diff --git a/paper/method/experiment/default.typ b/paper/method/experiment/default.typ index 4be7d69..4860836 100644 --- a/paper/method/experiment/default.typ +++ b/paper/method/experiment/default.typ @@ -55,5 +55,6 @@ todo 关于正入射和侧入射的对比：拟合得到结果、画曲线图、画箱图 极性模式对比。有两个方面需要对比。一个是，正、侧入射的不同，说明分裂的大小与我们的计算是否一致，LOPC是否会在其它偏振下出现；一个是，对正入射时E1的出现作解释。 +散射光路对不同偏振的响应不同，因此需要乘以一个系数。 探索：为什么对于A1的拟合，结果会差两倍？ \ No newline at end of file diff --git a/paper/result/perfect/default.typ b/paper/result/perfect/default.typ index 688b654..2ccd741 100644 --- a/paper/result/perfect/default.typ +++ b/paper/result/perfect/default.typ @@ -1,47 +1,19 @@ == Phonons in Perfect 4H-SiC -不同方向入射光的声子位置不同。我们只研究 Gamma 附近的那些。 +我们将声子被分为两类讨论： + 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； + 强极性声子模式，在拉曼光谱中电极性效应是可观测的，不可以被忽略。 -参与拉曼散射的声子的波矢等于入射光与散射光的波矢差。 -因此，在我们的实验（绿光和紫外光的背散射）中，参与拉曼散射的声子都位于 Gamma 点附近，且不同的入射方向对应的声子波矢不同。 -对于正入射，声子大致位于 Gamma-A 线上；对于沿x方向的边入射，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 - 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 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 lied approximately at the #sym.Gamma–A and #sym.Gamma–K lines, respectively. -For grazing incidence, - the relevant phonons did not reside on any high-symmetry lines and were therefore not depicted in the figure. - -#include "figure-discont.typ" - -每个点都有 21 个声子模式。我们把它分成 18 个极性很小的和 3 个极性很强的两类。 - -对于每一个 Gamma 附近的点，都有 21 个声子模式（简并模式按简并数计）。 -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 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), +These phonons were categorized into two groups and discussed separately, according to their electrical polarities: + phonons with negligible polarities (i.e., zero or very weak electrical polarity), 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, + and phonons with strong polarities 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 was also illustrated and compared with Raman experiment in @figure-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" +#include "figure-discont.typ" #include "non-polar/default.typ" #include "polar/default.typ" diff --git a/paper/result/perfect/figure-discont.typ b/paper/result/perfect/figure-discont.typ index afbb424..72278ba 100644 --- a/paper/result/perfect/figure-discont.typ +++ b/paper/result/perfect/figure-discont.typ @@ -4,8 +4,10 @@ (a) Phonon dispersion of 4H-SiC along the A–#sym.Gamma–K high-symmetry path. (b) Magnified view of the boxed region in (a). (c) Magnified view of the boxed region in (b). - The orange dashed lines mark the phonon wavevectors involved in Raman scattering - with green laser light under normal and edge incidence configurations. + The orange dashed lines marked the phonon wavevectors involved in Raman scattering + with green laser light (532 nm) under normal and edge incidence configurations. + The phonons relevant to grazing incidence configuration did not reside on any high-symmetry lines + and were therefore not depicted in the figure. ], placement: none, ) diff --git a/paper/result/perfect/non-polar/default.typ b/paper/result/perfect/non-polar/default.typ index f00a1f2..da62801 100644 --- a/paper/result/perfect/non-polar/default.typ +++ b/paper/result/perfect/non-polar/default.typ @@ -1,5 +1,7 @@ === Phonons with Negligible Polarities +对弱极性声子的分析首先从理论出发，然后结合 + 对弱极性声子的理论分析，首先使用 Gamma 点的声子来近似，然后再讨论不同入射方向导致的差异。 