The frequency response of a fractal photolithographic structure

The interest in fractal materials structure in recent years paved the way for the study of the electrical behavior of metallic samples having `fractal tree´ patterns. The unique characteristics of these structures, such as the self-similarity and the fractional dimension D _f, endow these materials with specific physical properties. The simulations and the measurements performed give evidence for the impedance of such a structure, a frequency response closely correlated with the sample structure itself and the so-called constant phase angle behavior of its phase. Indeed, during the characterization of the fractal sample in frequency, it is found that the real and the imaginary parts of the impedance obey the same law of variation beyond a certain frequency. This factor leads us to the relation (Z_e)/(Z_e )=tan (θ)=constant