Strong Influence of Ti Adhesion Layer on Electron−PhononRelaxation in Thin Gold Films: Ab Initio Nonadiabatic MolecularDynamicsXin Zhou,†,‡ Joanna Jankowska,‡,§ Linqiu Li,‡ Ashutosh Giri,∥ Patrick E. Hopkins,∥,⊥,#

and Oleg V. Prezhdo*,‡,¶

†College of Environment and Chemical Engineering, Dalian University, Dalian 116622, P. R. China‡Department of Chemistry and ¶Department of Physics and Astronomy, University of Southern California, Los Angeles, California90089, United States§Institute of Physics, Polish Academy of Sciences, 02-668 Warsaw, Poland∥Department of Mechanical and Aerospace Engineering, ⊥Department of Materials Science and Engineering, and #Department ofPhysics, University of Virginia, Charlottesville, Virginia 22904, United States

ABSTRACT: Electron−phonon relaxation in thin metal films is animportant consideration for many ultrasmall devices and ultrafastapplications. Recent time-resolved experiments demonstrate asignificant, more than a factor of five, increase in the electron−phonon coupling and acceleration in the electron−phonon relaxationrate when a narrow Ti adhesion layer is introduced between an Aufilm and a nonmetal substrate. Using nonadiabatic moleculardynamics combined with real-time time-dependent density functionaltheory, we identify the reasons that give rise to this strong effect.First, the Ti layer greatly enhances the density of states (DOS) in theenergy region starting at 1 eV below the Fermi level and extendingseveral electronvolts above it. Second, Ti atoms are four times lighterthan Au atoms and therefore generate larger nonadiabatic (NA)electron−phonon coupling. Because the transition rates depend oncoupling and DOS, both the factors accelerate the dynamics. Showing good agreement with the experiments, the time-domainatomistic simulations provide a detailed mechanistic understanding of the electron−phonon relaxation dynamics in thin goldfilms and related nanomaterials.

KEYWORDS: metallic films, adhesion layer, electron−phonon relaxation, nonadiabatic molecular dynamics,real-time time-dependent density functional theory, quantum dynamics

1. INTRODUCTIONThermal transport1−12 forms an increasingly important elementin various applications including microelectronics, thermo-electrics, and electro-optics. At interfaces comprising at leastone metal, the transfer of energy between electrons andphonons in the metal contributes an additional channel forthermal transport. If the other material forming the interface isa nonmetal, the predominant energy-transfer mechanism acrossthe metal/nonmetal interface at time scales when the electronsand phonons in the metal are in thermal equilibrium is phonon-mediated. If both materials are metals, the predominantmechanism involves electrons on the two sides.13 In bothcases, electron−phonon coupling can be an important factor inenergy transfer, and thus electron−phonon relaxation cannotbe ignored.To describe the heat flow and the resulting temperature

changes associated with the electron-to-phonon thermalconductance, one commonly considers a two-temperaturemodel (TTM),14,15 in which the electrons at temperature Te

exchange energy with phonons at temperature Tp. Underconditions of strong nonequilibrium between the electron andphonon subsystems, the energy transfer rate becomes propor-tional to the difference of the fifth power of the twotemperatures.14,15 Using the TTM, Majumdar and Reddy16

derived an analytical expression to obtain the role of electron−phonon coupling in metals on the thermal boundary resistanceacross metal/nonmetal interfaces. Gundrum et al.13 derived aversion of the diffuse mismatch model applied to the electron−electron scattering at metal/metal interfaces suggesting that thedistribution of energies around the Fermi energies of the metalsdictates the electron-interface conductance. This model hasbeen used to describe the measured thermal conductanceacross a variety of metal/metal interfaces but only considersthat the electrons and phonons are in near-equilibrium

Received: August 20, 2017Accepted: November 14, 2017Published: November 14, 2017

Research Article

www.acsami.orgCite This: ACS Appl. Mater. Interfaces 2017, 9, 43343−43351

© 2017 American Chemical Society 43343 DOI: 10.1021/acsami.7b12535ACS Appl. Mater. Interfaces 2017, 9, 43343−43351

