91 lines
6.1 KiB
XML
91 lines
6.1 KiB
XML
== Phonons in Perfect 4H-SiC
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Raman-active phonon modes were categorized into two groups,
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according to the distinct behaviors arising from different electrical polarities,
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including eight negligible-polarity modes (possessing zero or very weak polarity),
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and three strong-polarity modes.
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The negligible-polarity modes should exhibit minimal dependence on the wavevector direction,
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whereas the strong-polarity modes should show significant anisotropy.
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Consequently, the negligible-polarity modes were named
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according to their irreducible representations at the #sym.Gamma point and in order of increasing frequency,
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including A#sub[1]-1 to A#sub[1]-2, E#sub[1]-1 to E#sub[1]-2, and E#sub[2]-1 to E#sub[2]-4.
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In contrast, the strong-polarity modes were designated based on their polarization relative to the wavevector.
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Since the laser incidence direction was restricted to the x-z plane in this work, these modes were labeled as follows:
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TO-xz (polarized in the x-z plane and roughly perpendicular to the wavevector),
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TO-y (polarized along the y-axis), and LO (roughly parallel to the wavevector).
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// This distinction was clearly illustrated in @figure-discont,
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// where the phonon dispersion relations of negligible-polarity modes (gray solid lines)
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// were roughly continuous and flat at the #sym.Gamma point,
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// leading to only #sym.tilde 0.1 cm#super[-1] frequency variations and similar vibration patterns
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// across different incidence configurations.
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// In contrast, the strong-polarity modes (colored solid lines) displayed discontinuities at the #sym.Gamma point,
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// resulting in #sym.tilde 10 cm#super[-1] frequency shifts and distinct different vibration patterns
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// under different incidence configurations.
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Peaks corresponding to seven Raman-active negligible-polarity phonons were observed in our experiments
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(only the E#sub[2]-4 mode was not observed, see @figure-raman),
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which is more than all previous experiments (where only five or six peaks were typically reported).
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To explain the discrepancy in experimental results,
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first-principles calculations on Raman tensors were performed,
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and the result was compared with experimental data and summarized in @table-nopol.
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Our calculation showed that the mode of E#sub[2]-1, E#sub[2]-2, E#sub[1]-1, A#sub[1]-1 and E#sub[2]-3
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had relatively high Raman intensities and well-separated frequencies,
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making them observed in our experiments as well as most previous experiments.
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The A#sub[1]-2 mode was calculated to have very weak (0.01) and relatively strong (1.78) Raman intensity
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under in-plane polarization and z polarization, respectively,
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which is compatible with our experimental result
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that it could be observed clearly in the y(zz)#overline[y] configuration but hardly seen in our other experiments.
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This peek was reported to be observable in some experiments (cite) but not in others (cite),
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our calculation provided an explanation for this discrepancy.
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The E#sub[2]-4 modes was calculated
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to be located close to the most intense E#sub[2]-3 mode (< 10 cm#super[-1] away)
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and exhibit very weak Raman intensities (only 0.6% of the E#sub[2]-3 mode),
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making it not visible in our and all previous experiments.
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The E#sub[1]-2 mode was also located close to the E#sub[2]-3 mode and has weak Raman intensity,
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making it also unobservable in previous experiments.
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However, the E#sub[1]-2 mode was observable in our experiments of y(zx)#overline[y] with extended acquisition time,
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where the scattering of the E#sub[2]-3 mode was suppressed while that of the E#sub[1]-2 mode was enhanced,
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thanks to the different representations of these two modes.
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Our experiments reported the observation of the E#sub[1]-2 peak for the first time,
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and explained the discrepancy among previous experiments and ours with the help of our calculations.
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#include "figure-raman.typ"
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It is noteworthy that the large variation in Raman tensor magnitudes among different modes
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was not yet theoretically understood.
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For example, the Raman tensor of the E#sub[2]-3 mode was substantially larger
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than those of other negligible-polarity modes (over 30 times larger than that of the second-strongest).
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This highlighted a significant gap in established theory
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that rigorous symmetry analysis could only predict the non-zero components of the Raman tensors,
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but not their magnitudes.
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In order to address the limitations of existing theories,
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a method for estimating the magnitudes of Raman tensors was proposed.
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By analyzing the local environment of individual atoms,
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this approach decomposed their contributions to the Raman tensor into two parts:
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a dominant component (invariant across similar environments, denoted as $a_i$，where $i in {1, 2, 5, 6}$)
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and several secondary components (reflecting environmental variations,
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denoted as $epsilon_i$, $eta_i$, and $zeta_i$，where $i in {1, 2, 5, 6}$,
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and $|epsilon_i| + |eta_i| + |zeta_i| << |a_i|$ was assumed).
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Detailed derivations were provided in @appd-predict, with results summarized in @table-nopol and @table-pol.
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Notably, the E#sub[2]-3 mode was the only mode that retains the $a_i$ term,determine
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which indicating a constructive interference of contributions from the local environment of individual atoms.
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This stood in contrast to other negligible-polarity modes where such contributions tend to cancel out,
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explaining the exceptionally high Raman tensor magnitude observed for the E#sub[2]-3 mode.
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#page(flipped: true)[
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#include "table-nopol.typ"
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#include "table-pol.typ"
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]
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The mode frequency dependence on the wavevector were thoroughly investigated,
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including both thoretical calculations (@figure-rev a), experimental measurements (left part of @figure-rev b) and their comparisons (right part of @figure-rev b).
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The E#sub[2]-3 mode frequency was calculated to remaine distinct in all incidence geometries (@figure-rev a),
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making it an ideal calibration reference for experiments.
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Meanwhile,
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the E#sub[2]-1, E#sub[2]-2 and A#sub[1]-1 mode showed a relatively larger dependence on the incidence direction,
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which is in good agreement with our experimental observations (@figure-rev b).
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#include "figure-rev.typ"
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// TODO: 换个方案拟合，考虑不对称，看能不能把这个误差填上
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