We present ultrafast spectroscopic investigations of the coherent acoustic vibrations of Au/SiO2 and Au/TiO2 core–shell nanoparticles (NPs) upon excitation of the Au surface plasmon resonance. The oscillations are detected in the region of the interband transitions of Au in the deep-ultraviolet, where they appear in the form of intensity modulations with no changes in the spectra. For the Au/SiO2 NPs, the oscillation period (typically ∼10 ps) is similar to that of bare Au NPs having a size identical to that of the core, implying a negligible coupling of the core with the shell. For Au/TiO2 NPs, significantly slower (∼20 ps) oscillations appear, whose period is identical to that of a bare gold NP having the same total diameter, implying that the Au/TiO2 NPs can be treated as a single object. This may due to the strong chemical interaction at the gold/TiO2 interface. Finally, the amplitude modulations are a consequence of the modifications of the band structure of the Au NP, resulting from the strain due to the phonons, which may affect the joint density of states.

Studies of acoustic vibrations in nanoscale metals can provide fundamental insight into the mechanical properties of nanomaterials as a function of size, shape, composition, and surroundings, with potential applications in optical communication,1 photoacoustic imaging,2,3 nanoelectromechanical devices,4 sensor technology,5,6 etc. In this respect, it is important to investigate the role of the solid or liquid environment, as it will affect the mechanical behavior of the nanoparticle (NP).

Ultrafast pump-probe spectroscopy has emerged as a powerful tool for the investigations of acoustic phonons in metallic NPs.7–9 In these experiments, the pump laser primarily heats the electron gas and modifies the electron distribution within the particles. Electron–electron scattering occurs within tens of femtosecond (fs) leading to a “hot” Fermi–Dirac distribution. This is followed by cooling in a few picosecond via electron–phonon scattering, resulting in a rapid thermal expansion of the particle, and excitation of coherent acoustic phonons, which translate into a periodic variation in size and shape of the NP. Thereafter, the thermally expanded NP lattice dissipates energy to the environment.10–12 The strong optical absorption of the localized surface plasmon resonance (LSPR) and its sensitivity to changes in the size and shape of the NP result in modulations of the transmission of a time-delayed probe laser pulse in transient absorption (TA) experiments. In all of the above-mentioned studies where the coherent phonons in metallic NPs were probed via the LSPR band, a modulation of the latter's central energy was observed. Frequency and damping of the oscillations are, thus, directly reflecting the vibrational period of the breathing mode and its energy dissipation, respectively, and they are strongly dependent on the size and shape of the NPs, and on their composition.12 There are three mechanisms that translate the mechanical oscillations into changes in the LSPR frequency: (1) shape changes during oscillation; (2) electron density (ED) changes due to changes in the NP volume; (3) changes in interband transition energies through the deformation potential (DP).

The initial studies focused on bare nanospheres (in particular, Au NPs) and were then extended to various shapes and the presence of a surrounding medium. The experiments mainly focused on the frequency shift13–15 and damping16,17 of the LSPR modulated by the vibrations. Hartland and co-workers18 studied the coherent vibrational motion in ∼25 nm radius Au particles in an aqueous solution. They found the significant contribution of hot-electron pressure effects in the coefficient for thermal expansion of the particles, with the vibrational period being related to the NP mean radius and the damping time to the width of the size distribution. In their experiment, all the absorbed energy is assumed to go into expanding the NP, leading to a 0.4% increase in its radius for 400 nm pump pulses excitation (0.6 μJ/pulse). Pelton and co-authors16 used an array of highly uniform Au bipyramids and deduced that the damping is due to a combination of intrinsic (homogeneous) damping and damping by the surrounding solvent (e.g., water, methanol, ethylene, and glycerol), indicating that the widely considered dephasing due to the distribution of NP sizes is not as prominent as previously concluded.