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conditions (i.e., Te ≈ Tp). Hopkins et al.12 extended this metal/

metal electron conductance model to describe the conditions ofa strong electron−phonon nonequilibrium (i.e., Te ≫ Tp) onelectron−electron transmission across interfaces. However, inthese aforementioned metal/metal interface studies, the role ofelectron−phonon coupling has been ignored. However, theelectronic surface states that have been studied by detailedspectroscopic studies using angle-resolved photoemissionexperiments and supported by calculations17−24 have suggestedthat the electron−phonon coupling at metal interfaces cannotbe ignored, albeit the majority of these works have focused onmetal/nonmetal interfaces. Thus, this begs the question: whatrole does electronic nonequilibrium have on electron−phononcoupling at metal/metal interfaces? This question has not beenaddressed in any of these aforementioned studies, and we seekto answer this question in this current work.The fundamental understanding of how electronic non-

equilibrium affects electron−phonon relaxation at metal/metalinterfaces can be discussed through the qualitative frameworkof how electrons relax and energetically equilibrate inhomogeneous metals. Owing to the subpicosecond time scaleof the electron energy exchange, short-pulsed lasers have beenwidely used to advance this understanding.14 The absorption ofa laser pulse by a metal surface and the subsequent energyrelaxation process can be described by three characteristic timeintervals corresponding to (i) thermalization of the freeelectron gas, (ii) coupling between electrons and the lattice,and (iii) energy transport driven by the spatial gradient of theelectron and phonon temperatures, during which Te ≈ Tp.

25

The first observation of the nonequilibrium between theelectronic and vibrational states with short-pulsed, time-domainthermoreflectance was carried out by Eesley,26 who confirmedthe earlier theories that described the electrons and the latticeby two separate temperatures, thus validating the TTM.These ultrafast transient electron relaxation dynamics can be

influenced by the presence of interfaces and the resultingheterogeneity of the electronic and phononic states around theinterface. Indeed, these interfaces are ubiquitous in a range ofmodern technologies; for example, construction of metal/metaland metal/nonmetal interfaces is a key process in thefabrication of electronic and optoelectronic devices. Theatomistic features of the interfaces govern the interactionsbetween the electronic and phononic subsystems. A thintransition metal film is often inserted between an Au layer and a

substrate to improve the adhesive strength. Audino et al.studied three different thin evaporated film combinations Au/Cr, Au/Ti, and Au/Pd/Ti and found that Ti-based layers gavebetter resistance to interdiffusion with gold than Cr-basedlayers.27 Other researchers also reported that Ti is often morefavorable than Cr for optical applications because it provides alarger transmittance.28,29

Recently, Giri et al.30 utilized time-domain thermoreflectance(TDTR) experiments31 to report that the electron−phononcoupling increased by more than a factor of five with theinclusion of a thin Ti adhesion layer between an Au film and anonmetal substrate, and thus the electron−phonon energyrelaxation is notably accelerated. They showed that thedeposited thin Ti adhesion layer not only enhanced thebonding between the metal film and the dielectric substrate butalso provided a strong channel for the electron−phonon energyexchange near the interface, relative to the weak electron−phonon coupling characteristic of Au. Chang and co-workersused ultrafast laser pulses to launch acoustic phonons in singlegold nanodisks with variable Ti layer thicknesses and observedan increase in phonon frequencies as an adhesion layerfacilitated stronger binding to the glass substrate.32 With acombination of TDTR measurements of thermal boundaryconductance, picosecond acoustic measurements of acousticreflectivity, and Green’s function calculations of phononinterfacial transmission, Duda et al.33 demonstrated that theTi adhesion layer between Au and nonmetal substrates willenhance the vibrational energy transmission across metal/nonmetal interfaces.The present work reports an atomistic ab initio time-domain

simulation of the electron−phonon coupling and energyexchange in thin Au films with and without the Ti adhesionlayer. We apply the nonadiabatic molecular dynamics (NAMD)approach formulated within the framework of real-time time-dependent density functional theory (TDDFT) in the Kohn−Sham (KS) representation to investigate the dynamics ofphonon-induced relaxation of excited electrons in Au films. Thepaper is constructed as follows. The next section describes theessential theoretical background and computational detailsunderlying the NAMD simulation. The Results and Discussionsection comprises three parts, focusing on the geometric andelectronic structure, electron−phonon NA coupling (NAC),and electron relaxation dynamics. The simulation results are

