test-typst/main.typ

@@ -1,8 +1,10 @@
 #import "@preview/starter-journal-article:0.4.0": article, author-meta
 #import "@preview/tablem:0.2.0": tablem
 #set par.line(numbering: "1")
+// TODO: fix indent of first line
 #show figure.caption: it => {
   set text(10pt)
+  // TODO: how to align correctly?
   align(center, box(align(left, it), width: 80%))
 }
 #set page(
@@ -13,7 +15,8 @@
   // ],
   numbering: "1/1",
 )
-#set figure(placement: none)
+// TODO: why globally set placement not work?
+// #set figure(placement: none)
 #show: article.with(
   title: "Article Title",
   authors: (
@@ -71,6 +74,7 @@ Among these techniques,
   that near the #sym.Gamma point in reciprocal space.
 Studies in Raman scattering of 4H-SiC have been conducted since as early as 1983
   and have been widely employed to identification of different SiC polytypes.
+// TODO: 增加引用文献
 
 // 近年来，更多信息被从拉曼光谱中挖掘出来。
 // LOPC 已经被用于快速估计 n 型 SiC 的掺杂浓度。
@@ -87,37 +91,57 @@ Moreover, the potential effects of doping on Raman spectra have been explored.
 However, some unidentified peaks still appear in the Raman spectra,
   while certain phonon modes predicted by theory remain unobserved.
 In addition, the origins of newly emerged peaks induced by doping are often unclear or unexplained.
+// TODO: 多举例，增加引用文献
 
-In this paper, we do some things. We do something for the first time.
+In this paper, we do some things. Especially we do something for the first time.
+// TODO: 完善
 
 = Method
 
+// TODO
+
+calc
+
+experiment
+
 = Results and Discussion
 
 == Phonons in Perfect 4H-SiC
 
 // 拉曼活性的声子模式对应于 Gamma 点附近的声子模式。
 // 根据这些声子模式的极性，我们将这些声子分成两类。
-Raman scattering peeks correspond to phonons located near the #sym.Gamma point in reciprocal space.
-We classified these phonons into two categories based on their polarities:
-  (i) negligible-polar phonons (i.e., phonons with no polarity or very weak polarity),
-    whose dispersion curves are continuous near the #sym.Gamma point (as shown in @phonon),
-    and for which the effect of polarity can be ignored in the Raman scattering process;
-  and (ii) strong-polar phonons,
-    whose dispersion curves exhibit discontinuity near the #sym.Gamma point (also shown in @phonon),
+Raman scattering peeks correspond to atom vibrations (phonons) located near the #sym.Gamma point in reciprocal space,
+  and the exact location of these phonons is determined by the wavevectors of incident and scattered light.
+On each site of the Brillouin zone near the #sym.Gamma point,
+  there are 21 phonon modes in 4H-SiC.
+We classified these phonons into two categories based on their polarities.
+18 of 21 phonons are classified into negligible-polar phonons (i.e., phonons with zero or very weak polarity),
+    for which the effect of polarity can be ignored in the Raman scattering process;
+  and the other three phonons are strong-polar phonons,
     where the polarity gives rise to observable effects in the Raman spectra.
+This classification is based on the fact that
+  the four Si atoms in the primitive cell carry similar positive Born effective charges (BECs),
+  and the four C atoms carry similar negative BECs (see @table-bec).
+In the 18 negligible-polar phonons,
+  the vibrations of two Si atoms are approximately opposite to those of the other two Si atoms,
+  so do C atoms,
+  leading to cancellations of macroscopic polarity.
+While in the three strong-polar phonons,
+  all Si atoms vibrate in the same direction, so do C atoms,
+  leading to a net dipole moment.
 
 #figure(
-  image("/画图/声子不连续/embed.svg"),
-  caption: [
-    (a) Phonon dispersion of 4H-SiC along the A–#sym.Gamma–K high-symmetry path.
-      Gray lines represent negligible-polar phonon modes,
-      while colored lines indicate strong-polar phonon modes.
-    (b) Magnified view of the boxed region in (a).
-      The orange dashed lines mark the phonon wavevectors involved in Raman scattering
-        with incident light along the z- and y-directions.
-  ]
-)<phonon>
+  table(columns: 4, align: center + horizon,
+    table.cell(colspan: 2)[], table.cell(colspan: 2)[*BEC* (unit: |e|)],
+    table.cell(colspan: 2)[], [x / y direction], [z direction],
+    table.cell(rowspan: 2)[Si atom], [A/C layer], [2.667], [2.626],
+    [B layer], [2.674], [2.903],
+    table.cell(rowspan: 2)[C atom], [A/C layer], [-2.693], [-2.730],
+    [B layer], [-2.648], [-2.800],
+  ),
+  caption: [Born effective charges of Si and C atoms in A/B/C/B layers of 4H-SiC.],
+  placement: none,
+)<table-bec>
 
