MATERIALS SCIENCE AND CHEMISTRY

Direct bandgap silicon has been the holy grail of the semiconductor industry for many years, because it would allow integrating both electronic and optical functionalities on a silicon platform. Possible applications include silicon-based on-chip optical interconnects and a silicon-compatible quantum light source. Despite considerable effort, achieving light emission from group IV semiconductors has remained unattainable.

Recently, Botti’s group proved with ab initio calculations that Ge-rich hexagonal crystal phases of Si_xGe_1-x feature a direct bandgap, tunable in a frequency range coinciding with the low loss window for optical fiber communications [1]. At the same time, defect-free SiGe alloys have been grown using the crystal transfer method, in which a wurtzite gallium phosphide or gallium arsenide core nanowire is used as a template for the growth of lattice matched hexagonal silicon or germanium, respectively [2]. Combining different experimental techniques and calculations, efficient light emission from direct band gap SiGe has been finally proved this year [3]. These important developments were realized in the framework of the project “Silicon Laser”(SiLAS), funded by H2020 FET-Open Research and Innovation action (2017-2020). The research consortium of SiLAS gathers prominent groups at the Universities of Eindhoven, Oxford, Linz, Jena, and Munich, and at IBM in Zurich. The group of Prof. Botti at the Friedrich Schiller University Jena provides theoretical support and guide to experiments with accurate ab initio calculations of electronic excitations in SiGe alloys.

In connection to this project, Botti’s group required supercomputing power as provided at the Leibniz Supercomputing Centre (LRZ). They were assigned 4 660 000 hours on LRZ’s HPC system SuperMUC to perform a series of ambitious materials science calculations, that combine extensive structural prediction of defected structures and internal interfaces in SiGe alloys [4], together with accurate electronic structure and optical properties characterization [1,5]. The methods and computer codes employed in these studies are based on density functional theory. Most of the calculations have been performed with the code VASP [6], an efficient plane-wave code that implements density functional theory and many-body perturbation theory methods using PAW potentials. This code is well tested in HPC environments and can run efficiently in parallel.

Botti’s group first focused on the electronic properties of pure Ge hexagonal crystals, as accurate data on structural, electronic, and optical properties were not available in literature. They portrayed lonsdaleite Ge as a direct semiconductor with only weakly dipole-active lowest optical transitions, small band gap, huge crystal field splitting, and strongly anisotropic effective masses [1]. The unexpectedly small direct gap and the oscillator strengths of the lowest optical transitions were explained in terms of symmetry and back-folding of energy bands of the diamond structure.

Following this work, two different ways to engineer electronic properties of hexagonal Ge were considered, with the objective to increase its light emission: by applying strain and by chemical alloying.

Performing a very extensive series of calculations of effects of strain, the effect on electronic properties of hydrostatic pressure, symmetric biaxial strain, uniaxial strain, as well as other specific type of asymmetric biaxial strain were considered, investigating the direct/indirect character of the band gap and the selection rules for band-edge optical transitions [5]. This study revealed in which conditions moderate strain can significantly improve light emission. These predictions are now being experimentally tested by experimental partners of the SiLAS collaboration.

Alloying hexagonal germanium with silicon is another effective way to control the size of the band gap and light emission. Botti’s group studied alloy models using a cluster expansion approach, relying on density functional theory calculations. The crossover from indirect to direct band gap is found at about 60% Ge content. Alloying allows to break selection rules, and therefore increase the probability of optical transitions between the lowest conduction and the top valence band. This is true already for very small Si content [3]. Our calculations also considered the effect of defects on the optical properties of hexagonal SiGe alloys, combining crystal structure prediction and electronic structure calculations[4].

Efficient light emission from direct bandgap hexagonal Ge and SiGe alloys has been recently demonstrated by the SiLAS collaboration [3]. Selected results from calculations are shown in Fig.1.