Scaling considerations of the constitutive equations in a 2-D finite element heterojunction simulator PRISM

One of the problems while simulating heterojunction devices is the poor numerical stability due to the broad number range for concentrations and currents in the different materials. However, it is not obvious which scaling to apply as more than one material is involved. This paper presents a unified scaling system which circumvents the problem. This includes not only the extension of the general de Mari scaling but also an extra scaling with respect to local carrier concentrations. The idea provides a way to deal with the great number range of e.g., the carrier concentrations at heterojunctions. The developed algorithm is very efficient as the new scaling system can also be applied for bulk nodes without altering it. Finally, some examples prove the technique to be very stable and promising for future development