Nonlinear mathematical models are becoming increasingly important for new applications of low-dimensional semiconductor structures. Examples of such structures include quasi-zero-dimensional quantum dots that have potential applications ranging from quantum computing to nano-biological devices. In this contribution, we analyze presently dominating linear models for bandstructure calculations and demonstrate why nonlinear models are required for characterizing adequately opto- electronic properties of self-assembled quantum dots.
Melnik, Roderick V.N.; Lassen, Benny; Yan Voon, L.C. Lew; Willatzen, Morten; and Galeriu, Calin, "Accounting for Nonlinearities in Mathematical Modelling of Quantum Dot Molecules" (2005). Mathematics Faculty Publications. 34.