One of the major impedance spectrocopy books is "Impedance spectroscopy - emphazising solid materials an systems" by J. Ross Macdonald. It starts from the basics and covers a lot of the field.
If you have a two terminal electronic device having nonlinear I-V characteristics and you want to characterize it then there are three type of characterizations:
-The DC characterization by measuring its static I-V curve,
-The small signal ac characteristics by measuring its small signal impedance as a function of frequency. For its representation you just plot the imaginary versus the real part of the complex small signal impedance with the frequency as a parameter. An ideal p-n junction diode has an impedance diagram as a semicircle pointing out its small signal equivalent circuit as a parallel combination of small signal diode resistance parallel with its small signal junction resistance. It must be said that one has to keep the DC bias of the diode constant.
Lastly, it remains the dynamic or switching performance where one applies a unit step voltage voltage or current and measure the dynamic response as I(t) or V(t)
To see all these measurements including the impedance spectroscopy plot please see the link:Article A distributed SPICE-model of a solar cell
If the diodes are not ideal then one can get more than semicircle pointing out the presence of other interfaces than the major junction acting in series with it and contributing in limiting the current conduction in the diode.