This commit is contained in:
@@ -5,8 +5,8 @@
|
||||
|
||||
Phonon modes in defect-free 4H-SiC were first analyzed,
|
||||
which account for the majority of the observed Raman signals.
|
||||
Subsequently, we address the effects of defects and charge carriers,
|
||||
which manifest as additional minor peaks and modifications to the primary peaks in the Raman spectra.
|
||||
Subsequently, the effects of defects 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"
|
||||
#include "defect/default.typ"
|
||||
|
||||
@@ -7,14 +7,14 @@
|
||||
对于正入射，声子大致位于 Gamma-A 线上；对于边入射，声子大致位于 Gamma-K 线上。对于掠入射，声子不位于任何高对称线上。
|
||||
|
||||
The wavevectors of phonons participating in Raman scattering
|
||||
equal to the difference between the wavevectors of the incident and scattered light.
|
||||
equaled to the difference between the wavevectors of the incident and scattered light.
|
||||
Thus, in our experiments (back-scattering with green and UV light),
|
||||
the phonons involved are located very close to the #sym.Gamma point,
|
||||
the phonons involved were located very close to the #sym.Gamma point,
|
||||
with various wavevectors determined by the incidence configurations.
|
||||
As illustrated in @figure-discont, in Raman experiments of normal and edge incidence,
|
||||
the relevant phonons lie approximately at the #sym.Gamma–A and #sym.Gamma–K lines, respectively.
|
||||
the relevant phonons lied approximately at the #sym.Gamma–A and #sym.Gamma–K lines, respectively.
|
||||
For grazing incidence,
|
||||
the relevant phonons do not reside on any high-symmetry lines and are therefore not depicted in the figure.
|
||||
the relevant phonons did not reside on any high-symmetry lines and were therefore not depicted in the figure.
|
||||
|
||||
#include "figure-discont.typ"
|
||||
|
||||
@@ -24,17 +24,22 @@ For grazing incidence,
|
||||
我们将这 21 个声子模式分为两类：18 个极性可以忽略的声子模式（即极性为零或非常弱的声子），在拉曼散射过程中它们的电极性造成的效应可以忽略；
|
||||
和 3 个强极性声子模式，在拉曼光谱中电极性效应是可观测的。
|
||||
|
||||
At each position near the #sym.Gamma point, there are 21 phonon modes with non-zero frequency (counting degeneracies).
|
||||
At each position near the #sym.Gamma point, there were 21 phonon modes with non-zero frequency (counting degeneracies).
|
||||
These phonons were categorized into two groups according to their electrical polarities:
|
||||
18 negligible-polar phonons (i.e., zero or very weak electrical polarity),
|
||||
where atoms of the same species vibrate in opposite directions,
|
||||
where atoms of the same species vibrated in opposite directions,
|
||||
resulting in effective cancellation of electrical polarization during the Raman process
|
||||
(gray lines in @figure-discont);
|
||||
and three strong-polar phonons,
|
||||
where atoms of the same species vibrate in phase,
|
||||
where atoms of the same species vibrated in phase,
|
||||
resulting in strong electrical polarization and observable effects in Raman spectra
|
||||
(colored lines in @figure-discont).
|
||||
The categorized is also illustrated and compared with Raman experiment in @fig-raman.
|
||||
The categorized was also illustrated and compared with Raman experiment in @fig-raman.
|
||||
|
||||
极性不同的模式有着不同的行为，因此被分开讨论。
|
||||
|
||||
Negligible-polar and strong-polar phonons exhibited distinct behaviors
|
||||
and were therefore discussed separately in the following sections.
|
||||
|
||||
#include "figure-raman.typ"
|
||||
|
||||
|
||||
@@ -5,8 +5,7 @@
|
||||
|
||||
Negligible-polar phonons were theoretically analyzed,
|
||||
starting with the approximation using phonons at the #sym.Gamma point,
|
||||
followed by a discussion of variations arising from non-zero wavevectors
|
||||
(e.g. different incidence configurations in Raman experiments).
|
||||
followed by a discussion of modifications arising from non-zero wavevectors.
