  Gallium selenide (GaSe) is one of layered group-III metal monochalcogenides,
which has an indirect bandgap in monolayer and direct bandgap in bulk unlike
other conventional transition metal dichalcogenides (TMDs) such as MoX2 and WX2
(X=S and Se). Four polytypes of bulk GaSe, designated as beta-, epsilon-,
gamma-, and delta-GaSe, have been reported. Since different polytypes result in
different optical and electrical properties even for the same thickness,
identifying the polytype is essential in utilizing this material for various
optoelectronic applications. We performed polarized Raman measurement on GaSe
and found different ultra-low-frequency Raman spectra of inter-layer
vibrational modes even for the same thickness due to different stacking
sequences of the polytypes. By comparing the ultra-low-frequency Raman spectra
with theoretical calculations and high-resolution electron microscopy
measurements, we established the correlation between the ultra-low-frequency
Raman spectra and the stacking sequences for trilayer GaSe. We further found
that the AB-type stacking is more stable than the AA'-type stacking in GaSe.