 === Phonons with Negligible Polarities
 
@@ -131,49 +155,51 @@ Phonons at the #sym.Gamma point were used
 This approximation is widely adopted and justified by the fact that,
   although the phonons participating in Raman processes are not these strictly located at the #sym.Gamma point,
   their dispersion near the #sym.Gamma point is continuous with vanishing derivatives,
-  and their wavevector is very small (about 0.01 nm#super[-1] in this paper,
+  and their wavevector is very small (about 0.01 nm#super[-1] in back-scattering configurations with 532 nm laser light,
     which corresponds to only 1% of the smallest reciprocal lattice vector of 4H-SiC),
-  as shown by the orange dotted line in @phonon.
+  as shown by the orange dotted line in @figure-discont.
 Therefore, negligible-polar phonons involved in Raman processes
-  have nearly indistinguishable properties from those at the #sym.Gamma point.
-
-// 4H-SiC 在 Gamma 有 21 个distinct phonons。
-// 其中 18 个被归类为极性较弱的声子。这是因为，4H-SiC 的原胞中，4 个 Si 原子所带的有效电荷差别不大，四个 C 原子所带的有效电荷差别也不大。
-// 在这些声子模式中，原胞中的 2 个 Si 原子运动方向与另外 2 个 Si 原子相反，2 个 C 原子的运动方向与另外 2 个 C 原子相反，极性相互抵消。
-There are 21 distinct phonons at the #sym.Gamma point in 4H-SiC.
-Among them, 18 phonons are classified as negligible-polar phonons.
-This classification is based on the fact that
-  the four Si atoms in the primitive cell carry similar Born effective charges (BEC),
-  as do the four C atoms, as shown in @bec.
-In these 18 modes, the vibrations of two Si atoms are approximately opposite to those of the other two Si atoms,
-  and similarly for the C atoms,
-  leading to cancellations of macroscopic polarity.
+    have nearly indistinguishable properties from those at the #sym.Gamma point,
+  and the phonon participating in Raman processes of different incident/scattered light directions
+    are all nearly identical to the phonons at the #sym.Gamma point.
 
 #figure(
-  table(columns: 4, align: center + horizon,
-    table.cell(colspan: 2)[], table.cell(colspan: 2)[*BEC*],
-    table.cell(colspan: 2)[], [x / y direction], [z direction],
-    table.cell(rowspan: 2)[Si atom], [A/C layer], [2.667], [2.626],
-    [B layer], [2.674], [2.903],
-    table.cell(rowspan: 2)[C atom], [A/C layer], [-2.693], [-2.730],
-    [B layer], [-2.648], [-2.800],
-  ),
-  caption: [Born effective charges of Si and C atoms in A/B/C/B layers of 4H-SiC.]
-)<bec>
+  image("/画图/声子不连续/embed.svg"),
+  caption: [
+    (a) Phonon dispersion of 4H-SiC along the A–#sym.Gamma–K high-symmetry path.
+      Gray lines represent negligible-polar phonon modes,
+        while colored lines indicate strong-polar phonon modes.
+      The green, red and blue lines indicate the mode along the z-direction, y-direction and x-direction, respectively.
+      Along A-#sym.Gamma path, strong-polar modes along x- and y-directions are degenerated,
+        showing as a single purple line.
+    (b) Magnified view of the boxed region in (a).
+      The orange dashed lines mark the phonon wavevectors involved in Raman scattering
+        with incident light along the z- and y-directions.
+  ],
+  placement: none,
+)<figure-discont>
 
