Thin Ti adhesion layer breaks bottleneck to hot hole relaxation in Au films

Understanding electron-vibrational relaxation at interfaces is important for optimizing the efficiency of systems designed for a variety of applications, including thermoelectricity, microelectronics, and electro-optics.^1–4 Interfacial energy transfer can occur through energy exchange from the respective charge carriers and phonons in each material comprising the interface;^5–10 the transfer of energy between charge carriers and phonons across interfaces involving metals can contribute an additional channel for thermal transport, and corresponding energy losses cannot be ignored. Commonly, the two-temperature model (TTM) is used to describe the magnitude of electron-to-phonon thermal conductance,^1,11–13 in which electrons at temperature T_e exchange energy with phonons at temperature T_p. Since thermalization of excited electrons and phonons occurs very rapidly, short-pulsed lasers have been widely used to understand the scattering mechanisms of the fundamental energy carriers.^6,14–25

The nonequilibrium dynamics following excitation of electrons by a laser pulse exhibits three characteristic time scales, including thermalization of the charge carrier gas due to electron-electron scattering (∼tens of femtoseconds), energy exchange between the electrons and the lattice (∼hundreds of femtoseconds to a few picoseconds), and energy transport driven by the gradient in the lattice temperature (>picoseconds).^26,27 Eesley was the first to observe the nonequilibrium between the electronic and vibrational degrees of freedom using the short-pulsed, time-domain (TD) thermoreflectance (TR) technique^28,29 and confirmed the earlier theories that described electrons and the lattice by two separate temperatures,^23,24 validating the TTM.^30,31

Interfaces involving metal films and multilayer metal stacks constitute an essential component of electronic and optoelectronic and magnetic devices. Interactions among the various electron and phonon subsystems at metal interfaces are controlled by atomistic features of the interfaces. For example, to improve adhesive strength, a thin transition metal film is often inserted between a noble metal layer and its supporting substrate. Hohlfeld et al.³² studied three different evaporated thin film systems, Au/Cr, Au/Ti, and Au/Pd/Ti, and found that Ti-based layers gave better resistance to interdiffusion with gold than Cr-based layers. Other researchers also reported that Ti is often more favorable than Cr for optical applications because it provides a larger transmittance.^33,34 In terms of thermal transport, Kaganov et al.³⁵ demonstrated that the phonon-phonon thermal boundary conductance across Au/silicon interfaces can increase at over a factor of three with the inclusion of a Ti adhesion layer between the Au and silicon. More recent studies by Anisimov et al.³⁶ and Olson et al.³⁷ found that the oxygen stoichiometry of this Ti adhesion layer can also play a pronounced role in phonon coupling across Au/Ti/substrate interfaces for a wide array of substrates, including sapphire, MgO, quartz, and graphene.

While the dynamics of phonon thermal conductance at interfaces have been widely studied, including those with nanoscale thin films such as the aforementioned Ti adhesion layers, the mechanisms driving electron-phonon dynamics at and across interfaces have received much less attention. Several theories have been developed that treat this electron-phonon interface problem.^{19,36,38–41} Notably, Duda et al.⁴² found that the electron-phonon coupling increased by more than a factor of five with the inclusion of a thin Ti adhesion layer between the Au film and a nonmetal substrate and that the electron-phonon energy relaxation time notably accelerated. A following density functional theory (DFT)-based computational study identified two reasons for these experimental phenomena: the inclusion of a Ti layer greatly enhances the density of states (DOS) in the energy region starting at 1 eV below the Fermi level and extending several eV above it, and arguing that Ti atoms are four times lighter than Au atoms and therefore generate enhanced electron-phonon coupling.³⁷ Both factors accelerate the electron-phonon dynamics.

