Application of the k ⋅ p Method to Device Simulation

As electronic devices approach the sub 10-nm size and new device topologies emerge specifically exploiting quantum mechanical effects, new device simulation tools are needed addressing such issues. Among full quantum approaches, the k ⋅p model is known to provide a reasonably simple way to describe with good accuracy the complex system of valence and conduction bands of many semiconductors, including also their deformations induced by strain, which play a fundamental role in determining the electronic properties of the material. When used within the Non-Equilibrium Green’s Functions framework for the charge transport problem and coupled with Poisson’s equation, the k ⋅p model becomes a powerful tool for the simulation of full nanoelectronic devices featuring lateral confinement and quantum transport. In this chapter, a review of the k ⋅p model is presented, with special emphasis on its applications to the simulation of nanoelectronic devices. The mathematical model of the so called eight-band version is duly recalled first, including the correction terms accounting for strain. Examples of energy band calculations are provided for III–V semiconductors, which are of great potential for the future development of the nanoelectronic industry, relative to both bulk and confined structures. Significant examples of application of the k ⋅p model to full device simulation are then given, all of them relative to tunnel FETs. Specific topics include the investigation of strain in homojunction and heterojunction nanowire tunnel FETs, the optimization of complementary tunnel FETs and the evaluation of the performance of inverters built with the latter FETs, the investigation of the effect of interface traps on the same nanowire tunnel FETs. The main idea that this chapter would like to convey is that in the next future there will most likely be an increasing type and number of nanoelectronic devices for which the k ⋅ p model represents a well targeted simulation basis.