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陈浩南
2025-05-05 15:09:42 +08:00
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@@ -125,7 +125,7 @@ Phonons at the #sym.Gamma point were used
This approximation is widely adopted and justified by the fact that, This approximation is widely adopted and justified by the fact that,
although the phonons participating in Raman processes are not these strictly located at the #sym.Gamma point, although the phonons participating in Raman processes are not these strictly located at the #sym.Gamma point,
their dispersion near the #sym.Gamma point is continuous with vanishing derivatives, their dispersion near the #sym.Gamma point is continuous with vanishing derivatives,
and their wavevector is very small (about 0.01 nm#sub([-1]) in this paper, and their wavevector is very small (about 0.01 nm#super[-1] in this paper,
which corresponds to only 1% of the smallest reciprocal lattice vector of 4H-SiC), which corresponds to only 1% of the smallest reciprocal lattice vector of 4H-SiC),
as shown by the orange dotted line in @phonon. as shown by the orange dotted line in @phonon.
Therefore, negligible-polar phonons involved in Raman processes Therefore, negligible-polar phonons involved in Raman processes
@@ -138,12 +138,25 @@ There are 21 distinct phonons at the #sym.Gamma point in 4H-SiC.
Among them, 18 phonons are classified as negligible-polar phonons. Among them, 18 phonons are classified as negligible-polar phonons.
This classification is based on the fact that This classification is based on the fact that
the four Si atoms in the primitive cell carry similar Born effective charges (BEC), the four Si atoms in the primitive cell carry similar Born effective charges (BEC),
as do the four C atoms. // TODO: refer as do the four C atoms, as shown in @bec.
In these 18 modes, the vibrations of two Si atoms are approximately opposite to those of the other two Si atoms, In these 18 modes, the vibrations of two Si atoms are approximately opposite to those of the other two Si atoms,
and similarly for the C atoms, and similarly for the C atoms,
leading to cancellations of macroscopic polarity. leading to cancellations of macroscopic polarity.
These phonon modes correspond to twelve irreducible representations of the $\mathrm{C_{6v}}$ point group: $\mathrm{3A_1 + 4B_1 + 3E_1 + 4E_2}$. #figure(
table(columns: 4, align: center + horizon,
table.cell(colspan: 2)[], table.cell(colspan: 2)[*BEC*],
table.cell(colspan: 2)[], [x / y direction], [z direction],
table.cell(rowspan: 2)[Si atom], [A/C layer], [2.667], [2.626],
[B layer], [2.674], [2.903],
table.cell(rowspan: 2)[C atom], [A/C layer], [-2.693], [-2.730],
[B layer], [-2.648], [-2.800],
),
caption: [Born effective charges of Si and C atoms in A/B/C/B layers of 4H-SiC.]
)<bec>
// These phonon modes correspond to twelve irreducible representations of the $\mathrm{C_{6v}}$ point group: $\mathrm{3A_1 + 4B_1 + 3E_1 + 4E_2}$.
18 of them are classified as negligible-polar phonons, 18 of them are classified as negligible-polar phonons,