Letter pubs.acs.org/NanoLett
Universal Trapping Mechanism in Semiconductor Nanocrystals Marco Califano*,† and Francisco M. Gómez-Campos‡,§ †
Institute of Microwaves and Photonics, School of Electronic and Electrical Engineering, University of Leeds, Leeds LS2 9JT, United Kingdom ‡ Departamento de Electrónica y Tecnología de Computadores, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain § CITIC-UGR, C/Periodista Rafael Gómez Montero, no. 2, Granada, Spain S Supporting Information *
ABSTRACT: Size tunability of the optical properties and inexpensive synthesis make semiconductor nanocrystals one of the most promising and versatile building blocks for many modern applications such as lasers, single-electron transistors, solar cells, and biological labels. The performance of these nanocrystal-based devices is however compromised by efficient trapping of the charge carriers. This process exhibits different features depending on the nanocrystal material, surface termination, size, and trap location, leading to the assumption that different mechanisms are at play in each situation. Here we revolutionize this fragmented picture and provide a unified interpretation of trapping dynamics in semiconductor nanocrystals by identifying the origins of this so far elusive detrimental process. Our findings pave the way for a general suppression strategy, applicable to any system, which can lead to a simultaneous efficiency enhancement in all nanocrystal-based technologies. KEYWORDS: Trapping, surface, impurities, Auger processes, nanocrystal quantum dots, pseudopotential method
T
carrier trapping to surface-, interface-, and core-localized states. Coupling to phonons,18 energy transfer to high-frequency vibrational modes of the ligands,20 classical Marcus-like electron transfer,13 and Auger ionization10,11 are therefore invoked in turn, to explain different features in the observed decay dynamics of different systems. Accordingly, (i) the highly distributed surface trapping times,1,14−16 characterizing a multiexponential decay with six different components15 spanning five decades in time (from the subpicosecond to the nanosecond regime), observed in CdSe core-only NCs, (ii) the narrowly distributed trapping times, responsible for a biexponential decay with components in the subnanosecond range and separated by less than two decades, found in InAs/ ZnSe core/shell NCs,19 and (iii) the subpicosecond-fast trapping to core-localized impurities in doped CdSe:Te NCs,18 where, in analogy with surface traps, the hole becomes strongly localized around the Te atom(s),21,22 were all ascribed to different mechanisms.13,18,19 In contrast to this system-dependent picture, here we suggest that a single mechanism (Auger-mediated trapping, AMT) is responsible for trapping in all these systems, and show that, within an accurate atomistic description, its calculated rates can reproduce the observed decay rates in all the different configurations.
he surface of semiconductor nanocrystals (NCs) plays a central role in determining many of their physicochemical properties. Interactions taking place at this crucial interface between a NC and its environment profoundly influence its response to external excitations. Hence an accurate knowledge of surface states and of the mechanisms by means of which they are populated and contribute to optoelectronic processes in NCs of different materials is of paramount importance for any device application. Indeed, charge carrier trapping at the surface has been shown to represent a dominant contribution to the decay dynamics of exciton and multiexciton states in semiconductor nanocrystals (NCs),1 affecting the observed quantum yields of photoluminescence2,3 and carrier multiplication,4,5 limiting the optical gain,6−8 and hindering efficient charge transfer/transport for photovoltaic applications,9 among other effects. Yet, these surface processes are arguably the most poorly understood aspect of NC electronic structure and dynamics. Many models have been proposed to explain carrier trapping in semiconductor nanocrystals (NCs);1,10−19 however they are either purely qualitative,1,10,11,16,18,19 or largely empirical12−15,17 (i.e, all their parameters are extracted from fits to experimental data). As a consequence most of them are unable to provide quantitative predictions extending beyond the specific set of data for which the fitting was done. In particular none has so far been general enough to account for the seemingly incompatible features observed in the decay dynamics of nanocrystals of different materials and surface terminations or to be applied to © 2013 American Chemical Society
Received: January 24, 2013 Revised: April 22, 2013 Published: April 23, 2013 2047
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Auger mediated trapping (AMT)12,23 is a nonradiative decay process in which the energy of the trapping transition (i.e., the transition of the hole from a core-delocalized state to a localizedsurface, interface, or impuritystate in the gap) is transferred to the photogenerated conduction band edge electron promoting it to an excited state, as schematically depicted in Figure 1.
