# Ultrafast Hot-Carrier Dynamics in Ultrathin Monocrystalline Gold

Can O. Karaman Equal contributions Laboratory of Nanoscience for Energy
Technologies (LNET), STI, École Polytechnique Fédérale de Lausanne, 1015
Lausanne, Switzerland  Anton Yu. Bykov Equal contributions Department of
Physics and London Centre for Nanotechnology, King’s College London, London
WC2R 2LS, U.K  Fatemeh Kiani  Laboratory of Nanoscience for Energy
Technologies (LNET), STI, École Polytechnique Fédérale de Lausanne, 1015
Lausanne, Switzerland  Giulia Tagliabue Correspondence email address:
<EMAIL_ADDRESS>Laboratory of Nanoscience for Energy Technologies
(LNET), STI, École Polytechnique Fédérale de Lausanne, 1015 Lausanne,
Switzerland  Anatoly V. Zayats Correspondence email address:
<EMAIL_ADDRESS>Department of Physics and London Centre for Nanotechnology,
King’s College London, London WC2R 2LS, U.K

###### Abstract

Applications in photodetection, photochemistry, and active metamaterials and
metasurfaces require fundamental understanding of ultrafast nonthermal and
thermal electron processes in metallic nanosystems. Significant progress has
been recently achieved in synthesis and investigation of low-loss
monocrystalline gold, opening up opportunities for its use in ultrathin
nanophotonic architectures. Here, we reveal fundamental differences in hot-
electron thermalisation dynamics between monocrystalline and polycrystalline
ultrathin (down to 10 nm thickness) gold films. Comparison of weak and strong
excitation regimes showcases a counterintuitive unique interplay between
thermalised and non-thermalised electron dynamics in mesoscopic gold with the
important influence of the X-point interband transitions on the intraband
electron relaxation. We also experimentally demonstrate the effect of hot-
electron transfer into a substrate and the substrate thermal properties on
electron-electron and electron-phonon scattering in ultrathin films. The hot-
electron injection efficiency from monocrystalline gold into TiO2, approaching
9$\%$ is measured, close to the theoretical limit. These experimental and
modelling results reveal the important role of crystallinity and interfaces on
the microscopic electronic processes important in numerous applications.

##  1 Introduction

Monocrystalline (MC) metals have recently emerged as attractive materials for
a wide range of plasmonic applications, from sensing and imaging to
information processing and energy harvesting [1, 2, 3, 4]. In particular,
because of the highly ordered crystal structure and lack of grain boundaries,
they exhibit unique optical properties and allow for long-range plasmon
coherence and reduced optical losses [5, 6]. MC metals have in fact been shown
to result in higher resonance quality factors, longer surface plasmon
polariton propagation lengths, and superior electric field confinements
compared to their polycrystalline (PC) counterparts [7, 5, 8]. Concurrently,
advancements in the synthesis of MC metallic microflakes (MFs), in particular
Au MFs, towards larger lateral sizes and higher aspect ratios, has enabled the
study and exploitation of these outstanding physical properties in ultrathin
(sub 15 nm) films, which are difficult to realise with PC metals [2, 9].

Plasmonic-based charge transfer devices, such as photodetectors and
photoelectrodes [10, 11, 12] could uniquely benefit from ultrathin MC metals.
These systems indeed rely on the injection of photoexcited energetic charges
(hot electrons/holes) from the metal into an adjacent semiconductor or
adsorbed molecules [13, 14, 15]. Therefore, physical dimensions comparable to
hot-carrier mean-free paths (sub 20 nm) and reduced scattering losses could
favour ballistic hot-carrier transfer, significantly improving device
performance. Additionally, well-defined crystal facets in MC metals would help
clarify the interplay of catalytic properties and hot-carrier injection in
plasmonic photoelectrodes [16]. In order to design and optimize the
performance of hot-carrier devices, a detailed microscopic understanding of
the carrier properties and thermalization dynamics in the material is
essential.