Coherent acoustic vibrations were also reported in multi-material NPs, such as segregated bimetallic systems, e.g., core–shell Au–Pb, Au–Ag, Au–Pd, and Au–Ag particles.10,19–23 It was found that the frequency of the breathing mode was strongly dependent on the shell thickness10 and could be modeled using classical continuum mechanics.20 The bimetallic core–shell NPs can be assumed to be homogeneously heated by the pump laser pulse because of the efficient internal thermalization (for relatively small NP, up to ∼100 nm).10,21 Metal-dielectric core–shell NPs have also been investigated, such as Ag/SiO2 and Au/SiO2.10,24–28 The vibrational modes of the core–shell particle are described in terms of a weak or a strong mechanical coupling between the core and the shell.25–27 Indeed, in this case, the laser-generated heat is initially confined to the metal part, which may or may not couple to the dielectric.25 It is interesting to note that most of the theoretical efforts aimed at rationalizing the observation of coherent phonons in core–shell NPs have focused on the energy shifts of the LSPR,25,29,30 whereas vibrational amplitudes have received less attention.

In previous fs TA studies of Au NPs,31,32 we identified three bands in the hitherto unexplored UV region (3.4–4.5 eV), which we assigned to the interband X4 → X1 and L2 → L1 transitions and the intraband L5 → L2/L6 → L3 transitions. They exhibit coherent acoustic phonon oscillations riding on an exponentially decaying background. In these papers,31,32 we did not discuss the oscillatory response of the interband transitions. The goal of the present work is to examine them in detail in the case of Au/SiO2 and Au/TiO2 core–shell NPs dispersed in water. While coherent phonons have already been reported in the case of the former,27 the latter has not been investigated. However, one study has reported coherent oscillations of Au NPs embedded in a TiO2 film.33 Here, we find that while the coherent phonon oscillations in Au/SiO2 are the same as for bare Au NPs having the same size as the core, for Au/TiO2 NPs, they are identical to those of bare NPs having the same size as the entire core–shell NP. Furthermore, contrary to the case of the LSPR band where the coherent phonon oscillations affect the energy, the case of the interband transitions shows a modulation of the oscillator strength. Our results underscore the coupling between the core Au NP and the dielectric shell.

The sample preparation, description of the setup, and the calculations of the oscillation frequencies are presented in the supplementary material. The diameter of the NPs is ∼65 nm with a ∼25 nm diameter Au core and ∼20 nm thickness shell.

Time-energy TA maps are shown in Fig. 1 for Au/SiO2 NPs (a) and Au/TiO2 NPs (b). The traces clearly show the negative band at ∼3.8–3.85 eV and positive band at <3.6 eV, consisting of an exponential background, discussed in Refs. 31 and 32, and coherent oscillations, which are more prominent in the negative feature. For each system, the oscillation frequency is the same over the entire range of the negative band and the oscillations almost completely damp out within 120 ps for Au/SiO2 (a) and 80 ps for Au/TiO2 NPs (b). The oscillations show as a modulation of the width of the signal, whose central energy seems unchanged [see inset to Fig. 1(a), which shows the peak shift relative to 3.8 eV]. This is significantly different to the LSPR response whose central energy is modulated at the frequency of the phonons.16,18,29,30,34,35 In the case of Au/SiO2, the oscillation frequency is unchanged compared to that of bare Au NPs of identical radius as the core,10 in agreement with previous reports27 (Table I). The latter work also found that the oscillation frequency does not depend on the shell thickness. These two observations point to a weak coupling of the core with the SiO2 shell. In the case of Au/TiO2 NPs [Fig. 2(b)], the oscillatory pattern is very different compared to Fig. 2(a): the frequency is significantly smaller (almost half) and the damping time shorter.

FIG. 1.

Transient absorption maps of Au/SiO2 NPs (a) and Au/TiO2 NPs (b) as a function of probe energy and time delay between pump and probe. The inset in (a) shows the changes in the peak energy position of the ∼3.8 eV band with delay time (the relative shift: peak energy −3.78 eV, which is the peak energy).