 // 这18个声子对应于 $\mathrm{C_{6v}}$ 点群的 14 个表示：2A1 + 4B1 + 2E_1 + 4E2
-// 其中，B1 表示没有拉曼活性，它的拉曼张量为零；其它表示的拉曼张量不为零，但张量的大小是否足够大到可以在实验上看到，则还需要第一性原理计算，不能直接通过表示来判断。
+// 其中，B1 表示没有拉曼活性，它的拉曼张量为零；其它表示的拉曼张量不为零
+// 但张量的大小是否足够大到可以在实验上看到，则还需要第一性原理计算，不能直接通过表示来判断。
 The 18 negligible-polar phonons correspond to 14 irreducible representations of the C#sub[6v] point group:
   2A#sub[1] + 4B#sub[1] + 2E#sub[1] + 4E#sub[2].
-Phonons belonging to A#sub[1] and B#sub[1] representations are non-degenerate,
-  while phonons belonging to E#sub[1] and E#sub[2] representations are doubly degenerate.
+Phonons belonging to A#sub[1] and B#sub[1] representations vibration along z-axis and are non-degenerate,
+  while phonons belonging to E#sub[1] and E#sub[2] representations vibrate in plane and are doubly degenerate.
 Phonons belonging to B#sub[1] representation are Raman-inactive, as their Raman tensors vanish.
 In contrast, phonons belonging to other representations are Raman-active,
   the Raman tensors of them have non-zero components,
   indicating that these phonons might be visible in Raman experiment under appropriate polarization configurations.
+// 各个模式的声子可以使用怎样的偏振光看到（即拉曼张量的非零分量）可以联合考虑 C6v 和 C2v 的表示来判断，如表所示。
+// TODO: 翻译
 However, the actual visibility of each phonon depends on the magnitudes of its Raman tensor components,
-  which cannot be inferred solely from symmetry analysis.
+  which cannot be computed solely from symmetry analysis.
 
+// TODO: 画个表
+
+Here we propose a method to estimate the magnitudes of the Raman tensors of these phonons.
+
+// TODO: 写出来这个方法，并验证。
 /*
 这里应该有办法来估计。下面是我总结的规律：
 按照我们规定的 ABCB 层序，并将拉曼张量的大小归结为键长的变化的话：
@@ -191,12 +217,12 @@ However, the actual visibility of each phonon depends on the magnitudes of its R
 * 写出各个模式的拉曼张量（上面的线性组合）。即可以直接看到结果。
 */
 
-// 我们计算了拉曼活性声子的拉曼张量。
+// 我们计算了拉曼活性声子的频率及拉曼张量，并与实验对比，如表如图所示。
 // 其中有几个声子的拉曼活性较弱，有几个比较强。强的都可以在实验上看到；但弱的能否看到则取决于它是否恰好位于强模式的附近。
 // 其中，xxx 和xxx 位于强模式的附近，它们在实验上无法看到；xxx 只在 z 方向入射/散射时可以看到；xxx 则在任意方向都能看到。
 // 我们同样计算了这些声子在 300K 下的展宽，并与实验对比，结果如表所示。原子的振幅另外列于附录中。
 The Raman tensors of these Raman-active phonons were calculated using first-principles methods,
-  and the results are summarized and compared with experimental results in @nopol.
+  and the results are summarized and compared with experimental results in @table-nopol.
 Two Raman-active modes are not observed in our experiments,
   including the E#sub[1] mode at 746.91 cm#super[-1] and the E#sub[2] mode at 764.33 cm#super[-1],
   due to their relatively low Raman intensities, broad FWHM values, and their proximity to stronger modes.
@@ -205,7 +231,7 @@ The A#sub[1] phonon at 812.87 cm#super[-1] is Raman-active
   but it is only visible when both the incident and scattered light propagate along the z-direction (zz),
   as its Raman intensity in basal plane is too week to be distinguished from the noise.
 We also calculated the linewidths of these phonons at 300 K and compared them with experimental results,
-  as summarized in the @nopol.
+  as summarized in the @table-nopol.
 The atomic vibration amplitudes are listed separately in the Appendix.
 
 // TODO: 将一部分 phonons 改为 phonon modes
@@ -214,6 +240,8 @@ The atomic vibration amplitudes are listed separately in the Appendix.
 
