Size- and Temperature-Dependent Carrier Dynamics in Oleic Acid

Article pubs.acs.org/JPCC

Size- and Temperature-Dependent Carrier Dynamics in Oleic Acid Capped PbS Quantum Dots Peristera Andreakou,† Mael Brossard,† Chunyong Li,† Maria Bernechea,‡ Gerasimos Konstantatos,‡ and Pavlos G. Lagoudakis*,† †

School of Physics and Astronomy, University of Southampton, Southampton, United Kingdom ICFO - Institut de Ciències Fotòniques Castelldefels, Barcelona, Spain

‡

S Supporting Information *

ABSTRACT: In this work, we investigate the temperature dependence of the photoluminescence decay and integrated photoluminescence of oleic acid capped PbS quantum dots with diameters ranging from 2.3 to 3.5 nm over a broad temperature range (6−290 K). All the investigated samples exhibit similar behavior, consisting of three different temperature regimes. The low-temperature regime (250 K) is governed by quenched photoluminescence intensity and acceleration in the average lifetimes. We propose a three-level system, composed of bright, dark, and surface states, which describes the observed photoluminescence dynamics of oleic acid capped PbS QDs.

1. INTRODUCTION Quantum dots (QDs) have received great attention during the past decade because of their unique optical properties. Their discrete electronic transitions combined with their narrow emission spectrum have made them a significant material for fundamental research and the development of a range of applications such as photodetectors,1−5 light emitters,6,7 photovoltaics,8−12 and nanoprobes for labeling and sensing of biological targets.13−16 The optical properties of semiconductor QDs are determined by the ratio between the size of the QDs and the Bohr radius rB of the exciton. Depending on this ratio, three different regimes of quantization can be defined: weak (a ≫ rB), intermediate (a ≈ rB), and strong (a < rB). For the past decade, researchers have focused their interest on lead chalcogenide materials such as PbS, PbSe, and PbTe QDs since such materials offer the unique possibility to probe the strong confinement regime.17,18 This type of QD provides tunable electronic transitions which cover a wide spectral range, from the near-infrared to the visible. Multiple exciton generation has been observed in PbS QDs, a mechanism that could potentially lead to improved solar conversion efficiencies.19,20 An increase in the performance of both an ITO/PEDOT/PbSe/aluminum Schottky solar cell and a © XXXX American Chemical Society

hybrid bulk PDTPBT/PbS QD heterojunction photovoltaic device has been recently reported,9,21 showing the potential of this type of colloidal QD for photovoltaic applications. Due to the high technological interest of PbS QDs, understanding their optical properties is critical. The optical properties of PbS QDs have been extensively investigated. Olkhovets et al.22 reported the size dependence of the temperature coefficients of electron−hole pair energies in PbS and PbSe QDs. Lamaestre et al.23 studied the temperature dependence of the photoluminescence (PL) intensity and the decay rate of PbS QDs embedded in silicate glass. The PL intensity was enhanced for temperatures below 220 K and then quenched at higher temperatures, while the decay rate was increased with increasing temperature, suggesting carrier transitions from dark to bright states. The energy splitting between the dark and the bright state was estimated to be 37 meV. However, no interpretation was given for the complex observed PL behavior. Gaponenko et al.24 also performed temperature-dependent PL measurements on PbS QDs Received: June 2, 2012 Revised: December 3, 2012

A

dx.doi.org/10.1021/jp3054108 | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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Figure 1. Absorption (a) and emission (b) spectra of 2.3 nm (red), 2.6 nm (blue), 3.2 nm (green), and 3.5 nm (black) of PbS QDs. Inset: Stokes shift energy as a function of the diameter of PbS QDs.

