diff --git a/paper/result/default.typ b/paper/result/default.typ index 5f9c1d6..0b46482 100644 --- a/paper/result/default.typ +++ b/paper/result/default.typ @@ -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" diff --git a/paper/result/perfect/default.typ b/paper/result/perfect/default.typ index 9b9dfec..a588a39 100644 --- a/paper/result/perfect/default.typ +++ b/paper/result/perfect/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" diff --git a/paper/result/perfect/non-polar/default.typ b/paper/result/perfect/non-polar/default.typ index f453b7a..317acfb 100644 --- a/paper/result/perfect/non-polar/default.typ +++ b/paper/result/perfect/non-polar/default.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。 diff --git a/paper/result/perfect/polar/default.typ b/paper/result/perfect/polar/default.typ index 3eadd9c..b472dda 100644 --- a/paper/result/perfect/polar/default.typ +++ b/paper/result/perfect/polar/default.typ @@ -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. diff --git a/paper/todo.typ b/paper/todo.typ index b8ba596..d49fd10 100644 --- a/paper/todo.typ +++ b/paper/todo.typ @@ -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