使用Gamma 点的声子来近似，基于这样的事实：这些声子的色散曲线在 Gamma 点附近连续且非常接近 Gamma 点，并且已经被广泛使用 @_n-sic_2008。 @@ -8,7 +10,7 @@ Negligible-polar phonons were theoretically analyzed, 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. + and has been widely adopted in the literature @_n-sic_2008. 18 个声子属于 12 个表示。拉曼张量的形状可以确定，大小不能。 @@ -43,7 +45,7 @@ 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，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，这与实验和第一性原理计算结果一致。 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) @@ -55,26 +57,54 @@ 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]-3 mode (at about 756.25 cm#super[-1] in simulation) +Our analysis gave the result that the E#sub[2]-3 mode 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. + which is consistent with experimental and first-principles calculation results in the following text. 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. #include "table-nopol.typ" -我们使用第一性原理计算得到了频率和拉曼张量的大小，并与我们的结果进行了比较。 +我们做了计算，估计哪些峰可以看到、哪些峰看不到。 -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）。 +使用第一性原理计算得到了声子频率和拉曼张量的大小。 +我们的计算表明，E#sub[2]-1 E#sub[2]-2 E#sub[1]-1 A#sub[1]-1 E#sub[2]-3 模式的拉曼强度较高，并且被报道在绝大多数的拉曼实验中可以看到。 +A#sub[1]-2 被报道在一些实验中可以观测到而在另外一些实验中不可以观测到(cite)。 +我们的计算表明它在面内偏振下拉曼散射强度非常弱，但在 z 轴偏振下有可观测的强度； + 因此在正入射拉曼实验中可能难以看到，但在侧入射时通过选取合适的偏振配置应该可以观察到。 +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%），在报道的实验中都不可见。 +E#sub[1]-2 与最强模式 E#sub[2]-3 表示不同，我们认为，通过选取合适的偏振配置，可能可以在实验中观察到。 + +The Raman tensors and frequencies of the negligible-polar phonons were calculated using first-principles methods. +The results showed that + the E#sub[2]-1, E#sub[2]-2, E#sub[1]-1, A#sub[1]-1, and E#sub[2]-3 modes possess relatively high Raman intensities +The calculated phonon frequencies were in good agreement with experimental values, + with a slight underestimation of 2-5%, + which might be attributed to the known tendency of the PBE functional underestimating interatomic forces (cite). +The calculated Raman tensors were also consistent with both experimental and theoretical results. +Among negligible-polar modes, the E#sub[2]-3 mode showed the highest Raman intensity, + followed by four modes with lower intensities that were also visible in normal incidence Raman experiments, + including the E#sub[2]-1 mode, the E#sub[2]-2 mode, the E#sub[1]-1 mode, and the A#sub[1]-1 mode. +The E#sub[1]-2 mode and E#sub[2]-4 mode were not visible in our Raman experiments, + as they were located close to the most intense E#sub[2]-3 mode (only about 10 cm#super[-1] away) + with very weak Raman intensities (only 0.1% and 0.6% of the E#sub[2]-3 mode, respectively). +Additionally, + the A#sub[1]-2 mode had only a very weak Raman intensity under the incident light with in-plane polarization + (only 0.01), + but showed an observable intensity when the polarization is along the z-axis (1.78). +Thus, it was not typically observed in normal incidence Raman experiments (cite), + but could be clearly detected in edge incidence configurations in our experiments. + + +我们做了实验，比别人多看到了几个峰；和计算结果比对良好。 + +拉曼散射实验在衬底上进行，并与第一性原理计算结果进行了比较。 +在我们的实验中，除了 E#sub[2]-4 以外的弱极性模式对应的拉曼散射峰都被观察到，多于其它实验； + 这包括 A#sub[1]-2 在 xzzx 下可以观察到， + 以及 E#sub[1]-2 在 xzyx 下通过额外延长积分时间而观察到。 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]-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。 +计算的拉曼张量也与实验和理论结果基本一致。 