Figure 1. Side views of the simulation cells showing the geometries of the Au(111) slab and the Au(111) slab with absorbed Ti layer at 0 K (a) andduring the MDs run at 300 K (b). The distances between neighboring layers are shown on the left side of the structures.

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compared with the available experimental data. The keyfindings are summarized in the Conclusions section.

2. THEORY AND SIMULATION METHODSTo simulate the electron−phonon interactions in thin gold films, first,we identify the key electronic states involved in the photoinduceddynamics on the basis of experimental results and ab initio densityfunctional theory (DFT). Then, we perform the ground-state ab initioMD and compute electron−phonon NAC matrix elements. Finally, weperform time-domain simulations of the electron−phonon relaxationdynamics using a mixed quantum-classical technique, combining real-time TDDFT in the KS representation and fewest switches surfacehopping (FSSH).2.1. Ab Initio Electronic Structure Calculations and MDs. All

quantum-mechanical calculations and ab initio MDs are performedwith the Vienna Ab initio Simulation Package,34,35 which utilizes planewaves, and the ultrasoft pseudopotentials generated within thePerdew−Burke−Ernzerhof generalized the gradient DFT functional.36

The projector-augmented wave approach was used to describe theinteraction of the ionic cores with the valence electrons.37 The basisset energy cutoff was set to 400 eV.Aiming to mimic the experimentally studied Au films with and

without a narrow Ti adhesion layer30 and limit computationally thesimulation cell size, we build an Au(111) surface with seven layers ofAu atoms to simulate the gold film and add one layer of Ti on top ofthe Au surface to model the Au film with a narrow Ti adhesion layer,as shown in Figure 1. We further investigate the electronic structure ofthe Au film interacting with a layer of the Si substrate. We constructthe Au−Ti model as a 2 × 2 Au(111) surface supercell with the cellsurface dimension a = b = 5.76759 and a 2 × 2 Ti(001) layer withdimension a = b = 5.9012. The lattice mismatch between Au and Ti isonly 2.3%. In the Au−Si model, we used a 4 × 4 Au(111) supercellwith a = b = 11.53518 and a 3 × 3 Si(111) layer with a = b = 11.5203.Here, the lattice mismatch is only 0.1%. A vacuum layer of 20 Å isintroduced in the direction perpendicular to the surface to avoidspurious interactions between periodic slabs. The 5 × 5 × 1Monkhorst−Pack mesh was used for the structural optimization andMD, and the 7 × 7 × 1 mesh was employed for the density of states(DOS) calculations.After relaxing the geometry at 0 K, repeated velocity rescaling was

used to bring the temperature of the systems to 300 K, correspondingto the temperatures in the experiment.30 Following the 3 psthermalization dynamics, adiabatic MD simulations were performedin the microcanonical ensemble with a 1 fs atomic time step. Thelengths of the adiabatic MD trajectories were 7 ps for Au and 3 ps forAu−Ti. The adiabatic state energies and the NAC were calculated foreach step of the MD runs. Thousand geometries were selectedrandomly from the adiabatic MD trajectories and were used as initialconditions for nonadiabatic (NA) dynamics simulations.2.2. NAMD with Real-Time TDDFT in the KS Representation.

