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@@ -34,7 +34,7 @@ These phonons were categorized into two groups according to their electrical pol
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where atoms of the same species vibrated in phase,
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resulting in strong electrical polarization and observable effects in Raman spectra
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(colored lines in @figure-discont).
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The categorized was also illustrated and compared with Raman experiment in @fig-raman.
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The categorized was also illustrated and compared with Raman experiment in @figure-raman.
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极性不同的模式有着不同的行为,因此被分开讨论。
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@@ -84,14 +84,14 @@ The calculated phonon frequencies were in good agreement with experimental value
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with a slight underestimation of 2-5%,
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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 Raman tensors were also consistent with both experimental and theoretical results.
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Among negligible-polar modes, the E#sub[2]-3 mode exhibited the highest Raman intensity,
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Among negligible-polar modes, the E#sub[2]-3 mode showed the highest Raman intensity,
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followed by four modes with lower intensities that were also visible in normal incidence Raman experiments,
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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.
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The E#sub[1]-2 mode and E#sub[2]-4 mode were not visible in our Raman experiments,
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as they were located close to the most intense E#sub[2]-3 mode (only about 10 cm#super[-1] away)
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with very weak Raman intensities (only 0.1% and 0.6% of the E#sub[2]-3 mode, respectively).
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Additionally,
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the A#sub[1]-2 mode exhibited a very weak Raman intensity under the incident light with in-plane polarization
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the A#sub[1]-2 mode had only a very weak Raman intensity under the incident light with in-plane polarization
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(only 0.01),
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but showed an observable intensity when the polarization is along the z-axis (1.78).
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Thus, it was not typically observed in normal incidence Raman experiments (cite),
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@@ -100,16 +100,38 @@ Thus, it was not typically observed in normal incidence Raman experiments (cite)
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不同方向的入射配置会导致微小但可观测的峰位差异。
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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。
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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。
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我们的计算结果为xxx,实验结果为xxx。
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微小但可观测的峰位移动应该存在于不同入射配置的峰位中,因为非零的波矢长度。
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在我们的计算中,相比于正入射,肩入射的E2-1与E2-2的间距会减小0.49,同时A1-1会红移0.19。
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在实验中,E2-1与E2-2的间距减少0.36,A1-1红移了xxxx。
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// 186.38835388124227
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// 201.84270995851526
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Minor but observable peak shifts of negligible-polar phonons were expected between different incidence configurations,
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due to non-zero wavevector lengths.
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In our calculations, compared to normal incidence,
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the spacing between the E#sub[2]-1 mode and E#sub[2]-2 mode decreased by 0.49 cm#super[-1] under edge incidence,
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while the A#sub[1]-1 mode redshifted by 0.19 cm#super[-1].
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In our experiments, the spacing between the E#sub[2]-1 mode and E#sub[2]-2 mode decreased by 0.36 cm#super[-1],
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while the A#sub[1]-1 mode redshifted by xxxx cm#super[-1].
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// 191.77252066290447
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// 199.03816532139587
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#include "figure-nopo-diff.typ"
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E1为什么可以被看到。
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E1在正入射中可以看到,尽管理论上不应该。
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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。
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通过向不同方向倾斜衬底,我们可以使这个峰变高或变低,如附图所示。
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此外,考虑到斜切方向(x方向),E1模式应该更容易在zxxz和zyxz中看到,而在zyyz中更难看到,这与实验一致。
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The E#sub[1]-1 mode was observed in normal incidence Raman experiments, despite being theoretically forbidden.
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This was attributed to the fact that the incident light was not perfectly aligned along the z-axis,
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due to the substrate's slight tilt and the converging angle of the confocal setup.
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This was confirmed by tilting the substrate in different directions,
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which caused the peak to become more or less pronounced, as shown in the inset figure.
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Furthermore, considering the tilt direction (x-direction),
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the E#sub[1]-1 mode should be more easily observed in the zxxz and zyxz configurations,
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while being more difficult to detect in the zyyz configuration,
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which is consistent with our experimental observations.