(τAMT)−i 1 =
Γ ℏ
∑ n
⟨i|ΔH |fn ⟩ 2 (E f − Ei)2 + (Γ/2)2 n
(1)
where |i⟩ and |f n⟩ are the initial (delocalized) and final (trapped) excitonic states (see Figure 1), Ei and Ef n are their energies, ΔH is the Coulomb interaction, and ℏ/Γ is the lifetime of the final states. The resulting distributions of the transfer times to traps located at the core surface in both zinc-blende InAs/ZnSe core/ shell NCs and wurtzite CdSe core-only structures, presented in Figure 2a for NCs with R = 14.6 Å, agree well with experiment1,15,16,19 and reflect the observed contrast in the two systems. This feature is a consequence of the higher symmetry of zinc-blende InAs NCs, compared to wurtzite CdSe NCs, which leads to a larger number of equivalent sites (traps) on the surface (all of which have identical energies and similar wave functionsFigure 2dand almost identical coupling to the core-delocalized statesFigure 2c), therefore leading to a smaller spread in trapping times in the former system. Although these trapping times are distributed over about two decades (Figure 2b), we find the matrix elements relative to transitions to the different traps (i.e., the numerator of eq 1) to be very similar, with differences of less than an order of magnitude. The trapping efficiencies in InAs NCs are therefore mostly dictated by energy conservation (i.e., the denominator of eq 1), as shown in Figure 2c, where the matrix elements of the transitions relative to the four different traps in NCs with R = 14.6 Å are displayed as a function of the energy difference between the initial excitonic state |i⟩ and the energetically lowermost final excitonic state |f⟩ (Figure 1b). When this difference is negative (as it is the case for most transitions for R = 20 Å, see Figure S1, Supporting Information), energy is not conserved in the transition, as the initial states have all a lower energy than the final states. Conservation of energy is only attained for positive values of Ei(n) − Ef(1) < ε0, where ε0 = Ef(last) − Ef(1) is the spread of the final state energies (ε0 ≈ 40 meV for the InAs/ZnSe NCs considered here), in which case initial and final states can be in resonance. For Ei(n) − Ef(1) > ε0 (the case of R = 14.6 Å), the final states have a lower energy than the initial states, and again energy is not conserved in the transition. The most accurate estimates of trapping times available for InAs/ZnSe NCs are based on ultrafast transient absorption spectroscopic measurements, where the observed band edge transmittance transients were fitted by biexponentials,19 with fast components of the order of tens of picoseconds and slow components in the hundreds of picoseconds range (see Figure 3). To enable a fair comparison with these results we followed a similar procedure: we calculated the exciton population decay as a sum of N exponentials31 (N = 4 in the case of an InAs NC with R = 14.6 Å, and N = 6 in the case of R = 20 Å), each with a weight wi given by the number n(τi) of equivalent sites on the surface with a specific trapping time τi (see Figure 2b)
Figure 1. Schematics of the Auger-mediated trapping mechanism considered in this work. The energy ΔEht v of the hole transition |hs → tn⟩ from the band edge hs to the intragap trap site tn is transferred nonradiatively to the core band edge s-like electron, which is excited into one of the core p states, situated ΔEsp c higher in energy (all singleparticle states in both conduction and valence bands used in the calculations are included in the schematics). The different trap configurations investigated are also displayed: surface traps, traps at the core/shell interface, and impurities within the NC core.
Owing to the very localized nature of these trap states on length scales of the order of a few interatomic distances, an atomistic approach is indispensable for an accurate description of their properties. The semiempirical pseudopotential method used in this work24 is a state-of-the-art atomistic approach that has successfully been employed in the past to accurately reproduce many electronic and optical properties in semiconductor nanostructures of different sizes, shapes, and materials.3,25−28 Within this approach, the NC is built with bulk-like structure, starting from its constituent atoms, up to the desired radius. This procedure yields surface atoms with unsaturated bonds. Atoms with only one (saturated) bond are removed, as they are unstable for dissociation,29 leaving on the surface only atoms with one or two missing bonds. These surface dangling bonds are passivated by generic pseudohydrogenic, short-range potentials with Gaussian form. The effect of specific capping groups and inorganic shells is then captured through the use of appropriate dielectric constants.23 A hole surface trap state was created by removing a single passivant from a surface anion. The single-particle energies and wave functions were calculated using the plane-wave semiempirical pseudopotential method described in ref 24, including spin−orbit coupling, and excitonic effects were accounted for via a configuration interaction scheme.30 (More detailed information on the theoretical method can be found in our previous work23). AMT times were calculated using Fermi’s Golden Rule according to27
N
wi = n(τi)/∑ n(τi) i=1
and fitted the resulting curves with biexponentials (see Figure S2, Supporting Information). The theoretical decay times extracted with this procedure (Figure 3) yield long decay times (τ2) in excellent agreement with the experimental estimates for 2048
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Figure 2. Surface trapping in CdSe and InAs. (a) Distribution of calculated hole transfer times to traps located at the core surface in CdSe core only NCs (red bars) and InAs/ZnSe core/shell NCs (orange bars). The size of the cores is the same in both systems (R = 14.6 Å). (b) Atomistically accurate position-resolved map of the AMT times calculated, for an InAs/ZnSe NC with Rcore = 14.6 Å, by removing a single passivant (whose position is indicated by colored spheres) at a time. For clarity, shell atoms (i.e., Zn and Se) are not displayed. In and As atoms and In passivants are shown in gray. (c) AMT matrix elements calculated for transitions to all types of hole traps at the core/shell interface of InAs/ZnSe NCs with Rcore = 14.6 Å. The matrix elements are displayed as a function of the energy difference between the initial excitonic state Ei(n) and the lowermost final excitonic state Ef(1). The different regimes corresponding to the positive values of Ei(n) − Ef(1) are schematically depicted by the cartoons. (d) Charge density of the most efficient hole interface trap state in an InAs/ZnSe NC: the volume shown contains 75% of the charge density. Only As atoms are shown for clarity.