The nature and dynamics of charge carriers, e.g., electrons vs holes, in an electronic device depend on many factors, including chemical doping, operation and gate voltage, Fermi level alignment, and band bending at an interface. Our previous aforementioned DFT study focused on electrons,⁴³ rationalizing the observed acceleration of electron-phonon relaxation in Au due to a Ti adhesion layer reported by Majumdar and Reddy.³⁹ The properties of holes in Au are quite different from those of electrons. In particular, hole DOS is much higher than electron DOS. Additionally, holes are supported primarily by Au 5d orbitals, while electrons have strong contributions from both Au 6s and 6p orbitals. Furthermore, Ti electronic DOS is much higher in the energy range corresponding to Au electrons than holes. The dynamics of the hole is interesting by itself as it is a fingerprint of differences between electron and hole wavefunctions. Direct information on hole dynamics can be obtained experimentally by angle-resolved photoemission spectroscopy.^23,44–47 However, the role of these hole dynamics on carrier relaxation with a metal lattice has not been explicitly studied and is important to consider to garner a more holistic understanding of nonequilibrium energy transfer in metals and at metallic interfaces.

The present work reports an atomistic ab initio time-domain simulation of phonon-induced nonradiative relaxation of holes in thin Au films with and without a Ti adhesion layer. The simulations are performed using a nonadiabatic (NA) molecular dynamics (MD) approach formulated within the framework of real-time time-dependent density functional theory (TDDFT) in the Kohn-Sham (KS) representation. The paper is constructed as follows: Sec. II describes the essential theoretical background and computational details underlying the NAMD and real-time TDDFT simulations; Sec. III details the results and discussion, which is comprised of three parts—the geometric and electronic structure of the metal films, hole-phonon interactions, and nonradiative hole relaxation dynamics; finally, the key findings are summarized in the conclusions.

The simulations are carried out using a mixed quantum-classical technique. The electronic structure is described quantum mechanically, using ab initio DFT. The electronic evolution is modeled using real-time TDDFT. Nuclear motions are described by classical MD, and the electron-nuclear interactions are modeled using fewest switching surface hopping⁴⁸ (FSSH), which is the most common NAMD methodology.

All quantum-mechanical calculations and ab initio MD are performed with the Vienna Ab initio Simulation Package (VASP),^23,49 which utilizes plane waves and the ultrasoft pseudopotentials generated within the Perdew-Burke-Ernzerhof (PBE) generalized gradient DFT functional.⁵⁰ The interaction of the ionic cores with the valence electrons is described by the projector-augmented wave (PAW) approach.⁵¹ The plane wave basis energy cutoff is set to be 400 eV.

Considering computational limitations, the experimentally studied Au films with and without a narrow Ti adhesion layer⁵² are modeled with an Au (111) surface containing seven layers of Au atoms and one layer of Ti atoms (Fig. 1). 20 Å of vacuum are included perpendicular to the slabs to eliminate interactions between periodic images. The 5 × 5 × 1 Monkhorst-Pack mesh is used for geometry optimization and MD, and the 7 × 7 × 1 mesh is used to compute DOS.

After relaxing the geometry at 0 K, repeated velocity rescaling is employed to bring the temperature of the systems to 300 K, corresponding to common experimental conditions.⁵³ Following 3 ps of thermalization dynamics, adiabatic MD simulations are performed in the microcanonical ensemble with a 1 fs atomic time step. The adiabatic MD trajectories are 7 ps and 3 ps long for Au and Au–Ti, respectively.

