合并强极性模式的文本

paper/result/default.typ

@@ -1,11 +1,8 @@
 = Results and Discussion
 
-我们先讨论无缺陷的情况，再讨论有缺陷的情况。
-无缺陷的情况可以解释绝大多数拉曼信号，其它情况从拉曼中的小峰和峰的改变中看出。
-
 Phonon modes in defect-free 4H-SiC were first analyzed,
   which account for the majority of the observed Raman signals.
-Subsequently, the effects of defects and charge carriers were addressed,
+Subsequently, the effects of impurities and charge carriers were addressed,
   which manifested as additional minor peaks and modifications to the primary peaks in the Raman spectra.
 
 #include "perfect/default.typ"

paper/result/perfect/default.typ

@@ -7,22 +7,26 @@ These phonons were categorized into two groups and discussed separately, accordi
 
 The negligible-polarity phonons were initially analyzed at the #sym.Gamma point,
   disregarding the incidence configurations.
-This simplification is justified because the participating negligible-polarity phonon modes
+This simplification was justified because
-  are nearly identical across all Raman experiments,
+  the negligible-polarity phonon modes participated in Raman scattering
-  with their frequencies differing by only #sym.tilde 0.1 cm#super[-1] difference in frequency
+  were nearly identical across all incidence configurations,
-  (see gray lines in @figure-discont).
+  with their frequencies differing by only #sym.tilde 0.1 cm#super[-1]
+  (see the intersection of gray solid lines and orange dashed lines in @figure-discont b and c).
 
-There are eight Raman-active negligible-polar modes in 4H-SiC,
+There were eight Raman-active negligible-polarity modes in 4H-SiC at the #sym.Gamma point,
   corresponding to three irreducible representations of the C#sub[6v] group (A#sub[1], E#sub[1], and E#sub[2]).
 We named these modes as
   E#sub[2]-1, E#sub[2]-2, E#sub[1]-1, A#sub[1]-1, E#sub[1]-2, E#sub[2]-3, E#sub[2]-4, and A#sub[1]-2,
-  in order of increasing frequency.
+  in order of increasing frequency (see @figure-discont and @figure-raman).
 The Raman tensor forms of each mode were derived by further considering their representations in the C#sub[2v] group,
   and were summarized in @table-rep.
 
 #include "figure-discont.typ"
+#include "figure-raman.typ"
 #include "table-rep.typ"
 
+// negligible-polarity modes (only modes visible in our experiments are labeled)
+
 Peaks corresponding to seven Raman-active negligible-polarity phonons were observed in our experiments
   (only the E#sub[2]-4 mode was not observed),
   which is more than all previous experiments (where only five or six peaks were typically reported).
@@ -43,7 +47,7 @@ The E#sub[2]-4 modes was calculated
   making it not visible in our and all previous experiments.
 The E#sub[1]-2 mode was also located close to the E#sub[2]-3 mode and has weak Raman intensity,
   making it also unobservable in previous experiments.
-However, the E#sub[1]-2 mode was observable in our experiments of y(zx)#overline[y],
+However, the E#sub[1]-2 mode was observable in our experiments of y(zx)#overline[y] with extended acquisition time,
   where the scattering of the E#sub[2]-3 mode was suppressed while that of the E#sub[1]-2 mode was enhanced,
   thanks to the different representations of these two modes.
 Our experiments reported the observation of the E#sub[1]-2 peak for the first time,
@@ -58,51 +62,98 @@ For example, the Raman tensor of the E#sub[2]-3 mode was substantially larger
 This highlighted a significant gap in established theory
   that rigorous symmetry analysis could only predict the non-zero components of the Raman tensors,
   but not their magnitudes.
-
 In order to address the limitations of existing theories,
   a method for estimating the magnitudes of Raman tensors was proposed.
 By analyzing the local environment of individual atoms,
   this approach decomposed their contributions to the Raman tensor into two parts:
-  a dominant component (invariant across similar environments, denoted as $a_i$，where $i in {1, 2, 3, 4}$)
+  a dominant component (invariant across similar environments, denoted as $a_i$，where $i in {1, 2, 5, 6}$)
   and several secondary components (reflecting environmental variations, 
-    denoted as $epsilon_i$, $eta_i$, and $zeta_i$，where $i in {1, 2, 3, 4}$,
+    denoted as $epsilon_i$, $eta_i$, and $zeta_i$，where $i in {1, 2, 5, 6}$,
     and $|epsilon_i| + |eta_i| + |zeta_i| << |a_i|$ was assumed).
 Detailed derivations were provided in @appd-predict, with results summarized in @table-nopol.
 Notably, the E#sub[2]-3 mode was the only mode that retains the $a_i$ term,
-  indicating a constructive interference of contributions from the local environment of individual atoms.
+  which indicating a constructive interference of contributions from the local environment of individual atoms.
 This stood in contrast to other negligible-polarity modes where such contributions tend to cancel out,
-  thereby explaining the exceptionally high Raman tensor magnitude observed for the E#sub[2]-3 mode.
+  explaining the exceptionally high Raman tensor magnitude observed for the E#sub[2]-3 mode.
 
