大量小调整
This commit is contained in:
41
paper/others/table-pol-full.typ
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41
paper/others/table-pol-full.typ
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@@ -0,0 +1,41 @@
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#figure({
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set text(size: 9pt);
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set par(justify: false);
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let m(n, content) = table.cell(colspan: n, content);
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let m2(content) = table.cell(colspan: 2, content);
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let m3(content) = table.cell(colspan: 3, content);
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let A1 = [A#sub[1]];
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let A2 = [A#sub[2]];
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let B1 = [B#sub[1]];
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let B2 = [B#sub[2]];
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let E1 = [E#sub[1]];
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let E2 = [E#sub[2]];
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let NA = [Not Applicable]
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let lopc = [Yes#linebreak() (LOPC)];
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let overf = [Yes#linebreak() (overfocused)];
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table(columns: 19, align: center + horizon, inset: (x: 3pt, y: 5pt),
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m2[*Incident Direction*], m(4)[z], m(5)[y], m(8)[between z and y, 20#sym.degree to z],
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m2[*Vibration Direction*],
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// TODO: check LO-TO mixed
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[TO (x)], [TO (y)], m2[LO (z)], m3[TO (z)], [TO (x)], [LO (y)], m3[TO (y-z mixed)], [TO (x)], m(4)[LO (y-z mixed)],
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table.cell(rowspan: 2)[*Representation*],
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[C#sub[6v]], m2(E1), m2(A1), m(13, NA), [C#sub[2v]], B2, B1, m2(A1), m2(A1), B2, B1, m(9, NA),
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table.cell(rowspan: 2)[*Raman Tensor*],
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[Non-zero components],
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[xz], [yz], [xx, yy], [zz], // z
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[xx, yy], [zz], [xz], [yz], // y
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[xx], [yy], [yz], [zz], [xz], [xx], [yy], [yz], [zz], // 25 y&z
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[Simulation Result (a.u.)],
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// TODO: raman intensity, or raman tensor?
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m2[53.52], [58.26], [464.69], // z
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[58.26], [454.09], [53.52], [53.55], // y
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m2[53.71], [3.20], [425.98], [53.56], m2[3.60], [50.36], [27.99], // 45 y&z
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m2[*Visible in Common Raman Experiment*], m(17)[Yes],
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m2[*Wavenumber (Simulation) (cm#super[-1])*],
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// z y 45 y&z
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m2[776.57], m2[933.80], m2[761.80], [776.57], [941.33], m(4)[762.76], [776.57], m(4)[940.86],
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m2[*Electrical Polarity*], m(17)[Strong]
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)},
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caption: [Strong-polarized phonons near $Gamma$ point],
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)
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<table-pol>
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24
paper/others/table-rep.typ
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24
paper/others/table-rep.typ
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@@ -0,0 +1,24 @@
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#figure({
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set text(size: 9pt);
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set par(justify: false);
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let m2(content) = table.cell(colspan: 2, content);
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let A1 = [A#sub[1]];
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let A2 = [A#sub[2]];
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let B1 = [B#sub[1]];
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let B2 = [B#sub[2]];
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let E1 = [E#sub[1]];
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let E2 = [E#sub[2]];
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table(columns: 8, align: center + horizon,
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table.cell(rowspan: 2)[*Representation*],
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[C#sub[6v]], A1, B1, m2(E1), m2(E2),
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[C#sub[2v]], A1, B1, B2, B1, A2, A1,
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m2[*Vibration Direction*], [z], [z], [x], [y], [x], [y],
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m2[*Raman Tensor*],
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[$mat(a,,;,a,;,,b)$], [$0$],
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[$mat(,,a;,,;a,,;)$], [$mat(,,;,,a;,a,;)$], [$mat(,a,;a,,;,,;)$], [$mat(a,,;,-a,;,,;)$],
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)},
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caption: [
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Irreducible representations and raman tensors of phonons in 4H-SiC.
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],
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placement: none,
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)<table-rep>
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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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@@ -1,7 +1,7 @@
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#figure(
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image("/画图/拉曼整体图/embed.svg"),
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caption: [
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Phonon modes and corresponding Raman spectra of 4H-SiC.
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Raman-active phonon modes and corresponding Raman spectra of 4H-SiC.
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(a)-(b) Raman spectra with (a) normal and (b) edge incidence configurations.
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],
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placement: none
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@@ -1,18 +1,10 @@
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#figure(
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image("/画图/入射角度与偏移/embed.svg"),
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caption: [
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Phonon modes and corresponding Raman spectra of 4H-SiC.
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(a)-(b) Raman spectra with (a) normal and (b) edge incidence configurations.
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Frequency shifts of Raman-active modes depending on wavevectors.