By mapping an interacting many-body system onto a system of noninteracting particles moving in an effective potential, DFT expresses the ground state energy as a functional of electron density. In practical implementations, the density is constructed from single-particle Kohn-Sham (KS) orbitals, $Ψnr,t$⁠,

where N_e is the number of electrons. The evolution of $Ψnr,t$ is determined by the time-dependent variational principle, leading to the following equations of motion:

The equations are coupled and nonlinear since the Hamiltonian, $H[ρ(r,t)]$⁠, is a functional of the electron density, which is obtained by summing over many occupied KS orbitals [Eq. (1)]. By expanding the time-dependent KS orbitals, $Ψnr,t$⁠, in the adiabatic KS orbital basis, $Φkr;R(t)$⁠, obtained for a given nuclear configuration, R(t),

one takes advantage of the computational efficiency of time-independent DFT codes.^54–56 Substituting this expansion into Eq. (2) gives equations of motion for the expansion coefficients

where ε_k is the energy of the adiabatic state k and d_jk is the NA coupling between adiabatic states k and j. The latter arises from the orbital dependence on the atomic motion, R(t), and is calculated numerically as the overlap between wavefunctions k and j at sequential time steps via

The numerical evaluation of the time-derivative term on the right-hand-side of Eq. (5) provides significant computational savings if the off diagonal matrix elements of the gradient with respect to the nuclear coordinates, encountered in the middle of Eq. (5), are not available analytically. This NA coupling is a form of electron-phonon coupling as it reflects the dependence of the electronic wavefunctions on nuclear coordinates.

To model the hole relaxation process, one needs to employ a methodology capable of describing transitions between electronic states. NAMD and, in particular, trajectory surface hopping^54,56–59 provide an efficient method to describe electronic transitions in nanoscale systems. In this work, we utilize FSSH⁶⁰ in the classical path approximation (CPA), as implemented in the PYXAID package.^54,61 Note that solving real-time TDDFT equations, Eq. (2), is not sufficient for the present purpose, in particular, since they are reversible in time and do not obey detailed balance between transitions upward and downward in energy and thus cannot describe electron-phonon relaxation and approaches that assume thermodynamic equilibrium.

FSSH⁶² is an algorithm for modeling dynamics of mixed quantum-classical systems. It assigns a probability for hopping between quantum states based on the evolution of the expansion coefficients [Eq. (4)]. The probability of a transition from state j to another state k within the time interval dt is given in FSSH by⁶³ 

In cases where the calculated dP_jk is negative, the hopping probability is set to zero because, by construction, a hop from state j to state k can take place only when the occupation of state k increases and the occupation of state j decreases. This feature of the algorithm achieves “fewest switches” by minimizing the number of hops. A uniform random number between 0 and 1 is generated every time step and compared to dP_jk in order to decide whether or not to hop.

It is assumed that electrons and phonons exchange energy instantaneously during a hop. The energy balance is achieved by nuclear velocity rescaling; based on semiclassical arguments,⁶⁴ only the velocity component along the direction of the matrix element of the gradient vector, $Φj∇RΦk$⁠, is rescaled. If the magnitude of this component of the kinetic energy is too small to accommodate an increase in the electronic energy after a hop to a higher energy state, the hop is rejected. This velocity rescaling step gives rise to detailed balance between transitions up and down in energy, leading to Boltzmann statistics and quantum-classical thermodynamic equilibrium.⁶⁵ 

The classical path approximation (CPA) to FSSH^54,61 assumes that the nuclear dynamics are weakly dependent on the electronic evolution, for instance, as compared to thermally induced nuclear fluctuations. The CPA approximation allows great computational savings since the time-dependent potential that drives multiple FSSH realizations of the NA dynamics of the electronic subsystem can be obtained from a single MD trajectory. It is assumed further that the energy deposited into the nuclear modes along the direction of the NA coupling vector, $Φj∇RΦk$⁠, dissipates rapidly among all nuclear degrees of freedom such that the vibrational subsystem is always close to thermodynamic equilibrium. Then, the hop rejection feature of the original FSSH is replaced with multiplication of the FSSH probability up in energy by the Boltzmann factor. This maintains detailed balance and achieves thermodynamic equilibrium in the long time limit.^54,60

