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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,
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,
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),
as shown by the orange dotted line in @phonon.
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.
This classification is based on the fact that
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,
and similarly for the C atoms,
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,