The Raman tensors and frequencies of the negligible-polar phonons were calculated using first-principles methods, and the results were compared with both experimental data and theoretical predictions (@table-nopol). @@ -95,15 +125,20 @@ Additionally, Thus, it was not typically observed in normal incidence Raman experiments (cite), but could be clearly detected in edge incidence configurations in our experiments. -理想情况下不允许存在的效应被观察到。 -这包括不同入射方向下，弱极性峰位的微小移动，以及 E#sub[1]-1 模式在正入射中的可见性。 +#include "figure-raman.typ" + +E#sub[1]-1 模式在正入射中可见。 + +E#sub[1]-1 模式在正入射拉曼实验中被观察到尽管在理论上是不允许的，这被认为是因为入射光并非完全沿c轴入射。 +如图所示，由于非零的数值孔径，激光汇聚到样品上时存在一个锥形角度（不完全平行于c轴），使得 E#sub[1]-1 模式在正入射中总是可见的。 +由于衬底斜切（沿着x方向），对于 zxxz 和 zxyz 配置，入射光或散射光的偏振将具有更多的 z 分量，从而使 E#sub[1]-1 模式的强度增加。 +通过略微倾斜衬底可以补偿斜切导致的效应，如附图所示。 + +不同入射方向下弱极性峰位的微小移动被观察到，这是由于非零波矢长度的声子引起的。 在我们的计算中，从正入射到肩入射，E2-3的峰位几乎不变，E2-1与A1-1会有可观测的蓝移，同时E2-2会有可观测的红移。 实验结果与计算结果基本一致，如图如表所示。 -E1模式在正入射中可以看到，尽管理论上不应该。 -这被认为是因为入射光并非完全沿z轴入射，由于衬底斜切和共聚焦汇聚角。 -不同方向偏振的结果印证了我们的猜想，如图所示。同时，略微倾斜衬底可以使这个峰变高或变低，如附图所示，这印证了我们的猜想。 -Some effects absent in the ideal model were observed experimentally, +Some effects absent in previous theory were observed experimentally, including minor but observable peak shifts of negligible-polar phonons between different incidence configurations, and the observability of the E#sub[1]-1 mode in normal incidence Raman experiments. The peak shifts were considered caused by the non-zero wavevector lengths of phonons. diff --git a/paper/result/perfect/figure-raman.typ b/paper/result/perfect/non-polar/figure-raman.typ similarity index 100% rename from paper/result/perfect/figure-raman.typ rename to paper/result/perfect/non-polar/figure-raman.typ diff --git a/paper/result/perfect/non-polar/table-nopol.typ b/paper/result/perfect/non-polar/table-nopol.typ index c1a53a1..71a6756 100644 --- a/paper/result/perfect/non-polar/table-nopol.typ +++ b/paper/result/perfect/non-polar/table-nopol.typ @@ -39,7 +39,7 @@ [0.17], [1.13], [2.43], [2.83], [1.79], [0.09], [88.54], [0.50], [0.01], [1.78], [Experiment result #linebreak() (a.u.)], // E2 E2 E1 A1 E1 E2 E2 A1 - [0.15], [1.11], [0.68], [1.64], [3.15], [Invisible], [88.54], [Invisible], [Invisible], [2.97], + [0.15], [1.11], [0.68], [1.64], [3.15], [ ], [88.54], [Invisible], [Invisible], [2.97], table.cell(rowspan: 2)[*Raman Shift of Different Incidence Directions*], 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d50f2bf..4d719ad 100644 --- a/画图/拉曼结果拟合/251008/join_and_move.ipynb +++ b/画图/拉曼结果拟合/251008/join_and_move.ipynb @@ -1,3 +1,3 @@ version https://git-lfs.github.com/spec/v1 -oid sha256:46892a880300dc92dd9462f0cccc8f14cfef00f7d8cc072555a70d67dba036bc -size 2247986 +oid sha256:fcc5b3d6d45f7459c44d23c63bb77efaf52d13573da01af9216d5c4ea09a26e0 +size 4978241 diff --git a/画图/拉曼结果拟合/README.md b/画图/拉曼结果拟合/README.md index fb535a8..70f86fa 100644 --- a/画图/拉曼结果拟合/README.md +++ b/画图/拉曼结果拟合/README.md @@ -52,7 +52,13 @@ * 1: 摆拍几张照片 * 2: 衬底侧入射 xzzx xzyx 离焦 0 针孔 100 积分时间 5 积分次数 10 范围 150-650 580-1050 11 个点 * 3: 衬底正入射 zxxz zxyz 离焦 0 针孔 100 积分时间 5 积分次数 10 范围 150-650 580-1050 11 个点 +* 251019: + * 1: 衬底侧入射 xzyx 观察 E12 离焦 0 针孔 100 积分时间 30 积分次数 10 范围 600-790 5 个点 + * 2: 正入射衬底，将zxxz稍微垫高一点的结果。垫高x方向的某个方向。先分别测试不垫高和垫高的结果，确认有明显差别后再多测试几个点。 + * 3: 衬底正入射，离焦 0 针孔 100 积分时间 5 积分次数 10 范围 580-1050，1 是衬底，其余依次是 532 631 230 126 206 取 11 个点。 + * 4: 外延层侧入射， * 2510xx: * 1: 正入射衬底，将zxxz稍微垫高一点的结果。垫高x方向的某个方向。 * 2: 外延层侧入射。 + * 3: 衬底侧入射 xzyx 延长积分时间以得到 E12