incidence to the sample surface. Steady-state PL measurements were carried out using a charge-coupled device spectrometer with 1 nm resolution. PL decay kinetics of PbS QDs was found to exhibit a nonsingle exponential behavior that was satisfactorily described with the following double exponential function

embedded in glass. They observed an accelerated PL decay time and a decreased PL intensity with increasing temperatures. Their experimental results were explained through a three-level system. The acceleration in the PL decay rate was attributed to the transition of carriers from dark to bright states under the assumption that thermally activated carrier detrapping was the origin of thermal quenching at high temperatures. The bright to dark energy gap was estimated to be 21.8 meV. In all of these studies, the fine structure exciton splitting is estimated to be approximately an order of magnitude above the bulk PbS splitting. Recent studies in surface-passivated PbS QDs demonstrate temperature dynamics that differ from those of PbS QDs embedded in a glass matrix. The temperature dependence of the PL emission from thiol-capped PbS colloidal QDs showed an enhancement in the QD PL intensity for increasing temperatures up to 50 K and a further decrease for temperatures above 50 K. This PL behavior was explained by a thermally activated redistribution of carriers in the dots in the presence of a defect. However, no estimation of the fine structure splitting was derived from these observations.25 The fine exciton splitting in colloidal PbS QDs depends on the diameter of the dots, while the role of surface states is still unclear. In this work, we investigate the transient dynamics of oleic acid capped PbS QDs on glass substrates, for a wide size and temperature range. To interpret the experimental observations, we propose a model that considers the lowest exciton fine structures and the presence of a trap state. A global fit to the measured temperature- and size-dependent PL decay dynamics converges to a lowest exciton splitting of 3 meV that is within the range of theoretical expected values reported in the literature.18 The model also reveals a clear trend of oscillator strength transfer from the bright to dark exciton state with decreasing quantum dot diameter, in the strong confinement regime.

IPL(t ) = A1e−k1t + A 2 e−k 2t + C

(1)

The average decay rate is given by =

A1τ1 + A 2 τ2 A1τ12 + A 2 τ2 2

(2)

where τ1 = 1/k1 and τ2 = 1/k2, respectively. This value is used here to monitor the overall trend of the decay dynamics at different temperatures.

3. RESULTS AND DISCUSSION The absorption and emission spectra from four different diameters of PbS QDs in toluene are illustrated in Figure 1a,b. The maximum of the first exciton absorption is located at 620, 730, 830, and 920 nm for PbS QDs with diameters of 2.3, 2.6, 3.2, and 3.5 nm, respectively. The size of the quantum dots was theoretically calculated according to ref 18. The PL intensity maxima of these nanocrystals are red-shifted from their absorption maxima at 771, 856, 913, and 977 nm. The Stokes shift energy exhibits strong size dependence and is related to the size of the particles as illustrated in the inset of Figure 1a. Spectrally and time-resolved measurements were performed for PbS QDs deposited on glass substrates. Both the PL decay and the integrated intensity of the PbS QDs exhibit strong temperature dependence in the range of 6−290 K. The PL decays of these QDs follow a double exponential, indicating the existence of two radiative relaxation channels. The double exponential behavior of the PL decay has been previously observed and assigned to the lowest dipole transitions.24 The fine structure of the lowest-energy level is composed of a bright (triplet) and a dark (singlet) state, which are separated by an energy gap ΔE.18,27 The temperature dependence of the PL intensity peak and the decay rate for 3.2 nm PbS QDs are illustrated in Figure 2. The combined analysis of the decay curves and the PL intensity peaks allows the identification of three temperature regimes. The lowtemperature regime (up to 180 K) is characterized by a decrease in the PL intensity and an increase in the average decay rate. Temperature quenching of the PL of QDs has been commonly observed in colloidal suspensions and solvent-free systems such

2. EXPERIMENTAL METHODS PbS nanocrystals were synthesized following a slight modification of the previous reported method.26 The PbS nanoparticles were dissolved in octane at a concentration of 5 mg/mL and spin coated on the silica substrates. Time-resolved measurements were performed using a streak camera system with a temporal resolution of 30 ns. All QDs were excited nonresonantly at 400 nm with 150 fs pulses at 27 kHz repetition rate. Glass substrates with spin-coated PbS QDs were mounted on the coldfinger of a helium flow cryostat and excited at an oblique angle. The fluorescence was collected at normal B



