Electronic and optical properties of stacking faults in hexagonal germanium.

Direct-gap hexagonal (2H) Ge is most commonly realized by growing [0001]-oriented nanowires on a [111]-oriented cubic (3C) substrate [1]. The metastability of 2H-Ge has been observed to readily allow for defect formation via basal stacking faults (BSFs) in the (0001) plane [2]. Of these defects, the I3 BSF (a disruption of the twofold “AB” stacking sequence via a single “C” double layer) occurs frequently. Other BSFs [3], including intrinsic I1 and I2 defects (respectively consisting of one and two violations of twofold AB stacking), and extrinsic E defects (inclusion of an additional “C” double-layer), can potentially occur. We perform a systematic analysis of the impact of BSFs on the optoelectronic properties of 2H- Ge, using first-principles (density functional theory) calculations [4]. Specifically, we quantify the impact of BSFs on the (i) electronic structure, (ii) interband optical matrix elements, and (iii) spontaneous emission. The BSF electronic structure is interpreted via effective (zone unfolding) band structure calculations. Projecting the effective band structure (spectral function) onto atoms in pristine and faulted regions of BSF supercells allows to quantify carrier localization and its contribution to the perturbed band-edge states. We find that BSFs in 2H-Ge generally act as potential barriers, with the conduction and valence band edge states localizing outside of a given BSF. This suggests that BSFs in 2H-Ge are not expected to act as non-radiative (Shockley-Read-Hall) recombination centers. The calculated interband optical matrix elements and emission spectra demonstrate sensitivity to band hybridization. This band hybridization is induced by broken translational symmetry along [0001], a consequence of BSF formation, and makes the calculated properties sensitive to supercell size – i.e. to linear defect density along [0001]. For example, an I3 BSF can either decrease or increase the zone-center direct-gap optical matrix element, depending on defect density. Qualitative consequences of BSFs for device applications of 2H-Ge will be discussed