Figure 1: Optical properties of monocrystalline gold. a, The schematic
illustrations of monocrystalline and polycrystalline Au. b, Schematic of the
band diagram of Au. Red arrow indicates the transition from d-band to p-band
near the X-symmetry point, the green arrow indicates the transition near the
L-symmetry point. c, The simulated reflection, absorption and transmission
spectra of the 10-nm-thick MC Au (solid curves) and PC Au (dashed curves) on a
SiO2 substrate under normal illumination. The shaded area indicates a spectral
range of the excitation. d, Schematics of the degenerate pump-probe optical
measurements with back surface pumping and front surface probing. e, The
simulated $\Delta R/R$ (blue curve) for a 10-nm-thick MC Au flakes on a SiO2
substrate at the laser fluence of 3.5 Jm-2 and 8-fs-long pulses and its
components $\Delta R_{T}/R$ (orange curve), $\Delta R_{NT}/R$ (yellow curve),
$\Delta R_{D-Te}/R$ (violet curve), and $\Delta R_{D-Tl}/R$ (green curve).

Hot carriers initially generated in metal by light absorption have non-thermal
energy distribution (which cannot be described by the Fermi-Dirac
distribution) with energies that depend on the incident photon energy and the
material band structure [17]. They are generated via intraband and interband
absorption described by the dielectric function of the metal,
$\epsilon=\epsilon_{1}+i\epsilon_{2}$, and augmented by geometric effects in
nanoscale structures [18]. Non-thermal carriers subsequently undergo a
thermalization process that involves carrier-carrier scattering (typical
carrier thermalization time $\tau_{th}$ of few hundreds of femtoseconds) and
carrier-phonon relaxation ($\tau_{e-ph}$ of few picoseconds) [19, 20, 21],
ultimately dissipating the photon energy into lattice heating. Ultra-fast
transient absorption spectroscopy studies of polycrystalline metal films and
monocrystalline (colloidal) nanoparticles have shown that the substrate
thermal conductivity as well as hot-carrier extraction strongly alter the
overall thermalization dynamics [22, 23, 24, 25, 26, 27, 28]. Interestingly,
nanoparticle-based studies have recently shown that the size and metal
crystallinity can alter the electron-phonon coupling time [29, 30, 31, 32].
Yet, because of limitations in the temporal resolution, there remains a lack
of understanding of how the crystallinity affects the early thermalization
stages (sub 100 fs), where electron-electron scattering is dominant. No study
to date has investigated the hot-carrier dynamics in MC ultrathin films and
transfer to semiconductors, both of which are essential for applications.

In this work, we study hot-carrier generation, relaxation, and transfer
dynamics in ultrathin MC Au microflakes under different excitation conditions.
We perform transient reflectance spectroscopy of these films with near-IR 8-fs
pulses, providing new insights into the hot-carrier thermalization dynamics on
ultrashort timescales. In particular, we observe a decrease in electron
scattering rate in MC gold, which suggests that grain boundaries may play a
role in this process. Our results also demonstrate several new features of
hot-electron dynamics in the equilibrium regime, such as the dynamic
renormalization of the interband absorption peak at the X high symmetry point
in the Brillouin zone as well as a strong contribution of hot-electron
scattering on polar phonons in the substrate, caused by the electron spill-out
and manifested by the dependence of the relaxation rate on the thermal
conductivity of the substrate and thickness of gold crystals. The latter
behaviour is reversed for stronger optical excitation due to the increasingly
higher energy stored in the hot-electron gas. Finally, we use the MC gold
flakes as a platform for ultrafast hot-electron transfer into the adjacent
semiconductor material (TiO2) and demonstrate the injection efficiency as high
as $\approx$ 9$\%$, close to the theoretical limit, despite the Au surface is
atomically flat. This finding is highly promising for hot-carrier transfer
devices with monocrystalline metals, allowing high-quality factor surface
plasmon resonances thanks to the low optical loss and their atomically flat
surfaces. We also show the impact of the excitation regime (weak or strong
perturbation) resulting in the suppression of the electron spill-out effect on
the electron-phonon relaxation time as perturbation increases. The obtained
results reveal important effects of crystallinity on hot-carrier dynamics,
providing new opportunities for development of plasmonic hot-carrier devices.

