Plasmon-Induced Hot Carriers Transport in Metallic Ballistic Junctions

Article pubs.acs.org/JPCC

Plasmon-Induced Hot Carriers Transport in Metallic Ballistic Junctions Michal Vadai and Yoram Selzer* School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel ABSTRACT: The recent surge of theoretical research and experimental effort to devise plasmon-induced hot-carrier devices for radiation harvesting relies on the capability to separate charges at metal−semiconductor interfaces; however, the demand for momentum conservation of hot carriers at these interfaces sets an inherent limit to the quantum yield of such devices, making them currently less efficient than commonly used solar cells. Here we report experiments that suggest that ballistic whole-metal plasmon-induced hot carriers junctions based on atomic contacts could potentially be as efficient as semiconductor-based photovoltaic devices.

1. INTRODUCTION The most commonly used solar cells have an average efficiency in the range of 16−20%.1 One appealing approach in the continuous effort to improve the efficiency, that is currently being extensively explored, is to make solar cells based on plasmon-induced hot-carrier generation at metal−semiconductor interfaces.2−6 The same approach is also used for efficient infrared detection.7,8 Consider the Schottky barrier depicted in Figure 1a. Light harvesting of wavelengths longer than the

creates coherent oscillations of conduction electrons in a skinlayer of the metal structures, known as localized surface plasmons (LSPs), which, in turn, form hot carriers by nonradiative (Landau dumping) decay processes. The energy distribution of the initially formed hot carriers has been a subject of intensive theoretical research.9−13 These suggest that hot carriers formed by interband transitions (such as d-band to s-band in Au) have a limited lifetime of the d-holes and low energy of the s-electrons. In contrast, intraband (sband to s-band) transitions result in long-lived s-electrons and holes with energy up to 2.0 eV above and below the Fermi energy and with a characteristic mean free path of 20−40 nm limited by electron−electron (e−e) and electron−phonon (e− p) inelastic scattering events. Under such energy-distribution conditions, a possible quantum yield value for hot-carrier devices as high as 22% has been suggested assuming a density of states on the metal side that favors preferential excitation of electronic levels close to the Fermi level.14 Then, the number of “wasted” excitations of carriers from deep below the Fermi energy to final energy values that are still below the Schottky barrier is minimized. The rather high possible yield in this study was based on the assumption that the transmission probability of sufficiently high hot electrons to cross the interface (process 3 in Figure 1a) is 1. This assumption, however, was recently scrutinized based on momentum matching considerations.15 Because of a difference in the number of available states in momentum space in the metal and in the semiconductor (see Figure 1b), only hot carriers that reach the interface within an escape cone can cross it, while all of the rest are totally reflected. Under these

Figure 1. (a) Band diagram of a metal−semiconductor Schottky barrier. Photons with energy smaller than the band gap of the semiconductor can create plasmons (shown as a red ellipse) within the metal side, which by Landau dumping (process 1) create hot carriers that transport to the interface (process 2), and a fraction of them has a sufficient kinetic energy to cross the barrier to the semiconductor side (process 3). (b) Constant energy contours for hot electrons in the metal (left) and semiconductor (right). Transfer across the barrier is confined to an angle Ω that is determined by the maximum allowed momentum in the semiconductor.

corresponding energy gap of the semiconductor can be achieved by efficient generation of hot carriers within the metal with sufficient kinetic energy to be injected over the barrier. While direct absorption of photons in noble metals in the requested wavelength regime is rather low, it can be immensely enhanced by using properly designed plasmonic metal nanostructures. Absorption of photons in this case © XXXX American Chemical Society

Special Issue: Richard P. Van Duyne Festschrift Received: April 7, 2016 Revised: May 23, 2016

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of G0, where G0 = 2e2/h is the quantum of conductance. A small deviation of the peak position from the exact quantized value has been discussed by some authors18−21 and attributed to the contact’s internal configuration, additional electron reflection due to an abrupt contact geometry, and the presence of adsorbates. Creation of plasmons within the gap of the SBJ is achieved in a Kretschmann configuration by attaching a BK7 glass prism to the bottom slide. Plasmon resonance conditions are found by varying θ, the incident angle of a p-polarized light with respect to the surface normal, and by monitoring the intensity of the reflected light. Maximum plasmon coupling appears as a minimum in the reflectivity. A previous study that used a similar approach to couple light into an air−Au−insulator−Au−glass structure resulted in a plasmon located predominantly at the air−metal interface.2 In our case, the plasmon mode created in the symmetric structure of the SBJ has an enhanced field located within the gap with a symmetric behavior of the field on both metal−glass interfaces (see Figure 3).