The FSSH-CPA calculations are performed by first computing the adiabatic state energies and NA coupling along the MD trajectories, and then randomly selecting 1000 geometries as initial conditions for NAMD; 100 realizations of the stochastic FSSH process are sampled for each initial condition. FSSH has been implemented within real-time KS-TDDFT,⁵⁴ tested,⁶⁵ adapted to the CPA,^62,66 released in public software,⁶⁰ and applied to various nanoscale systems.^{59–61,66–72}

The geometries of the Au films with and without the Ti adhesion layer have been optimized at 0 K first. As shown in Fig. 1, introducing a layer of Ti results in a very minor distortion of the Au film geometry. The largest increase in the distance between adjacent Au layers is less than 0.06 Å. The average length of the bond between the nearest Au and Ti atoms is 2.791 Å; this value is close to those observed and calculated for the Au–Ti bond lengths in alloys and clusters.^73,74 The intralayer Au–Au bond length is 2.884 Å, in good agreement with the experimental value.⁷⁵ 

As the temperature increases from 0 K to 300 K, both slabs expand and the average distance between the Au slab and the Ti adhesion layer increases by 0.05 Å, while the distance between Au layers increases by at most 0.26 Å. The top layer of the Au film distorts notably due to interaction with the Ti layer. The metal layers vibrate horizontally with respect to each other (Fig. 1). Heating does not perturb the bonding pattern, as it does in other nanoscale systems.^76,77 At the same time, adding a Ti layer breaks the Au slab symmetry, influences wavefunction localization, and enhances electron-phonon coupling.

Figure 2 presents the hole DOS of the Au and Au–Ti slabs. Shown are the total DOS (TDOS) and partial DOS (PDOS) for the optimized geometry. The zero of energy is set at the Fermi level. Since Au and Ti are metals, the systems have no bandgaps. Parts (a) and (b) of Fig. 2 demonstrate that the TDOS of Au undergoes a sharp drop in the energy range between −2 and −1 eV and that the holes are supported primarily by Au 5d atomic orbitals. Such a dramatic decrease in the DOS should have a strong influence on the charge-phonon energy exchange as holes at energies below −2 eV relax to the Fermi level.

Adding a narrow Ti adhesion layer has a minor effect on the TDOS, whose overall shape does not change, parts (c) and (d) of Fig. 2. However, the adhesion layer has a strong effect on the charge-phonon relaxation dynamics, as demonstrated and discussed below. Upon a closer inspection of Figs. 2(c) and 2(d), one observes that the contribution of Ti to the TDOS rises exactly where the Au PDOS decreases; Ti PDOS is negligible below −2 eV. However, at −1 eV and above, Au and Ti have nearly equal PDOS, even though the number of Ti atoms is seven times smaller than the number of Au atoms (Fig. 1).

Hole relaxation dynamics depends on NA coupling between electronic states induced by nuclear motions, and coupling strength is related to localization of hole wavefunctions [Eq. (5)]. According to the excitation energy employed in many two-color pump-probe experiments,^23,24,78,79 we consider the energy range between −3 and 0 eV. Since the DOS undergoes a rapid change around −1.5 eV (Fig. 2), we separate the total energy range further into the −3 to −2 eV interval of high DOS, the −1 to 0 eV interval of low DOS, and the high-to-low DOS transition interval from −2 to −1 eV. We compute hole charge densities for each interval by averaging over charge densities of all KS orbitals within each energy range (Fig. 3).

The wavefunctions of the pristine Au film are symmetric; however, the density distribution between inner and surface regions of the slabs changes with energy (Fig. 3). Far below the Fermi level at energies with high DOS (Fig. 2), the charge density is distributed nearly evenly across the slab. In the region from −2 to −1 eV, in which the Au DOS decreases sharply and the Ti DOS grows, the Au charge density is localized toward the surface of the slab, and therefore, the Au wavefunctions can couple strongly to the Ti adhesion layer. The Au charge density is localized toward the middle of the slab at energies close to the Fermi level.