Article

structure of the lowest-energy state is represented by a bright and a dark exciton with radiative decay rates kB and kD, respectively. The energy splitting ΔE between these two states is in the range of a few meV, depending on the size and shape of the QDs.18 A trap surface state as described in Figure 4 is introduced. A barrier of height E1 from the bright exciton to the trap prevents total quenching of the bright states, rendering this surface state thermally activated.28 According to the proposed model, the increase in PL decay rate in the first regime is due to the splitting between dark and bright states. With increasing temperature, the probability of carriers to relax from bright to ground states dominates over the dark to ground radiative relaxation channel, and consequently, the average decay rate is increased. On the other hand, the presence of the trap state causes the PL peak intensity to decrease as the temperature increases. Carriers with thermal energy E2 > KBT > E1 become trapped in the defect and consequently the total number of radiatively relaxing carriers. For temperatures above 180 K (regime 2), the thermal energy of the trapped carriers is sufficient to overcome the E2 barrier and populate the dark and bright states. Carriers can then relax from the dark and bright states to the ground state by increasing the PL peak intensity. In the third regime, we observe that the PL intensity is quenched again, suggesting the existence of a nonradiative channel from the trap state. The average decay rate shows a complex trend for temperatures above 180 K due to interplay between trapping and detrapping rates. We calculate the corresponding nonradiative relaxation decay rates from the bright (κB−T) and dark (κD−T) states to the trap state with the absorption or emission of phonons

Figure 2. PL peak intensity (a) and PL decay rate (b) of 3.2 nm PbS QDs as a function of temperature. The error bars for the graph (a) correspond to the standard deviation of the experimental data with a Gaussian fit. The error bars for the graph (b) correspond to the standard deviation of the experimental data with a double exponential fit.

as QDs deposited on glass substrates and is attributed to surface states.24 For the range of temperatures from 180 to 250 K, the PL intensity recovers, and the average decay rate decreases. For temperatures above 250 K, the PL intensity quenches, and the average PL decay rate increases again. The last two temperature regimes have been previously observed, but the involved dynamics remain elusive. These three regimes were observed for all PbS QD sizes (Figure 3).

κB − T

⎛ ⎛ Eph ⎞ ⎞−E1/ Eph = ko⎜⎜exp⎜ ⎟ − 1⎟⎟ ⎝ ⎝ KBT ⎠ ⎠ ⎛ ⎞ E2 / Eph Eph exp K T ⎜ ⎟ B ⎟ ×⎜ ⎜⎜ exp Eph − 1 ⎟⎟ KBT ⎝ ⎠

( ) ( ( ) )

Figure 3. PL peak intensity (a) and PL decay rate (b) of PbS QDs with a diameter of 2.3 nm (red), 2.6 nm (blue), 3.2 nm (green), and 3.5 nm (black) of PbS QDs as a function of temperature. The error bars for the graph (a) correspond to the standard deviation errors of the experimental data with a Gaussian fit. The error bars for the graph (b) correspond to the standard deviation errors of the experimental data with a double exponential fit.

(3)

and κD − T

Herein, we propose a simple model to describe the temperature dependence of photoluminescence in oleic acid capped PbS QDs, which is summarized in Figure 4. The fine

⎛ ⎛ Eph ⎞ ⎞−E1+ΔE / Eph = ko⎜⎜exp⎜ ⎟ − 1⎟⎟ ⎝ ⎝ KBT ⎠ ⎠ ⎛ ⎞ E2 / Eph Eph exp K T ⎜ ⎟ B ⎟ ×⎜ ⎜⎜ exp Eph − 1 ⎟⎟ KBT ⎝ ⎠

( ) ( ( ) )

(4)

where KB is the Boltzmann constant; ko is a rate constant, which characterizes the efficiency of the thermally induced nonradiative relaxation processes; (exp(Eph/(KBT)) − 1)−n is the probability for a carrier to absorb n phonons of energy Eph; and [(exp(Eph/ (KBT)))/((exp(Eph/(KBT)) − 1))]m = [(1/(exp(Eph/(KBT)) − 1)) + 1]m is the probability for a carrier to emit m phonons of energy Eph. The number of phonons (Np) with energy equal to Eph is given by Bose−Einstein statistics Np = [(1/(exp(Eph/ (KBT)) − 1)]. Nonradiative processes also take place from the trap state to the bright (κT−B) and dark (κT−D) states with rates given by

Figure 4. Schematic representation of the exciton relaxation processes. C



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Figure 5. PL decay curves and PL peak intensity fitted with the proposed theoretical model for the 2.3 nm (a,b), 2.6 nm (c,d), 3.2 nm (e,f), and 3.5 nm (g,h) diameter PbS QDs.