##  2 Results

Ultra-thin MC Au MFs with pristine (no ligand) and atomically smooth
$\\{111\\}$ surfaces are grown on glass by a wet chemistry method [2]. The
studied range of the flake thicknesses is 10 nm to 20 nm, as determined by
atomic force microscopy (Supplementary Fig. 4). The high aspect ratio of the
flakes concurrently ensures lateral sizes larger than 10 $\mu$m, suitable for
optical spectroscopy. Separately, complementary 10-nm-thick, continuous PC Au
films were prepared by sputtering. The hot-electron injection into TiO2 was
studied by transferring the chemically synthesized MC Au flakes onto a 40-nm-
thick TiO2 film, deposited on borosilicate glass (see Methods). Calculated
reflection, absorption and transmission spectra of the 10-nm-thick MC Au (the
dielectric function from Ref. [33]) and PC Au (the dielectric function from
Ref. [34]) films on a SiO2 substrate show small but distinguishable
differences (Fig. 1c). In the spectral range of the pump beam used in the
experiments, the mean absorption for PC films ($A$ = 0.071) is slightly higher
than that of MC films ($A$ = 0.066).

Hot-carrier dynamics was investigated using transient reflectance measurements
(Fig. 1d, see Methods). An 8 fs pump-pulse laser allows to measure the whole
thermalization process, including at sub-100 fs time-scales. Both the pump and
probe beam have central photon energy of 1.7 eV. In Au, this corresponds
mainly to the intraband hot-carrier excitation regime, which results in a
near-uniform non-Fermi distribution of non-thermal carriers from the Fermi
level up to the energy of the excitation photon [17, 35, 36, 19]. At photon
energies higher than 1.8 eV, the interband transitions dominate the optical
response and include transitions at X-point ($\approx$ 1.8 eV, d-band to
p-band transition) and at L-point ($\approx$ 2.4 eV, d-band to p-band and
$\approx$ 3.5 eV, p-band to s-band)(Fig. 1b, Supplementary Fig. 1).

The relaxation dynamics of the hot carrier ensemble can be well-described
using a three-process model [17, 37] that evaluates the time evolution of the
energy density of the non-thermal hot carriers, $N_{e}$, the temperature of
the thermalized electron gas, $T_{e}$, and the temperature of the lattice,
$T_{l}$. This model, combined with a semiclassical theory of optical
transitions in the solids, allows to establish a link between the non-
equilibrium energy transfer and the measured changes in the dielectric
function $\Delta\epsilon(\hbar\omega,t)$ of the metal and, therefore, the
measured reflectance signal (see Supplementary Information Section 1 for the
details of the model) [17, 21]. The changes in permittivity $\Delta\epsilon$
can be split in three distinct contributions from (i) the non-thermal hot
carriers ($\Delta\epsilon_{NT}$), (ii) the thermalized electrons with the
elevated temperature ($\Delta\epsilon_{T}$), and (iii) the Drude damping
modification ($\Delta\epsilon_{D}$) as in [17]:

$\Delta\epsilon(\hbar\omega,t)=\Delta\epsilon_{NT}(\hbar\omega,t)+\Delta\epsilon_{T}(\hbar\omega,t)+\Delta\epsilon_{D}(\hbar\omega,t)$
(1)

The importance of these contributions changes with the time after the
excitation. The first two terms account for the transient change of the
single-particle interband absorption peak due to the pump-induced change in
the electron-hole occupancy and the electron temperature, respectively, while
the last term accounts for the many-body free-electron response manifested by
the change in the optical Drude damping. In the spectral range above the
interband offset threshold the main contribution is given by the
$\Delta\epsilon_{T}$, and a characteristic "slow" rise is observed in the
optical constants as the internal equilibrium is being reached within the hot-
electron gas (i.e., $\tau_{rise}\approx\tau_{th}$). In a highly non-
equilibrium Fermi gas, which can be obtained at higher optical fluences the
thermalisation time decreases due to stronger electron-electron scattering
[38]. At longer wavelengths, on the other hand, $\Delta\epsilon_{NT}$
dominates the response and exhibits an almost instantaneous $\tau_{rise}$,
irrespective of the strength of the excitation, which depends on the average
scattering rate of the non-thermal electrons [39, 40] (Supplementary Fig 2.).

