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Silver sulfide (Ag2S) nanoparticle (NP) is a promising material for quantum-dot-based hot-carrier solar cell, yet the hot carrier dynamics of the mate...
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Observation of Hot Carriers Existing in Ag2S Nanoparticles and Its Implication on Solar Cell Application S. Lin,† Y. Feng,*,† X. Wen,*,† T. Harada,‡ T. W. Kee,‡ S. Huang,† S. Shrestha,† and G. Conibeer*,† †

School of Photovoltaics and Renewable Energy Engineering, UNSW Australia, Sydney 2052, Australia Department of Chemistry, The University of Adelaide, Adelaide, South Australia 5005, Australia

‡

S Supporting Information *

ABSTRACT: Silver sulfide (Ag2S) nanoparticle (NP) is a promising material for quantum-dot-based hot-carrier solar cell, yet the hot carrier dynamics of the material has not been thoroughly studied for this purpose. In this work, carrier cooling dynamics of Ag2S NP thin film were measured and analyzed using the transient absorption (TA) spectrometer. The NPs exhibit a relatively high carrier temperature and long carrier cooling time. This result was further verified by the carrier temperature extraction from steady-state photoluminescence (ssPL) spectrum. The long carrier cooling time in Ag2S NPs can potentially lead to efficiency of 33.6%, demonstrating potential application for the high-efficiency hot-carrier solar cell.

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INTRODUCTION

In this work we report the synthesis of monodispersed 1dodecanethiol capped Ag2S NPs using a high-temperature solution-phase method. Ultrafast transient absorption (TA) spectroscopy is applied to investigate the carrier thermalization dynamics in the Ag2S NPs. We report the observation of hotcarriers existing in Ag2S NPs with a relatively high carrier temperature and a long thermalization time. The hot carrier dynamics are studied by TA spectroscopy, which is in good agreement with the carrier temperature extracted from steadystate photoluminescence (ssPL) spectrum. Overall, by experimental and theoretical study of the carrier thermalization dynamics and optical properties of Ag2S NPs, we are able to demonstrate a potential material for hot-carrier solar cell absorber.

Since the concept of the hot-carrier solar cell was first presented by Ross and Nozik,1 many advanced methods have been developed to improve the solar cell efficiency based on this concept. The advantage of hot-carrier solar cell is specifically designed to reduce the energy loss of photocarriers by slowing their thermalization rate before they are extracted to the selective energy contact. A preferred hot-carrier solar cell absorber requires large phononic bandgap to suppress the Klemens decay,2 thus slowing down the thermalization process. Nanostructures are considered as potential approaches for the high-efficiency hot-carrier solar cell.3,4 In a quantum confined system, the increasing electronic energy spacing requires the emission of multiple phonons to conserve energy in the phonon-assisted relaxation process.5 This results in a slow carrier cooling rate in nanostructures compared with that in bulk semiconductor material, due to the low transition rates of higher-order perturbative multiphonon processes. In the last decades, only few available semiconductor nanoparticle (NP) materials were investigated for the application of hot-carrier solar cells.6−8 Most of the solution-processed nanoparticle thin film solar cells were based on the multiple exciton generation (MEG) in Pb(S,Se) and Cd(Se,S,Te) quantum dots.9−14 The dynamics of hot carrier cooling of those materials have been extensively studied and the relaxation times are determined to be around a few picoseconds.15 Silver sulfide (Ag2S) is a nontoxic semiconductor material, which displays a premier bandgap with around 1 eV and relatively large absorption coefficients.16 To our knowledge Ag2S NPs have not yet been exploited for the application of the hot-carrier solar cell either theoretically or experimentally. © XXXX American Chemical Society

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SYNTHESIS OF AG2S NANOPARTICLES Ag2S nanoparticles used in this study are synthesized according to the fabrication process described in a previous study (see SI for details).17 Philips CM200 field-emission-gun high-resolution transmission electron microscope (HRTEM) was used to image the monodispersed NP array, and the particle size is estimated to be 5.7 ± 0.7 nm (Figure 1a). The HRTEM image reveals clear lattice fringe of as-fabricated samples, implying high crystallinity of the Ag2S NPs. The lattice constant is estimated to be 2.4 Å and aligns along the {121} plane.18 This was further confirmed by the X-ray diffraction (XRD) spectroscopy measurement (Figure 1b). The XRD spectrum displays strongest diffraction peak at a 2θ angle of 34.5° along Received: March 13, 2016 Revised: April 29, 2016

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Figure 1. (a) TEM and HRTEM image of synthesized Ag2S NPs; (b) XRD patterns show high crystallinity of NPs; (c) UV−visble−NIR absorption spectra of Ag2S NPs; (d) 2D AFM image of monolayer NPs fabricated with LB technique.