FIG. 1.

Transient absorption maps of Au/SiO2 NPs (a) and Au/TiO2 NPs (b) as a function of probe energy and time delay between pump and probe. The inset in (a) shows the changes in the peak energy position of the ∼3.8 eV band with delay time (the relative shift: peak energy −3.78 eV, which is the peak energy).

Close modal
TABLE I.

Oscillation frequencies, amplitudes (A1, A2), and damping constants (τ1, τ2) of the oscillatory traces of Au/SiO2 and Au/TiO2 NPs (Fig. 2).

Sample Ω1 (GHz) Ω2 (GHz) A1 A2 τ1 (ps) τ2 (ps)
Au/SiO2  101 ± 6.7  ⋯  ⋯  ⋯  43.6 ± 5.3  ⋯ 
Au/TiO2  55.8 ± 6.7  111 ± 3.4  78%  22%  18.4 ± 1.7  17.1 ± 5.1 
Sample Ω1 (GHz) Ω2 (GHz) A1 A2 τ1 (ps) τ2 (ps)
Au/SiO2  101 ± 6.7  ⋯  ⋯  ⋯  43.6 ± 5.3  ⋯ 
Au/TiO2  55.8 ± 6.7  111 ± 3.4  78%  22%  18.4 ± 1.7  17.1 ± 5.1 
FIG. 2.

(a) and (c) Oscillatory traces of the Au/SiO2 and Au/TiO2 NPs upon LSPR excitation. The probe energy is 3.8 eV. (b) and (d) Power spectra of the traces in panels (a) and (c), obtained by Fourier transformation, blue rectangles for experimental traces, and solid black lines for the fit traces.

FIG. 2.

(a) and (c) Oscillatory traces of the Au/SiO2 and Au/TiO2 NPs upon LSPR excitation. The probe energy is 3.8 eV. (b) and (d) Power spectra of the traces in panels (a) and (c), obtained by Fourier transformation, blue rectangles for experimental traces, and solid black lines for the fit traces.

Close modal

Using Eq. (S1), we subtracted the exponential part of the transient band around 3.8 eV and extracted the oscillatory part, which is shown in Fig. 2. The fit parameters are given in Table I. The red circles represent the experimental data, and the solid black lines are the fits. Note that the inconsistency in Fig. 2(a) between the fits and experiment data at t <10 ps is due to the strong TA background signal at early time delays that affects the extraction of the oscillatory part. For Au/SiO2, the fit with only one mode having a period of ∼ 9.9 ps (ω: ∼101 GHz) and a damping constant of 43.6 ± 5.3 ps (Table I) reproduces the oscillatory pattern after 10 ps. The power spectra obtained by Fourier transformation of the experimental and fitted traces are shown in Fig. 2(b). They mainly show a peak at a frequency of ∼101 GHz with a width of 21.2 GHz. For Au/TiO2, the fit of the oscillatory component [Fig. 1(c)] yields the parameters given in Table I, with two modes of τ: ∼8.9 ps (ω: ∼111 GHz) and τ: ∼17.9 ps (ω: ∼55.8 GHz) and damping constants of 17.1 ± 5.1 and 18.4 ± 1.7 ps, respectively. This is also confirmed by the power spectra in Fig. 2(d), which clearly shows two oscillation frequencies: the fundamental at ∼56 GHz and its first harmonic at ∼111 GHz, at a ratio of 0.78:0.22 and with widths of 41.9 and 38.9 GHz, respectively. Compared to bare or to Au/SiO2 NPs, this change of oscillation frequency for Au/TiO2 NPs10 is much larger than reported in the case of core–shell Au–Pb NPs where it decreases by ∼25% for the largest shell thicknesses, or in the case of Ag/SiO2 where it decreases by ∼15%.