Figure 1e illustrates the contributions of the above introduced
excitation/relaxation processes to the transient reflection, $\Delta R/R$.
Initially, the photon absorption results in a sudden change in the electron
occupancy and creates a nonequilibrium, nonthermal electron distribution,
which causes the rapid increase of the signal by $\Delta R_{NT}/R$. The
nonthermalised electrons interact inelastically with each other and also with
’cold’ electrons, not perturbed from their initial thermal equilibrium,
resulting in the thermalized electron distribution after approximately 100s of
fs. The contribution $\Delta R_{T}/R$, which accounts for the interband
transitions, is associated with this new electron distribution, thermalised at
a higher electron temperature. The thermalized electrons also have an impact
on the Drude response of the electron gas resulting in $\Delta R_{D-Te}/R$.
The thermalized electrons collide with the lattice of a metal, and their
excess energy is transferred to phonons. Therefore, a lattice temperature
increases over a few ps time, determined by the electron-phonon coupling
constant of the system, G. As a consequence,the $\Delta R_{D-Tl}/R$
contribution is built up. The excited phonons interact with the room
temperature phonons of the lattice and also the substrate phonons and their
energy is dissipated until the thermal equilibrium with the surroundings is
established.

###  2.1 Electron-Electron Relaxation

Figure 2:  Electron-electron scattering effects. a, Transient reflection from
a 10-nm-thick MC Au MF (violet curves) and a PC Au (green curves) on SiO2
substrate at the pump fluence F = 3.6 J/m2 (dashed curves) and F = 5.7 J/m2
(solid curves). The inset shows the low perturbation regime measurements with
F = 0.4 J/m2. b, Transient change in the imaginary part of the dielectric
function of Au at $\hbar\omega$ = 1.7 eV due to nonthermalised
$\Delta\epsilon_{NT}$ (blue curves) and thermalised $\Delta\epsilon_{T}$
(orange curves) electron distributions, simulated with the three process
model. c, Simulated (cyan curves) and measured (gray curves) $\Delta R/R$ from
a 10-nm-thick PC Au film on SiO2. d, The JDOS at the X-symmetry point of the
Brillouin zone of the MC Au at different electron temperatures (left) and the
JDOS at the X-symmetry point for MC (purple curves) and PC (green curves) Au
(right). e, Simulated (cyan curves) and measured (gray curves) $\Delta R/R$
for a 10-nm-thick monocrystalline Au MF on SiO2. In (a,c,e), dashed curves
correspond to $F$ = 3.6 J/m2 and solid curves to $F$ = 5.7 J/m2 (solid
curves). Insert in (a) show the case of a weak perturbation regime at $F$ =
0.4 J/m2.

We first compare the behaviour of highly nonequilibrium hot electrons in MC
and PC gold generated under strong excitation conditions (Fig. 2a). At low
fluences, both samples exhibit exactly the same charge carrier dynamics. In
particular, we observe a rapid rise, ($\tau_{rise}$ = 150 fs
$<<\tau_{th}\approx$ 500 fs), dictated by the non-thermal electron dynamics
$\Delta\epsilon_{NT}$, as expected for the nonresonant (with respect to the
interband transitions) probing conditions. However, when the fluence
increases, two intriguing phenomena emerge: (i) counter-intuitively,
$\tau_{rise}$ increases and, most significantly, (ii) $\tau_{rise}$ in the MC
sample becomes longer than in the PC one, despite its lower absorption. This
indicates different early-stage thermalization dynamics in MC and PC films.

