Electronic structure of interface defects in epitaxially grown germanium on silicon

A number of devices rely on epitaxially grown germanium on silicon, including photodetectors, Stark modulators and lasers. There is a 4.2\% lattice mismatch between these materials, hence germanium grown epitaxially on silicon will contain defects within some distance from the interface. Line defects are either misfit dislocations - lines of dangling bonds where a mismatched plane terminates parallel to the heterointerface - or threading dislocations which occur where the side edges of the misfit dislocation terminate and usually glide along the (111) plane. Defect structures create `trap states'- allowed energy states within the forbidden band gap. Traps may act as recombination centres, inhibit transport over the interface, limit the repetition rate of devices such as photodetectors, and may contribute to noise currents from detrapping of carriers outside the normal operating regime of a device. Density functional theory (DFT) offers one means of characterising the electronic structure of defects and hence the available states for carrier recombination and transport. METHOD The CASTEP code is used to calculate the electronic bandstructure for silicon, germanium, and epitaxial interfaces of these materials, both for pure bulk and for cells containing extended misfit dislocations. First-principles calculations impose practical limits to the number of atoms which may be simulated, however CASTEP relies on periodic boundary conditions, hence a misfit placed within a limited-size supercell will be replicated across the structure, and one challenge is to ensure that calculated electronic states due to a dislocation are not unduly influenced by an adjacent periodic dislocation. In order to increase the spatial separation of dislocations while retaining practical numbers of atoms for simulation, a rhombohedral cell of germanium was used, in which the dislocation propagates along the [100] direction. The dislocation was placed centrally to offset the effect of adjacent cells. In this orientation, a supercell one unit cell deep in the plane of the dislocation may be created, allowing greater spatial separation in the remaining dimensions. The electronic bandstructure for bulk germanium using the primitive unit cell was been calculated using the CASTEP code, applying a library norm-conserving pseudopotential and using the PW91 exchange-correlation functional. This calculation has been repeated using 6x4x1 and 12x8x1 rhombohedral cells, both for pure bulk material and for cells containing a single extensive misfit dislocation. Comparison of these electronic structures allows identification of electronic states due to extended misfit dislocations in germanium. DISCUSSION For a supercell constructed of multiple primitive cells the effective Brillouin zone represents only a portion of the Brillioun zone of the primitive cell, and band folding is observed at the zone edge. A number of additional energy states are observed in the bandgap relative to the electronic structure for bulk material.