-To further investigate the Raman spectra,
+To achieve a more precise investigation of the Raman spectra
-  an analysis of negligible-polarity phonons off the #sym.Gamma point was conducted
+    and prepare for analyzing impurity and charge carrier effects,
+  the analysis of negligible-polarity phonons off the #sym.Gamma point was conducted
   by comparing experimental and calculated results under various lazer incidence directions.
 The E#sub[2]-3 peak searved as a calibration reference under various experiments,
-  since its position remained virtually invariant between normal and edge incidence
+  since its position was calculated to be virtually invariant between normal and edge incidence
   (with a shift of only #sym.tilde 0.004 cm#super[-1]).
-
-The E2​-1, E2​-2, and A1​-1 modes exhibited observable frequency shifts. These experimental results are in good agreement with our calculations, as shown in Figure X and Table Y."
-
-#include "figure-e12.typ"
-
 The E#sub[2]-1, E#sub[2]-2, and A#sub[1]-1 modes exhibited observable shifts,
-  and the experimental results were in good agreement with our calculations, as shown in figure and table.
+  and the experimental results were in good agreement with our calculations, as shown in @fig-nopo-diff.
 Our results further confirmed the accuracy of both our experiments and calculations.
 
 #include "figure-nopo-diff.typ"
 
-为了进一步探索拉曼光谱，离开Gamma点的弱极性声子的分析也被进行，通过比对不同方向入射下的实验和计算结果。
+=== Strong-polar Phonons
+
+沿着不同方向入射的话，强声子的模式是不同的。
+
+// 在半导体的极性声子模式中，原子间存在长距离的库伦相互作用，导致散射谱在 Gamma 附近不再连续（引用），如图中的彩色线所示。
+// 这导致不同方向的入射/散射光的声子模式不同。
+// 具体来说，当入射光/散射光沿着 z 方向时，起作用的是 A-Gamma 线上的声子模式（图中的左半边的橘线），它们适用于群 C6v。
+// 这时会有一个 E1 模式（TO，振动方向在面内）和一个 A1 模式（LO，沿 z 振动）。
+// 而当沿着 y 方向入射时，起作用的是 Gamma-K 线上的声子模式（图中的右半边的橘线），它们不再适用于群 C6v，而只适用于群 C2v；
+// 它会分裂成沿x、y、z 方向的三个声子模式（图中的右半边的蓝线），它们分别对应于群 C2v 的 A1、B1 和 B2 表示 TODO: 确认这个几个表示的名字。
+// 若考虑到到入射光不是严格沿着 z 方向，而是有一个小的角度（例如 10 度），则此时有一个声子模式沿着 x 方向，另外两个声子模式则为 y-z 两个方向的混合。
+// (没有在图上表示)
+
+半导体中的强极性声子模式强烈地依赖于入射光的方向，
+  这是由于半导体中原子之间的长程库伦相互作用所致，
+  表现在散射光谱中，Gamma点附近不连续（见@figure-discont）。
+具体来说，当入射光沿着 z 方向时，起作用的是 A-Gamma 线上的声子模式（图中的上半部分的橘线），它们适用于群 C6v。
+这时会有一个 TO 模式（C6v 中的 E1）和一个 LO 模式（C6v 中的 A1）。
+而当沿着 y 方向入射时，起作用的是 Gamma-K 线上的声子模式（图中下半部分的橘线），它们不再适用于群 C6v，而只适用于群 C2v；
+这时将会出现三个模式，包括一个LO（沿y方向振动，对应C2v中的A1）和两个TO模式（根据振动方向，命名为B2-x和B2-y，对应C2v中的B1和B2）。
+当入射光不是严格沿着坐标轴方向，而是在xOy面内呈现一定的夹角时（掠入射，以及考虑了斜切的正入射），则此时有一个声子模式沿着 x 方向，另外两个声子模式则为 y-z 两个方向的混合。
+
+Strong-polarity phonon modes caused by different incident light directions are different,
+  due to long-range Coulomb interactions between atoms in semiconductors,
+  showing discontinuity in the scattering spectra near the #sym.Gamma point (see @figure-discont).
+For incident light propagating along the z direction (phonon modes on the A-#sym.Gamma line),
+  symmetry of C#sub[6v] point group applies and leading to two modes (two peeks in Raman spectra),
+  including an E#sub[1] mode (pink line in @figure-discont, vibration in-plane)
+    and an A#sub[1] mode (green line in @figure-discont, vibration along z-direction).
+When the light is incident along other directions, symmetry in plane was broken and C#sub[6v] symmetry no longer holds,
+  and there will be three phonon modes in theory.
+For example, when the light is incident along the y direction (phonon modes on the #{sym.Gamma}-K line),
+  symmetry of C#sub[2v] applies and three modes exist in dispersion curves,
+  including an A#sub[1] mode (green line in @figure-discont, vibration along z direction),
+  a B#sub[2] mode (blue line in @figure-discont, vibration along x direction),
+  and a B#sub[1] mode (red line in @figure-discont, vibration in y direction).
+When the light is incident along a direction between z and y,
+  three phonon modes will exist, but vibration in the mixed direction.
+
+将理论/计算结果与实验对比。
+
+我们将计算与实验结果进行了对比。衬底中的LO峰与plasmon耦合形成LOPC峰，因此与计算结果大不相同。
+对于TO峰，在正入射中，它与E2-3模式的距离为xxx；在掠入射中，它与E2-3模式的距离为xxx。
+
+Many Raman experiments on 4H-SiC with incident light along the z direction have observed two peaks.
+However, no experiments have reported three peaks with incident light along other directions.
+In our experiment, we found the third, and it satisfied properties we expected.
+In our experiments, we found that the third peak only appears when focusing inside the sample.
+
+E1 的情况。
+
+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。
+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。
+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。
+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。
+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。
+其中某个模式会怎样怎样，另一个会怎样怎样。
+
+// 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。
+// 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。
+
+#include "table-pol.typ"
+
 