⎛ ⎛ Eph ⎞ ⎞−E2 / Eph κT − B = ko⎜⎜exp⎜ ⎟ − 1⎟⎟ ⎝ ⎝ KBT ⎠ ⎠ ⎛ ⎞ E1/ Eph Eph exp K T ⎜ ⎟ B ⎟ ×⎜ ⎜⎜ exp Eph − 1 ⎟⎟ KBT ⎝ ⎠

( ) ( ( ) )

where Eesc is the energy required for a carrier to escape the QD from the surface state. Furthermore, we consider the transition of a carrier from dark to bright states (κD−B) as well as the transition from bright to dark (κB−D), due to the absorption or emission of n = ΔE/Eph phonons of energy Eph. The corresponding nonradiative rates are described by the equations

(5)

⎛ ⎛ Eph ⎞ ⎞ κT − D = ko⎜⎜exp⎜ ⎟ − 1⎟⎟ ⎝ ⎝ KBT ⎠ ⎠

−E 2 / Eph

⎛ ⎞ E1+ΔE / Eph Eph exp ⎜ ⎟ KBT ⎟ ×⎜ ⎜⎜ exp Eph − 1 ⎟⎟ KBT ⎝ ⎠

( ) ( ( ) )

κD − B

ΔE / Eph ⎛ ⎛E ⎞ ⎛ ⎛E ⎞ ⎞⎞ ph ph κB − D = ko⎜⎜exp⎜ ⎟ /⎜⎜exp⎜ ⎟ − 1⎟⎟⎟⎟ ⎠⎠ ⎝ ⎝ KBT ⎠ ⎝ ⎝ KBT ⎠

(6)

(8)

(9)

Moreover, the populations of the dark, bright, and trap state can be described by the following rate equations

while carriers from the trap state can thermally escape the dot with a rate ⎛ ⎛ Eph ⎞ ⎞ kesc = ko⎜⎜exp⎜ ⎟ − 1⎟⎟ ⎝ ⎝ KBT ⎠ ⎠

⎛ ⎛ Eph ⎞ ⎞−ΔE / Eph = ko⎜⎜exp⎜ ⎟ − 1⎟⎟ ⎝ ⎝ KBT ⎠ ⎠

dnbright

−Eesc / Eph

dt

= −(kB + kB − T + kB − D)nbright + kD − Bndark + k T − Bntrap

(7) D



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Table 1. Fitting Parameters Used in the Proposed Model d = 2.3 nm d = 2.6 nm d = 3.2 nm d = 3.5 nm

ΔE (meV)

E1 (meV)

E2 (meV)

Eesc (meV)

kB (s−1)

kD (s−1)

ko (s−1)

3 ± 0.033 3 ± 0.0075 3 ± 0.0072 2 ± 0.0016

6.5 ± 0.166 4.5 ± 0.193 3 ± 0.684 1 ± 0.056

115 ± 4.83 115 ± 4.945 96 ± 0.096 60 ± 0.63

10 ± 5.0 95 ± 7.6 110 ± 3.3 120 ± 0.168

1.1 × 10 ± 18513 1.65 × 106 ± 10120 1.65 × 106 ± 16500 2 × 106 ± 22000

6.5 × 10 ± 27170 1.5 × 104 ± 555 1.5 × 104 ± 660 0.8 × 104 ± 24.8

4.6 × 105 ± 13000 1.5 × 106 ± 11700 1.5 × 106 ± 19500 1.5 × 106 ± 11100

+ k T − Dntrap

where nbright, ndark, and ntrap are the carrier populations of the bright, dark, and trap states, which are time and temperature dependent, and kB and kD are, respectively, the radiative relaxation rates of carriers from the bright and dark states. The population of the bright and dark states at t = 0 is assumed to follow the Boltzmann distribution ((nbright/ndark) = e(−ΔE)/(KBT)), while the initial total population is set to be Ntotal(t = 0) = nbright + ndark. The initial populations of bright and dark states are given by

