Carrier dynamics in silicon and Germanium nanocrystals

Abstract

This is a computational work on the Si and Ge nanocrystals (NCs) embedded in wide band gap host matrices. As the initial task, extensive ab initio work on the structural and electronic properties of various NC host matrices, namely, SiO2, GeO2, Si3N4, and Al2O3 are preformed. The structural parameters, elastic constants, static and optical dielectric constants are obtained in close agreement with the available results. Furthermore, recently reported high density cubic phase of SiO2 together with GeO2 and SnO2 are studied and their stable highdielectric constant alloys are identified. Based on the ab initio study of host matrices, two related high field phenomena, vital especially for the electroluminescence in Si and Ge NCs, are examined. These are the hot carrier transport through the SiO2 matrix and the subsequent quantum-confined impact ionization (QCII) process which is responsible for the creation of electron-hole pairs within the NCs. First, the utility and the validity of the ab initio density of states results are demonstrated by studying the high field carrier transport in bulk SiO2 up to fields of 12 MV/cm using the ensemble Monte Carlo technique. Next, a theoretical modeling of the impact ionization of NCs due to hot carriers of the bulk SiO2 matrix is undertaken. An original expression governing the QCII probability as a function of the energy of the hot carriers is derived. Next, using an atomistic pseudopotential approach the electronic structures for embedded Si and Ge NCs in wide band-gap matrices containing several thousand atoms are employed. Effective band-gap values as a function of NC diameter reproduce very well the available experimental and theoretical data. To further check the validity of the electronic structure on radiative processes, direct photon emission rates are computed. The results for Si and Ge NCs as a function of diameter are in excellent agreement with the available ab initio calculations for small NCs. In the final part, non-radiative channels, the Auger recombination (AR) and carrier multiplication (CM) in Si and Ge NCs are investigated again based on the atomistic pseudopotential Hamiltonian. The excited electron and excited hole type AR and CM and biexciton type AR lifetimes are calculated for different sized and shaped NCs embedded in SiO2 and Al2O3. Asphericity is also observed to increase the AR and CM rates. An almost monotonous size-scaling and satisfactory agreement with experiment for AR lifetime is obtained considering a realistic interface region between the NC core and the host matrix. It is further shown that the size-scaling of AR can simply be described by slightly decreasing the established bulk Auger constant for Si to 1.0×10−30cm6 s −1 . The same value for germanium is extracted as 1.5×10−30cm6 s −1 which is very close to the established bulk value. It is further shown that both Si and Ge NCs are ideal for photovoltaic efficiency improvement via CM due to the fact that under an optical excitation exceeding twice the band gap energy, the electrons gain lion’s share from the total excess energy and can cause a CM. Finally, the electron-initiated CM is predicted to be enhanced by couple orders of magnitude with a 1 eV of excess energy beyond the CM threshold leading to subpicosecond CM lifetimes.