Adding a Ti layer breaks the symmetry of the wavefunctions. Most importantly, the system’s charge density has strong contributions from the Ti layer in the regions where the Au DOS is low, i.e., between −2 and 0 eV. At energies below −2 eV, where Au DOS is high, the charge density is localized away from the Ti adhesion layer. This situation favors rapid relaxation of holes because the lighter and faster Ti atoms can couple to the holes exactly in the energy regions with low Au DOS (>−2 eV), where hole relaxation in pure Au alone would be slow.

Nonradiative relaxation of holes by coupling to phonons appears in the simulations as a sequence of NA transitions between energy levels occupied by the holes. Each elementary transition reflects the strength of the NA coupling between the states. The NA coupling fluctuates along the trajectory and depends on the time-derivative overlap between the corresponding adiabatic wavefunctions [Eq. (5)].

Table I summarizes the averaged absolute values of the NA coupling in the Au and Au–Ti systems. The canonical averaging is performed over both the overall energy range from −3 to 0 eV and over the three energy windows considered previously (Fig. 3). Considering the pristine Au slab, we observe that the NA coupling decreases significantly, by a factor of 5, in the region from −1 to 0 eV with low Au DOS, relative to the energies farther away from the Fermi level. This effect can be understood by considering the fact that the NA coupling is inversely proportional to the gap between the corresponding energy levels [Eq. (5)]. Note that the DOS also changes by a factor of 5–6 between −2 and −1 eV (Fig. 2). The decrease in both DOS and NA coupling results in a dramatic slowing down of the nonradiative hole relaxation.

Addition of a thin Ti adhesion layer has a strong effect on the NA coupling values (Table I), changing the hole relaxation dynamics. On the one hand, the overall NA coupling magnitudes are 5–9 times larger in the presence of the Ti layer. On the other hand, the difference in the NA coupling values between the high and low energy regions is much smaller, roughly a factor of 2, compared to the factor of 5 for pure Au. Furthermore, the NA coupling is largest in the energy region of rapidly changing DOS, −2 to −1 eV, in which nonradiative relaxation of holes in pure Au is slow. The NA coupling grows significantly in the presence of Ti because the Ti atom is about 4 times lighter than the Au atom and the coupling is proportional to the nuclear velocity [Eq. (5)]. In addition, the states become more localized in the presence of Ti (Fig. 3), and localized states exhibit stronger electron-phonon coupling than delocalized states. This is consistent with previous simulations of pure metals that predict that transition metals with Fermi energies intersecting the d-band PDOS have larger electron-phonon coupling factors than free electron metals with s- and/or p-band PDOS at the Fermi level.⁸⁰ 

In order to characterize the phonon modes that couple to the electronic subsystem and the relative strengths of the hole-phonon coupling for different modes, we compute Fourier transforms of the energy gaps between states sampled at −3 eV, −2 eV, −1 eV, and the Fermi level. The spectra shown in Fig. 4 are known as influence spectra or spectral densities.^80–82 The heights of the peaks characterize the strength of hole-phonon interaction at the corresponding frequencies. As can be seen from Fig. 4(a), the phonon modes that couple to the electronic subsystem in pristine Au have low frequencies, indicating that the acoustic modes exhibit stronger coupling than the higher frequency optical phonons. The dominant peaks below 100 cm⁻¹ seen in the influence spectra of pristine Au can be assigned to acoustic phonon modes involving core Au atoms.⁸³ The strength of the hole-phonon coupling decreases as holes get closer to the Fermi level, in agreement with the NA coupling values shown in Table I. Introduction of the narrow Ti layer changes the influence spectrum completely (Fig. 4(b)). In this case, the signal extends to 500 cm⁻¹, with the dominant peaks seen around 300 cm⁻¹. The change occurs because Ti atoms are much lighter than Au atoms and because the hole states delocalize from the Au slab to the Ti layer (Fig. 3). The faster motions seen in the influence spectra of the Au–Ti system generate stronger NA coupling (Table I), which depends on nuclear velocity [Eq. (5)]. The simulation agrees with the shift to higher frequencies seen in experiments with gold disks in contact with adhesion layers.²³ 

