NANODYN · Theory of Dynamical Processes in Semiconductor Nanostructures

Theory of Dynamical Processes in Semiconductor Nanostructures

The goal of this project was to develop a computational method, base on first-principles and empirical pseudopotentials that is, unlike any other method, able to treat the relevant size range of semiconductor nanostructures (i.e., between 1000 and 10,000 atoms), on an atomistic footing, including dynamical effects. The method development shall follow a bottom-up approach, i.e., starting from the most accurate description available such as density functional theory. The vibrational and electronic properties obtained this way for small clusters constitute the back-bone of the method and shall be used to construct a robust and accurate description, based on classical force fields (for the phonons) and semiempirical pseudopotentials (for the electrons). From the resulting electronic wave functions and phonon eigenmodes a wide range of new physical effects will be available, such as electronic relaxation times, spin relaxation times, temperature effects, Raman spectra, Polaron couplings, photon linewidth, which are key components in fields such as quantum information/computing, spintronics, lasers, nano-electronic devices, photovoltaic and even medicine. Besides its relevance for nanotechnology, the development presented here will have a significant impact for basic science research. Many of the concepts valid in solid-state physics are challenged at the nanometer scale and many fundamental discoveries can be expected that cross the boundary of physics to chemistry and biology. In the first year, we derived a classical interatomic potential for the calculation of phonon spectra in III-V semiconductor nanostructures. In the initial phase, we validated the results for bulk and small clusters against density functional theory (DFT) calculations. The classical description is less transferable than the ab initio approach but allows us to span a large range of nanostructure, up to 100,000 atoms. In the second year, we developed a formalism for the calculation of the electron-phonon coupling elements that can be used for electronic and vibrational states calculated from either empirical potential calculations or from DFT. The formalism has been implemented into a modern computer code. We validated the results for small clusters against density functional perturbation theory (DFPT) calculations. In the third year, we studied the electronic relaxation processes in colloidal semiconductor nanoclusters using the electron-phonon coupling matrix elements calculated using the methodology we developed in the first period of this project. The dynamical processes are described using the Liouville-von Neumann equation including a phenomenological Lindblad decay term. In the fourth year, we studied the band gap renormalization in colloidal semiconductor nanoclusters via electron-phonon interactions. We calculated the zero-point motion band gap renormalization and the temperature dependence of the band gap in carbon and silicon nanoclusters using our own approach and codes based on a frozen-phonon method and ab initio density functional theory (DFT).

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