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9 changed files with 73 additions and 34 deletions

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@@ -34,7 +34,7 @@ These phonons were categorized into two groups according to their electrical pol
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 @fig-raman.
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。

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@@ -84,14 +84,14 @@ The calculated phonon frequencies were in good agreement with experimental value
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 exhibited the highest Raman intensity,
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 exhibited a very weak Raman intensity under the incident light with in-plane polarization
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),
@@ -100,16 +100,38 @@ Thus, it was not typically observed in normal incidence Raman experiments (cite)
不同方向的入射配置会导致微小但可观测的峰位差异。
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。
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
在我们的计算中,相比于正入射,肩入射E2-1与E2-2的间距会减小0.49同时A1-1会红移0.19
在实验中E2-1与E2-2的间距减少0.36A1-1红移了xxxx。
// 186.38835388124227
// 201.84270995851526
Minor but observable peak shifts of negligible-polar phonons were expected between different incidence configurations,
due to non-zero wavevector lengths.
In our calculations, compared to normal incidence,
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,
while the A#sub[1]-1 mode redshifted by 0.19 cm#super[-1].
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],
while the A#sub[1]-1 mode redshifted by xxxx cm#super[-1].
// 191.77252066290447
// 199.03816532139587
#include "figure-nopo-diff.typ"
E1为什么可以被看到。
E1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。
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。
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。
The E#sub[1]-1 mode was observed in normal incidence Raman experiments, despite being theoretically forbidden.
This was attributed to the fact that the incident light was not perfectly aligned along the z-axis,
due to the substrate's slight tilt and the converging angle of the confocal setup.
This was confirmed by tilting the substrate in different directions,
which caused the peak to become more or less pronounced, as shown in the inset figure.
Furthermore, considering the tilt direction (x-direction),
the E#sub[1]-1 mode should be more easily observed in the zxxz and zyxz configurations,
while being more difficult to detect in the zyyz configuration,
which is consistent with our experimental observations.
#include "figure-e1.typ"
// 其它峰在其它章节中解释。
//

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@@ -11,6 +11,15 @@
// 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。
// (没有在图上表示)
半导体中的强极性声子模式强烈地依赖于入射光的方向,
这是由于半导体中原子之间的长程库伦相互作用所致,
表现在散射光谱中Gamma点附近不连续@figure-discont)。
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。
这时会有一个 TO 模式C6v 中的 E1和一个 LO 模式C6v 中的 A1
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
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
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。
Strong-polar phonon modes caused by different incident light directions are different,
due to long-range Coulomb interactions between atoms in semiconductors,
showing discontinuity in the scattering spectra near the #sym.Gamma point (see @figure-discont).
@@ -28,15 +37,25 @@ 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.
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
理论/计算结果与实验对比
// 实验发现的确是这样的。
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。
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。
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.
In our experiment, we found the third, and it satisfied properties we expected.
In our experiments, we found that the third peak only appears when focusing inside the sample.
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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@@ -15,7 +15,7 @@
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(4)[y], m(9)[between z and y, 20#sym.degree to z],
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)],

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@@ -44,21 +44,13 @@
* 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 170-6501 是衬底,其余依次是 532 631 230 126 206。
* 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。
* 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)。
* 2509xx:
* 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。
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
1. 测试正入射数据
* 使用上面选定的共焦针孔、积分时间、离焦距离
* 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。
* 范围170-1100
* ==提前准备好拟合脚本==
2. 测试肩入射数据。
* 测试衬底的肩入射数据。测试五个点。
* 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。
Si 共焦针孔 200
* 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。
* raw:
* 1: 正入射 zxxz 前半
* 2: 正入射 zxxz 后半。
* 3: 侧入射 yxxy 前半。
* 4: 侧入射 yxxy 后半。
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。
* 2: 衬底正入射zxxz略微垫起一些使得E1减小
* 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
*