|
||||
This approximation is based on the fact that
|
||||
the dispersion of these phonons is continuous and very close to the #sym.Gamma point,
|
||||
and has been widely adopted in the literature @_n-sic_2008.
|
||||
@@ -44,7 +43,7 @@ It should be noted, however, that the observability in Raman experiment depends
|
||||
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，756 附近的峰应该比其它峰具有更强的拉曼强度，这与实验一致。
|
||||
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）。
|
||||
|
||||
A method to estimate the magnitudes of the Raman tensors of each mode from their vibration patterns (eigenvectors)
|
||||
@@ -56,9 +55,10 @@ Furthermore, the absolute amplitude differences among atoms of the same type wit
|
||||
and only their vibrational directions were considered.
|
||||
This enables a preliminary estimation of the Raman tensor magnitudes prior to detailed first-principles calculations,
|
||||
with the results summarized in @table-nopol.
|
||||
Our analysis gave the result that the E#sub[2] mode at 756.25 cm#super[-1] in simulation (mode 8)
|
||||
should possess a much higher Raman intensity than the others,
|
||||
which is consistent with experimental observations.
|
||||
Our analysis gave the result that the E#sub[2]-3 mode (at about 756.25 cm#super[-1] in simulation)
|
||||
should possess a much higher Raman scattering intensity than the others,
|
||||
which is consistent with experimental observations,
|
||||
where at about 776 cm#super[-1] a very strong E#sub[2] peak is observed.
|
||||
Our result showed that
|
||||
the high Raman intensity of this mode arises from the constructive interference of contributions from all bonds,
|
||||
in contrast to other negligible-polar modes where contributions tend to cancel each other out.
|
||||
@@ -69,17 +69,12 @@ Our result showed that
|
||||
|
||||
声子频率和拉曼张量的大小被使用第一性原理计算，并与实验结果和理论预测进行了比较（@table-nopol）。
|
||||
计算的声子频率与实验数据有很好的吻合，误差在 2-5% 之间，这个误差可能是由于 PBE 泛函对原子间力的低估（cite）。
|
||||
计算的拉曼张量也与实验和理论结果基本一致，这包括强度最高的模式 E#sub[2] 776 cm#super[-1]（模式 8），
|
||||
其次是四个强度较低但在实验中清晰可见的模式，
|
||||
包括 E#sub[2] 模式在 195.5 cm#super[-1]（模式 1）和 203.3 cm#super[-1]（模式 2），
|
||||
E#sub[1] 模式在 269.7 cm#super[-1]（模式 3），
|
||||
和 A#sub[1] 模式在 609.5 cm#super[-1]（模式 6）。
|
||||
在 746 cm#super[-1]（模式 7）计算的 E#sub[1] 模式
|
||||
和 756.25 cm#super[-1]（模式 9）计算的 E#sub[2] 模式
|
||||
被预测具有更弱的拉曼强度，并且位于最强模式（模式 8）附近，使得它们在实验光谱中难以区分。
|
||||
此外，在 812.87 cm#super[-1]（模式 10）计算的 A#sub[1] 模式
|
||||
在基面极化配置（xx 和 yy，仅为 0.01）中具有非常弱的拉曼强度，
|
||||
但当偏振沿 z 轴时（1.78）则显示出可观的强度。
|
||||
计算的拉曼张量也与实验和理论结果基本一致，这包括强度最高的模式 E#sub[2]-3，
|
||||
其次是四个强度较低但在实验中清晰可见的模式，包括 E#sub[2]-1、E#sub[2]-2、E#sub[1]-1 和 A#sub[1]-1。
|
||||
E#sub[1]-2 和 E#sub[2]-4 模式位于最强模式 E#sub[2]-3 附近，且具有很弱的拉曼强度（分别为最强模式的0.1%和0.6%），
|
||||
使得它们在实验光谱中难以区分。
|
||||
此外，A#sub[1]-2 模式在基面极化配置（xx 和 yy，仅为 0.01）中具有非常弱的拉曼强度，这导致它在正入射的拉曼实验中通常不可见；
|
||||
但当偏振沿 z 轴时（1.78）则显示出可观测的强度。这与我们的实验结果一致。
|
||||
|
||||
The Raman tensors and frequencies of the negligible-polar phonons were calculated using first-principles methods,
|
||||
and the results are compared with both experimental data and theoretical predictions (@table-nopol).