Using $\epsilon_{Au}(\omega)$ for PC Au [34] and the electron-electron
scattering rate ($\gamma_{e-e}$, which has a quadratic dependence on electron
energy [40, 41]), we obtain an excellent agreement between the experimental
and theoretical transient reflectance (Fig. 2c). Importantly, at higher
fluences and hence higher $T_{e}$ of the thermal carriers, the joint density
of states (JDOS) for the interband transitions at the X-point of the Brillouin
zone broadens in energy, so that the spectral overlap with the probe beam
spectrum used in the measurements increases (Fig. 2d). In other words, when a
high $T_{e}$ is established, the probe pulse can transiently access interband
absorption at the X-point, becoming more sensitive to the thermal-carrier
contribution ($\Delta\epsilon_{T}$) similar to the resonant probing conditions
of the interband transitions. The interplay between the evolution of
$\Delta\epsilon_{T}$ and $\Delta\epsilon_{NL}$ then produces a "delayed" rise
time, observed in the experiment. To confirm this conclusion, we compare the
fluence dependence of $\Delta\epsilon_{NT}$ and $\Delta\epsilon_{T}$ (Fig. 2b
and Supplementary Fig. 2). At low fluences ($F$ = 0.4 J/m2), the contribution
from $\Delta\epsilon_{T}$ is negligible, and the response is dominated by the
fast $\Delta\epsilon_{NT}$. However, at stronger excitation, the magnitude of
$\Delta\epsilon_{T}$ increases rapidly, reaching nearly 25% of the nonthermal
contribution for a fluence of 5.7 J/m2. We conclude, therefore, that the
observed experimental trends and their dependence on the excitation fluence
showcase an overlooked unique interplay between equilibrium and non-
equilibrium electron dynamics in mesoscopic gold. We can speculate that the
stronger role of X-point in the dielectric function of MC gold is what allows
us to more clearly observe it at higher fluences in the transient spectra
(Fig. 2a).It is worth noting that we do not observe the decrease (increase) of
$\tau_{th}$ ($\gamma_{e-e}$) that follows from the Fermi liquid theory [40,
35] due to the predominantly nonresonant nature of the experiment, which is
only partially sensitive to the non-equilibrium dynamics
($\tau_{rise}<<\tau_{th}$).

For strongly perturbative excitation at higher excitation fluences, the rise
of $\Delta R/R$ in the PC Au film is faster than in the MC Au MF. Treating the
average scattering rate of the nonthermalised electrons,
$\overline{\gamma_{e}}$, as a free parameter of the dynamic three-process
model (see Supplementary Information Section 1) and noting the larger JDOS at
the X-point for MC than PC Au (Fig. 2d), we can reproduce the measured
electron dynamics in MC gold (Fig. 2e). The greater spectral weight of the
interband transitions in MC Au means a stronger contribution of the slow
$\Delta\epsilon_{T}$ term to the measured dynamics with the obtained
$\overline{\gamma_{e,MC}}$ = 18 THz smaller than $<\overline{\gamma_{e,PC}}$ =
24 THz. This difference in $\overline{\gamma_{e}}$ arises from the additional
contributions from scattering on lattice defects and grain boundaries in PC
Au, which are the additional energy loss channels for electrons [42, 43, 44].
The studied PC Au film has the average grain size of 50 nm Supplementary Fig.
5) which is much smaller than the pump beam size ($\approx$ 10 $\mu m$ and
thus multiple grain boundaries contribute. We can, therefore, attribute the
longer $\tau_{rise}$ in MC Au to the combination of (i) a decrease in
$\overline{\gamma_{e}}$ and (ii) an increase of the contribution of the
interband optical transitions at the X-point. The former also results in
longer thermalization of electrons in MC Au.

Figure 3:  Effect of hot-carrier transfer on the electron dynamics. a, The
schematic illustration of hot-electron transfer from Au to TiO2 and the
respective energy band diagramme. b, Transient reflection measured for 10 nm
thick monocrystalline Au MF on SiO2 (purple curves) and on TiO2 (red curves)
at a pump fluence F = 3.6 J/m2 (dashed curves) and F = 5.7 J/m2 (solid
curves). Inset shows the low perturbation $\Delta R/R$ measurement at F = 0.4
J/m2.

To visualize the effect of hot-carrier extraction on the early-stage
thermalization dynamics of hot carriers, we compare a 10-nm-thick Au MF on
SiO2 and TiO2 substrates. At an Au/TiO2 interface, a Schottky barrier of
approximately 1.2 eV is formed [45, 46, 47] (Fig. 3 a), enabling hot-electron
separation across the metal/semiconductor interface. Under these conditions,
regardless of the pump fluence, the rise of $\Delta R/R$ is slower than on
SiO2. This is related to the transfer of the non-equilibrium hot electrons
with the energies exceeding the Schottky barrier from Au to TiO2 in the first
100 fs, increasing the thermalisation time governed by the electrons closer to
the Fermi level. In fact, $\gamma_{e-e}$ is quadratically proportional to the
excited electron energy, and lower energy carriers have a longer lifetime (see
Supplementary Information Section 2) [21, 40, 41]. Since the remaining
electrons are less energetic, they will live longer. This effect occurs at all
levels of excitation as hot-carrier transfer is always present in Au/TiO2
system. However, it is fundamentally different from the power-dependent
phenomena discussed above, and it survives even in the regime of low
perturbation excitation (Fig. 3 b).