 
-为了检验我们实验和计算的准确性，我们测量和计算了不同入射方向下弱极性峰位的微小移动。
-在我们的计算中，对比于正入射，肩入射中，E2-1与A1-1会有可观测的蓝移，同时E2-2会有可观测的红移。
-E2-1 E2-2 的计算结果与实验吻合较好，A1-1与实验结果略有出入。
-这可以被解释为频率移动的原因不同。
-对于 E2 模式，其极性为零，色散曲线在 Gamma 点附近连续，因此频率取决于色散曲线在Gamma附近的曲率；
-而 A1 模式具有弱但非零的极性，它在 Gamma 点附近不连续，
-  计算频率偏移需要同时考虑色散曲线曲率和阶跃大小的影响。
-在 A1-1 模式中，阶跃大小占主导。
-而在重掺杂n型衬底中，阶跃大小被载流子屏蔽显著减小，因此导致理想模型的计算结果与实验结果不符。
-通过将载流子屏蔽效应纳入计算，计算结果与实验结果吻合较好，如图所示。
 
 在强极性声子中：
 

paper/result/perfect/non-polar/default.typ

@@ -1,24 +0,0 @@
-
-
-我们提出了一个新的办法来估计拉曼张量大小。
-
-我们提出了一个办法来快速估计拉曼张量的大小。
-这个办法基于对称性分析，并加入了以下假设：
-  每个原子对拉曼张量的贡献主要取决于第一近邻原子（它们的贡献记为 $a_i$），更远的原子则归结为小量（记为 $epsilon_i$ $eta_i$ $zeta_i$)。
-  此外，我们忽略了同一个振动模式中，同种原子振幅的绝对值的差异，只考虑它们振动方向的不同。
-因此，拉曼张量的大小可以在进一步的第一性原理计算之前给出，结果总结在表中。
-我们的结果表明，E2-3 模式的拉曼散射强度远高于其它振动模式，这与实验和第一性原理计算结果一致。
-我们的研究表明，这个峰的高拉曼强度来自于所有键的贡献的相长干涉，这与其他弱极性模式不同（他们的贡献相互抵消）。
-
-
-
-
-
-#include "figure-raman.typ"
-
-不同入射方向下有微小移动。
-
-为了检验我们实验和计算的准确性，我们测量和计算了不同入射方向下弱极性峰位的微小移动。
-在我们的计算中，从正入射到肩入射，E2-3的峰位几乎不变，E2-1与A1-1会有可观测的蓝移，同时E2-2会有可观测的红移。
-实验结果与计算结果基本一致，如图如表所示。
-