(840−1120 nm) giving very negative ΔODs (deviation of optical density from its static value) in the regime, as indicated by the red color in Figure 2a. With the time proceeding, most of the excited carriers in higher energy bands are thermalized to lower energies close to the conduction band minimum and accumulate at bands around 1060 nm before being recombined. More detailed information on the observed carrier dynamics are illustrated in Figure 2b,c. Figure 2b suggests the variation of transient absorbance at different time delays t. The excitation occurs at t = 0 ps, which pumps valence electrons to the excited states. The temporary bleaching of light absorption is assumed attributed to the excited carriers’ occupation in conduction bands. The broad transient bleaching reaches its maximum at around 1.3 ps centering at 920 nm and then decreases, accompanied by the bleaching center red-shifting to 1060 nm in line with the first allowed energy transition. At this stage the electrons initially occupying higher excited states thermalize to the edge of the conduction band. At long decay time, a negative signal in ΔOD is still observed in Figure 2b, indicating that some electrons stay in the lowest excited state (1060 nm) suggesting a long recombination time. The time evolution of ΔOD (at different detector wavelength illustrated in Figure 2c) is considered as being contributed by a variety of carrier processes. Due to the

the {121} plane direction, and the other diffraction peaks all agree with the published results.19 Figure 1c shows a continuous absorbance spectrum of Ag2S NPs solution (in chloroform) covering the whole wavelength range from infrared to ultraviolet (UV). An uniformly close-packed NPs monolayer is fabricated using Langmuir−Blogett (LB) technique,20 and its surface roughness is imaged by atomic force microscopy (AFM) in both 2D and 3D sections (Figure 1d). Details of the LB deposition are explained in the SI. The high quality of Ag2S NPs thin film as fabricated lays the foundation of further exploration measurement.

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HOT CARRIER DYNAMICS OF AG2S NANOPARTICLES The next step is to retrieve the carrier lifetime of Ag2S samples deposited on quartz by performing the femtosecond pump− probe experiment. We utilized TA spectroscopy (FemtoFrame II, IB Photonics) with 400 nm excitation pump pulses and 800−1200 nm probe range to study the dynamics of carrier cooling process in Ag2S NPs. The details of TA experimental setup are explained in SI. Figure 2a shows the color mapping of transient absorbance changes over pump−probe time delay. This provides information on the time evolution of photocarrier distributions in Ag2S NPs. Short after the pump, the photoexcited carriers are populated over a wide energy range B

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Figure 2. (a) Color mapping of transient absorbance change over pump−probe time delay and (b) at different instants after pump; (c) time evolution of the optical density variation at 920 and 1060 nm and relaxation-time-approximation (RTA) fitting of transient absorption spectroscopy measurement to obtain time constants; (d) transient carrier temperatures after photoexcitation (retrieved from measured TA spectra using RTA fitting description for inset).

uniformity of the synthesized NPs as measured with TEM, the diffusion of carriers (i.e., charge transfer) between NPs is not a major contributor to the observed dynamics. More importantly, according to our previous publication17 the variation of energy level between different sizes NPs is insignificant due to the small Bohr radius, as a result the coupling effects of Ag2S NPs are not important as it does not have much contribution to the TA spectra. All of these allow us to study the dynamics of different processes using the relaxation time approximation (RTA)21 as if the material is homogeneous. This kinetic model based on RTA was previously applied to the efficiency calculation of hot carrier solar cells.22−24 Here we reverse this model to fit the observed TA results. This allows us to find the relaxation times for carrier processes including photocarriers generation, Auger process, thermalization, and recombination of carriers. The mathematical form of the RTA model is expressed by two differential equations:

E[β(t ), μ(t )] − E[βrm , μth (t )] dE[β(t ), μ(t )] =− dt t th −

β (t ) =

(2)

1 kBT (t )

(3)

where kB is the Boltzmann constant. This allows us to express the particle density of carriers N and the energy density of carriers E in simple analytical forms:

N[β(t ), μ(t )] − N (βrm , 0) tre

tre

This set of differential equations describes the time evolution of the photogenerated carriers in the semiconductor. Due to the ultrafast renormalization process, we assume the carriers’ energy can be described by a Fermi−Dirac function after the pumping. The Fermi−Dirac function takes two parameters, a time-evolving temperature T(t) and a time-evolving electrochemical potential η(t). In eq 1 and eq 2, we use an alternative representation of the carrier temperature:

N[β(t ), μ(t )] − N[βau(t ), 0] dN[β(t ), μ(t )] =− dt tau −

E[β(t ), μ(t )] − E(βrm , 0)

N (β , μ) =

(1) C

NcNv exp( −βEg ) exp(βμ)

(4)

DOI: 10.1021/acs.jpcc.6b02607 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The first term at the right side of eq 1 reflects the dynamics of the Auger recombination. Auger recombination requires the combination of e−h pairs and transfer the energy to a third free carrier; therefore, the total energy remains the same while carrier population is changed. The electrochemical potential of electrons and holes are shifted to the same state resulting in μ(t) = 0. This condition together with the energy conservation allows us to calculate the equilibrium temperature of the Auger process (βau(t)). The thermalization process is incorporated in the first term of eq 2. The cooling of photoexcited carriers reduces the total energy of the carriers to room temperature while the total number of carriers is conserved as the bandgap effectively prevents the recombination of e−h pairs. As a result, the carriers at the end of thermalization process have an equilibrium electrochemical potential splitting (μth(t)) and share the same temperature with the environment (βrm). The second term at the right sides of both differential equations refer to the dynamic process of the carrier recombination. The recombination process leads to both thermal equilibrium (to room temperature) and chemical equilibrium. Therefore, the equilibrium state is characterized by the room temperature βrm and an electrochemical potential splitting of 0. In semiconductor-based system, the TA spectra at any time after the ultrafast renormalization process can be described by a Bose−Einstein function:

(5)

where Nc, Nv are the effective densities of states for conduction and valence band; Eg is the bandgap that is known as parameter; and 3/β is the average kinetic energy of electrons and holes. For the purpose of analyzing the TA spectrum, we can assume that the electrons and the holes share the same temperature due to the ultrafast process of intercarrier scattering. However, electrons and holes may have different electrochemical potentials, namely, μe(t) and μh(t). As a result, the particle density of carriers N and the energy density of carriers E can be expressed as functions of the temperature parameter β(t) and the splitting of electrochemical potentials μ(t) = ηe(t) − ηh(t) (Table 1). Table 1. Definition of Parameters for eq 1 and eq 2 parameter

definition

N E β(t) μ(t)

particle density of photoexcited carriers energy density of photoexcited carriers parameter that represents the time-evolving carrier temperature splitting of the electrochemical potentials between electrons and holes temperature parameter for carrier population equilibrated by the Auger process carrier temperature parameter at the room temperature electrochemical potential splitting for population equilibrated by thermalization Auger relaxation time of carriers (relaxation time for the Auger process) thermalization time (relaxation time for the thermalization process) recombination time (relaxation time for band-to-band recombination)

βau(t) βrm μth(t) tau(t) tth(t) tre(t)

Iε(t ) ∝ {exp[β(t )(ε − μ(t ))] − 1}−1

(6)

where Iε(t) is the time evolution of TA signal at energy ε. After the pump, β(0) and μ(0) are first established, and the carrier distribution at each subsequent process can be determined by solving the differential equation. The fitting process is carried by solving those equations together to determine tth, tau, and tre. The fitting results demonstrate that the initially excited hot carriers in Ag2S NPs have a thermalization relaxation time (tth) of 40.9 ps, a Auger/impact-ionization relaxation time (tau) of 27.9 ps, and a band-to-band recombination (tre) time of 3 ± 1 ns. Compared with the carrier cooling time of other materials reported in the literature,25−29 the Ag2S NPs demonstrate a significant reduction on carrier cooling rates. The longer thermalization time is possibly due to the effective phonon confinement in Ag2S NPs, which hinders the phonon-assisted relaxation process.5,30 The transient process of carrier temperature decay is illustrated in Figure 2d, calculated using the same