=

(e

Ntotal −ΔE / KBT

e−ΔE / KBT Ntotal (e−ΔE / KBT + 1)

+ 1)

4

Gaponenko et al.24 but remains in a good agreement with the theoretical predictions mentioned previously. The exciton lifetimes of the dark state were observed to range between 60 and 8 ms for different sizes of PbS QDs. Within the effective mass approximation, the singlet (dark) exciton lifetimes are described to be size independent and radiationless. However, the finite observed lifetimes can be explained by considering the spin orbit coupling, QD asymmetry, and the associated violation of selection rules. The spin−orbit coupling as well as the asymmetric shape of the QDs change the excitonic fine structure and consequently lead to mixing of triplet and singlet exciton states. Through this process, the latter acquires finite optical oscillator strength, leading to measurable dark exciton lifetimes. With increasing QD size, we observe a trend of decreasing radiative dark exciton rates as it is expected toward the limit of infinite size crystal (bulk) where singlet states are forbidden optical transitions. The transfer of optical oscillator strength from the triplet to singlet states is also evident in the size dependence of the radiative rate of bright (triplet) excitons. Indeed, we observe that the radiative rate of bright excitons follows the trend opposite to that of dark excitons that is an increasing radiative rate with increasing size of QDs. The energy of the trap states of the oleic acid capped PbS QDs was found to decrease as the size of the QDs increases. This trend could be due to the increased concentration of dangling bonds as the size of the QDs decreases. Smaller QDs contain a higher number of outer atoms and consequently a larger concentration of dangling bonds. Therefore, carriers can be easily trapped to smaller sized QDs as is reported by Talapin et al.33 The escape energy, which describes the thermal energy needed by a carrier to escape the surface of the QD, was shown to decrease for smaller nanocrystals. The ko rate, which introduces the efficiency of the thermally nonradiative relaxation processes, was constant for most of the QD sizes. The higher value found for the smallest QDs can be explained by an increase in the confinement and the associated modification in the electron−phonon coupling constant.18

dndark = kB − Dnbright − (kD + kD − T + kD − B)ndark dt

nbright(t = 0, T ) =

6

and ndark (t = 0, T )

(11)

However, we note that the overall dynamics of the carriers is independent of the initial carrier distribution and is only affected by the thermal energy of carriers and therefore temperature. For the range of excitation densities under consideration, the number of carriers per QD remains less than one. The integrated PL intensity (Figure 5) is directly proportional to the number of radiative recombinations (nexciton,r). The integrated PL is thus derived from the solution of the differential equation (dnexciton,r)/ (dt) = kBnbright + kDndark, and the PL decay is calculated by the sum of (kBnbright + kDndark). We apply this model to our experimental data by setting Eph equal to the LO-phonon energy ELO = 26.6 meV. The best fit was found for the set of parameters presented in Table 1 for all the different sizes of PbS QDs. Each of the error bars shown in the table changes by 1‰ the goodness of the fit. The variation of all the values inside the errors bars alters the goodness of the fit by 0.92%. The estimated value of the bright−dark state energy gap ΔE was found to be equal to 3 meV for most of the particles, while it decreased to 2 meV for the 3.5 nm diameter particles. A strong size and shape dependence of the bright−dark splitting has been predicted by Efros et al.29 The electron−hole exchange interactions mix direct excitons in the same valley, direct excitons of two different valleys, and direct and indirect excitons. Kang et al.18 estimated the lowest direct exciton splitting for PbS QDs, by considering the effect of the Coulomb and exchange interactions. For a bulk exchange strength of 10 meV, the dark− bright splitting was calculated to be around 4 meV for 2 nm diameter PbS particles, a value close to the one estimated from our simulations.18 In our case, no strong correlation could be found between the dark−bright splitting and the particle size. This can be attributed to possible variations in the shape of the nanocrystals, which has been theoretically shown by Efros et al.29 The shape asymmetry of the PbS QDs has been reported by refs 26 and 30−32. The estimated value of the bright−dark energy gap (ΔE = 3 meV) is lower than the value reported by