spanning five decades in time and covering exactly the range spanned by our theoretical predictions in Figure 2a. We found23 that this range shifts toward higher times for larger NC sizes, in broad agreement with the experimental observations by Sewall et al.33 (A more detailed comparison with experimental data for CdSe is provided elsewhere.23) We have therefore shown that the different features observed in the trapping process to localized states on the core surface, in materials with different crystal structure (wurtzite vs zincblende), band gap (wide vs narrow), and surface termination (organic vs inorganic capping), can be explained in terms of a single trapping mechanism. We will now show that the very same mechanism can also reproduce the observed efficient transfer time of the valence band hole to an impurity-localized state in the NC core. Recent experimental investigations by Avidan et al.18 estimated the hole transfer to a Te impurity within the CdSe core (which evolved from an initial CdTe cluster to a doped CdSe:Te spherical structure, with a very small Te content, close to the single-atom limit), to occur in subpicosecond times. In order to reproduce the experimental conditions, for our calculations we chose the smallest cluster possible made of a binary compound (the five-atom structure shown in the inset of Figure 4b), in the configuration which provides the highest
Figure 3. InAs/ZnSe trapping times: comparison of theory and experiment. Comparison of the fast (τ1) and slow (τ2) components extracted from the fits to the experimental (solid symbols)19 and theoretical (empty symbols) data, for different NC sizes.
both sizes considered,32 and short times (τ1) in the same order of magnitude as experiment and which correctly reproduce the observed trend with size. In contrast to this “bi-modal” decay, in CdSe NCs six decay components were recently identified15 2049
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on an undoped CdSe core (Figure 5), where the combined effects of decreased Auger coupling and increased energy
Figure 5. Surface trapping times: Dependence on surface termination and dielectric environment. Comparison of AMT times calculated for transitions to trap states at the surface of CdSe core only (red circle), CdSe/CdS (Rcore = 10.2 Å, red/black circle), and CdSe/ZnS (Rcore = 14.6 Åred/green circle and 10.2 Åred/blue circle) NCs with the same total size R = 19.2 Å and different core radii and shell thicknesses. The cartoons illustrate the volume occupied by the carriers band edge wave functions in the different structures: In coreonly NCs both electron and hole sample the whole NC volume; in CdSe/CdS NCs only the electron samples the whole volume, including the shell surface, whereas the hole is confined within a region larger than the core, but smaller than the whole volume (orange dashed line) and cannot access the shell surface;34 in CdSe/ZnS NCs both electron and hole are confined to the core region and cannot sample the shell surface. The combined effect of (i) reduced wave function overlap between surface trap state and core-delocalized band edge states and (ii) increased energy dephasing between initial and final state energies induced by the different dielectric environments, leads to a progressive increase in the trapping times of about 1 order of magnitude at each step (i.e., for each different structure), up to a total increase of over 3 orders of magnitude from ∼80 ps to ∼100 ns.
