Polymer electronics increasingly needs circuit design tools based on simple but accurate device models. It also needs scaling rules and ultimately its own form of Moore's Law.
Such models must include accurate conduction equations. Here we begin the development of device models based on the Universal Mobility Law which is itself the basis of roadmapping. This law is the physical manifestation of variable range hopping and this is widely recognized as a dominant mechanism, except perhaps at the highest doping levels. By interpreting this law in terms of the relationship between mobility and carrier density the gradual channel equation is redeveloped below and above pinch-off. It is immediately apparent that mobility is not an appropriate measure of the speed of circuits. Two new parameters K1 and m are introduced. They can be found from accurate measurements on Schottky barriers and give the maximum possible performance. Real performance is always less than this. The values of K and m for a particular process can be assessed above pinch-off and with stable polymer they can be used to accurately predict the output characteristics.