Category theory and organic electronics

Inorganic semiconductors and conducting polymers are described by band conduction models with delocalized electrons, whereas small-molecule organic compounds are described by hopping conduction between localized molecular orbitals. However, the latter devices can reproduce fully the characteristics of semiconductor devices. Why are they so different and yet so similar? We will try to answer this question using Category theory and considering the meaning of electrical transport in electronic materials. The meaning of the category theory in physics is to consider different mathematical entities under a common mathematical structure.

In this paper, the basic idea of category theory is first explained in detail using the example of complex impedance, and then four examples of its application are discussed. The derivation of the Mott-Gurney equation and the negative capacitance in OLED are discussed as examples of solving problems by moving to different categories. After those simple examples of formal rewriting from physical entity to mathematical entity, it is shown that electrical connection and electrical contact lead to direct sums and direct products of conducting states, based on the duality concept. We conclude that small-molecule organic compounds are not a mere branch of semiconductors, but rather equal counterparts of semiconductors in duality that are necessary to clarify the origin of the difference and similarity between organic electronics and semiconductor physics. Finally, by considering the electrical responses of OLEDs and OFETs in the immittance category, we show that they can be described under a common operating dynamic and propose a new operating model for OFETs.