大量小调整

This commit is contained in:
2026-01-06 17:00:37 +08:00
parent 549ba6f87a
commit 4855cae854
17 changed files with 108 additions and 141 deletions

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@@ -0,0 +1,41 @@
#figure({
set text(size: 9pt);
set par(justify: false);
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]];
let B2 = [B#sub[2]];
let E1 = [E#sub[1]];
let E2 = [E#sub[2]];
let NA = [Not Applicable]
let lopc = [Yes#linebreak() (LOPC)];
let overf = [Yes#linebreak() (overfocused)];
table(columns: 19, align: center + horizon, inset: (x: 3pt, y: 5pt),
m2[*Incident Direction*], m(4)[z], m(5)[y], m(8)[between z and y, 20#sym.degree to z],
m2[*Vibration Direction*],
// TODO: check LO-TO mixed
[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)],
table.cell(rowspan: 2)[*Representation*],
[C#sub[6v]], m2(E1), m2(A1), m(13, NA), [C#sub[2v]], B2, B1, m2(A1), m2(A1), B2, B1, m(9, NA),
table.cell(rowspan: 2)[*Raman Tensor*],
[Non-zero components],
[xz], [yz], [xx, yy], [zz], // z
[xx, yy], [zz], [xz], [yz], // y
[xx], [yy], [yz], [zz], [xz], [xx], [yy], [yz], [zz], // 25 y&z
[Simulation Result (a.u.)],
// TODO: raman intensity, or raman tensor?
m2[53.52], [58.26], [464.69], // z
[58.26], [454.09], [53.52], [53.55], // y
m2[53.71], [3.20], [425.98], [53.56], m2[3.60], [50.36], [27.99], // 45 y&z
m2[*Visible in Common Raman Experiment*], m(17)[Yes],
m2[*Wavenumber (Simulation) (cm#super[-1])*],
// z y 45 y&z
m2[776.57], m2[933.80], m2[761.80], [776.57], [941.33], m(4)[762.76], [776.57], m(4)[940.86],
m2[*Electrical Polarity*], m(17)[Strong]
)},
caption: [Strong-polarized phonons near $Gamma$ point],
)
<table-pol>

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@@ -0,0 +1,24 @@
#figure({
set text(size: 9pt);
set par(justify: false);
let m2(content) = table.cell(colspan: 2, content);
let A1 = [A#sub[1]];
let A2 = [A#sub[2]];
let B1 = [B#sub[1]];
let B2 = [B#sub[2]];
let E1 = [E#sub[1]];
let E2 = [E#sub[2]];
table(columns: 8, align: center + horizon,
table.cell(rowspan: 2)[*Representation*],
[C#sub[6v]], A1, B1, m2(E1), m2(E2),
[C#sub[2v]], A1, B1, B2, B1, A2, A1,
m2[*Vibration Direction*], [z], [z], [x], [y], [x], [y],
m2[*Raman Tensor*],
[$mat(a,,;,a,;,,b)$], [$0$],
[$mat(,,a;,,;a,,;)$], [$mat(,,;,,a;,a,;)$], [$mat(,a,;a,,;,,;)$], [$mat(a,,;,-a,;,,;)$],
)},
caption: [
Irreducible representations and raman tensors of phonons in 4H-SiC.
],
placement: none,
)<table-rep>