paper/result/perfect/polar/default.typ

@@ -1,62 +0,0 @@
-=== Strong-polar Phonons
-
-沿着不同方向入射的话，强声子的模式是不同的。
-
-// 在半导体的极性声子模式中，原子间存在长距离的库伦相互作用，导致散射谱在 Gamma 附近不再连续（引用），如图中的彩色线所示。
-// 这导致不同方向的入射/散射光的声子模式不同。
-// 具体来说，当入射光/散射光沿着 z 方向时，起作用的是 A-Gamma 线上的声子模式（图中的左半边的橘线），它们适用于群 C6v。
-// 这时会有一个 E1 模式（TO，振动方向在面内）和一个 A1 模式（LO，沿 z 振动）。
-// 而当沿着 y 方向入射时，起作用的是 Gamma-K 线上的声子模式（图中的右半边的橘线），它们不再适用于群 C6v，而只适用于群 C2v；
-// 它会分裂成沿x、y、z 方向的三个声子模式（图中的右半边的蓝线），它们分别对应于群 C2v 的 A1、B1 和 B2 表示 TODO: 确认这个几个表示的名字。
-// 若考虑到到入射光不是严格沿着 z 方向，而是有一个小的角度（例如 10 度），则此时有一个声子模式沿着 x 方向，另外两个声子模式则为 y-z 两个方向的混合。
-// (没有在图上表示)
-
-半导体中的强极性声子模式强烈地依赖于入射光的方向，
-  这是由于半导体中原子之间的长程库伦相互作用所致，
-  表现在散射光谱中，Gamma点附近不连续（见@figure-discont）。
-具体来说，当入射光沿着 z 方向时，起作用的是 A-Gamma 线上的声子模式（图中的上半部分的橘线），它们适用于群 C6v。
-这时会有一个 TO 模式（C6v 中的 E1）和一个 LO 模式（C6v 中的 A1）。
-而当沿着 y 方向入射时，起作用的是 Gamma-K 线上的声子模式（图中下半部分的橘线），它们不再适用于群 C6v，而只适用于群 C2v；
-这时将会出现三个模式，包括一个LO（沿y方向振动，对应C2v中的A1）和两个TO模式（根据振动方向，命名为B2-x和B2-y，对应C2v中的B1和B2）。
-当入射光不是严格沿着坐标轴方向，而是在xOy面内呈现一定的夹角时（掠入射，以及考虑了斜切的正入射），则此时有一个声子模式沿着 x 方向，另外两个声子模式则为 y-z 两个方向的混合。
-
-Strong-polar phonon modes caused by different incident light directions are different,
-  due to long-range Coulomb interactions between atoms in semiconductors,
-  showing discontinuity in the scattering spectra near the #sym.Gamma point (see @figure-discont).
-For incident light propagating along the z direction (phonon modes on the A-#sym.Gamma line),
-  symmetry of C#sub[6v] point group applies and leading to two modes (two peeks in Raman spectra),
-  including an E#sub[1] mode (pink line in @figure-discont, vibration in-plane)
-    and an A#sub[1] mode (green line in @figure-discont, vibration along z-direction).
-When the light is incident along other directions, symmetry in plane was broken and C#sub[6v] symmetry no longer holds,
-  and there will be three phonon modes in theory.
-For example, when the light is incident along the y direction (phonon modes on the #{sym.Gamma}-K line),
-  symmetry of C#sub[2v] applies and three modes exist in dispersion curves,
-  including an A#sub[1] mode (green line in @figure-discont, vibration along z direction),
-  a B#sub[2] mode (blue line in @figure-discont, vibration along x direction),
-  and a B#sub[1] mode (red line in @figure-discont, vibration in y direction).
-When the light is incident along a direction between z and y,
-  three phonon modes will exist, but vibration in the mixed direction.
-
-将理论/计算结果与实验对比。
-
-我们将计算与实验结果进行了对比。衬底中的LO峰与plasmon耦合形成LOPC峰，因此与计算结果大不相同。
-对于TO峰，在正入射中，它与E2-3模式的距离为xxx；在掠入射中，它与E2-3模式的距离为xxx。
-
-Many Raman experiments on 4H-SiC with incident light along the z direction have observed two peaks.
-However, no experiments have reported three peaks with incident light along other directions.
-In our experiment, we found the third, and it satisfied properties we expected.
-In our experiments, we found that the third peak only appears when focusing inside the sample.
-
-E1 的情况。
-
-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。
-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。
-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。
-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。
-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。
-其中某个模式会怎样怎样，另一个会怎样怎样。
-
-// 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。
-// 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。
-
-#include "table-pol.typ"