immittance spectroscopy is widely applied, commonly used strategies of analysing its measured data do not exhaust its full potential. In this work, a novel method of analysing immittance spectra is presented that resolves typical drawbacks of previous approaches. In comparison, it allows the extraction of meaningful physical parameters instead of effective parameters, the distinction of different parts in the complete system under investigation and, most importantly, it results in unambiguous electrical equivalent circuits (EECs). By introducing the dependence on external parameters in Maxwell’s extension of Ampere’s law, an EEC for a homogeneous piece of material is derived that allows replacing idealised lumped components, like resistors and capacitors, by (non-linear) process-specific physical models dependent on external parameters. Utilising these models for measurements over a range of external parameters in combination with global fits, that do optimise relevant physical parameters describing all varied external conditions simultaneously instead of resistances and capacitances per condition, allows identifying as well as understanding the underlying physical processes whilst, furthermore, extracting aforementioned physically relevant parameters. These are better comparable between different experiments and, additionally, due to the physical meaning they carry, more easily verifiable as reasonable in comparison to e.g. resistances and capacitances. Such meaningful physical parameters can be simultaneously present in multiple models, even shared between dielectric and electric models. This enables joint fitting of a parameter value across the different models for the corresponding processes, in the same piece of the system, and makes the presented method predestined to test the self-consistency of the measured data or the development of unified theories for electric and dielectric properties. The novel approach, presented in this work, was successfully applied in the analysis of heterostructures with a thin film of tetrahedral-amorphous carbon on different crystalline p-type silicon substrates where as many mutual parameters as possible were fitted jointly. Specificly the joint parameters of the dielectric and electric model of the thin film were used to verify a correction (suggested in this work) in the calculation of the superimposed field from the externally applied potential difference of the Frenkel-Poole model, that resolves an over 50 year old quantitative deviation of this model. It was often argued that the reason for the deviations are the too simple assumptions and limited physical concepts of the Frenkel-Poole model, especially since it ignores processes like the tunnelling of charges between states. The suggested correction, however, is within the physical concept of the Frenkel-Poole model. Explanations why the correction obtains reasonable results within the physical concept of the Frenkel-Poole model and without extending it with additional physical concepts are discussed in this work, as well.