To model the electron relaxation process, one needs to employ amethodology capable of describing transitions between electronicstates. NAMD and, in particular, trajectory surface hopping38,39

provide an efficient method that describes electronic transitions innanoscale systems. In this work, we utilize FSSH39,40 in the classicalpath approximation, as implemented in the PYXAID package.41,42

DFT expresses the ground-state energy in terms of the properties ofelectron density. The latter is obtained from single-particle KS orbitals,Ψn(r, t)

∑ρ = |Ψ |=

t tr r( , ) ( , )n

N

n1

2e

(1)

Here, Ne is the number of electrons. The equations-of-motion for thetime-dependent KS orbitals is derived using the time-dependentvariational principle

ρℏ ∂∂

Ψ = Ψit

t H t tr r r( , ) [ ( , )] ( , )n n (2)

These equations are nonlinear and are coupled because theHamiltonian itself, H[ρ(r, t)], depends on the occupied KS orbitals(eq 1). The time-dependent KS orbitals, Ψn(r, t), are expressed in theadiabatic KS orbital basis, Φk(r; R(t)), computed for a given nuclearconfiguration, R(t)

∑Ψ = Φt C t tr r R( , ) ( ) ( ; ( ))nk

kn

k(3)

using standard DFT codes.41−43 Substitution of eq 3 into eq 2produces equations-of-motion for the expansion coefficients

∑ ε δℏ ∂∂

= +it

c t C t d( ) ( )( )jn

kk

nk jk jk

(4)

where εk is the energy of the adiabatic state k and djk is the NACbetween adiabatic states k and j. The latter arises from the orbitaldependence on the atomic motion, R(t), and is calculated numericallyas the overlap between wave functions k and j at sequential time steps

= − ℏ⟨Φ|∇ |Φ ⟩· = − ℏ Φ ∂∂

Φd it

it

Rddjk j k j kR

(5)

The numerical evaluation of the derivative on the rightmost side of eq5 provides significant computational savings, if the analytic gradientmatrix elements, appearing in the middle of eq 5, are not available. TheNAC is the electron−phonon coupling because it arises from thedependence of the wave functions on nuclear coordinates.

FSSH39 is an approach for modeling dynamics of quantum-classicalsystems. FSSH was implemented in the real-time KS-TDDFT,43

tested,44 released in public software,41 and applied to various nanoscalesystems.42,45−55 FSSH provides a probability for hopping betweenquantum states based on the evolution of the expansion coefficients(eq 4). Specifically, the probability of a transition from state j toanother state k within the time interval dt is given in FSSH by39

=− *

= *A d

At A c cP

Rd

2 Re( )d ;jk

jk jk

jjjk j k

(6)

If the calculated dPjk is negative, the hopping probability is reset tozero. A hop is possible only when the occupation of the initial state jdiminishes and the occupation of the final state k grows. This featureminimizes the number of hops, leading to “fewest switches”. A uniformrandom number on the [0, 1] interval is generated in every step tocompare with dPjk and decide whether to hop.

The quantum-classical energy is conserved by nuclear velocityrescaling. On the basis of semiclassical arguments,56 only the velocitycomponent along the direction of the matrix element of the gradientvector, ⟨Φj|∇R|Φk⟩, is rescaled. If the magnitude of this component ofthe kinetic energy is too small to account for the electronic energyincrease after a hop, the hop is rejected. The velocity rescalingprocedure gives a detailed balance between up and down transitions.The detailed balance is needed to achieve the Boltzmann statistics andthermodynamic equilibrium.40

The classical path approximation to FSSH41,45 assumes that thenuclear dynamics is weakly dependent on the electronic evolution, forinstance, as compared to thermally induced nuclear fluctuations. Thisapproximation generates great computational savings because thetime-dependent potential that drives multiple FSSH realizations isobtained from the single MD trajectory. It is assumed further that thenuclear subsystem is close to the thermodynamic equilibrium and inparticular that the energy deposited into the nuclear modes along thedirection of the ⟨Φj|∇R|Φk⟩ vector dissipates rapidly among all nucleardegrees of freedom. Then, the hop rejection feature is replaced withmultiplication of FSSH probability upward in energy by the Boltzmannfactor. This maintains the detailed balance and achieves thermody-namics equilibrium in the long-time limit.41,45