constrains, the overall yield of a device is expected to be merely 1%; however, for thin-metal films that have a thickness in the order of the mean free path of the hot carriers for e−e scattering, the yield can be enhanced significantly by reflections at the boundaries. In addition, e−p scattering can enhance the yield by redirecting the momentum of hot carriers into the escape cone with little loss of energy. The overall yield is therefore estimated to be, under favorable conditions, as high as ∼10%. Experimental studies, however, do not report yield values higher than ∼5%.2,3,5,6 Considering all of the above it seems that in order for hot carriers devices to be at least as efficient as state of the art semiconductor-based solar cells three conditions need to be met: (i) efficient plasmon-induced creation of hot carriers, (ii) ballistic transport of the carriers to the interface, and (iii) relief of the momentum-space limitation at the interface. A recent experimental study from the Van Duyne group16 shows plasmon-induced charge separation in molecular junctions, where their transmission-energy landscape dictates the energy of the hot carriers that can ballistically cross the interface. Inspired by these results, we wish to demonstrate here using ballistic metal quantum atom-contact junctions that when all of the above necessary conditions are met, the resulting effective yield could be as high as ∼30%.

2. EXPERIMENTAL SECTION To demonstrate our approach, we use a squeezable break junction (SBJ) setup operating at room temperature under ambient conditions.17 The SBJ consists of two 40 nm thick gold films evaporated on top of 1 mm BK7 glass slides, facing each other, with an initial gap of 500 nm, as depicted in Figure 2.

Figure 3. Calculated dispersion of two out of a total three plasmonic modes that can be excited by the Kretschmann configuration in an IMIMI configuration.17 The dielectric constants of the prism and air are 1.512 and 1, respectively. The relevant Johnson and Christy values were taken for Au. The light (prism) line is in blue, and two modes, symmetric and antisymmetric, are shown in green and orange. The additional momentum needed for 1.59 eV photons to match the momentum of plasmons within the gap is supplied by local roughness. The arrow indicates that roughness with periodicity of ∼1 μm is sufficient to create the symmetric mode within the gap. The inset depicts the field distribution, where the two glass−Au interfaces are located at 0 and 80 nm.

Figure 2. Squeezable break junction (SBJ) setup. (a) Schematics of the experimental approach. Coupling between free photons and surface plasmons confined within the gap is established by a prism and by laser illumination in the total reflectance regime. The wavelength of the continuous wave laser used in all experiments was 781 nm, the power was 10 mW, and the beam focused to a spot with a radius of 80 μm. (b) Conductance histogram of Au atomic contacts showing peaks around multiple integers of G0. The inset shows typical conductancetime traces.

The advantage of using the squeezable setup for this study can be described in the following way. The generation of efficient plasmon-induced current within a certain junction sets two demands for the energy (wavelength) of the photons that should be used for this purpose. On one hand, the transmission properties of the junction, as will be elaborated below, determine the necessary energy (above or below the Fermi level) of the hot carriers that can contribute additional current to the one induced by the applied bias. On the other hand, efficient absorption of these photons necessitates that the used wavelength is within the plasmon resonance of the junction, which is determined by its geometry on roughly the scale of the wavelength. This geometry cannot be easily changed or controlled in “traditional” single molecule devices such as mechanical or STM-based break junctions.16 The squeezable

The gap size can be mechanically controlled with high accuracy by applying a squeezing force on the top slide, allowing it to flex. Conductance traces are initiated by squeezing the top slide until it contacts the bottom surface and then by measuring the conductance (typically at 0.1 V) while letting the top slide moving back (up) in steps of 10 pm. Conductance histograms are constructed from thousands of traces without any data selection or processing. Figure 2 depicts a typically obtained histogram for Au atomic contacts, revealing a quantized conductance behavior with clear peaks around integer values B

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The conductance gap between the two peaks is angledependent, as revealed in Figure 5. The dip in reflectance is

setup used here solves this problem: For each chosen wavelength, as determined by the electrical transmission properties, plasmon resonance can be achieved by the angledependent prism-coupling setup. The typical roughness of deposited Au films provides momentum matching for all possible wavelengths between the prism-induced momentum of the free photons and the corresponding value of the surface plasmons. Without the prism and the “knob” of angledependent illumination, plasmons cannot be created within the gap. In a previous study17 we presented (as supporting information) Fourier analysis of AFM images of Au films, such as the ones used here. Roughness was shown to have a broad spectrum of wavevectors, which enables momentum matching for plasmons creation with all visible and near-IR wavelengths. While the experiments described here can essentially be performed with any plasmon-active metal, the use of Au in this study originates in the fact that theoretical formulation of the conductance properties of atom contacts formed with this metal22 is well established. This understanding, as will be discussed below, is essential for quantitative interpretation of the results.