Table II compares the oscillation frequencies reported here to those of bare NPs of identical diameter to the core only or to the core–shell NP. It can be noted that for Au/SiO2 NPs with a core diameter of 25 nm and a shell thickness of 20 nm, the oscillation frequency is to within 10%–20% similar to that of the bare NP having a diameter of 25 nm.18 For Au/TiO2 NPs, the oscillation frequency is almost identical (to within 10%–15%) to that of a large bare Au NP having a diameter of 60 nm. Thus, while in the case of the SiO2 shell, the core appears decoupled from the shell, for the case of the TiO2 shell, the core–shell NP behaves as a bare Au NP having the same total diameter, reflecting a strong coupling of core and shell.

TABLE II.

Comparison between experimental oscillation frequencies of bare Au,18 and Au/SiO2 and Au/TiO2 NPs.

Sample Au radius/shell thickness (nm) Total diameter (nm) Ω1 (GHz) Ω2 (GHz)
Bare Au in water18   12.5  25  120   
Bare Au in water18   25  50  62.5   
Bare Au in water18   30  60  57.1   
Au/SiO2 (this work)  12.5/20  65  101 ± 6.7   
Au/TiO2 (this work)  12.5/20  55.8 ± 6.7  111 ± 3.4 
Sample Au radius/shell thickness (nm) Total diameter (nm) Ω1 (GHz) Ω2 (GHz)
Bare Au in water18   12.5  25  120   
Bare Au in water18   25  50  62.5   
Bare Au in water18   30  60  57.1   
Au/SiO2 (this work)  12.5/20  65  101 ± 6.7   
Au/TiO2 (this work)  12.5/20  55.8 ± 6.7  111 ± 3.4 

It has been suggested that the acoustic vibrational frequency in core–shell NPs provides a good criterion of mechanical contact, and the comparison of Table II provides a unique criterion to that effect for core–shell NPs.29 In addition, it was reported that for shell thicknesses smaller than or of the order of the core radius, the fundamental radial mode of the full core–shell NP dominates the time-domain signal,25 which is in agreement with the measured Au/TiO2 sample. However, in the Au/SiO2 particles, the measured frequency is within 20% that of the breathing mode of the bare Au NP [Fig. 2(a)], suggesting a poor mechanical coupling between core and shell. This poor mechanical coupling for Au/SiO2 has been reported by several authors.29,36,37

In the case of good coupling, the presence of the shell modifies the observed phonon frequencies of the metallic core in two ways: (a) the mass of the shell lengthens the vibrational period of the core38 and (b) additional energy is required to vary the volume of the shell.29 In time-resolved experiments, the laser-induced hot electrons in the metal core quickly transfer their energy to the lattice. This creates a nonequilibrium situation with a hot core surrounded by a cold shell, which translates into a non-uniform thermal stress in the full core–shell particle and makes it evolve toward a new equilibrium configuration characterized by a larger size.39 The Au core used here is identical for both Au/SiO2 and Au/TiO2 samples. Anatase TiO2 is widely reported to have strong interactions with Au NPs.40,41 According to first principles calculations,40 the Au/TiO2 (001) interface is essentially dominated by Au–O, Au–Ti, and Au–Au bonding. As the bond length of Au–Ti is close to that of Au–Au, the lattice mismatch between Au and TiO2 (001) is mild, which is critically important for the formation of a solid interface, and the breaking of Ti–O bonds directly leads to strong Au–Ti interactions. In addition, such an interaction has an Au NP size dependence. Indeed, by establishing a surface tension dependent thermodynamic equilibrium model,33 it was found that the Au–Ti interaction is more prone to occur on large Au NPs (∼9 and ∼13 nm) than on small ones (∼3 and ∼7 nm). Thus, the strong chemical interactions at the interface could explain the good mechanical contact in Au/TiO2 core–shell NPs.

