You need to use Z-view plot to do fitting of your nyquist plots. Z-view is a free software which you you can download it from the web.Instant fit in the Z-view is very easy way to get the equivalent circuit.

There are numerous parameter which we can obtain from the fitting of the Nyquist plot like solution resistance, electron transfer resistance and CPE-P and CPE-T will be useful in obtaining the electrochemically active surface area of the you material.

hope this is helpful.

In a trilayer system this is a difficult job to do. First you need to measure the impedance over the available frequency (f) range at various temperatures (T). You then need to rationalize the current path in your sample, because this is what the impedance analyzer effectively measures: the amplitude and the phase shift of the current as a response to the applied alternating voltage signal. You need to determine, which parts of your sample are connected in series, and which are connected in parallel to each other, considering your measurement geometry. I recommend to use an out-of-plane measurement geometry (parallel-plate capacitor arrangement), so your 3 layers would always be strictly in series with each other. In this case, each layer should be represented with a resistor and capacitor in parallel, the so-called RC element. Possibly, some interfaces between your layers may need to be represented by an additional RC element. By measuring Si/TiO2/Au layers in the out-of-plane direction, you would expect at least 2 series RC elements: one for the Si, one for the TiO2, the Au layer should not be visible due to low resistance. Additionally, you would expect more series RC elements for all the relevant interfaces. Some interfaces may give you an additional contribution (i.e. possibly a Schottky type barrier), some others may not. To fit your data, you may have to replace each capacitor with a constant-phase element (CPE) to account for the non-ideality of your sample. You should then fit the data to the equivalent circuit model, possibly 3 R-CPE elements in series. I recommend to use Z-View software to display and model your data. You then extract the resistance and capacitance values from the fitting process, and by repeating this process for the data sets collected at different temperatures, you get the resistance vs T and capacitance vs T dependencies. This should give you a clear indication, which R-CPE element needs to be associated with which layer or interface in your sample. The whole process is very difficult and can take a long time. I recommend studying the literature first. 

Thanks Santosh and Reiner for the response. Reiner your explanation is quite straight forward and detailed. Actually the Au is the contact. I have a series of samples prepared at different temperatures with TiO2 changing from anatase to rutile phase. The Nyquist data I measured changes from almost diagonal line with positive slope (as-deposited samples) to a semicircle for the rutile/annealed samples. See attached file for an example of two Nyquist plots.

At the moment I am studying some literature. One challenge is that most papers I get cover electrochemically obtained data, while my samples are thin film layers. I will appreciate any suitable references you may recommend for me to read.

Thanks again.

Dear Albert, Rainer has presented very detailed explanation and there is no doubt that he is absolutely right saying that your equivalent circuit should have some RC series. I would add only that it would be useful to analyse C-V and I-V curves because in some cases you can neglect one or two elements within your equivalent circuit. For instance, based on my experience, I have measured Impedance spectra of a Si-LiNbO3-Al heterostructure at the zero bias and at the same time as it followed from the C-V curve this heterostructure have been similar to MOS structure in the mode of accumulation. As a result, I have removed from the consideration RC series related to the Si-LiNbO3 heterojunction and taking into account that in my case Al-LiNbO3 is an Ohmic contact I have interpreted my Nyquist plot considering only LiNbO3 layer properties. Also, I have dealt with TiO2 based heterostructures and we have proposed an equivalent circuit that may be interesting for you. You can visit my profile to find this article. Good luck!

Thanks Maxim for the additional remarks which I found quite helpful. I have requested for your papers to see your analysis and discussion of your work.

In addition, I would like to know the relevance of doing impedance measurements as a function of bias voltage and temperature. For temperature dependance, one could get activation energies of the defects or dielectric relaxation times. In disordered materials we often have a distribution of defects instead of decrete energy states. How can one obtain these information on the distribution of defect states using impedance experiments?

Thanks

Dear Albert,

Certainly, Rainer and Maxim have already presented detailed responses which would be very valuable. I could only recommend you to be attentive when choosing the correct equivalent circuit. Usually there are more than one circuit fitting the same electrical response and the use of software like Z-View could drive you into ambiguous interpretations. The most important part when modelling impedance data and discerning between several equivalent circuits is accurately assign each element of the circuit to regions in your material. This is why Rainer’s recommendation about measuring in a parallel plate capacitor configuration is very important (by making this you can be sure that at least there should be three RC elements connected in series representing three different sections in a three layer). Concerning the CPE elements, I agree with Rainer, it is almost necessary to use them if you deal with non-ideal relaxations. However, you must be careful and never forget that if you simply replace a capacitor by a CPE element then the physical meaning of the circuit will be insignificant. This, because you need an element able to characterize the low and high frequency limits in the imaginary part. Replacing only capacitors by CPE’s (which would derive into RCPE’s circuits) would underestimate this important fact. In my experience it is better to connect a CPE element in series together with each RC circuit, so you would obtain RCCPE’s sub-circuits with more accurate physical meaning for each non-ideal region.

You can read A. R. West and coworkers work which has been a lot of help for me; in spite most of their work is focused on bulk systems it could also help modelling your impedance data: Appl. Phys. Lett. 108, 152901 (2016) (https://doi.org/10.1063/1.4946008); Adv. Mater. 2, 132 (1990) (https://doi.org/10.1002/adma.19900020304). As well, I highly recommend you read important literature in this field: J. Ross Macdonald, Impedance Spectroscopy: Emphasizing Solid Materials and Systems, (Wiley Interscience Publication, New York, 1987); A.K. Jonscher, Dielectric Relaxation in Solids, (Chelsea Dielectric Press, London, 1983).

Greetings!