Figure 5. Conductance gap between the peaks as a function of incidence angle (blue). The corresponding reflectance is shown in black. The difference in the width of the two curves can be explained by considering radiative damping of the plasmons, a process that does not contribute to the hot carriers generation. This competing effect is taken into account in the semiquantitative model that explains the results (red curve). See the text for details.

3. RESULTS AND DISCUSSION Figure 4 shows that upon irradiation, the 1G0 peak in the conductance histogram splits into two peaks. Splitting occurs

accompanied by a peak in the conductance-splitting gap. Importantly, the relative intensity of the two peaks does not change with the incident angle. This rules out the possibility that the peaks correspond to different structural conformations of the atomic contacts that are thermally activated and populated because then the gap between conductance peaks would have been constant and only their relative intensity should have changed. In a previous paper, the effect of irradiation on the conductance of Au atom contacts was analyzed by us using a photoassisted transport (PAT) mechanism.23 In PAT, adiabatic coupling between states on the two sides of a junction, located within integer multiplication of the photon energy from one another, is induced by the oscillating electromagnetic field within the gap. To be effective, this mechanism requires high fields, that is, high laser intensities. Indeed, in our former study the laser intensity was more than 5000 times higher than the one used here. The use of the PAT mechanism is not justified in this study. In fact, fitting of the results by this model (see ref 23 for details) necessitates nonphysical plasmonic field enhancement of above 10 000. Instead, the results are explained by considering plasmoninduced generation of hot carriers within the SBJ. For the creation of a hot electron−hole pair to take place, an electron with an energy E1 and wavevector k1 below the Fermi level needs to be excited to a state with energy E2 = E1 + ℏω and a wavevector k2 (see Figure 6a). The resulting wavevector mismatch Δk is on the order of Δk ≈ ω/νF, where the Fermi velocity νF for Au is 1.4 × 108 cm/s. Thus, for a 1.59 eV photon (780 nm) the wavevector mismatch is ∼0.02 nm−1. This value, although much larger than the wavevector of free photons, is within the range of momentum values supplied by the rough Au films.17 Thus, the LSPs are responsible for the “diagonal” transition in Figure 6a, that is, the Landau damping processes within the junctions. The rates of this process depend on the spectrum of roughness-induced wavevectors Δq values according to ∼ΔqνF.10

Figure 4. Conductance histograms measured without (a) and with (b) laser irradiation at the indicated incident angle θres. Upon irradiation, the 1G0 peak splits into two peaks with equal populations located above and below the initial conductance value of 1G0. (c) Reflectivity curve measured, as explained in Figure 2. The angle of minimum reflectance, that is, maximum plasmons creation, is θres. (d) Individual conductance traces taken from the set of traces from which the doublepeaked histogram in panel b was constructed. Traces with the conductance steps of 1G0 (blue) values are shown. For reference, a trace with a conductance step at 1G0 (black) is also shown, taken from the set of traces comprising the 1G0 histogram (a).

only with p-polarized illumination, while with s-polarized light, under which plasmons cannot be created, no splitting is observed. The traces in Figure 4d reveal conductance steps that correspond to the two peaks in the histogram. In general, the traces do not show fluctuations between the two conductance values of the peaks. Instead, each can be associated with one of the peaks. Thus, roughly in half of the measurements events the conductance is higher than 1G0, while in the other it is lower than 1G0. C

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enhancement of the field within the gap of the SBJ. We find that all results can be fitted using one enhancement factor of 600. This value is on par with former measurements of molecular junctions.26 The current is calculated by a Landauer theory expression according to I=

Under all of these conditions, the electronic distribution within the leads formed by Landau damping can be described by16,24 (1)

where the equilibrium Fermi−Dirac function, feq, reflects the electronic temperature, Te, and f p is the nonequilibrium distribution of carriers formed by Landau damping. Thus, under steady-state conditions electron−hole pairs created by plasmons annihilation with an energy distribution defined by f p continuously relax by damping their excess energy into the surrounding electrons bath, creating a Fermi Dirac distribution feq with an effective Te, which is higher than the surroundings. The Fermi distribution is defined by 1 feq (ε , μ) = (ε − μ)/ kBTe (2) 1+e eV

where μ is the chemical potential of the lead, μ = E F ± 2 , EF and V are the Fermi energy and the applied bias, respectively, and kB is the Boltzmann constant. Assuming that all electronic transitions are equally probable, and in the case of CW radiation, the steady-state form of the nonequilibrium plasmon-induced component takes the form of fp (ε , μ) =

