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@@ -41,12 +41,12 @@ We propose a method to estimate the magnitudes of the Raman tensors of these pho
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This approach is founded on the assumption that the change in polarizability induced by atomic displacements in 4H-SiC
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is primarily determined by the first- and second-nearest neighbors of the atom and the sign of the atomic charge,
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while other factors (mass, bond length, etc.) only have small contributions.
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As a result,
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the phonon modes with the strongest Raman intensities can be predicted
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prior to first-principles calculations and experiments (appendix),
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and the Raman tensors of the calculated phonon modes can be estimated
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before additional first-principles computations.
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Further details are provided in the appendix.
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Consequently, the Raman tensors of the calculated phonon modes can be estimated
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before additional first-principles computations (see appendix for details),
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and the results are summarized in @table-nopol.
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The parameters $a_i$ exhibit significantly larger absolute values compared to $epsilon_i$, $eta_i$, and $zeta_i$,
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indicating the E#sub[2] mode at 756.25 cm#super[-1] in simulation (mode 8)
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possess a much higher Raman intensity than the others.
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The Raman tensors and frequencies of the negligible-polar phonons were calculated using first-principles methods,
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and the results are compared with both experimental data and theoretical predictions (@table-nopol).
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@@ -78,24 +78,13 @@ The peek at 796 and 980 are caused by strong-polar phonons which will be discuss
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Besides, there are small peeks at xxx,
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which could not be explained in perfect 4H-SiC and will be discussed in the next section.
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The method only takes the vibration directions of each atom in each phonon mode,
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leaving the amplitudes unconsidered (see appendix for details),
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and the result was summarized in @table-predmode.
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In the Raman tensors in @table-predmode,
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$a_i$ corresponding to the change of polarizability caused by movement of the Si atoms in A and C layers,
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$epsilon_i$, $eta_i$ and $eta_i$ corresponding to the difference between different bilayers and different atoms.
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Due to the similarity of environment in different bilayers and around different atoms,
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the absolute values of $epsilon_i$, $eta_i$ and $zeta_i$ are expected to be much smaller than that of $a_i$,
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thus the Raman tensors containing $a_i$ are expected to be much larger than those not containing $a_i$.
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// TODO: 将一部分 phonons 改为 phonon modes
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// 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。
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// 也就是说,简并的里面有两个或者无数个 phonon,但只有一个 mode
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#include "table-nopol.typ"
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#include "raman.typ"
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#include "figure-raman.typ"
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// 实验与计算基本相符。对于声子频率,计算总是低估大约 3%。
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// 此外,一些较强的模式在预测无法看到的偏振中也可以看到。例如,一些在 xy 偏振中不应该看到的模式可以被看到了。
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@@ -63,5 +63,5 @@
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// E2 E2 E1 2B1 A1 E1 E2 E2 A1 2B1
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m2[*Polarity*], m(4)[None], m2[Weak], m2[None], m(4)[Weak], m(4)[None], m2[Weak], m2[None],
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)},
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caption: [Negaligible-polarized Phonons at $Gamma$ Point],
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caption: [Negaligible-polarized Phonons at $Gamma$ Point.],
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)<table-nopol>]
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