###  2.2 Electron-Phonon Scattering and Hot-Electron Transfer Efficiency

Figure 4: Electron-phonon scattering. a, Measured transient reflection from a
10-nm-thick MC Au MF (violet curve) and a PC Au film (green curve) on a SiO2
substrate, and a MC Au MF on a TiO2 substrate (red curve) at the excitation
fluence $F$ = 5.7 J/m2. b, The dependence of $\tau_{e-ph}$ of a 10-nm-thick MC
Au MF on SiO2 (violet diamonds), on TiO2 (red squares), and a PC Au film on
SiO2 (green dots) on the excitation fluence. The dotted curves obtained from
eq. 2 for G${}_{MCAu/TiO_{2}}$ = 1.6x1016 Wm-3K-1 (red), G${}_{PCAu/SiO_{2}}$
= 2x1016 Wm-3K-1 (green), G${}_{MCAu/SiO_{2}}$ = 2.2x1016 Wm-3K-1 (purple).
Inset shows the comparison of the fluence dependence of $\tau_{e-ph}$ of a
10-nm-thick MC Au MF on TiO2 with the simulations for different $P_{i}$
values. c, Thickness dependence of measured $\tau_{e-ph}$ for MC Au MFs on
SiO2 in strong (dots), and weak (diamonds) perturbation regimes. Solid curves
are the calculated electron temperatures Te achieved in strong (upper) and
weak (lower) perturbation regimes. Error bars in panels b and c represent
standard deviation.

To complete the picture of the role of crystallinity and hot-electron
extraction on the overall carrier thermalization dynamics, we analyze the
temporal response of optical properties of MC and PC films governed by the
electron-phonon scattering (Fig. 4b). Electron- phonon relaxation time
$\tau_{e-ph}$ increases with the excitation fluence for all the samples since
the free-electron heat capacity depends on thermalized Te, and, therefore, the
relaxation is slower for higher initial values of Te [25, 48, 31]. For the
same excitation fluence, $\tau_{e-ph}$ is slightly shorter in the MC Au MFs
compared to the PC Au thin films. We can estimate the electron-phonon coupling
constant from the intersect of its dependence on the excitation fluence as
GMCAu= (2.2$\pm$0.1)x1016 Wm-3K${}^{-1})$ and GPCAu= (2.0$\pm$0.1)x1016
Wm-3K${}^{-1})$, for MC and PC samples, respectively. Since both films are on
the same substrate, the change in an electron-phonon coupling constant
originates from the difference in crystallinity. In particular, grain
boundaries can affect the phonon density of states and frequencies [49],
therefore, impacting the rate of energy transfer from electrons to phonons
[49], showcasing the importance of using robust single crystal platforms for
the design of plasmonic hot-carrier devices.

A second practically important observation is a slower electron-phonon
relaxation in MC Au on TiO2 and a drastic difference in the electron-phonon
coupling constants for the identical MC gold films deposited on SiO2 (GMCAu=
(2.2$\pm$0.1)x1016 Wm-3K-1) and TiO2 (GMCAu/TiO2= (1.6$\pm$0.1)x1016 Wm-3K-1).
Several studies have reported a major effect of the environment on
$\tau_{e-ph}$ in Au NPs and Au thin films interfaced with dielectric materials
[23, 24, 50, 51, 52, 53]. In particular, it has been shown that $\tau_{e-ph}$
decreases in an environment with higher thermal conductivity which is likely
to be related to the scattering of Au electrons on the phonons in the
substrate [51]. Therefore, we expect smaller $G_{MCAu/TiO2}$ to partially
originate from the lower thermal conductivity of thin TiO2 film compared to
bulk SiO2 [54]. Hot-electron injection is also expected to modify
$\tau_{e-ph}$. Since the most energetic electrons will be transferred, the
thermalised electron gas temperature will increase less in the presence of
hot-carrier transfer. Therefore, one could also expect a decrease in
$\tau_{e-ph}$ in the case of a Au film on TiO2, as it depends on the electron
temperature.