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#include "figure-e1.typ"
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// 其它峰在其它章节中解释。
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//
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@@ -11,6 +11,15 @@
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// 若考虑到到入射光不是严格沿着 z 方向,而是有一个小的角度(例如 10 度),则此时有一个声子模式沿着 x 方向,另外两个声子模式则为 y-z 两个方向的混合。
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// (没有在图上表示)
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半导体中的强极性声子模式强烈地依赖于入射光的方向,
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这是由于半导体中原子之间的长程库伦相互作用所致,
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表现在散射光谱中,Gamma点附近不连续(见@figure-discont)。
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具体来说,当入射光沿着 z 方向时,起作用的是 A-Gamma 线上的声子模式(图中的上半部分的橘线),它们适用于群 C6v。
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这时会有一个 TO 模式(C6v 中的 E1)和一个 LO 模式(C6v 中的 A1)。
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而当沿着 y 方向入射时,起作用的是 Gamma-K 线上的声子模式(图中下半部分的橘线),它们不再适用于群 C6v,而只适用于群 C2v;
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这时将会出现三个模式,包括一个LO(沿y方向振动,对应C2v中的A1)和两个TO模式(根据振动方向,命名为B2-x和B2-y,对应C2v中的B1和B2)。
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当入射光不是严格沿着坐标轴方向,而是在xOy面内呈现一定的夹角时(掠入射,以及考虑了斜切的正入射),则此时有一个声子模式沿着 x 方向,另外两个声子模式则为 y-z 两个方向的混合。
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Strong-polar phonon modes caused by different incident light directions are different,
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due to long-range Coulomb interactions between atoms in semiconductors,
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showing discontinuity in the scattering spectra near the #sym.Gamma point (see @figure-discont).
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@@ -28,15 +37,25 @@ For example, when the light is incident along the y direction (phonon modes on t
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When the light is incident along a direction between z and y,
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three phonon modes will exist, but vibration in the mixed direction.
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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。
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将理论/计算结果与实验对比。
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// 实验发现的确是这样的。
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我们将计算与实验结果进行了对比。衬底中的LO峰与plasmon耦合形成LOPC峰,因此与计算结果大不相同。
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对于TO峰,在正入射中,它与E2-3模式的距离为xxx;在掠入射中,它与E2-3模式的距离为xxx。
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Many Raman experiments on 4H-SiC with incident light along the z direction have observed two peaks.
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However, no experiments have reported three peaks with incident light along other directions.
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In our experiment, we found the third, and it satisfied properties we expected.
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In our experiments, we found that the third peak only appears when focusing inside the sample.
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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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@@ -15,7 +15,7 @@
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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(4)[y], m(9)[between z and y, 20#sym.degree to z],
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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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@@ -44,21 +44,13 @@
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* 3: 测试外延片和衬底。离焦 0 针孔 100 积分时间 5 积分次数 10 范围 170-650,1 是衬底,其余依次是 532 631 230 126 206。
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* 第一次测试正常完成,全程不移动光谱,但光谱仍然出现偏移。因此仍然需要以某个峰为基准,进行测量。
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* 第二次测试一半时软件崩溃,导致光谱发生移动。此后测试时,需要禁止软件启动时初始化,并且在设定好参数后,立即重启软件(使得软件崩溃后再打开,不需要移动光谱)。
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* 2509xx:
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* 1: 测试衬底数据,用来给论文的无缺陷数据使用。包括正入射 zyyz yzxz,肩入射 yzxy yzzy,以及一个用来自己比对(不写到论文里)的 yxxy。
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离焦 0 针孔 100 积分时间 5 积分次数 10 范围 170-1100 测试三个点,忽略光谱移动等误差,论文用三个来平均。
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1. 测试正入射数据。
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* 使用上面选定的共焦针孔、积分时间、离焦距离。
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* 依次换片:硅片,衬底,12345号片,硅片。然后再反过来。一次只测试一个点。
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* 范围:170-1100
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* ==提前准备好拟合脚本==
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2. 测试肩入射数据。
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* 测试衬底的肩入射数据。测试五个点。
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* 按照某一个标准,测试各个样品的肩入射数据。仅测试yy和yz偏振。
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Si 共焦针孔 200
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* 250923: 对衬底结果的一些补充。离焦 0 针孔 100 积分时间 5 积分次数 10 范围 170-650 580-1000 测试11个点。
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* raw:
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* 1: 正入射 zxxz 前半。
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* 2: 正入射 zxxz 后半。
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* 3: 侧入射 yxxy 前半。
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* 4: 侧入射 yxxy 后半。
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离焦 0 针孔 100 积分时间 5 积分次数 10 范围 170-650 550-1000 各测试11个点。
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* 2: 衬底正入射zxxz,略微垫起一些,使得E1减小。
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* 3: 测试外延层正入射数据。离焦 0 针孔 100 积分时间 5 积分次数 10 范围 170-1000 测试十个点,手动移动光谱并手动对齐。
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*
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