 #page(flipped: true)[#figure({
   let m(n, content) = table.cell(colspan: n, content);
+  let m2(content) = table.cell(colspan: 2, content);
+  let m3(content) = table.cell(colspan: 3, content);
   let A1 = [A#sub[1]];
   // let A2 = [A#sub[2]];
   let B1 = [B#sub[1]];
@@ -223,16 +251,15 @@ The atomic vibration amplitudes are listed separately in the Appendix.
   table(columns: 27, align: center + horizon, inset: (x: 3pt, y: 5pt),
     // [*Direction of Incident & Scattered Light*],
     //   m(26)[Any direction (not depend on direction of incident & scattered light)],
+    // TODO: 整理表格，使用 m2 m3 来代替
     [*Number of Phonon*],
-      // E2         E2            E1        2B1       A1
-      [1], m(2)[2], [3], m(2)[4], [5], [6], [7], [8], m(3)[9],
-      // E1       E2              E2              A1        2B1
-      [10], [11], [12], m(2)[13], [14], m(2)[15], m(3)[16], [17], [18],
+      // E2       E2          E1        2B1       A1     E1          E2            E2            A1        2B1
+      [1], m2[2], [3], m2[4], [5], [6], [7], [8], m3[9], [10], [11], [12], m2[13], [14], m2[15], m3[16], [17], [18],
     [*Vibration Direction*],
       // E2       E2            E1        2B1      A1
-      [x], m(2)[y], [x], m(2)[y], [x], [y], [z], [z], m(3)[z],
+      [x], m2[y], [x], m(2)[y], [x], [y], m(2)[z], m(3)[z],
       // E1     E2            E2            A1       2B1
-      [x], [y], [x], m(2)[y], [x], m(2)[y], m(3)[z], [z], [z],
+      [x], [y], [x], m(2)[y], [x], m(2)[y], m(3)[z], m(2)[z],
     [*Representation #linebreak() in Group C#sub[6v]*],
       m(3, E2), m(3, E2), m(2, E1), B1, B1, m(3, A1), m(2, E1), m(3, E2), m(3, E2), m(3, A1), B1, B1,
     [*Raman-active or Not*],
@@ -279,8 +306,8 @@ The atomic vibration amplitudes are listed separately in the Appendix.
       // E2 E2    E1          2B1         A1 E1       E2 E2       A1          2B1
       m(6)[None], m(2)[Weak], m(2)[None], m(5)[Weak], m(6)[None], m(3)[Weak], m(2)[None],
   )},
-  caption: [Weak- and None-polarized phonons near $Gamma$ point],
-)<nopol>]
+  caption: [Negaligible-polarized Phonons at $Gamma$ Point],
+)<table-nopol>]
 
 #figure(
   image("/画图/拉曼整体图/main.svg"),
@@ -294,8 +321,29 @@ The atomic vibration amplitudes are listed separately in the Appendix.
   ]
 )<raman>
 
+// TODO: 画一个模拟的图，与实验图对比。
+
+// 实验与计算基本相符。对于声子频率，计算总是低估大约 3%。
+// 此外，一些较强的模式在预测无法看到的偏振中也可以看到。例如，一些在 xy 偏振中不应该看到的模式可以被看到了。
+// 这个现象可以由 4度的斜切所解释：我们将材料略微踮起一些角度，就可以使得该模式减小。
+// 这个现象也可以由材料或偏振片的微小角度来解释。
+// 例如，我们将偏振方向转动 5 度，就可以得到这个模拟结果。
+// 此外，由于使用的材料是沿着 c 轴切片的，所以我们在测量 y 入射时不得不将片子以略小于 90 度（约 75 度）的角度放置。这也导致实验与计算的偏差。
+// TODO: 翻译成英文
+
+=== Strong-polar Phonons
+
+// 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。
+
 #page(flipped: true)[
   #figure({
+    // 使用 m2 m3
     let m(n, content) = table.cell(colspan: n, content);
     let A1 = [A#sub[1]];
     let A2 = [A#sub[2]];
@@ -303,7 +351,7 @@ The atomic vibration amplitudes are listed separately in the Appendix.
     let B2 = [B#sub[2]];
     let E1 = [E#sub[1]];
     let E2 = [E#sub[2]];
-    let NA = [Not Applicable];
+    let NA = [Not Applicable]
     let yzmix = [y-z mixed#linebreak() (LO-TO mixed)];
     let lopc = [Yes#linebreak() (LOPC)];
     let overf = [Yes#linebreak() (overfocused)];
@@ -339,4 +387,8 @@ The atomic vibration amplitudes are listed separately in the Appendix.
   )
 ]
 
+// TODO: 这句话放哪里？
+// whose dispersion curves exhibit discontinuity near the #sym.Gamma point (also shown in @phonon),
+
+
 #bibliography("./ref.bib", title: "Reference", style: "american-physics-society")