3. RESULTS AND DISCUSSION3.1. Geometric and Electronic Structure. The structures

of the thin Au films with and without the Ti adhesion layer

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were first optimized at 0 K. The optimized structures shown inFigure 1a indicate that adding a layer of Ti has a very minoreffect on the Au film geometry. The geometry of the Ti layeralso changes slightly because of the interaction. The largestatomic displacement along the vertical direction is less than0.06 Å. The distance between the Ti layer and the nearest Aulayer is 2.270 Å. The calculated Au−Ti bond length is 2.791 Å,which is close to the observed and calculated Au−Ti bondlengths in clusters and alloys.57,58 The intralayer Au−Au bondlength is 2.884 Å, in good agreement with the experimentaldata.59 The influence of the Au−Ti interaction on the systemgeometry is much weaker than thermal effects.The geometries of both slabs change considerably owing to

thermal expansion, when the temperature is elevated to 300 K(Figure 1b). The distance between the Au layers increases byabout 0.2 Å, whereas the distance between the Ti adhesionlayer and Au slab grows by 0.05 Å. In addition to thermalexpansion, the finite temperature geometries exhibit small-scalesliding motions of layers with respect to each other, includingboth Au and Ti layers. Even though the bonding patterns donot change at the finite temperature relative to the optimizedstructure, in contrast to some other nanoscale systems,60,61 theadditional symmetry breaking introduced by thermal fluctua-tions influences localization of the wave functions, generatingNAC.Figure 2 characterizes the electronic structure of the Au−Ti

slabs by presenting the projected density of states (PDOS)

obtained using the optimized geometry at 0 K. All three panelsin Figure 2 show the same DOS in different representations.The Fermi level is set to zero. The system has no bandgapbecause it is a metal. The most obvious observation is that theAu DOS is significantly larger than the Ti DOS in the energyrange between −7 and −1.5 eV. This is the range dominated byAu 5d states, which contributes much more than Au 6s, 6p, andTi 3d states to the overall DOS.The second and the most important observation is that the

Ti DOS is about equal to the Au DOS in the −1.5 to 4 eVenergy range. This is quite remarkable because the systemcontains 7 times more Au atoms than Ti atoms. The Ti DOS in

this energy range arises from Ti 3d states whereas the Au DOSis determined by about equal contributions of Au 6s, 6p statesand the tail of the 5d states PDOS. One can conclude that, ingeneral, d states produce much higher DOS than s and p states.Similar to the −7 to −1.5 eV range that exhibits high DOSowing to 5d contributions of Au, the 3d states of Ti contributesignificantly in the −1.5 to 4 eV energy range. We focus on thepreviously mentioned pump−probe experiments performed byGiri et al. using a pump excitation energy of 3.1 eV.30 In theenergy range from 0 to 3.1 eV (Figure 2c), the contribution ofTi states is comparable to and even more important than thatof Au states. Considering that Ti atoms constitute only 1/8 ofall atoms, we conclude that the Ti adhesion layer significantlyinfluences the electronic states in the experimentally relevantenergy region.Thin gold films are usually evaporated onto nonmetal

substrates, such as crystalline, fused silica.30,62 To explore theeffect of a nonmetal substrate on the electronic states of thegold film, we constructed a model with one layer of Si adsorbedonto the same Au(111) surface slab and calculated the PDOSof every component (Figure 3). Part (c) of Figure 3 shows

clearly that the contribution of Si to the overall DOS isnegligible over the whole considered energy range between −7and 6 eV. The PDOS in Figure 3b indicates that thecontributions of Si 3s and 3p states are much smaller thanthe contributions of Au 5d, 6s, and 6p states. We conclude thata nonmetal substrate, such as Si, has little effect on theelectronic DOS of Au films in the relevant energy range.The electron relaxation rate depends on the phonon-induced

