Environmental Engineering Reference
In-Depth Information
Figure 1.26
Amplitude of the FFT of the long-time region of normalized
HCACF. The black lines in all figures draw the zero-axis for reference.
(a) Ge/Si core-shell NWs. (b) The high-frequency oscillation peaks for
Ge/Si core-shell NWs. The black arrows pinpoint the different oscillation
frequencies.
time region of normalized HCACF. Figure 1.26 shows the FFT of
normalized HCACF for different structures. The FFT amplitude for
Ge/Si core-shell NWs exhibits a dominant peak at low frequency,
which is denoted as
f
0
. All the FFT amplitudes shown here are
normalized by the amplitude of the dominant peak. Moreover, there
exist multiple high-frequency peaks, with much smaller amplitude
compared to that of the dominantpeak.
Themultipleoscillationpeaksobservedinthefrequencydomain
for core-shell NWs are very similar to the confinement effect of
the acoustic wave (coherent long-wavelengthphonon) in a confined
structure. We record the high-frequency peaks marked by the
black arrows in Fig. 1.26, and compare them with the frequency
of the dominant peak
f
0
. We find that the relation between the
frequencies of these high-frequency peaks and the dominant peak
f
0
is very close to the eigenfrequency of the transverse modes
for a wire with the square cross-section. This good agreement of
oscillation frequency suggests that the intriguing oscillation effect
results from the frequency quantization of the transverse modes as
a consequenceof structure confinementin the transverse direction.
In single-component homogeneous NWs, atoms on the same
cross-section plane have the same sound velocity, so that the
transversemotionisdecoupledfromthelongitudinalmotion.Thisis
whytheoscillationsignalisnotprobedbythelongitudinalHCACFin
SiNWs.However,incore-shellNWs,atomsonthesamecross-section