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(a) Calculated results.
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(b) Experimental results and theoretical comparison.
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],
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placement: none
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)<figure-rev>
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// #figure(
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// image("/画图/弱极性不同方向偏移/embed.svg"),
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// caption: [
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// Frequency shifts of negligible-polar phonon modes under different incidence configurations.
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// (a) Experimental results under z(yy)#overline[z] and x(yy)#overline[x] configurations. Solid lines and dots represent distribution and value of experimental data, respectively.
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// (b) Comparison between experimental and calculated frequency shifts. The baby blue bars and error bars represent the mean and standard deviation of experimental results, respectively; the purple bars represent theoretical calculations.
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// ],
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// placement: none
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// )<fig-nopo-diff>
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@@ -1,5 +1,5 @@
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// 拟合结果位于 画图/拉曼结果拟合/250923
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#page(flipped: true)[#figure({
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#figure({
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set text(size: 9pt);
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set par(justify: false);
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let m(n, content) = table.cell(colspan: n, content);
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@@ -50,8 +50,7 @@
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)},
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caption: [
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Negaligible-polarized Phonons at $Gamma$ Point.
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The calculated phonon frequencies had a slight underestimation of 2-5% comparing to experimental values,
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which might be attributed to the known tendency of the PBE functional underestimating interatomic forces (cite).
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// The calculated phonon frequencies had a slight underestimation of 2-5% comparing to experimental values,
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// which might be attributed to the known tendency of the PBE functional underestimating interatomic forces (cite).
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],
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)<table-nopol>]
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)<table-nopol>
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@@ -1,10 +1,10 @@
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#page(flipped: true)[
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#figure({
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set text(size: 9pt);
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set par(justify: false);
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let m(n, content) = table.cell(colspan: n, content);
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let m2(content) = table.cell(colspan: 2, content);
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let m3(content) = table.cell(colspan: 3, content);
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let m2(content) = m(2, content);
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let m3(content) = m(3, content);
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let m4(content) = m(4, content);
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let A1 = [A#sub[1]];
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let A2 = [A#sub[2]];
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let B1 = [B#sub[1]];
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@@ -15,12 +15,12 @@
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let lopc = [Yes#linebreak() (LOPC)];
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let overf = [Yes#linebreak() (overfocused)];
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table(columns: 19, align: center + horizon, inset: (x: 3pt, y: 5pt),
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m2[*Incident Direction*], m(4)[z], m(5)[y], m(8)[between z and y, 20#sym.degree to z],
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m2[*Vibration Direction*],
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// TODO: check LO-TO mixed
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[TO (x)], [TO (y)], m2[LO (z)], m3[TO (z)], [TO (x)], [LO (y)], m3[TO (y-z mixed)], [TO (x)], m(4)[LO (y-z mixed)],
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m2[*Incident Direction*], m4[z], m4[x], m(9)[between z and x, 20#sym.degree to z],
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m2[*Notation of Mode*], [TO-x], [TO-y], m2[LO], m2[TO-z], [TO-y], [LO], m4[TO-xz], [TO-y], m4[LO],
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table.cell(rowspan: 2)[*Representation*],
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[C#sub[6v]], m2(E1), m2(A1), m(13, NA), [C#sub[2v]], B2, B1, m2(A1), m2(A1), B2, B1, m(9, NA),
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[C#sub[6v]], m2(E1), m2(A1), m4(NA), table.cell(rowspan: 2, colspan: 9, NA),
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[C#sub[2v]], B1, B2, m2(A1), m2(A1), B2, B1,
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// TODO: 以下数据需要重新计算,因为x和y换过一次
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table.cell(rowspan: 2)[*Raman Tensor*],
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[Non-zero components],
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[xz], [yz], [xx, yy], [zz], // z
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@@ -31,12 +31,10 @@
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m2[53.52], [58.26], [464.69], // z
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[58.26], [454.09], [53.52], [53.55], // y
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m2[53.71], [3.20], [425.98], [53.56], m2[3.60], [50.36], [27.99], // 45 y&z
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m2[*Visible in Common Raman Experiment*], m(17)[Yes],
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m2[*Wavenumber (Simulation) (cm#super[-1])*],
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// z y 45 y&z
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m2[776.57], m2[933.80], m2[761.80], [776.57], [941.33], m(4)[762.76], [776.57], m(4)[940.86],
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m2[*Electrical Polarity*], m(17)[Strong]
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m2[776.57], m2[933.80], m2[761.80], [776.57], [941.33], m(4)[762.76], [776.57], m(4)[940.86]
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)},
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caption: [Strong-polarized phonons near $Gamma$ point],
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)
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<table-pol>]
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<table-pol>
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