NAC between electronic states. The strength of the coupling isrelated to the corresponding wave function overlap (eq 5).Therefore, we investigate the shape of the electron densities atdifferent energies (Figure 4). The plotted densities are squaresof the adiabatic KS orbitals that enter eq 5. The pump−probeexperiments employ 3.1 eV excitation energy.30,62 Accordingly,we consider approximately the 0−3.1 eV energy range anddivide it into three intervals, 0−1, 1−2, and 2−3 eV. Figure 4shows the charge densities of the highest occupied molecularorbital (HOMO) at the Fermi energy, as well as the

Figure 2. PDOS of the Au(111) slab with adsorbed Ti layer (a) overbroad energy range from −10 to 6 eV, (b) over narrower energy rangefrom −2 to 5 eV, and (c) split into Au and Ti contributions. TheFermi level is set to zero and shown by the dashed line.

Figure 3. PDOS of the Au(111) slab with adsorbed Si layer (a) overbroad energy range from −10 to 6 eV, (b) over narrower energy rangefrom −1 to 4 eV, and (c) split into Au and Si contributions. The Fermilevel is set to zero and shown by the dashed line.

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representative states picked randomly 1, 2, and 3 eV above theFermi level for both Au and Au−Ti. The wave functions of thepristine Au film are symmetrical and localized on the bulk layerswith little surface contribution. The symmetry is broken in theAu−Ti system by the Ti layer. The surface layers nowcontribute to the majority of states, which can be localizedeither on the Ti side or on the opposite side of the film. Theorbital localization changes as atoms move along the trajectory,and an averaging over initial conditions is required to reproduceall situations. The states localized on the Ti side haveconsiderable contributions from Ti, as expected based onPDOS (Figure 2). Typically, electron−phonon NAC matrixelements (eq 5) are larger for more localized states becausechanges in wave functions induced by nuclear motions aremore significant if wave functions are localized.3.2. Electron−Phonon Interactions. Electron−phonon

relaxation appears in the trajectory surface hopping as asequence of NA transitions between electronic energy levels.Each elementary transition reflects the strength of the NAC andthe detailed balance factor for transitions upward anddownward in energy. The NACs are obtained along thetrajectory based on the adiabatic wave functions for the currentmoment in time, according to eq 5.Table 1 compares the absolute values of NAC averaged over

all electronic states involved in the relaxation to those averagedonly over the neighboring states. Different energy ranges inboth Au and Au−Ti systems are considered. The most strikingobservation is that the NAC magnitudes are much larger for

Au−Ti compared to Au. Even a thin Ti adhesion layer changesthe NAC by a factor of 3−5 and even more. The differencearises because Ti is a factor of 4 times lighter than Au, and thenuclear velocities directly affect the equation for NAC (eq 5);at a given temperature, which determines the nuclear kineticenergy, the velocity is inversely proportional to the square rootof the atomic mass. This dependence predicts a factor of 2difference in NAC arising from Ti compared to Au. Further, asingle layer of Ti doubles the DOS of the 7-layer Au slab withinthe relevant energy range (Figure 2). Generally, NAC betweenstates that are close in energy is larger. Indeed, the absoluteNAC averaged over the nearest neighbor states is a factor of 2−4 larger than the absolute NAC averaged over all states,compare the first two lines in Table 1. Similarly, NAC betweendenser states in Au−Ti is larger than between sparser states ofpristine Au. Thus, the Au and Ti mass difference, together withthe difference in the DOS, can explain why electron−phononcoupling is much larger in Au−Ti than Au, in agreement withthe experiment.30

One might argue that an adhesion layer of Si on a Au filmshould also increase NAC because Si is much lighter than Au.This is not the case because Si contributes very little to theoverall DOS in the relevant energy region (Figure 3). Eventhough Si atoms are light, they do not affect the electronic wavefunctions and the NAC matrix elements that depend on thewave function overlap (eq 5). This result is consistent with theexperimental observation that semiconducting substrates havelittle effect on the electron−phonon relaxation in Au films.30

Figure 4. Charge density of the representative states: HOMO, 1, 2, and 3 eV above the Fermi level for bare Au(111) and Au(111) with adsorbed Tilayer in their optimized structures. The isosurface value is set to 0.001 e/A3.

