Numerical simulation of the electrical characteristics of semiconductor devices has become an invaluable tool for the understanding of device behavior, the optimization of device performance, and the development of new device concepts. Classical technology CAD has reached a mature state and is widely used in semiconductor industry. The advent of semiconductor nanostructures and the growing importance of optoelectronic devices, however, prompts for the development of new simulation tools based on full quantum mechanical models.
In the first work package the photo response of semiconductor nanowires will be numerically modeled. Axial heterostructures are used to create the built-in fields for the separation of the photo-generated electron-hole pairs. To explore the physics of such devices the non-equilibrium Green's function technique will be employed. Both a ballistic and a dissipative quantum transport model will be implemented. Electron-photon interaction is taken into account through an appropriate self-energy term. In the dissipative case, the relevant scattering mechanisms are cast into additional self-energy terms.
The quantum cascade laser (QCL), first demonstrated in 1994, is now at the verge of commercial application. The second work package of this project deals with the quantitative modeling of electronic transport and the optical field in QCLs. A quantum transport model for QCLs has to include coherent effects and dissipative effects on equal footing. The transport model should also be efficient so as to enable the simulation of bigger portions of the QCL. The Pauli Master equation will be chosen as a trade-off between physical rigor and computational efficiency. The basis functions for the representation of the density matrix are calculated using VSP, the Schrödinger-Poisson solver developed in the first project period. Dominant scattering processes in a QCL are due to polar optical phonons, interface roughness, ionized impurities, alloy disorder and electron-electron interaction. Transition rates are calculated from Fermi's golden rule based on the weak-interaction and long-time limits. Band structure effects are included via a tight-binding or k*p Hamiltonian. Open system boundary conditions for the Pauli master equation should be developed, exploiting the periodicity of the QCL layer structure. Furthermore, a numerical solver for the optical field will be developed and coupled to the electronic transport simulator. The electronic and optical systems are coupled via a photon rate equation. The optical problem is described by a Helmholtz eigenvalue equation which will be numerically solved by the finite-element method.