4. CONCLUSIONS The size and temperature dependences of the exciton dynamics in PbS QDs on a glass substrate have been investigated. Three different regimes have been recognized, regardless of the size of the particles. The low-temperature regime (250 K) due to the enhanced nonradiative processes, while the PL rate increases, demonstrating that the bright to ground transition dominates. Our experimental results were fitted with a simple model, and we E



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(16) Wu, C.; Bull, B.; Szymanski, C.; Christensen, K.; McNeill, J. ACS Nano 2008, 2, 2415−2423. (17) Wise, F. W. Acc. Chem. Res. 2000, 33, 773−780. (18) Kang, I.; Wise, F. J. Opt. Soc. Am. B 1997, 14, 1632−1646. (19) Ellingson, R. J.; Beard, M. C.; Johnson, J. C.; Yu, P.; Micic, O. I.; Nozik, A. J.; Shabaev, A.; Efros, A. L. Nano Lett. 2005, 5, 865−871. (20) Farrell, D. J.; Takeda, Y.; Nishikawa, K.; Nagashima, T.; Motohiro, T.; Ekins-Daukes, N. J. Appl. Phys. Lett. 2011, 99, 111102. (21) Ma, W.; Swisher, S. L.; Ewers, T.; Engel, J.; Ferry, V. E.; Atwater, H. A.; Alivisatos, A. P. ACS Nano 2011, 5 (10), 8140−8147. (22) Olkhovets, A.; Hsu, R.; Lipovskii, A.; Wise, F. Phys. Rev. Lett. 1998, 81, 3539−3542. (23) Espiau de Lamaëstre, R.; Bernas, H.; Pacifici, D.; Franzó, G.; Priolo, F. Appl. Phys. Lett. 2006, 88, 181115. (24) Gaponenko, M.; Lutich, A.; Tolstik, N.; Onushchenko, A.; Malyarevich, A.; Petrov, E.; Yumashev, K. Phys. Rev. B 2010, 82, 125320. (25) Turyanska, L.; Patanè, A.; Henini, M.; Hennequin, B.; Thomas, N. R. Appl. Phys. Lett. 2007, 90, 101913. (26) Hines, M. A.; Scholes, G. D. Adv. Mater. 2003, 15, 1844−1849. (27) An, J. M.; Franceschetti, A.; Zunger, A. Nano Lett. 2007, 7, 2129− 2135. (28) Pankove, J. I. Optical processes in semiconductors; Dover Publications Inc.: New York, 1971. (29) Efros, A. L.; Rosen, M. Annu. Rev. Mater. Sci. 2000, 30, 475−521. (30) Lingley, Z.; Lu, S.; Madhukar, A. Nano Lett. 2011, 11, 2887−2891. (31) Sargent, E. H. Nat. Photonics 2012, 6, 133−135. (32) Xu, F.; Ma, X.; Haughn, C. R.; Benavides, J.; Doty, M. F.; Cloutier, S. G. ACS Nano 2011, 5, 9950−9957. (33) Talapin, D. V.; Murray, C. B. Science 2005, 310, 86−89.

estimated that the lowest-energy splitting for the smallest particles is 3 meV. The simplicity of this model and its capacity to explain the observed nonmonotonous intensity and fluorescence decay rate dynamics of PbS colloidal quantum dots increases our confidence in the validity of the converged parameters describing the exciton fine structure. An interesting transfer of oscillator strength from bright to dark states has also been observed and predicted by our model. Understanding the exciton dynamics in PbS colloidal QDs can allow for fine-tuning of their size and passivation toward improved light harvesting and IR photodetector applications.

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ASSOCIATED CONTENT

S Supporting Information *

The PL spectra of the different sizes of PbS QDs at 6 K and the PL decays of the different sizes of QDs fitted with the proposed theoretical model. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge support by FP7 through ITN- ICARUS and Network of Excellence, N4E GA.248855. P.A. is indebted to D. Emmanoulopoulos for the useful discussions regarding Mathematica. Konstantatos G. and Bernechea M. acknowledge Fundacio Privada Cellex for financial support.

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ABBREVIATIONS QD, quantum dot; PL, photoluminescence; PbS, lead sulfide. REFERENCES

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Size- and Temperature-Dependent Carrier Dynamics in Oleic Acid

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