Table 1. Absolute Value of the NAC Averaged over the Nearest States (Ni,i+1abs ) and over All States (Ntotal

abs ) and Electron−PhononRelaxation Times in the Au and Au−Ti Systems at 300 K

Au Au−Ti

0−1 eV 0−2 eV 0−3 eV 1−2 eV 2−3 eV 0−1 eV 0−2 eV 0−3 eV 1−2 eV 2−3 eV

Ni,i+1abs (meV) 7.15 6.64 6.19 4.99 5.90 20.31 20.40 27.32 21.76 40.28

Ntotalabs (meV) 2.60 1.84 1.26 2.30 1.95 7.48 8.11 8.46 11.81 19.11

decay time(ps) 1.83 0.45

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To characterize the frequencies of the phonon modes thatcouple to the electronic subsystem and the relative strength ofelectron−phonon coupling for different modes, we computethe Fourier transforms of the energy gaps between HOMO atthe Fermi energy and the three states sampled at 1, 2, and 3 eVabove the Fermi energy (Figure 5). The densities of these states

are shown in Figure 4 for the optimized slab geometries. Theheights of the peaks in Figure 5 characterize the strength of theelectron−phonon interaction at the corresponding frequencies.The spectra shown in Figure 5 are known as influence spectraor spectral densities.63,64

The phonon modes that couple to the electronic subsystemhave low frequencies, with the lower frequency acoustic modesshowing stronger coupling than the higher frequency opticalphonons, consistent with the semiclassical theory. Oursimulations provide important insight into the quantum-mechanical mechanism driving this electron-low frequency

phonon interaction, more specifically, that the electronic wavefunctions are quite delocalized (Figure 4). Local displacementsof atoms with respect to each other, characteristic of higherfrequency optical modes, have little effect on the delocalizedwave functions. (The effect averages out on the scale of wavefunction delocalization.) In comparison, larger scale acousticmotions induce a stronger wave function change. Recall that itis the phonon-induced change in the wave function that causesthe electron−phonon NAC (eq 5).The dominant peaks below 100 cm−1 seen in the influence

spectra of pristine Au can be assigned to acoustic phononmodes involving core Au atoms.65 Introduction of the Ti layerincreases the frequency range of active vibrations. The higherfrequency modes appear because Ti atoms are much lighterthan Au atoms. Our simulation agrees well with theexperimental shift to higher phonon frequencies observedupon inclusion of adhesion layers on gold nanodisks.32

3.3. NA Relaxation Dynamics of Photoexcited Elec-trons. The electrons photoexcited to about 3.1 eV, as in theexperiment,30 were allowed to relax from the nonequilibriumstates to the Fermi energy by coupling to phonons. Theelectron−phonon relaxation dynamics was simulated usingFSSH implemented with real-time TDDFT in the KSrepresentation, as described in section 2.2 and in more detailin refs 41-42. The evolution of the photoexcited electronenergies in the Au and Au−Ti systems is shown in Figure 6.Note that the x-axis scales are different in parts (a,b). Here, thezero of energy is again set at the Fermi level. The reported timeconstants were obtained by the exponential fitting. Note thatthe early time dynamics in Figure 6 is Gaussian rather thanexponential, which is typical of quantum dynamical systems;66

however, the exponential regime is achieved relatively fast.The electron−phonon relaxation dynamics is a factor of 4

faster in Au−Ti than in Au. The difference between pristine Auand Au with a Ti adhesion layer is more pronounced in thecalculation than in the experiment, compare Figure 6 of thispaper with Figure 2 of ref 30. This discrepancy could be due tothe small size of the simulation cell compared to theexperimental system. The narrow slab used in the simulationemphasizes the coupling of Au states to Ti atoms. In thicker

Figure 5. Fourier transforms of the energy gaps from the Fermi levelto electronic levels at 1, 2, and 3 eV above it, in (a) Au and (b) Au−Tisystems.