The evolution of the average energy of the holes excited to about −3.1 eV, according to the excitation energy employed in the pump-probe experiments,^23,24,81 is shown for the Au and Au–Ti systems in Fig. 5; note the difference in the x-axis scales in parts (a) and (b). The nonradiative relaxation of holes in the pristine Au slab is clearly bi-phasic. In the region with high Au DOS (Fig. 2), at energies between −3 and −1.5 eV, the hole relaxation is fast. The relaxation slows down by a factor of 30 in the region of low Au DOS close to the Fermi energy. Attempting to fit the curve in Fig. 5(a) with a single exponent equation fails completely, while a bi-exponential fit does a good job describing the simulation data. The transition from subpicosecond relaxation to dynamics in tens of picoseconds can be qualified as the phonon bottleneck to hot-hole relaxation.^84–87 Such slow relaxation of hot charge carriers can be exploited to increase the efficiency of solar cells.^88–90 

The relaxation is much faster in the presence of the Ti adhesion layer (Fig. 5(b)). Thus, one can state that the Ti adhesion layer breaks the phonon bottleneck and provides new, efficient pathways for relaxation of hot holes. In this case, a single exponential fit does a good job describing the data. Rigorously, quantum dynamics is always Gaussian at early times,⁸⁵ as can be seen in the discrepancy between the exponential fit represented by the dashed line and the raw data shown by the solid line. Exponential decay develops when quantum dynamics evolve to include multiple states in the Hilbert space. Nevertheless, one can assign a single time scale to the hole relaxation in the Au–Ti system; by 0.5 ps, the vast majority of the charges have decayed to within 0.2 eV of the Fermi level (Fig. 5(b)). In comparison, even after 6 ps, the average hole energy is 1 eV below the Fermi level in the pure Au slab (Fig. 5(a)).

The qualitative and quantitative differences in the nonradiative hole relaxation in the Au and Au–Ti systems can be rationalized by considering DOS (Fig. 2) and NA coupling (Table I). The Ti layer, with 7 times fewer atoms than the Au slab, doubles the system’s hole DOS between −1.5 eV and the Fermi level. Ti atoms also contribute significantly to the charge densities of the hole states in this energy range (Fig. 3), especially between −2 and −1 eV where the Au DOS drops dramatically and the relaxation bottleneck develops in pristine Au. Ti atoms are lighter and thus move faster than Au atoms (Fig. 4). Consequently, the Ti layer increases the NA coupling (Table I), especially in the energy range around −1.5 eV, where hole relaxation undergoes a transition from fast to slow decay.

One can attempt to explain the differences in the calculated time scales using Fermi’s golden rule, whereby the relaxation rate is a quadratic function of the coupling and a linear function of the DOS. On comparing the 0.53 ps and 16.29 ps relaxation times in pure Au to the observed 0.23 ps characteristic time scale in Au–Ti, the hole-phonon relaxation dynamics is found to be a factor of 2.3 and 70.8 faster in Au–Ti than in Au (Fig. 5). The NA coupling is different in the Au and Au–Ti films by a factor of 3.7–8.5 (Table I). Ignoring the changes in DOS (Fig. 2), which are much smaller than this difference in coupling, and squaring the NA coupling, we obtain a predicted factor of 13–72 faster dynamics in Au–Ti than Au. This shows reasonable agreement with 2.3 and 70.8 estimated from the fitted time scales (Fig. 5). The deviations can be ascribed to several factors. First, the DOS is a function of energy and changes rapidly around −1.5 eV (Fig. 2). One needs to exclude this region of rapidly changing DOS from consideration and apply Fermi’s golden rule to energy ranges with relatively constant DOS (or use integral versions of Fermi’s golden rule); the NA coupling fluctuates along the trajectory, and comparison of average absolute values or root-mean-square values can lead to different conclusions. Additionally, the localization of the charge density depends on the energy and presence of the Ti layer (Fig. 3). For instance, between −3 and −2 eV, where DOS is relatively constant (Fig. 2), the charge is localized on roughly twice fewer atoms in Au–Ti compared to Au (Fig. 3). Thus, the effective DOS is twice smaller in Au–Ti and Au for this energy range. The fact that rate expressions such as Fermi’s golden rule cannot fully explain the calculated results emphasizes the need for quantum dynamics simulations.