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@@ -1,7 +1,5 @@
== Phonons in Perfect 4H-SiC
// 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。
Raman-active phonon modes were categorized into two groups,
according to the distinct behaviors arising from different electrical polarities,
including eight negligible-polarity modes (possessing zero or very weak polarity),
@@ -51,6 +49,8 @@ However, the E#sub[1]-2 mode was observable in our experiments of y(zx)#overline
Our experiments reported the observation of the E#sub[1]-2 peak for the first time,
and explained the discrepancy among previous experiments and ours with the help of our calculations.
#include "figure-raman.typ"
It is noteworthy that the large variation in Raman tensor magnitudes among different modes
was not yet theoretically understood.
For example, the Raman tensor of the E#sub[2]-3 mode was substantially larger
@@ -72,103 +72,19 @@ Notably, the E#sub[2]-3 mode was the only mode that retains the $a_i$ term,deter
This stood in contrast to other negligible-polarity modes where such contributions tend to cancel out,
explaining the exceptionally high Raman tensor magnitude observed for the E#sub[2]-3 mode.
#page(flipped: true)[
#include "table-nopol.typ"
#include "table-pol.typ"
]
The mode frequency dependence on the wavevector were thoroughly investigated,
including both thoretical calculations (@figure-rev a), experimental measurements (@figure-rev b)
and their comparisons (@figure-rev c).
including both thoretical calculations (@figure-rev a), experimental measurements (left part of @figure-rev b) and their comparisons (right part of @figure-rev b).
The E#sub[2]-3 mode frequency was calculated to remaine distinct in all incidence geometries (@figure-rev a),
making it an ideal calibration reference for experiments.
Meanwhile,
the E#sub[2]-1, E#sub[2]-2 and A#sub[1]-1 mode showed a relatively larger dependence on the incidence direction,
which is in good agreement with our experimental observations (@figure-rev c).
// TODO: 图中标注强调是拉曼活性的模式
// TODO: b 图的标题歪了
#include "figure-raman.typ"
#include "table-nopol.typ"
#include "table-pol.typ"
// TODO: 合并两个表格到一页,删除 polar 中的多余信息
which is in good agreement with our experimental observations (@figure-rev b).
#include "figure-rev.typ"
#include "figure-discont.typ"
The E#sub[2]-3 peak was calculated to be having virtually invariant frequency,
and thus served as a calibration reference under various experiments.
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,
thus was uesd to compare the frequency shifts between different incidence configurations.
// TODO: 增加图例:各种入射激光
// TODO: 增加 TO-zOx 的讨论
// TODO: 条形图画成两个方向的
// TODO: 换个方案拟合,考虑不对称,看能不能把这个误差填上
// 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。
// 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。
// 第四段:声子模式的强度可以从理论上得到解释。
=== Negligible-polarity Phonons
To achieve a more precise investigation of the Raman spectra
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 was calculated to be virtually invariant between normal and edge incidence
(with a shift of only #sym.tilde 0.004 cm#super[-1]).
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 fig.
Our results further confirmed the accuracy of both our experiments and calculations.
=== Strong-polarity Phonons
The Strong-polarity phonon modes participated in Raman scattering
exhibited significant variations depending on the incidence configurations
(see the intersection of colored solid lines and orange dashed lines in @figure-discont b and c).
For incident light propagating along the z direction,
the C#sub[6v] point group applied and two modes were present,
marked as normal-TO and normal-LO,
and they were corresponding to the E#sub[1] and A#sub[1] representations
and vibrations along the basle plane and z direction, respectively.
The normal-LO would subsiquently couple with plasmons to form LOPC modes in n-type 4H-SiC.
For incident light propagating along other directions,
the C#sub[6v] group no longer held and three modes were present.
Specifically, for incident light propagating along x direction, the C#sub[2v] group applied,
and the three modes was named as edge-TO-z, edge-TO-y and edge-LO,
which were corresponding to A#sub[1], B#sub[2] and B#sub[1] representations
and vibrations along z, y and x directions, respectively.
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。

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@@ -1,7 +1,7 @@
#figure(
image("/画图/拉曼整体图/embed.svg"),
caption: [
Phonon modes and corresponding Raman spectra of 4H-SiC.
Raman-active phonon modes and corresponding Raman spectra of 4H-SiC.
(a)-(b) Raman spectra with (a) normal and (b) edge incidence configurations.
],
placement: none