Figure 6. Average electron energy decay at 300 K in the (a) Au and (b) Au−Ti systems.

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slabs, Au wave functions should be less delocalized onto the Tiadhesion layer. This discrepancy could also be due to thechemistry of the Ti layer in the prior experimental work and thepotential for oxygen defects or TiOx phases in Ti layer.The thickness of the Au film used in the experiment is about

16 nm, and the thickness of the Ti adhesion layer is 2.8 nm (seeTable 1 of ref 30). The experimental Au−Ti thickness ratio is5.7. The current simulation uses seven atomic layers of Au andone atomic layer of Ti, giving a similar ratio. If the thickness ofthe Ti adhesion layer is increased, one can expect that theelectron−phonon relaxation in the Au−Ti system will becompletely dominated by Ti. On the one hand, the PDOS of asingle Ti layer is already similar in magnitude to the PDOS ofseven Au layers, at energies around and above the Fermi energy(Figure 2). The Ti PDOS will be dominant for a larger numberof Ti layers. On the other hand, Ti atoms are significantlylighter than Au atoms, and therefore, they create strongerelectron−phonon coupling than Au atoms.Fermi’s golden rule, employed successfully to rationalize

other NAMD simulations,67 cannot explain the fourfolddifference in the relaxation times observed in this work. Ingeneral, the initial stage of quantum dynamics is Gaussianrather than exponential because the time-derivative of thequantum population is 0 at t = 0, see early times in Figure 6.The nonexponential initial stage of quantum dynamics givesrise to the so-called quantum Zeno effect,66 in which theinteraction with the environment dramatically slows down thedynamics. According to the Fermi’s golden rule, the transitionrate is proportional to the coupling squared. In the currentsystems, the NAC in the Au and Au−Ti films is alreadydifferent by a factor of 3−5, see Table 1. The DOS on Au−Ti isalso larger than the DOS of Au, see Figure 2. Thus, Fermi’sgolden rule should predict a factor of 10−20 times fasterdynamics in Au−Ti, as opposed to a factor of 4. A similarsituation is observed experimentally: the difference in therelaxation times, Figure 2 of ref 30, is much less than thedifference between the squares of the corresponding electron−phonon couplings (with and without Ti), Figure 3 of ref 30.The fact that rate expressions such as Fermi’s golden rulecannot explain the experimental observations emphasizes theneed for quantum dynamics simulations coupled closely withthe well-controlled experiments.

4. CONCLUSIONSBy performing the time-domain ab initio simulations, weinvestigated the electron−phonon relaxation process in thingold films with and without a Ti adhesion layer and establishedthe factors responsible for the difference in the observedrelaxation rates in the two systems. Understanding of thesefactors is important for the successful application of thin goldfilms and related systems in various electro-optical devices. Thesimulation supports the experimental observation that therelaxation between electrons and phonons accelerates signifi-cantly when a Ti adhesion layer is deposited on a Au film. Thedifference stems from two factors. First, Ti contributes verysignificantly, about seven times more per atom than Au, to thedensity of electronic states in the relevant energy window.Second, Ti atoms are about four times lighter than Au atoms,generating faster nuclear velocities that determine theelectron−phonon NAC. By contrast, semiconducting sub-strates, such as Si, SiO2, or Al2O3, have no effect onelectron−phonon relaxation, even though they are alsocomposed of light atoms. This is because they have no states

near the Fermi energy of Au. The reported results show goodagreement with the experiment data and provide a detailedatomistic understanding of the electron relaxation processesneeded for designing novel materials and devices.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: prezhdo@usc.edu.ORCIDXin Zhou: 0000-0002-4385-8379Ashutosh Giri: 0000-0002-8899-4964Oleg V. Prezhdo: 0000-0002-5140-7500NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSX.Z. acknowledges the support from the National NaturalScience Foundation of China, grant no. 21473183 and ChinaScholarship Council. O.V.P. and P.E.H. acknowledge thefinancial support from the US Department of Defense,Multidisciplinary University Research Initiative, grant no.W911NF-16-1-0406.

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