Equation 1 and eq 2 illustrate the time evolution of the particle density and the change of the energy density, respectively. Together they determine the time evolution of the carrier energy distribution toward its equilibrium. It is noted that this transition is contributed by several carrier processes. The rates of these processes are characterized by their respective relaxation times, including the thermalization time (tth), the Auger relaxation time (tau), and the band-to-band recombination time (tre).

Figure 3. (a) Time evolution of the carrier density variation at different band energy; (b) the variation of carrier distribution as a function of band energy at different time delays. D

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product of the absorption coefficient and the Maxwell− Boltzmann statistical function. The denominator originates from the sigmoidal form of the absorption coefficient function.31 Band-tail effects and phonon-assisted transitions are incorporated with a finite spreading energy Δ. The Maxwell−Boltzmann statistical term is provided in the numerator, describing the energy distribution of state-filling probabilities. The measured ssPL spectra have been fitted using the expression described as shown in Figure 4a. Compared with TA experiment, the red shift of the PL emission peak indicates Stokes shift occurring in Ag2S NPs. Five material parameters have been retrieved from the fitting procedure and are recorded in Table 2, including the relative intensity of excitonic emission Q, excitonic emission spreading σ, band gap energy Eg, carrier temperature T, and absorption edge broadening Δ. According to Table 2, the steady-state carrier temperature under the illumination of ssPL is 495 K, about 200 K higher than the room temperature. Since no obvious state filling effects were observed, one reason for the elevated carrier temperatures is the confinement or localization of phonons in NPs.32,33 This phonon localization reduces the thermal conductivity and thus the overall rate of energy dissipation. Immediately after excitation, the hot photocarriers lose their energies by emitting polar phonons, which then decay into lower phonon branches. In NPs the populated phonons diffuse slowly due to the threedimensional confinement, resulting in energy being fed back into carriers. To verify the relaxation time results retrieved from the TA measurement, we use them to estimate the steady carrier temperature under ssPL. The model used for this estimation is essentially the same RTA dynamics model adopted for the TA data analysis, involving two respective equations for carrier number conservation and energy conservation (see SI for details). The result is presented in Figure 4b, which illustrates the relation between the carrier temperature and the incident power intensity of the monochromatic illumination at 450 nm. The power intensity of the ssPL setup is estimated to be around 50 μW/cm2 (see SI for details). Under such excitation, it is predicted from the relaxation time values shown in Figure 2c that the carriers in the ssPL measurement could reach 518 K. This is similar to the actual measured temperature 495 K. This provides further evidence on the accuracy of the three relaxation time constants of carriers in Ag2S NPs. The significantly slowed carrier cooling time is a merit of Ag2S NPs that can be utilized for the purpose of realizing the high-efficiency hot carrier solar cell. Based on the device modeling work on the hot carrier solar cell (Figure 5a), this time scale of thermalization can potentially lead to solar energy conversion efficiency of 33.6% for hot carriers being extracted at an elevated energy level of 1.2 eV (Figure 5b).34 This calculation follows the method in the literature (see SI for detailed calculation).22−24 The improvement over the Shockley−Quessier efficiency limit is because of the excess thermal energy of hot carriers, which is retained by the prolonged carrier cooling time (40.9 ps).

RTA model. Two distinct features are observed, including an initial fast temperature decay from 954 to 700 K in a short time range around 50 ps, followed by a much slower decay process (up to 2 ns) starting from 700 K. This results from the fact that Auger processes constantly pump electrons up to higher energies, thus mitigating the fast thermalization process. Further analysis of hot carrier thermalization process is based on the extraction of nonequilibrium carrier distribution in the conduction band at different time delays after excitation. Figure 3a shows the time evolving population of carriers lying at different energy levels. With the time proceeding the total density of carriers decreases due to the recombination processes (including both nonradiative and radiative). Compared with other energy states, the carrier density at 0.05 eV are higher than other energy levels. Lower carrier distribution is observed at 0.001 eV, which is due to the less enough density states available near the band edge. In agreement with Figure 3a, Figure 3b illustrates that shortly after the excitation, the electrons are excited to the high excited states in the conduction band, initializing a hot-carrier distribution peaking at 0.05 eV above the edge of the conduction band. The peak position is followed by a red-shift toward 0.02 eV indicating the fast thermalization of excited carrier population and thus decrease the average energy of hot carriers.