⎛ (ε − μ)β ⎞ L(ω) Ṅ (ω)τe(ε) e ⎟ tanh⎜ ρ (ε) 2 ⎠ ℏω ⎝ cosh(ℏωβe) − 1 cosh(ℏωβe) + cosh((ε − μ)βe)

+∞

∫−∞

dε [f1 (ε , μ1) − f2 (ε , μ2 )]Τ(ε)

(4)

where e is the electron charge, f j(ε, μj) (j = 1,2) is the electronic distribution in electrode j, μj is the chemical potential of the eV electrode defined as μj = ± 2 , and T(ε) is the transmission function at energy ε (see Figure 6b). The nonequilibrium between the electrodes results from, in addition to the applied bias V, the fact that at each measurement event Landau damping is taking place in only one of the electrodes. This is based on the observation that the traces do not show fluctuations between the two conductance values of the peaks and also due to the fact that plasmon damping necessitates, as described above, certain local roughness to bridge the momentum gap, which statistically occurs on one side of each formed atomic contact. From eq 1, assuming that Landau damping occurs in electrode 1, f1(ε, μ1) − f 2(ε, μ2) = feq(ε, μ1) − feq(ε, μ2) + f p(ε, μ1). The difference feq(ε, μ1) − feq(ε, μ2), which reflects the difference in the electronic temperatures, Te, between the two electrodes (a direct result of the Landau damping on one electrode in each measurement event), gives rise to a possible thermoelectric response. An estimated upper limit for Te can be made based on the following reasoning. In the diffusion limit according to the two temperatures model,27,28 which describes the time and space evolution of the electron and lattice temperatures (Te and Tl, respectively) in response to light absorption in a metal, the behavior of the lattice temperature is described by Cl∂Tl/∂ t = g(Te − Tl) where Cl is lattice heat capacity and g is the electron−phonon coupling constant. Clearly, under the steady state, CW illumination, conditions that prevail in our experiments: Te = Tl. Because in our system measurements of 1G0 contacts at different bath temperatures set a limit ∼400 K, above which these contacts cannot be formed, we may assume that Te (for the illuminated electrode) cannot exceed this temperature value. Considering the theoretical curve in Figure 6b, because the conductance of a Au atomic contact is 1G0 within an energy range of ±1 eV around the Fermi energy, it is clear that with a maximal temperature difference of 100 K between the two electrodes no photothermoelectric effect is expected. The contribution of the feq(ε, μ1) − feq(ε, μ2) term to the measured conductance is most likely negligible. Further support for this argument is found in the fact that the experimentally determined Seebeck coefficient of Au atomic contacts is ≤10 μV/K.29,30 The largest measured conductance peak splitting, according to Figure 5, is 0.05G0. Because the applied voltage is 0.1 V, this peak splitting should correspond to a thermovoltage of 5 mV, which necessitates a temperature difference of at least 500 K based on the Seebeck value. As previously described, atomic contacts cannot be formed in our setup at such elevated temperatures. Hence, the observed peak splitting is entirely due to the nonequilibrium hot carriers distribution, f p, that is formed in the leads by Landau damping. Splitting results from the fact that hot-carrier generation can form current that flows either

Figure 6. (a) Phonon- or impurity-assisted absorption of a photon with wavevector k, which (compared with the wavevectors of electron) is ∼0, and a direct absorption of LSP with a large wavevector k (Landau damping). (b) Calculated transmission of a Au atomic contact as a function of energy.21 The shaded area covers the energy range in which hot carriers are created by 1.59 eV photons (assuming momentum matching is provided). On the basis of this curve, enhancement of conductance is due to hot holes.

f (ε , μ) = feq (ε , μ) + fp (ε , μ)

e πℏ

(3)

−1

Here ρ (0.1 eV per atom) and τe (ε) are the density of states and the relaxation time of the hot carriers, respectively. For simplicity, we later assume that both parameters are energyindependent. This assumption is corroborated by other studies13,25 that show that within energy values of ±2 eV around the Fermi level of Au, ρ ≈ 0.1 eV−1 per atom and τe ≈ 10 fs. Ṅ is the number of incident photons per second per atom, βe = (kBTe)−1, and L(ω) is the absorption line shape, taken here for plasmons as 1. The value of Ṅ inserted into the equation is Ṅ calculated from the laser intensity factorized by the incident angle (as described below) multiplied by the square of a free parameter, which represents the plasmonic D