|
||||
@@ -113,12 +108,16 @@ Among the negligible-polar modes, the E#sub[2] mode at 776 cm#super[-1] (mode 8,
|
||||
|
||||
Additionally, the A#sub[1] mode at 812.87 cm#super[-1] (mode 10) exhibits a very weak Raman intensity in the basal-plane polarization configurations (xx and yy, only 0.01), but shows a significantly higher intensity (1.78) when the polarization is aligned along the z-axis. Since most Raman measurements are performed in a backscattering geometry with incident light along the z-direction (i.e., in-plane polarization) and photon energies well below the band gap, this mode is typically not observed (cite). However, it may become detectable if the incident light has a polarization component along the z-direction (as in our experiment), or under resonance excitation conditions (cite).
|
||||
|
||||
其它峰在其它章节中解释。
|
||||
非零长度的波矢（i.e. 参与散射的声子不在 Gamma 点）导致不同入射配置的峰位具有微小但可观测的差异，如色散图所示。
|
||||
相比于正入射，肩入射时，E2-1与E2-2的间距会减小、E2-2会展宽；E2-3会展宽，同时略微蓝移动。我们的计算结果为xxx，实验结果为xxx。
|
||||
|
||||
Besides, there are other peeks in the experiment.
|
||||
The peek at 796 and 980 are caused by strong-polar phonons which will be discussed later.
|
||||
Besides, there are small peeks at xxx,
|
||||
which could not be explained in perfect 4H-SiC and will be discussed in the next section.
|
||||
|
||||
// 其它峰在其它章节中解释。
|
||||
//
|
||||
// Besides, there are other peeks in the experiment.
|
||||
// The peek at 796 and 980 are caused by strong-polar phonons which will be discussed later.
|
||||
// Besides, there are small peeks at xxx,
|
||||
// which could not be explained in perfect 4H-SiC and will be discussed in the next section.
|
||||
|
||||
// TODO: 将一部分 phonons 改为 phonon modes
|
||||
// 在论文中我们这样来称呼：phonon 对应某一个特征向量，而 modes 对应于一个子空间。
|
||||
|
||||
@@ -28,7 +28,9 @@ For example, when the light is incident along the y direction (phonon modes on t
|
||||
When the light is incident along a direction between z and y,
|
||||
three phonon modes will exist, but vibration in the mixed direction.
|
||||
|
||||
实验发现的确是这样的。
|
||||
理论上预测，不同入射时，会发生什么改变，峰之间的差距有多少；实验中观测到的，差距有多少。
|
||||
|
||||
// 实验发现的确是这样的。
|
||||
|
||||
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.
