This results are consistent with the very recent reports of unstable r8-Ge [3] and its “annealing” to a more stable hd-Ge phase at room temperature [4]. Since there is considerable disagreement in the literature on the assignment of Raman peaks from indented Ge (as discussed in chapter 1), experimental Raman peak positions from family ‘a’ spectra with calculations from density functional perturbation theory (DFPT) was undertaken by our collaborators Malone and Cohen [5]. As it was a concern that some of the end phases in the family ‘a’ case may be unstable (see previous section) Raman spectra was taken immediately after indentation. Figure 3.6 shows such an experimental Raman spectrum from a typical family ‘a’ case. The path of the spectrum in the 100-400 cm-1 wave number range can be fitted with a series of seven Gaussian line-shapes. Given the clear presence of the broad a-Ge Raman spectrum arising from the underlying a-Ge substrate, the a-Ge line-shape is included in the fit. The metastable high pressure end phases give rise to peaks with Raman frequencies of 85.4±0.5, 202.3±0.7, 224±1, 246.3 cm-1(errors are the standard deviation from six separate indents studied). The 202.3 cm-1 line has a small shoulder at 213 cm-1. A broad band is also observed centered at 150 cm-
1.
As indicated earlier (outline more fully in section 3.5), the end phases in the family ‘a’ case are unstable at room temperature and rapidly transform. Most of the Raman lines observed initially in Fig 3.6 decrease significantly in intensity whilst being observed at room temperature while the band at 287-295 cm-1 increases. This band arises presumably
from hd-Ge consistent with the XTEM SADP’s in the previous section.
In order to investigate the nature of the experimental Raman peaks, a comparison of the Ge spectra may be made to the r8/bc8 Si Raman spectrum. This is shown in Fig. 3.7, noting that the Si data has been appropriately scaled to match the Ge spectrum [6]. It can be seen in Fig. 3.7 that the metastable phases of Si and Ge are similar. Both r8 and bc8 are expected to coexist in a Si indent [6] formed under condition similar to those used for Ge family ‘a’. It is well known that the main line observed here at 349 cm-1 in the Si
spectrum arises from the r8 phase. The normalised Raman frequency of this line is 201.6 cm-1 in Fig 3.9, which is in excellent agreement with the 202.3 cm-1 line for Ge. For Si, the transition pressure for the r8 to bc8 transition is 2 GPa. According to the DFPT calculations, Ge makes this same transition on pressure release at the lower pressure of 0.65 GPa [5]. It might therefore be expected that the Ge indent, confined within the
substrate, may contain a greater volume of r8 than the equivalent Si indent, and thus it may well be possible that r8 alone is present after final indentation pressure release.
To further aid the interpretation of the experimental results, DFPT calculations have been performed to give Raman peak positions of dc, st12, bc8 and r8 phases of Ge. The Raman frequencies determined by DFPT are shown in Fig. 3.8 and compared to the experimentally determined line positions extracted from Fig. 3.6. The DFPT results are not corrected for the 2.4 cm-1 difference between the experimental (300.6 cm-1) and
theoretical Raman mode (298.2 cm-1) in dc-Ge. The metastable phases crystals in the transformed zone of the family ‘a’ case are expected to be 5-30 nm in diameter so that confinement effects may shift the Raman frequencies down [6]. An upper limit is calculated to be -2 cm-1 for dc-Ge with the phonon confinement model [7]. It can be seen that the frequency of the dominant Raman peak at 202.3 cm-1 is in excellent agreement with the r8 line at 202.8 cm-1. No other calculated Raman lines are observed in the vicinity. We therefore suggest that r8, giving rise to the dominant 202.3 cm-1 line, is present after pressure release in the family ‘a’ case. In addition, other observed lines at 85 cm-1, 95 cm-1, 213 cm-1, 224 cm-1, 246 cm-1 and 277 cm-1 are also very close to the calculated peak positions for r8-Ge. Similar Raman line-shapes have also been observed in DAC experiments by Coppari et al. at pressures in the range of 3-8 GPa [8], suggesting that the phases observed are similar to those produced in the present study. However, in this earlier work, the end phase was assigned to st12-Ge and not r8, based on DFT calculations. The st12 Raman intensities were also calculated and are shown in Fig 5.8 (b) and compared to previous calculations. Note that similar theoretical intensities cannot be obtained for r8 and bc8 phases since they are Raman active. The peak positions appear to be underestimated in the earlier calculation, where the dominant calculated line is close to our experimental r8 line at 202.3 cm-1 which presumably led to an incorrect assignment
in the earlier work. We also note that the observed Raman peaks at 224 cm-1 and 246 cm-
1 are not close to the calculated st12 lines from the Coppari calculation. The discrepancy
between the Coppari calculation and the DFPT calculations for st12-Ge is not known, but note that the dc Raman peak in that work was calculated as 292 cm-1 compared to here at 298.2 cm. Furthermore, the two dominant lines at 249 cm-1 and 275 cm-1 in the calculated st12 spectrum agree well with the experimentally determined Raman peak positions of st12-Ge formed in a DAC by Kobliska et al. [9] at 246 cm-1 and 273 cm-1. It is therefore clear from the above calculations and arguments that the family ‘a’ indents do not contain any detectable trace of st12; rather it is observed a dominant r8 phase which is the only
phase that gives rise to the dominant line at 202 cm-1 in the Raman spectrum. The other Raman lines also agree well with those calculated for the r8 phase shown in Fig 3.8 (a). However, as might be expected for a phase with a similar structure, four of these peaks also agree with those calculated for the bc8 phase so that the presence of bc8 cannot be ruled out entirely. Finally, the r8-Ge phase is unstable and, as it decays, the Raman band at 285-295 cm-1 grows which corresponds to the calculated band for hd-Ge, as shown in
later section 3.5.
Figure 3.6: (colour online). Experimental Raman spectra of the indented a-Ge immediately after indentation fit with a series of Gaussian fits (solid lines). An a-Ge line shape was included in the fit (dashed line). The inset shows the low frequency region from (i) the indented a-Ge and (ii) pure a-Ge showing the broad transverse acoustic a-Ge Raman band [3].
Figure 3.7: Experimental Raman spectra (i) from Fig. 3.6 compared to (ii) that of an indent formed under similar conditions in a-Si. The Raman shift has been scaled for comparison. The inset shows the low frequency region from the indented (i) a-Ge and (ii) a-Si [3].
Figure 3.8: (colour online). (a) Raman-active mode frequencies decided by DFPT for various Ge phases. The upper bars are the experimentally observed peak positions, the width of the bar being the associated standard deviation of the six indents measured. (b) The calculated st12 Raman spectra. The r8 and bc8 intensities could not be calculated since they are metallic within the calculations [3].