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which they lose at each event an energy in the order of a phonon energy (∼20 meV). On the basis of the transmission curve, a total energy loss of 500 meV would bring a hot hole back to a conductance value of 1G0. Thus, the maximum traveling distance is (500 meV/20 meV) × 15 nm = 0.375 μm. Setting the latter value to be the diameter of the effective irradiated area, the resulting yield is 43%, in fair agreement with the former calculation. We note that a yield of 30% was recently reported for an imaging technique based on hot carriers formed at a scanning tip.33 In conclusion, while the SBJ is clearly not suitable for real applications, we believe that the results presented here suggest that efficient radiation harvesting by ballistic whole-metal plasmon-induced hot carriers devices is quite a promising approach. Their main advantage is in the fact that they eliminate the (impedance) momentum-mismatch that always exists in metal−semiconductor interfaces, which appears to impede their charge-separation efficiency. Additional work is under progress to expand the wavelength range of this approach and to fabricate multicontact structures suitable for applications.

with or against the current formed by the applied bias, depending on which side of each formed junction Landau damping occurs. Applying the above semiquantitative model to explain the results (red curve in Figure 5) necessitates also considering the fact that the width of the reflectance dip in Figure 5 is wider than the corresponding value of the conductance-splitting peak. This behavior is not revealed in eq 3, according to which the relative changes in Ṅ as a function of incident angle should follow the reflectance behavior. This discrepancy is resolved by noting that the reflectance resonance curve contains two contributions: the Landau nonradiative damping (with a damping constant of ΓL) and radiation damping (with a damping constant of ΓR) that does not contribute to the creation of hot carriers. As a result, the width of the reflectance curve (at half value of the dip) is ΓR + ΓL. The model (red) curve in Figure 5 was calculated by making a reasonable assumption that ΓR = ΓL and by describing the changes in Ṅ as a function of incident angle according to the following Lorentzian behavior31 ⎛ ⎞ 4ΓLΓL ⎟ Ṅ (θ ) = Ṅ ⎜1 − m 2 2 (kx − kx ) + ΓL ⎠ ⎝ ω

■

(5)

Corresponding Author

ω

where kx = c n sin θ , kxm = c n sin θres , n is the reflective index of glass, and θres defined in Figure 4c. The quantum yield cannot be calculated directly from the laser intensity and the shift of the 1G0 peak (translated into current) because the radius of the laser spot is 80 μm and consequently the excitation of hot carriers takes place across a large area that on only a small fraction of which the single-point contact junction is formed. Hot carriers generated away from the point contact junction will degrade their energy through e− e and e−p collisions and will not arrive “hot” enough to affect its conductivity. Thus, to calculate the quantum yield under these circumstances, we estimate the effective traveling distance based on the escape probability of the hot carriers at a coordinate x. This has been shown to be proportional to ∼exp(−μx), where μ is a reciprocal escape length defined by32 μ=

⎛⎛ ⎞2 ⎛ ⎞⎞ ⎜⎜ 1 + 1 ⎟ − 1 × ⎜ 1 + 1 ⎟⎟ ⎜⎜⎝ le − e le − p ⎟⎠ le − p ⎜⎝ le − e le − p ⎟⎠⎟ ⎝ ⎠

AUTHOR INFORMATION

*E-mail: [email protected]. Tel: +972-36407361. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Partial support by the ISF (grant no. 1666/14) and the GIF (grant no. 1146-73.14) for this research is gratefully acknowledged.

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REFERENCES

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(6)

where le−e and le−p are the mean free path values of the corresponding processes. On the basis of the transmission curve in Figure 6b, hot holes located 1.59 eV below the Fermi energy are responsible for the apparent shift in the 1G0 conductance peak under irradiation. For these carriers and in contrast with former understanding, a recent calculation shows that their transport is affected equally by e−e and e−p processes with a resulting mean free path of l ≈ 15 nm, that is, 1/l = 1/le−e + 1/le−p, where le−e = le−p ≈ 30 nm.13 Considering the above exponentially decreasing escape probability, we conservatively assume that only hot carriers that are formed within a distance of three times the escape distance, that is, 3 × 1 , from the point contact are responsible for the additional μ

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