As previously mentioned, so far the acoustic vibrations in Au NPs have only been reported in the LSPR region.17,42 The estimated temperature increase in the Au core NP is between 30 and 300 K,18,27 resulting in a particle dilatation between 0.04% and 0.4%. Thus, the maximal vibration amplitudes are estimated to be between 0.005 and 0.05 nm. The NP volume change further leads to a change of electron density (resulting in the shift of plasmon band), the strain, and periodic variations of the absorption from the pump laser pulses, and possible other factors such as lattice temperature, elastic constants, sound speed in Au, etc. In the present case (Fig. 1), the same coherent phonon oscillation shows up as a modulation of the interband transition intensity, but the central energy position remains unaffected. In our previous studies, we showed that the temperature-induced changes of dielectric function in Au NPs in the region of the interband transitions are small.32 Therefore, the behavior of the coherent oscillations in the deep-UV TA signal is unlikely to reflect a variation of the dielectric constant. The strain has been proved to modify the band structure43 by changing the valence band (VB) structure and hole effective masses44 in semiconductor materials, since the joint density of states in the VB is reduced with the reduction in effective mass, and it becomes comparable to that in the conduction band (CB)45 that is, altering the transparency of current density. Although we cannot conclude if the amplitude modulation is due to the change of joint density of states in Au, the experimental results are quite remarkable.

The damping time (Table I) can be attributed to two mechanisms: (a) an inhomogeneous dephasing of the vibrations due to the polydispersity (in size and shape) of the NPs16 and (b) homogeneous damping due to energy loss to the solvent. As far as polydispersity of the NPs is concerned, for Au/SiO2 NPs where the vibrations are due to the Au core, only the polydispersity of the core should be important. For the Au/TiO2 NPs where the entire particle vibrates, both the polydispersity of the core and the shell would be important. It can be seen in Fig. 2 that, indeed, the Au/TiO2 NPs appear less homogeneous in size and shape than the Au/SiO2 NPs. An analysis of the size distributions of the samples would be needed, which is beyond the scope of this paper. Therefore, one can conclude that the distribution in sizes and shapes of core–shell NPs plays a role in the damping. However, this is not the only cause of damping. Indeed, when the NP is surrounded by extended media, a first damping channel is the acoustic radiation of phonons into the surroundings.46 In a solvent environment, an additional damping channel arises from its viscosity,47 which leads to energy dissipation via “external” friction. Mechanical coupling of the sphere with its environment and the outgoing energy flow into the latter (due to the outgoing spherical acoustic wave) introduce a damping of the sphere's vibrations, due to acoustic energy transfer at the particle interface.48,49 Thus, in addition to polydispersity, the faster damping time in Au/TiO2 NP supports that the oscillations damp away for the system as a whole object, while in Au/SiO2, the two constituents are not strongly coupled, and the damping is slower.

In conclusion, coherent acoustic phonons in core–shell Au/dielectric nanoparticles have been observed upon excitation of the surface plasmon resonance of the Au core. They exhibit a dramatic decrease in oscillation frequency and damping constant of the oscillations from Au/SiO2 to Au/TiO2. The latter behaves as a single object, i.e., with the vibration modes involving motion of the entire core–shell nanoparticle, due to good contact between Au and TiO2, while this is not the case with Au/SiO2 NPs. Finally, contrary to the case of the surface plasmon resonance where the central energy is modulated, it is the intensity of the interband transitions that is modulated. This, we believe, is a consequence of the modifications of the band structure of the Au NP, resulting from the strain due to the phonons, which may affect the joint density of states.

See the supplementary material for sample preparation, laser setup, data acquisition, and fit procedures.

This work was supported by the Swiss NSF via the NCCR: MUST and the European Research Council Advanced Grant DYNAMOX. L.W. acknowledges support from the China Scholarship Council (CSC).

The authors have no conflicts to disclose.