|
||||
|
||||
@@ -3,13 +3,32 @@
|
||||
#import "@preview/cheq:0.2.2": checklist
|
||||
#show: checklist
|
||||
|
||||
以下进度并不是指，将论文写成完成的稿件；而是指，将论文写成初稿、等待别人给我提意见的状态。
|
||||
|
||||
- [x] 排版：如何让图片固定在原位置？10分钟。
|
||||
- [ ] 排版：旋转内容而不是旋转页面。10分钟。
|
||||
|
||||
剩余工作量估计：
|
||||
|
||||
- introduction：1 小时
|
||||
- method：25.5 小时
|
||||
- results：
|
||||
- 无缺陷：15小时
|
||||
- 弱极性：5小时
|
||||
- 强极性：10小时
|
||||
- 带缺陷：先不做，先做无缺陷的。
|
||||
- conclusion：1 小时
|
||||
- appendix：
|
||||
|
||||
- [/] 文本
|
||||
- [/] introduction
|
||||
- [x] 第一段
|
||||
- [x] 第二段
|
||||
- [/] 第三段
|
||||
- [x] 完成大致结构
|
||||
- [ ] 等待完成论文主体内容后，再完善内容（要强调什么），估计 30
|
||||
- [ ] 第四段，等待主体内容完成，估计 30
|
||||
- [/] method
|
||||
- [x] 几个外延片
|
||||
- [x] 中文
|
||||
- [x] 英文
|
||||
- [x] 调整语言
|
||||
- [/] 坐标轴定义
|
||||
- [x] 中文，20
|
||||
- [x] 考虑图片怎么画，10
|
||||
@@ -22,15 +41,20 @@
|
||||
- [x] 英文，20
|
||||
- [x] 调整画图，20
|
||||
- [x] 调整图片描述，10
|
||||
- [ ] 补充参考文献
|
||||
- [ ] 补充参考文献，估计要两个小时。
|
||||
- [/] 几个外延片
|
||||
- [x] 中文
|
||||
- [x] 英文
|
||||
- [x] 调整语言
|
||||
- [ ] 文章主体内容完成后，根据用到的内容，再调整。估计 30 分钟。
|
||||
- [/] 拉曼实验
|
||||
- [x] 仪器设置
|
||||
- [x] 中文
|
||||
- [x] 英文
|
||||
- [x] 调整语言
|
||||
- [x] 三个入射配置
|
||||
- [ ] 偏振
|
||||
- [/] 建模
|
||||
- [ ] 根据主体内容，补充、调整（缺少对偏振的描述），估计 60 分钟。
|
||||
- [/] 建模，等待主体内容完成再继续补充，估计需要两天（16x60）。
|
||||
- [x] 模型总述
|
||||
- [x] 无缺陷和点缺陷的模型大小、结构
|
||||
- [x] 中文
|
||||
@@ -41,20 +65,20 @@
|
||||
- [ ] 确定要展示哪些结构
|
||||
- [ ] 点缺陷画图（复杂缺陷）
|
||||
- [ ] 面缺陷的模型大小、结构
|
||||
- [/] 第一性原理计算和声子计算的工具
|
||||
- [/] 第一性原理计算和声子计算的工具，等待主体内容完成再继续补充，估计需要120分钟。
|
||||
- [x] 中文
|
||||
- [ ] 英文
|
||||
- [ ] 填充数据和引用
|
||||
- [ ] 拉曼强度的计算
|
||||
- [ ] 拉曼强度的计算，到时候写到模拟中去，估计需要4x60分钟。
|
||||
- [/] results
|
||||
- [x] 总述
|
||||
- [/] 无缺陷
|
||||
- [/] 总述
|
||||
- [/] 声子位置与实验对应
|
||||
- [x] 声子位置与实验对应
|
||||
- [x] 中文
|
||||
- [x] 英文
|
||||
- [x] 调整语言
|
||||
- [ ] 调整画图
|
||||
- [x] 调整画图
|
||||
- [x] 每个位置有 21 个模式
|
||||
- [x] 中文
|
||||
- [x] 英文
|
||||
@@ -68,19 +92,15 @@
|
||||
- [x] 中文
|
||||
- [x] 英文
|
||||
- [x] 调整语言
|
||||
- [/] 表示的表格
|
||||
- [x] 表示的表格
|
||||
- [x] 大致内容
|
||||
- [ ] 可见性
|
||||
- [/] 估算拉曼张量
|
||||
- [x] 中文
|
||||
- [x] 英文
|
||||
- [x] 调整语言
|
||||
- [ ] 填充最终结果
|
||||
- [ ] 模式的表格
|
||||
- [x] 可见性
|
||||
- [/] 模式的表格
|
||||
- [x] 大致内容
|
||||
- [ ] 调整、填充数据
|
||||
- [/] 第一性原理计算
|
||||
- [x] 中文
|
||||
- [ ] 调整、填充数据，估计2小时
|
||||
- [ ] 非零长波矢导致的结果，估计3小时。
|
||||
- [ ] 对比数据，确定要提的内容
|
||||
- [ ] 中文
|
||||
- [ ] 英文
|
||||
- [ ] 调整语言
|
||||
- [ ] 强极性
|
||||
|
||||
Reference in New Issue
Block a user