(Invited) Emission from Strained Germanium Nanocrystals
Authors: Rowell Nelson L. , Lockwood David J. 
Published: February 2020

A silicon-compatible group IV coherent light source remains the missing link in Si-based photonics, despite much effort. Recently lasing and high efficiency photoluminescence (PL) have been shown for germanium (Ge), a material with a relatively small indirect to direct bandgap (BG) difference.
We previously had observed a very intense, low temperature PL in dozens of samples for MBE-grown Si1-xGex epitaxial layers with x from 0.05 to 0.53, with quantum efficiencies up to 5%. This PL was neither defect nor dislocation related, but appeared to be strong with a large lifetime due to localization effects. As shown in Fig. 1, the PL consisted of a broad peak with asymmetry to low photon energies. With Ge fraction this peak was constant in shape and tracked the BG variation, but was ~80 meV below the indirect BG for strained SiGe. The width of this peak at ~50 meV was too small to be due to a no phonon (NP) line with its TO phonon replica if the material were Si or SiGe as the NP-TO spacing is about 58 meV for those materials. Fig. 1 shows that for higher Ge fractions the PL is emitted at energies significantly below those for bulk Ge, with its BG of 744 meV. This broad, intense PL peak has been unexplained, although a morphological origin was suggested by TEM. Here we will show from PL data that the peak is due to Ge nanocrystals (NCs) imbedded in SiGe layers (see Fig. 2).
Epitaxy requires that the SiGe epilayers and the Ge NCs be lattice matched to Si (001) in the x-y plane, so that both the SiGe and NCs are under compression in that plane. Unconstrained in the vertical (z) direction, the epilayer is under tensile strain, leading to a vertical lattice constant that increases with Ge fraction and is larger than that for unstrained SiGe. Here the volume of the unit cell for the epitaxial SiGe is assumed to be the same as that for unstrained SiGe. The lattice of the Ge NCs is constrained to match the SiGe epilayer vertically. For relatively Si-rich SiGe, the Ge NCs are under compression vertically, but for more Ge-rich SiGe the vertical lattice constant of the strained SiGe exceeds that of bulk Ge. At this point the vertical strain in the Ge NC becomes tensile, which first occurs for a Ge fraction in the SiGe of 0.36 (Fig. 3 - red trace).
The BG variation in Ge with uniaxial strain can be computed using deformation potential theory. As the strain becomes more strongly tensile both the direct and indirect gap energies decline, with the direct energy decreasing more rapidly than the indirect one. As shown in the blue traces of Fig. 3, the direct gap crosses the indirect at a tensile uniaxial strain of 4.4%, resulting in a direct gap semiconductor, a highly desirable outcome. Our results with PL point the way to this transition point, but the maximum vertical tensile strain for the present Ge NCs is not much greater than 2.1%. Nonetheless, the fact that we see PL below the indirect BG of bulk Ge is explained by the Ge NCs being under tensile strain vertically, reducing their BG. The broad peak width and shape can be curve resolved with two peaks, each ~30 meV wide, separated by ~35 meV, i.e., very near the momentum conserving TO phonon energy for Ge.The NP peak is wide (25-30 meV) due in part to confinement shift variations from size variability and to alloy disorder broadening in the SiGe.
To test our hypothesis further, we have calculated the emission energy in a numerical model that includes the effects of strain on the Ge BG and of the confinement blue shifts on exciton energy for both the SiGe layers and the imbedded NCs, the latter assumed to be of a single vertical size (2.5 nm). The calculated energies for over 45 samples of varying composition are compared with the measured PL energies in Fig. 4, where the slope is somewhat different from the expected value of unity due to possible lower order influences, such as variations in the NC size and deviations from the linear deformation potential model for the strained BG. However, we do have very good general agreement between our computed emission energies and those observed in PL, which provides validation for our theory that imbedded Ge NCs have given rise through carrier localization in three dimensions to the intense, broad PL observed in MBE grown SiGe.

Figure 1