Lijie Wang: Data curation (lead); Formal analysis (lead); Investigation (lead); Writing – original draft (equal); Writing – review & editing (equal). Malte Oppermann: Investigation (equal); Methodology (equal); Validation (equal). Michele Puppin: Investigation (equal); Methodology (equal); Validation (equal). Benjamin Bauer: Investigation (equal); Methodology (equal). Tsz Him Chow: Investigation (equal); Methodology (equal). Jianfang Wang: Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Supervision (equal); Validation (equal). Majed Chergui: Conceptualization (lead); Funding acquisition (lead); Methodology (equal); Project administration (lead); Supervision (lead); Validation (lead); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

1.
Y.
Seol
,
A. E.
Carpenter
, and
T. T.
Perkins
,
Opt. Lett.
31
,
2429
(
2006
).
2.
W.
Li
and
X.
Chen
,
Nanomedicine
10
,
299
(
2015
).
3.
Y.-S.
Chen
,
W.
Frey
,
S.
Kim
et al,
Nano Lett.
11
,
348
(
2011
).
4.
J.-H.
Song
,
S.
Raza
,
J.
van de Groep
et al,
Nat. Commun.
12
,
48
(
2021
).
5.
R.
Marty
,
A.
Arbouet
,
C.
Girard
et al,
Nano Lett.
11
,
3301
(
2011
).
6.
Z.
Wang
,
H.
Kim
,
M.
Secchi
et al,
Phys. Rev. Lett.
128
,
048003
(
2022
).
7.
M.
Nisoli
,
S.
De Silvestri
,
A.
Cavalleri
et al,
Phys. Rev. B
55
,
R13424
(
1997
).
8.
J. H.
Hodak
,
I.
Martini
, and
G. V.
Hartland
,
J. Chem. Phys.
108
,
9210
(
1998
).
9.
N.
Del Fatti
,
C.
Voisin
,
F.
Chevy
et al,
J. Chem. Phys.
110
,
11484
(
1999
).
10.
J. H.
Hodak
,
A.
Henglein
, and
G. V.
Hartland
,
J. Phys. Chem. B
104
,
5053
(
2000
).
11.
J. H.
Hodak
,
A.
Henglein
, and
G. V.
Hartland
,
J. Phys. Chem. B
104
,
9954
(
2000
).
12.
A.
Crut
,
P.
Maioli
,
N.
Del Fatti
et al,
Phys. Rep.
549
,
1
(
2015
).
13.
G. V.
Hartland
,
Chem. Rev.
111
,
3858
(
2011
).
14.
G. V.
Hartland
,
Phys. Chem. Chem. Phys.
6
,
5263
(
2004
).
16.
M.
Pelton
,
J. E.
Sader
,
J.
Burgin
et al,
Nat. Nanotechnol.
4
,
492
(
2009
).
17.
P. V.
Ruijgrok
,
P.
Zijlstra
,
A. L.
Tchebotareva
et al,
Nano Lett.
12
,
1063
(
2012
).
18.
G. V.
Hartland
,
J. Chem. Phys.
116
,
8048
(
2002
).
19.
B.
Dacosta Fernandes
,
M.
Spuch-Calvar
,
H.
Baida
et al,
ACS Nano
7
,
7630
(
2013
).
20.
J. E.
Sader
,
G. V.
Hartland
, and
P.
Mulvaney
,
J. Phys. Chem. B
106
,
1399
(
2002
).
21.
M. F.
Cardinal
,
D.
Mongin
,
A.
Crut
et al,
J. Phys. Chem. Lett.
3
,
613
(
2012
).
22.
L.
Wang
,
A.
Kiya