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JUSTIFICATION OF RELAXATION TIME WITH SSPL MEASUREMENT To further justify the relaxation time results retrieved from the TA measurement, we examine the steady-state photoluminescence (ssPL) of Ag2S NPs. The optical emission spectra were studied by infrared photoluminescence spectroscopy with an exciton wavelength of 450 nm. The details of experimental conditions of ssPL are further explained in SI. The ssPL spectra were fitted with a line shape function to estimate the exciton binding energies and carrier temperatures,31 where the term definition of parameters are illustrated in Table 2. I(E) =

⎡ (E − E )2 ⎤ exp[(Eg − E)/kT ] Q X ⎥+ exp⎢ − 2 2π 1 + exp[(Eg − E)/Δ] 2σ ⎣ ⎦ (7)

Table 2. PL Fitting Results of Ag2S Nanoparticles Using the Lineshape Function particle diameter (nm)

excitonic relative intensity Q (au)

excitonic spread σ (eV)

band-toband energy Eg (eV)

carrier temperature T (K)

absorption broadening Δ (eV)

5.7

0.5883

0.0452

1.0532

495

0.0283

The former term in this equation corresponds to the excitonic emission of Ag2S nanoparticles. It is approximated by a Gaussian distribution function with its standard deviation denoted by σ. The momentum conservation of light absorption ensures that the exciton−photon coupling only happens for the excitonic state close to the Γ point. As a result, the excitonic energy is fixed at 0.95 eV, corresponding to the shoulder position of the PL signals (Figure 4a). The independence between the exciton energy and the particle size originates from its small excitonic Bohr radius (approximately 1.15 nm). The band-to-band emission is included in the latter term of eq 7. The band-to-band recombination intensity is given by the

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CONCLUSION In summary, closed-packed uniform nanoparticle monolayer is fabricated with wet-chemistry Langmuir−Blodgett technique. The carrier thermalization dynamics of Ag2S nanocrystals are studied with ultrafast transient absorption spectroscopy. A slow carrier thermalization time as long as 40.9 ps is retrieved from the measured transient absorption spectra based on a E

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Figure 4. (a) Fitting of the measured steady-state photoluminescence signals using the line shape function; (b) simulated carrier temperatures and quasi-Fermi level splitting under steady-state illumination with different power intensities using the relaxation time constants obtained by fitting the transient absorption spectra shown in Figure 2c.

Figure 5. (a) Schematic drawing of hot carrier solar cell with Ag2S NPs being an absorber; (b) current−voltage curves and respective efficiency figures for a hot carrier solar cell using an ideal Ag2S NP absorber with hot carriers being extracted at an elevated energy level of 1.2 eV.

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comprehensive dynamics model. The characterized relaxation time results are further justified by steady-state photoluminescence measurement. The high carrier temperature obtained from ssPL with line shape function is in agreement with the temperature retrieved from adjusted relaxation-timeapproximation model based on extracted time constants. Our results demonstrate that Ag2S nanoparticles can be a potential material for fabricating the high-efficiency hot-carrier solar cell.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Tel: +61-02-9385-7120. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is financially supported by the Australia Government through the Australian Renewable Energy Agency (ARENA). We are also thankful to the Mark Wainwright Analytical Centre, University of New South Wales, Australia, and Department of Chemistry, University of Adelaide, Adelaide, South Australia, Commonwealth Scientific and Industrial Research Organization (CSIRO), Lindfield, Sydney, New South Wales, for providing characterization facilities for this research.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b02607. Fabrication of Ag2S nanoparticles; Langmuir−Blodgett deposition of NPs monolayer; TA and ssPL experimental setup and conditions; steady-state carrier temperature calculation using RTA; theoretical efficiency calculation based on measured thermalization lifetime (PDF)

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REFERENCES

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