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@@ -1,18 +1,10 @@
#figure(
image("/画图/入射角度与偏移/embed.svg"),
caption: [
Phonon modes and corresponding Raman spectra of 4H-SiC.
(a)-(b) Raman spectra with (a) normal and (b) edge incidence configurations.
Frequency shifts of Raman-active modes depending on wavevectors.
(a) Calculated results.
(b) Experimental results and theoretical comparison.
],
placement: none
)<figure-rev>
// #figure(
// image("/画图/弱极性不同方向偏移/embed.svg"),
// caption: [
// Frequency shifts of negligible-polar phonon modes under different incidence configurations.
// (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.
// (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.
// ],
// placement: none
// )<fig-nopo-diff>

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@@ -1,5 +1,5 @@
// 拟合结果位于 画图/拉曼结果拟合/250923
#page(flipped: true)[#figure({
#figure({
set text(size: 9pt);
set par(justify: false);
let m(n, content) = table.cell(colspan: n, content);
@@ -50,8 +50,7 @@
)},
caption: [
Negaligible-polarized Phonons at $Gamma$ Point.
The calculated phonon frequencies had a slight underestimation of 2-5% comparing to experimental values,
which might be attributed to the known tendency of the PBE functional underestimating interatomic forces (cite).
// The calculated phonon frequencies had a slight underestimation of 2-5% comparing to experimental values,
// which might be attributed to the known tendency of the PBE functional underestimating interatomic forces (cite).
],
)<table-nopol>]
)<table-nopol>

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@@ -1,10 +1,10 @@
#page(flipped: true)[
#figure({
set text(size: 9pt);
set par(justify: false);
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 m2(content) = m(2, content);
let m3(content) = m(3, content);
let m4(content) = m(4, content);
let A1 = [A#sub[1]];
let A2 = [A#sub[2]];
let B1 = [B#sub[1]];
@@ -15,12 +15,12 @@
let lopc = [Yes#linebreak() (LOPC)];
let overf = [Yes#linebreak() (overfocused)];
table(columns: 19, align: center + horizon, inset: (x: 3pt, y: 5pt),
m2[*Incident Direction*], m(4)[z], m(5)[y], m(8)[between z and y, 20#sym.degree to z],
m2[*Vibration Direction*],
// TODO: check LO-TO mixed
[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)],
m2[*Incident Direction*], m4[z], m4[x], m(9)[between z and x, 20#sym.degree to z],
m2[*Notation of Mode*], [TO-x], [TO-y], m2[LO], m2[TO-z], [TO-y], [LO], m4[TO-xz], [TO-y], m4[LO],
table.cell(rowspan: 2)[*Representation*],
[C#sub[6v]], m2(E1), m2(A1), m(13, NA), [C#sub[2v]], B2, B1, m2(A1), m2(A1), B2, B1, m(9, NA),
[C#sub[6v]], m2(E1), m2(A1), m4(NA), table.cell(rowspan: 2, colspan: 9, NA),
[C#sub[2v]], B1, B2, m2(A1), m2(A1), B2, B1,
// TODO: 以下数据需要重新计算因为x和y换过一次
table.cell(rowspan: 2)[*Raman Tensor*],
[Non-zero components],
[xz], [yz], [xx, yy], [zz], // z
@@ -31,12 +31,10 @@
m2[53.52], [58.26], [464.69], // z
[58.26], [454.09], [53.52], [53.55], // y
m2[53.71], [3.20], [425.98], [53.56], m2[3.60], [50.36], [27.99], // 45 y&z
m2[*Visible in Common Raman Experiment*], m(17)[Yes],
m2[*Wavenumber (Simulation) (cm#super[-1])*],
// z y 45 y&z
m2[776.57], m2[933.80], m2[761.80], [776.57], [941.33], m(4)[762.76], [776.57], m(4)[940.86],
m2[*Electrical Polarity*], m(17)[Strong]
m2[776.57], m2[933.80], m2[761.80], [776.57], [941.33], m(4)[762.76], [776.57], m(4)[940.86]
)},
caption: [Strong-polarized phonons near $Gamma$ point],
)
<table-pol>]
<table-pol>

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