To disentangle the two contributions, we consider the relationship between
$\tau_{e-ph}$ and the hot-electron injection probability, $P_{i}$, [31, 48]:

$\tau_{e-ph}\approx\frac{\gamma
T_{l}}{G_{MCAu/TiO_{2}}}+\frac{(1-P_{i})U}{2G_{MCAu/TiO_{2}}T_{l}}$ (2)

where $\gamma$= 66 Jm-3K-2 is the electron heat capacity for Au, and $U$ is
the initial energy density absorbed by the electrons $U=A\times F/L$, where
$A$ and $L$ are the absorbance of the film and its thickness, respectively.
Using $P_{i}$ as a fitting parameter, the dependence of the electron-phonon
relaxation time on the excitation fluence can be fitted to the experimental
data with $P_{i}$ = 0.09$\pm$0.03 (Fig. 4b). On the other hand, the
theoretical hot-electron injection probability from a monocrystalline Au MF
into TiO2 can be evaluated, assuming $\Phi_{b}$ = 1.2 eV and $\hbar\omega$ =
1.7 eV, as $P_{i}$ = 0.1 (see Supplementary Information Section 2 for the
details of the calculations). Surprisingly, there is an excellent agreement
between the hot-electron injection probability obtained from the theoretical
estimates under fully-relaxed momentum conservation and the one extracted from
the experimental $\tau_{e-ph}$ dependence.

Several studies demonstrated the increase in the hot-electron transfer
efficiency due to electron-surface-defect scattering which causes the electron
momentum randomization if the surface is rough or due to a grain structure of
PC metals [55, 56]. However, our results suggests that, despite their
atomically smooth surfaces, MC Au MFs provide good hot-electron extraction
efficiency ($\approx$ 10$\%$). This agrees well with the reduced hot-electron
scattering rate measured above, as it would favor the ballistic collection of
the highly energetic electrons. Additionally, for the thicknesses lower than
the electron mean-free-path, which is electron-energy-dependent and higher
than 30 nm at 1.7 eV photon energy [56], quasi-elastic electron-phonon
scattering can efficiently redirect the momentum of hot electrons, which
increases the transfer efficiency even in the absence of other momentum
relaxing mechanisms, such as lattice defects, grain boundaries and rough
surface scattering. Therefore, we assume the relaxation of the momentum
conservation during hot-electron transfer, which shows good agreement with the
measured efficiency. It should be noted that an ideal theoretical limit of the
injection probability in the considered system can be obtained assuming
$\Phi_{b}$ = 0 eV, zero-thickness of Au film and angular momentum for all the
hot electrons directed towards to the film interface to be $P_{i,max}$ = 0.53.

Finally, we compare the electron-phonon relaxation times $\tau_{e-ph}$ for
monocrystalline Au MF with different thicknesses (Fig. 4c). In a low
perturbation regime ($F$= 0.4 J/m2), the increase of the electron temperature
$T_{e}$ is simulated to be stronger for the thinner films. However,
interestingly, $\tau_{e-ph}$ decreases as the thickness decreases. While the
contribution of surface acoustic [57] or electronic [58] states on highly
oriented (111) Au surfaces may become relevant with the increase of a surface-
to-bulk ratio, multiple previous theoretical and experimental works have
failed to observe their role in hot-electron dynamics on surfaces even for
much higher surface-to-bulk ratios than in the studied MC Au films [59, 60,
58]. Moreover, since the experimental studies are performed here at ambient
conditions, the surface states are likely to be passivated by molecular
contaminants [61]. Therefore, we attribute the decrease of $\tau_{e-ph}$ with
the increase in thickness to the increased contribution of the electron spill-
out effects, which reduces the average electron density for the thinner films
[62]. This leads to reduced screening and stronger interaction between the
electrons and the ionic lattice [63, 38]. The opposite behavior is observed at
higher fluences in the strong perturbation regimes: $\tau_{e-ph}$ increases as
the thickness decreases. The reason is that the non-negligible increase in Te
(Fig. 4c), overpowers the contribution of the electron spill-out effect on
$\tau_{e-ph}$: as the thickness decreases, the hot-electron temperature
$T_{e}$ significantly increases in a high perturbation regime and its increase
is stronger for thinner films because of the smaller volume where the energy
is absorbed, resulting in longer electron-phonon relaxation.

