Modeling the Impact of Metallic Plasmonic Resonators on the Solar

Oct 8, 2018 - Department of Chemical Engineering, University of Michigan , Ann Arbor , Michigan 48109 , United States. J. Phys. Chem. C , Article ASAP...
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Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

Modeling the Impact of Metallic Plasmonic Resonators on the Solar Conversion Efficiencies of Semiconductor Photoelectrodes: When Does Introducing Buried Plasmonic Nanostructures Make Sense? Paul A. Hernley and Suljo Linic*

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Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States S Supporting Information *

ABSTRACT: It is well established that plasmonic nanoparticles embedded in a semiconductor can, under certain conditions, increase the rate of charge carrier collection in electrocatalysts bound to the semiconductor surface by changing the depth at which photons are absorbed in the semiconductor. One mechanism that leads to this effect is the injection of photon energy into the semiconductor by near-field and scattering effects induced by plasmonic metal nanoparticles. It is also well-known that these metallic plasmonic materials are also photon absorbers that can dissipate the incident electromagnetic energy into heat, which can make them into relatively efficient parasitic absorbers. Therefore, it is not clear under what circumstances plasmonic nanostructures should enhance the quantum efficiencies of semiconductors. We have developed a physically transparent model to demonstrate when introducing buried plasmonic metal nanoparticles into semiconductors is beneficial to improving the photon conversion efficiency. The model captures the influence of the thickness, optical, and charge carrier transport properties of the semiconductor as well as the depth of the buried plasmonic metal nanoparticles. We demonstrate the utility of the model by probing the impact of buried metal plasmonic nanoparticles on the efficiency of three vastly different semiconductors: TiO2, BiVO4, and Si. Using this model, we recommend strategies for improving the efficiency of available semiconducting materials by introducing buried plasmonic antennas.

INTRODUCTION The development of efficient ways to store solar energy in the form of chemical bonds is crucial for a sustainable future. A promising family of materials for this application is semiconductor light absorbers coupled with metal electrocatalysts at the surface of the semiconductor.1−12 The generation of charge carriers through photon absorption in the semiconductor and the transport of these carriers to the reaction sites on the electrocatalysts are processes that must be efficient to achieve acceptable external quantum efficiencies (EQE). In general, different semiconductors possess very diverse optical and charge transport properties that have a significant impact on the EQE. The reflectance of the semiconductor dictates the fraction of incoming light that enters the semiconductor, while the photon absorption depth dictates the fraction of photons absorbed by the semiconductor at a given depth. Once a photon is absorbed in the bulk of the semiconductor, the resulting charge carriers (electrons and holes) must be separated and transported to the reactive centers at the surface of semiconductor. Each semiconductor has a unique charge carrier diffusion length that corresponds to the distance a charge carrier can travel in the bulk before recombining. If a photon is absorbed at a depth away from the semiconductor surface that is greater than the charge carrier diffusion length, the charge carriers are likely to recombine before arriving at the reaction site. If the photon absorption © XXXX American Chemical Society

depth is large relative to the electrode thickness, the EQE is limited by inefficient absorption. Both of these scenarios could be improved if photon absorption is enabled closer to the reaction centers (i.e., electrocatalysts at the semiconductor surface). Metal nanoparticles can interact strongly with light of certain wavelengths as a result of localized surface plasmon resonance (LSPR). This excitation of LSPR results in strong electric fields near the surface of the particle. These electric fields can lead to the scattering of light by the particle to the far field or the absorption of light in the nanoparticle. The resonant wavelengths depend on the composition, size, and shape of the nanoparticles, as well as their local environment. Au and Ag nanoparticles can achieve these optical responses across the visible light spectrum.13−20 There have been a number of examples demonstrating that these plasmonic, noble metal nanoparticles can be coupled with some semiconductors to enhance the EQE, particularly at the LSPR wavelengths.21−26 It has been demonstrated that these enhancements are the result of a transfer of energy from the excited metal nanoparticles to the semiconductor, which leads to high rates of charge carrier generation in the semiconductor close to the Received: July 26, 2018 Revised: October 3, 2018 Published: October 8, 2018 A

DOI: 10.1021/acs.jpcc.8b07214 J. Phys. Chem. C XXXX, XXX, XXX−XXX


The Journal of Physical Chemistry C

data (Figure S2) for a number of flat semiconductors. The Fresnel equation is most appropriate for flat and smooth surfaces (monocrystalline Si wafers) while experimental data are more appropriate for rough, particle-based surfaces (for example, films of TiO2 and BiVO4 nanoparticles). We use the Beer−Lambert Law, shown in eq 1, to compute the probability of photon absorption in the semiconductor as a function of the semiconductor depth. ÄÅ ÉÑ ÅÅ x ÑÑÑ ÑÑ A(λ , x) = 1 − expÅÅÅÅ− ÅÅÇ d(λ) ÑÑÑÖ (1)