,
Y.
Okuno
et al,
J. Chem. Phys.
134
,
054501
(
2011
).
23.
S.-J.
Yu
and
M.
Ouyang
,
Nano Lett.
18
,
1124
(
2018
).
24.
H.
Portales
,
L.
Saviot
,
E.
Duval
et al,
Phys. Rev. B
65
,
165422
(
2002
).
25.
D.
Mongin
,
V.
Juvé
,
P.
Maioli
et al,
Nano Lett.
11
,
3016
(
2011
).
26.
A.
Crut
,
V.
Juvé
,
D.
Mongin
et al,
Phys. Rev. B
83
,
205430
(
2011
).
27.
B. D.
Fernandes
,
N.
Vilar-Vidal
,
H.
Baida
et al,
J. Phys. Chem. C
122
,
9127
(
2018
).
28.
M.
Hu
,
X.
Wang
,
G. V.
Hartland
et al,
Chem. Phys. Lett.
372
,
767
(
2003
).
29.
A.
Ahmed
,
M.
Pelton
, and
J. R.
Guest
,
ACS Nano
11
,
9360
(
2017
).
30.
O.
Saison-Francioso
,
G.
Lévêque
, and
A.
Akjouj
,
J. Phys. Chem. C
124
,
12120
(
2020
).
31.
L.
Wang
,
T.
Rossi
,
M.
Oppermann
et al,
J. Phys. Chem. C
124
,
24322
(
2020
).
32.
L.
Wang
,
D.
Zare
,
T. H.
Chow
et al,
J. Phys. Chem. C
126
,
3591
(
2022
).
33.
W.
Qian
,
L.
Lin
,
Y. J.
Deng
et al,
J. Appl. Phys.
87
,
612
(
2000
).
34.
B.
Uthe
,
J. F.
Collis
,
M.
Madadi
et al,
J. Phys. Chem. Lett.
12
,
4440
(
2021
).
35.
L.
Bonacina
,
A.
Callegari
,
C.
Bonati
et al,
Nano Lett.
6
,
7
(
2006
).
36.
C.
Guillon
,
P.
Langot
,
N.
Del Fatti
et al,
Nano Lett.
7
,
138
(
2007
).
37.
D. A.
Mazurenko
,
X.
Shan
,
J. C. P.
Stiefelhagen
et al,
Phys. Rev. B
75
,
161102
(
2007
).
38.
A. J.
Mork
,
E. M.
Lee
,
N. S.
Dahod
et al,
J. Phys. Chem. Lett.
7
,
4213
(
2016
).
39.
C.
Voisin
,
N.
Del Fatti
,
D.
Christofilos
et al,
J. Phys. Chem. B
105
,
2264
(
2001
).
40.
C.
Sun
and
S. C.
Smith
,
J. Phys. Chem. C
116
,
3524
(
2012
).
41.
X.
Du
,
Y.
Huang
,
X.
Pan
et al,
Nat. Commun.
11
(
1
),
5811
(
2020
).
42.
M.
Perner
,
S.
Gresillon
,
J.
März
et al,
Phys. Rev. Lett.
85
,
792
(
2000
).
43.
S. W.
Corzine
,
R. H.
Yan
, and
L. A.
Coldren
,
Appl. Phys. Lett.
57
,
2835
(
1990
).
44.
E.
Yablonovitch
and
E.
Kane
,
J. Lightwave Technol.
4
,
504
(
1986
).
45.
P.
Bhattacharya
,
R.
Fornari
, and
H.
Kamimura
,
Comprehensive Semiconductor Science and Technology
(
Newnes
,
2011
).
46.
K.
Yu
,
P.
Zijlstra
,
J. E.
Sader
et al,
Nano Lett.
13
,
2710
(
2013
).
47.
L.
Saviot
,
C. H.
Netting
, and
D. B.
Murray
,
J. Phys. Chem. B
111
,
7457
(
2007
).
48.
C.
Voisin
,
N.
Del Fatti
,
D.
Christofilos
et al,
Appl. Surf. Sci.
164
,
131
(
2000
).
49.
V. A.
Dubrovskiy
and
V. S.
Morochnik
,
Izv. Earth Phys.
17
,
494
(
1981
).
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