##  3 Discussion

We interrogated the temporal dynamics of hot carriers in ultrathin
monocrystalline and polycrystalline Au films on passive and active substrates.
Our findings revealed that a relative contribution of thermalised and
nonthermalised electrons to transient optical properties depends on the
crystallinity of a gold film. We found longer electron thermalization in
monocrystalline Au due to a decrease in $\overline{\gamma_{e}}$, which was
caused by the absence of grain boundaries and lattice defects. Contrary to
general perception, in the near-IR spectral range, the interband transitions
in gold at the X-point of the Brillouin zone significantly affect hot-carrier
dynamics and must be taken into account in monocrystalline gold, especially in
a strong perturbation regime at the high excitation fluences. This results in
the increase of the contribution of long-lived thermalized electrons to the
optical response and, therefore, its slower dynamics. We also showed that the
presence of hot-electron transfer from Au to TiO2 suppresses the nonthermal
electron contribution to the optical properties and leads to much longer
electron-phonon relaxation on a thermally low conductive substrate. We
demonstrated that the perturbation regime highly affects the thickness
dependence of the electron-phonon scattering $\tau_{e-ph}$. While
$\tau_{e-ph}$ decreases as thickness decreases in a low perturbation regime
owing to the electron spill-out effect, it increases in a high perturbation
regime because of the non-negligible increase in $\Delta T_{e}$ for smaller
thicknesses. Our findings also revealed that hot-electron injection efficiency
is approximately 9$\%$, which agrees with the estimates under momentum
relaxation assumptions, even though the Au surface is atomically flat. This
result indicates a potential for using monocrystalline metals in hot-carrier
transfer devices [64, 45, 65], as it supports high-quality factor plasmonic
resonances. Overall, the results contribute to a deeper understanding of the
non-equilibrium carrier dynamics in monocrystalline metals.

##  4 Methods

Sample preparation: High-aspect ratio ultrathin (10–25 nm) monocrystalline Au
MFs are fabricated by the procedure described in Ref. [2]. The used substrate
is 180-$\mu$m-thick borosilicate glass. MFs have atomically smooth and well-
defined $\\{111\\}$ crystallographic surface and face-centered cubic crystal
structure (Supplementary Fig. 5). The RMS roughness of the MF surface is
measured to be $\approx$ 250 pm. To study hot-electron transfer, chemically
synthesized flakes are transferred to 40-nm-thick TiO2 films on borosilicate
glass by the PMMA transfer method [66], followed by the exposure to an oxygen
plasma (4 min, 500 W) to remove any PMMA residue left from the transfer step.
The detailed characterization of the MC Au-TiO2 interface can be found in our
recent study [67]. To compare the effect of crystallinity on hot-carrier
dynamics, 10-nm-thick Au films were fabricated on the same type of substrates
by sputtering. AFM imaging verifies that these films are continuous with the
RMS surface roughness around 1.5 nm (Supplementary Fig. 5). The average grain
sizes of the polycrystalline Au films are measured as around 50nm.
Degenerate pump-probe measurements: Transient optical measurements were
conducted using a femtosecond laser (Laser Quantum Venteon) and a degenerate
pump-probe setup (Supplementary Fig. 5). The laser produces approximately 8 fs
pulses with a repetition rate of 80 MHz and an average power of 0.5 W. The
spectrum of such a short laser pulse covers a range from 650 to 950 nm
(Supplementary Fig. 5). The pump and probe beams were cross-polarized in order
to prevent coherent interactions during the measurements. The measurements
were performed using a lock-in amplifier using a modulated pump at 1 kHz
frequency, which allowed for accurate measurements with a precision of 10-6 to
10-7. The optical path included a dispersion control system (Sphere Photonics
D-Scan) in order to control the dispersion of the ultrashort pulses. To assure
consistency, $\Delta R/R$ traces of each sample were measured several times
over a few different days.

## Acknowledgements

This work was supported in part by the SNSF Eccellenza Grant #PCEGP2_194181,
the ERC iCOMM project (789340), and the UK EPSRC project EP/W017075/1.

## Data Availability Statement

All the data supporting the findings of this study are presented in the
Results section and Supplementary Materials and Available from the
corresponding authors upon reasonable request.

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