The field-effect Transistor has evolved since its advent in 
from a humble barely working proof of concept device to an innumerable and indispensable basis for modern technology. After five decades of constant improvement and miniaturization, enabling new devices and applications, one can see the physical limits in the near future. However, the field-effect devices are still improving every generation cycle and many exciting possibilities of the field-effect concept are still uncharted.
The very powerful field-effect concept enables a vast area of possible applications. In this work four promising and interesting aspects of gate stack modeling are presented and described in detail. First with high-k materials utilized by modern CPU manufactures like Intel or IBM are reviewed. Special emphasis is layed on the description of the gate stacks for switching transistors and for non-volatile memory applications. Thereby, flash gate stacks are compared with alternative gate stack structures, which are able to facilitate the next technology node. Then an overview of different commonly employed strain techniques which enable one of the major mobility boosts in state of the art devices, is given. The discussion of ferroelectric gate stacks for non-volatile memory applications follows as a promising candidate for a flash gate stack replacement. Thereafter, a short introduction to electrolytic interfaces and the biologically sensitive field-effect transistor (BioFET) is presented.
Starting with the concept of stress and strain in general, a focus on the mathematical description of strain in semiconductors and thereafter on quantization effects in ultra-thin body FETs follows. This is realized by a two-band k.p model and the assumption of a confinement potential. The resulting model is able to predict the band structure in strained silicon up to about
quite well and delivers effective masses for the primed and unprimed subbands. The big advantage of the employed model compared to other available methods lies in the reduced computational effort.
Finally, the still young field of biologically sensitive field-effect transistors (BioFETs) is presented. These devices enable the sensing of biochemical processes from start to finish via electronic means. At first all the major effects of ionic transport in electrolytes and their mathematical modeling, is given, followed by examples of simulations for various applications, and their corresponding mathematical models.