Comparing the hole relaxation dynamics studied here to the electronic relaxation investigated previously in the same Au and Au–Ti systems,^85,91 we observe that electrons in the Au film relax uniformly across the whole energy range, in contrast to holes. The electron relaxation time is 1.8 ps, which is between the time scales for the fast and slow hole relaxation components. The electron DOS is similar to the hole DOS near the Fermi level (Fig. 2). However, the electron charge densities are distributed more evenly^87,91 than those of the holes (Fig. 3), generating better wavefunction overlap and larger NA coupling. The significantly longer time scale associated with nonradiative relaxation of holes near the Fermi energy makes them better candidates for extraction of hot charge carriers, compared to electrons. The Ti adhesion layer accelerates both electron and hole relaxation, leading to subpicosecond energy losses to heat and greatly reducing the possibility of utilization of hot charge carriers.

By performing time-domain ab initio simulations, we demonstrate that nonradiative relaxation of excited holes in an Au film undergoes a sharp transition from the subpicosecond to tens-of- picoseconds regime at 1.5 eV below the Fermi level. The bottleneck to this nonradiative relaxation arises due to a rapid decrease in the DOS and hole-phonon coupling in this energy range. Hole localization changes with energy as well; deep inside the valence band, the hole is delocalized over the whole Au film. In the energy region of rapidly changing DOS, it is localized near the film surface. Close to the Fermi energy, the hole is localized toward the middle of the film. The nonradiative relaxation of the hole is mediated by Au acoustic modes with frequencies below 100 cm⁻¹.

The situation completely changes in the presence of a narrow Ti layer that is used in applications to improve adhesion to a substrate. The bi-phasic fast-slow hole relaxation switches to a single exponential decay that takes 0.23 ps. The relaxation is accelerated because Ti contributes very significantly to the DOS in the critical region in which the dynamics in pure Au is slow because the Au states localized near the film surface strongly mix with Ti states and since Ti atoms are much lighter and move faster than Au atoms. Hole relaxation in the Au–Ti system is facilitated by modes that extend to 500 cm⁻¹, and the hole-phonon coupling grows by a factor of 3.7 at energies far from the Fermi level and 8.5 near the Fermi energy.

The hole relaxation bottleneck present in the pristine Au film can be utilized to extract hot charge carriers, reducing energy losses and increasing efficiencies of optoelectronic devices. In order to extend the lifetime of high energy carriers in the presence of adhesion layers, these layers should be made of relatively heavy chemical elements, compared to Au, and/or have relatively small DOS in the relevant energy range. Inversely, narrow adhesion layers of Ti atoms assist heat dissipation, providing advantages in electronics applications. The detailed atomistic time-domain analysis of the nonradiative charge relaxation reported in this work is directly related to time-resolved spectroscopy experiments and emphasizes the highly nonequilibrium nature of the relaxation dynamics. By establishing the mechanism of the nonradiative charge relaxation, and characterizing the electronic states and phonon modes involved, the study facilitates fundamental understanding of energy flow at engineered nanoscale interfaces, guiding future experiments and providing principles for design of more efficient materials and devices.

The research was funded by the US Department of Defence, Multidisciplinary University Research Initiative, Grant No. W911NF-16-1-0406. X.Z. acknowledges support of the National Natural Science Foundation of China, Grant No. 21473183.