limited regime could be related to the magnitude of the splitting between the direct and indirect valleys of the conduction band. Theoretical calculations have found the strain in nanowires to be important in increasing the splitting between the Γ conduction band valley and the bulk indirect X direction valley[60, 61]. For pillars with diameters less than 10 nm experiencing tensile strain in the radial and circumferential direction, the splitting between these two minima is several times the room temperature thermal energy (depending on the wire diameter and the amount of strain), as seen in the solid lines of 5.17. This large splitting allows the excited electrons to sit in the Γ valley, allowing for a faster, direct optical transition. For un-strained or compressively strained pillars (dotted line in 5.17) the splitting between the two valleys is closer to the thermal energy forcing carriers to sit both in the Γ as well as the X valley, requiring a longer phonon-assisted recombination. Furthermore, by tuning the size of the pillars to be on order of or smaller than the free-space electron wavelength, it is possible to increase the overlap between the hole and electron wave functions and therefore increase the recombination rate[70]. By examining the variation of radiative lifetime with temperature in future experiments it would be possible to determine the influence of the non-radiative decay as well.
Guichard et al.[59] have shown that the bimolecular bound exciton Auger recombination coefficient of VLS-grown nanowires scales with both temperature and the density of excitons. Since the pillars investigated in our report are both larger and smaller than the 4.9 nm ground state exciton radius in silicon[71] it may be possible to see the onset of this effect as the size of the pillars crosses this threshold. Furthermore these pillars could serve as a platform to investigate the recombination dynamics of the “bulk-like” excitons (excitons in structures larger than the exciton Bohr radius) as they transition into their 1D counterparts.
69 oxide.
Figure 5.18: Finite element model of the strain distribution in a 4 nm diameter pillar before and after the anneal.
Once the high temperature anneal was performed, microphotoluminescence was once again mea- sured. It was found that the pillars with core diameters in the range of 2-5 nm red-shifted roughly 100 meV after the anneal. Furthermore it was found that the larger core pillars ceased to emit light.
Figure 5.20 shows the red-shift in the smaller core diameter pillars; as predicted by the tight binding simulations, relief of the strain would bring the conduction band edge closer to the valence band.
Figure 5.21 shows the results of tight binding simulations for the effects of tensile (blue), neutral (black), and compressive (red) strain on the silicon core.
This result has several implications. The first concerns the fact that the larger diameter pillars ceased to emit light. It was found during tight binding simulations that more tensile strain on the silicon core would not only blue-shift the bandgap but also increase the splitting between the Γ and X direction valley. When that tensile strain was released through the anneal it is possible that the simple quantum confinement was not sufficient to make silicon behave as a direct bandgap material.
If the bandgap of a sub-10 nm diameter silicon whisker has an indirect valley at or below the energy of the Γ valley then the material will have a blue-shifted (when compared to bulk silicon), indirect, bandgap. An indirect or almost indirect bandgap will quench the photoluminescence as excited carriers are more likely to thermalize down to the valence band instead of recombining with holes.
Furthermore the influence of strain on the peak emission wavelength gives us another degree of freedom in tuning the pillars to an ideal emission wavelength. Figure 5.22 illustrates the range of peak
Figure 5.19: Lateral cross-section of the strain profile found in a 4 nm diameter annealed and unannelaed pillar.
Figure 5.20: Peak emission energy before and after anneal. The theoretical plot was obtained by performing a tight binding simulation with a small amount of compressive strain imparted to the core.
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Figure 5.21: Calculated band-structure for a pillar under (blue) tensile, (red) compressive, (black) no strain.
emission energy that can be obtained by setting the core diameter with self-terminating oxidation and the residual strain. The two dotted lines show the regions of strain that were measured and plotted as a fit to data in figures 5.20 and 5.15.
This experiment should be repeated with a method to continuously vary the strain incorporated in the pillars in order to experimentally probe the effects of strain on the luminescent emission.
Further work needs to be done to accurately quantify the strain found in the nanopillars. Raman or X-ray diffraction (XRD) techniques[73] can be used to probe deformation of atoms at the Si-SiO2
interface. XRD techniques found inTakeuchi et al.[73] have shown that the interface and the body of the silicon core of oxidized nanowires are subjected to tensile strain as high as 0.5%. Unfortunately the nanowires studied in their work were horizontal and trapezoidal and an order of magnitude larger than those we fabricated and were not oxidized to their self-limiting state as seen in 5.23;
it is found that the strain scales as the inverse square of the decreasing radius of curvature[17, 18]
so size effects are more severe in our case. For the luminescent nanopillars accurate TEM studies need to be performed to actually examine the lattice deformation and lattice spacing of the silicon cores. Unfortunately the scattering of electrons in the amorphous oxide prevents precise HRTEM measurements; however we could thin the oxide with a gentle hydrofluoric acid vapor based etch to decrease the amount of oxide the electrons have to pass through.
Figure 5.22: Peak emission wavelengths for a span of strain and core diameter as predicted by a tight binding simulation. The two white lines correspond to theory used to fit the data.
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Figure 5.23: Lateral cross-section TEM of the oxidation of a trapezoidal nanowire. The pictures are taken pre-oxidation, 1 hour into oxidation and 5 hours into oxidation. The left frame shows the XRD diffraction curves for different oxidation times used to estimate the interfacial strain. Oxidation in this work was performed at 850oC.