大量小调整
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@@ -1,7 +1,5 @@
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== Phonons in Perfect 4H-SiC
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// 第一段：弱极性与强极性声子模式表现截然不同。如图所示，弱极性声子模式几乎不依赖于波矢方向，而强极性声子模式则表现出显著的各向异性。
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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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@@ -51,6 +49,8 @@ However, the E#sub[1]-2 mode was observable in our experiments of y(zx)#overline
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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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@@ -72,103 +72,19 @@ Notably, the E#sub[2]-3 mode was the only mode that retains the $a_i$ term,deter
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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 (@figure-rev b)
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and their comparisons (@figure-rev c).
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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 c).
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// TODO: 图中标注强调是拉曼活性的模式
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// TODO: b 图的标题歪了
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#include "figure-raman.typ"
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#include "table-nopol.typ"
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#include "table-pol.typ"
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// TODO: 合并两个表格到一页，删除 polar 中的多余信息
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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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#include "figure-discont.typ"
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The E#sub[2]-3 peak was calculated to be having virtually invariant frequency,
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and thus served as a calibration reference under various experiments.
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The peek of E#sub[2]-1, E#sub[2]-2, A#sub[1]-1 and TO-zOx modes were observable in both normal and edge incidence,
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thus was uesd to compare the frequency shifts between different incidence configurations.
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// TODO: 增加图例：各种入射激光
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// TODO: 增加 TO-zOx 的讨论
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// TODO: 条形图画成两个方向的
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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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// 第二段：我们具体计算了模式对极性的依赖。可以看到，弱极性声子的变化极小。与实验比较，也验证了我们实验的准确性。
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// 第三段：有两个弱极性模式还没有在实验上看到过。我们通过计算知道了它们的强度，并看到了其中一个。
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// 第四段：声子模式的强度可以从理论上得到解释。
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=== Negligible-polarity Phonons
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To achieve a more precise investigation of the Raman spectra
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and prepare for analyzing impurity and charge carrier effects,
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the analysis of negligible-polarity phonons off the #sym.Gamma point was conducted
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by comparing experimental and calculated results under various lazer incidence directions.
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The E#sub[2]-3 peak searved as a calibration reference under various experiments,
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since its position was calculated to be virtually invariant between normal and edge incidence
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(with a shift of only #sym.tilde 0.004 cm#super[-1]).
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The E#sub[2]-1, E#sub[2]-2, and A#sub[1]-1 modes exhibited observable shifts,
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and the experimental results were in good agreement with our calculations, as shown in fig.
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Our results further confirmed the accuracy of both our experiments and calculations.
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=== Strong-polarity Phonons
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The Strong-polarity phonon modes participated in Raman scattering
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exhibited significant variations depending on the incidence configurations
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(see the intersection of colored solid lines and orange dashed lines in @figure-discont b and c).
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For incident light propagating along the z direction,
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the C#sub[6v] point group applied and two modes were present,
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marked as normal-TO and normal-LO,
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and they were corresponding to the E#sub[1] and A#sub[1] representations
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and vibrations along the basle plane and z direction, respectively.
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The normal-LO would subsiquently couple with plasmons to form LOPC modes in n-type 4H-SiC.
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For incident light propagating along other directions,
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the C#sub[6v] group no longer held and three modes were present.
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Specifically, for incident light propagating along x direction, the C#sub[2v] group applied,
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and the three modes was named as edge-TO-z, edge-TO-y and edge-LO,
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which were corresponding to A#sub[1], B#sub[2] and B#sub[1] representations
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and vibrations along z, y and x directions, respectively.
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E1 的情况。
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注意到在正入射中，理论上不能被观察到的E#sub[1]-1模式也被观察到了。
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与弱极性的 E1-1 模式类似，我们也认为这是由于入射光并非完全沿 z 轴入射所致。
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但与弱极性 E1-1 模式不同的是，强极性 E1-1 模式在 xy 的偏振下并没有更强反而更弱。
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这是因为E1这时不再是严格的E1模式，而是分裂成了两个相近的模式。
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我们的计算表明，在2度的入射角下，E1分裂的两个模式非常接近。
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其中某个模式会怎样怎样，另一个会怎样怎样。
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// 我们预测，随着入射方向偏移，LO 峰会向着高频方向移动。此外，我们也注意到 LO 也会与载流子产生影响。
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// 在 n 型半导体中，LOPC 模式将代替 LO 模式；在 p 型半导体中，LO 模式仍然单独存在，但它的半高宽会受到载流子浓度的影响。
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