Direct Simulation of Quantum Transport in Semiconduct

The semiconductor fabrication technology is proceeding very fast. Due to the downscaling of semiconductor devices and the progress in epitaxial growth techniques, devices which are strongly influenced by quantum effects are becoming more and more important. For modern electronic engineering, efficient computational methods which include quantum effects are required to obtain a deeper understanding of the device characteristics. Recently, some research groups, including my own, have created new deterministic methods to solve the semiclassical Boltzmann equation. It has turned out that these techniques are interesting alternatives with some advantages over the Monte Carlo schemes usually used for device simulation. In the framework of this project, we intend to investigate several quantum transport scenarios by means of deterministic schemes for solving the governing transport equations. Therefore, quantum transport models containing the relevant physics must be established and new computational methods must be developed. In modern semiconductor devices, quantization effects and reduced dimensionality play an important role. Here, we will break new grounds by simulating these phenomena by means of model equations based on either the (quantum-corrected) Boltzmann equation or the Wigner equation. When applying the Wigner formalism, the contact regions are usually assumed to be in thermal equilibrium, and the carrier inflow into the device is modeled by using Fermi-Dirac distributions. We will study the influence of improved boundary conditions as well as phase-breaking contacts on the transport properties of mesoscopic devices. Resonant interband tunneling diodes (RITDs) exploit the phenomenon of transitions between the conduction and valence band states. They are of growing importance for the application in high-speed and miniaturized systems. We will investigate the contribution of interband current in RITDs by means of a two-band Wigner transport model. A further research issue concerns the influence of scattering on the device operating properties. Here, it is our special interest to find out whether and how the results obtained by regarding quantum corrected collision terms differ from those with semiclassical electron-phonon interaction terms. The developed numerical tools will be used on non-uniform grids in order to resolve suitably regions of the device, where the important aspects of quantum transport take place, but also to save computational power in regions, where semiclassical low-field transport occurs. This approach allows an efficient investigation of semiconductor devices which are characterized by a complicated interplay of semiclassical and quantum transport. For instance, MOSFETs and HFETs belong to this type of semiconductor devices. Our cooperation with experimental research groups will enable us to validate the numerical methods by comparing them with measurements. Finally, we will apply them to scenarios which closely follow the recent trends in semiconductor device technology.

The progress in epitaxial growth technique and new functional materials will lead to a remarkable miniaturisation of electronic devices. Quantum effects will increasingly more influence the charge carrier transport. The great challenge to predict the current distribution in such devices motivated us to develop new quantum transport models and appropriate methods for their solution. The phase space formulation of quantum mechanics offers the possibility to describe quantum phenomena with a language similar to that used in the classical kinetic theory. Our suggested models are, therefore, mainly based on the formalism introduced by E. Wigner and H. Weyl. This approach has the advantage that interesting questions of the quantum-classical correspondence can be directly investigated. In order to fulfil this requirement, we derived, at first, a Liouville-like evolution equation governing the quantum phase space dynamics. Further, an asymptotic expansion of the multiband Wigner function was performed. It is designed to describe the dynamics in nanoscaled semi-conductor devices in the presence of conduction band-to-valence band tunneling, In addition, we developed a semiclassical kinetic model for simulating the coupled high-field transport of electrons and phonons in graphene, As an alternative, we choose a pseudo-spin phase space approach in the framework of the Wigner-Weyl formalism to treat the ballistic transport of electrons in graphene. Interesting results were obtained by suggesting a new perturbative ansatz aiming at an approximated description of the phase space dynamics.In conventional nanoelectronics, the charge and the magnetic moment (spin) of electrons are used for different purposes. Logical operations are implemented via the control of charge transport by means of electric fields, whereas the magnetic properties are used mainly for the purpose of long-term data storage in hard disc drives. Promising concepts for novel devices take advantage of the combined usage of the charge- and spin-degree of freedom in so-called spintronic applications. In these devices one uses either an electric field to control magnetic properties or a magnetic field to regulate the charge transport. Hence, a further challenge of this project was to derive new spin transport models from basic principles and to develop numerical algorithms for their solution in order to study interesting phenomena in spintronic applications. We established a matrix Boltzmann equation that allows for the description of the spin-coherent electron transport at the kinetic level. Moreover, we rose to the challenge of deriving appropriate matrix collision operator from first principles. Impressive results were obtained by investigating the ion-spin relaxation mediated by spin exchange mechanisms. Finally, we performed a numerical study of a quantum-diffusive, two-component spin model for the transport in a two-dimensional electron gas with Rashba spin-orbit coupling.