plasmonic nanoparticle.21,22,27−29 These plasmon-induced enhancements of the EQE have, so far, been experimentally demonstrated mainly for semiconductors that have very short minority charge carrier diffusion lengths (such as Fe2O3 and doped TiO2) and that, in general, exhibit relatively low EQEs. While there are many reports of the positive impact of the plasmonic metal nanoparticles on the measured EQE, there are no clear, physically transparent guidelines about when these EQE enhancements should be expected and what their magnitude should be. We note that metallic nanoparticles are characterized by various pathways that lead to the parasitic loss of the light energy (i.e., heating of the nanoparticles). In light of these complexities, it is important to determine when and how plasmonic metal nanoparticles should be used in particular systems to improve the EQE of different families of semiconductors.10,22,30,31 In this contribution, we present a simple, physically transparent photon conversion (PC) model that sheds light on the impact of plasmonic nanoparticles on the EQE of different families of planar semiconductor photoelectrodes. In our analysis we have focused on three different semiconductors (TiO2, BiVO4, and Si), which represent three different families of light absorbers in terms of the charge carrier diffusion and photon absorption lengths. The photon conversion (PC) model captures the optical (absorption, emission, and reflection) and bulk recombination properties of the semiconductor and evaluates the effect of placing idealized plasmonic metal nanoparticles at a specific depth in the planar semiconductor electrode.

The probability of absorption in the semiconductor, A, at a given wavelength, λ, is exponentially dependent on the quotient of the depth into the semiconductor, x, and the photon absorption depth, d. The photon absorption depth is defined as the distance at which the number of incident photons has been attenuated to 1/e of its initial number. This is equivalent to the reciprocal of the absorption coefficient and is dependent on the wavelength and the imaginary component of the refractive index (see the Supporting Information). In our PC model, none of the photons that traverse the entire semiconductor (i.e., are not absorbed) are reflected back into the semiconductor (i.e., they are transmitted) unless stated otherwise. To account for the inclusion of plasmonic metal nanoparticles at a depth xp in the semiconductor, we modify the semiconductor absorption probability calculation using eq 2. In this calculation, we assume that the photon energy that reaches the particle is either transferred into the SC at xp (e.g., via LSPR-mediated near-field effect), producing energetic charge carriers in the SC at this depth, or it is dissipated as heat in the particle.32,33 ÄÅ ÉÑ l ÅÅ o x ÑÑÑ o Å o Å ÑÑ, (0 ≤ x < xp) o 1 − expÅÅ− o o ÅÅÇ d(λ) ÑÑÑÖ o o A (λ , x ) = m o ÅÄÅ x ÑÉÑ o o o ÅÅÅ− p ÑÑÑ, (x ≥ x ) o 1 (1 f ( ) f )exp λ − − · o ÅÅ Ñ p o et l o ÅÇÅ d(λ) ÑÑÖÑ o n

THEORETICAL METHODS The PC model, described in detail in the Supporting Information, is built upon compounding the probabilities of several processes that occur in series. For an incoming photon to be useful, it must enter the semiconductor, be absorbed at a specific depth, and generate electrons and holes that reach the active centers before recombining. For a pure semiconductor, these probabilities are respectively related to the wavelengthdependent reflectance of the semiconductor, photon absorption depth (inverse of the absorption coefficient), and effective charge carrier diffusion length. We describe the impact of plasmonic nanostructures embedded in a semiconductor by modeling them as “light concentrators”, where these structures interact strongly with light. We assume that these materials can either efficiently transfer the energy of light to the nearby semiconductor, causing enhanced absorption in the semiconductor at the location of the nanoparticles, or alternatively convert the light energy into a parasitic heat loss in the nanoparticle. Our model essentially captures the action of the electromagnetic field around the nanoparticles, which can lead to either the enhanced absorption in the semiconductor or a parasitic heat loss in the nanoparticle. We neglect the potential of the energetic charge carrier that is created in the nanoparticle being transferred to the semiconductor. This is a reasonable assumption since a large fraction of charge carriers formed in the nanoparticle lose their energy rapidly through the collisions with electrons or by exciting phonon modes (heating the nanoparticle). To describe the optical behavior of a semiconductor, we use its complex refractive index (n + i·κ). Figure S1 shows the wavelength-dependent values of κ and n for the TiO2, BiVO4, and Si semiconductors used in this work. We estimate the reflectance, R, using a simplified version of the Fresnel equation (eq S2) or experimentally published reflectance


f l is the probability of absorption in the semiconductor through the LSPR-mediated energy transfer process The sum of this probability (f l) and the probability for the parasitic absorption in the metal (fa) is assumed equal to 1. When f l is 1, all the energy is injected into the SC. When f l is 0, all the energy is dissipated as heat in the nanoparticle. An energy transfer parameter (fet) is included to allow the plasmonic particleinduced transfer of energy to the semiconductor only when the incident photon energy is greater than the semiconductor band gap energy. It takes a value of 1 when the extinction coefficient (κ) of the semiconductor is ≥10−5 and a value of 0 when the extinction coefficient is