Figure 4. Trapping to localized impurity states within a CdSe core. AMT times (a) and matrix elements (b) calculated for transitions to selected impurity states located at different positions (center, red; periphery, cyan, and intermediate between these two, black, see Figure S4 in the Supporting Information) within the core of a CdSe NC with R = 14.6 Å. The trapping times are plotted as a function of the variation of the trap depth δΔE, around its calculated position δΔE = 0. Values of δΔE ≠ 0 account for the effects of size/shape anisotropy in the sample and/or other external causes (such as local electric fields). The inset in b displays the five-atom cluster considered as substitutional impurity in the calculations.
dephasing lead to orders of magnitude increase in the trapping times. We will therefore focus our discussion on impurities located at the NC center. In Figure 4a (and S3a, Supporting Information) we account for possible variations δΔE in the trap depth (or equivalently, however with the opposite sign, in the calculated value of ΔEsp c ), around its calculated position (δΔE = 0), due to size/ shape anisotropy in the sample and/or external causes (such as local electric fields): A variation of about 20 meV in this value brings the trapping time for the smaller NC in the subpicosecond range, and for δΔE ∼ 30 meV (corresponding to a size distribution of about 10%, consistent with experiment18), our calculated rates match the experimental data very closely. Our calculations also reproduce the observed trend of decreasing trapping times with increasing size, as the theoretical trapping times for the R = 19.2 Å NC (Figure S3a, Supporting Information) agree well with experiment for δΔE = ± 10 meV. This effect is easily explained in terms of energetics of the trapping transition: the s−p splitting in the conduction band ΔEsp c is larger than the energy separation between hole band edge and intragap impurity state ΔEht v (see Figure 1a) for small NCs; however it decreases much faster than ΔEht v , with increasing size. This leads to a decrease in the energy dephasing
localization for the hole (a central anion surrounded by four cations), and placed it as a substitutional impurity in different locations within a wurtzite CdSe spherical NC (see Figure S4 in the Supporting Information). We find (Figure 4a and Figure S3a, Supporting Information) that trapping is most efficient for impurities located close to the NC center, due to a combination of stronger coupling (i.e., larger wave function overlap) with the core-delocalized valence band edge, and lower energy dephasing between initial and final states (Figure 4b and Figure S3b, Supporting Information). In fact our calculated intragap energy levels become increasingly shallower (i.e., closer to the valence band edge), the closer the impurity atom is placed to the surface, consistent with recent findings.22 This causes the trapping transition energy ΔEht v to decrease compared to the s-p splitting in the conduction band ΔEsp c (the electron excitation energy, Figure 1), which is much less sensitive to the defect position, leading to an increase in the energy dephasing between initial and final states in the transition. At the same time the wave function overlap with the valence band edge decreases with increasing distance from the NC center. A similar situation is found in the case of surface states when shells of various semiconductor materials are grown 2050
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between initial and final states, as, with increasing size, the energy of the hole trapping transition approaches the excitation energy of the electron (vertical arrows in Figure 1b). Another feature worth noticing in Figure 4a (Figure S3a, Supporting Information) is the effect of the presence of a ZnS shell: trapping times extracted from experiment show an increase of a factor of ∼2.5 for CdSe:Te/ZnS structures compared with CdSe:Te NCs.18 This effect, together with the observed size dependence of the trapping rates, prompted the experimentalists to suggest a combined relaxation mechanism involving LO phonons and surface traps. The observed shell-induced increase is well reproduced by our calculations (except very close to resonance, due to the combined effect of a large gradient of the curves in that region and the difference in the position of the peaks for the core-only and core/shell structures), as a natural consequence of the increase in the dielectric constant of the surrounding material, from that of the solvent [ϵ(octadecene) = 2.07] to that of the shell [ϵ(ZnS) = 8.2]. In fact, given that all states involved in this process have low kinetic energy, their wave functions do not have a large amplitude on the surface region, and as a consequence the effect of the surface termination is expected to be small (consistent with the observed factor of 2.5 increase in the trapping times). In contrast, should surface-localized states be involved in the transition, as suggested by Avidan et al.,18 the expected increase in the transfer time would be much larger (∼1 order of magnitude, based on our results for undoped CdSe presented in Figure 5). Unlike any other trapping mechanism proposed in the literature to date, AMT is therefore not only capable to reproduce the observed hole transfer rates to surface-, interface-, and core-localized states in different material systems and topological configurations, but also naturally explains many features of these processes, such as their dependence on size and on surface termination, in terms of energetics, coupling strength, and dielectric environment. Its dependence on the latter factors demonstrated throughout this study suggests that one of the most effective strategies for AMT suppression could be to increase the energy dephasing between initial and final states, (i.e., to detune the s−p splitting in the conduction band from the trap depth in the gap). This could be achieved by varying the NC shape,35 its dielectric environment, or by inducing local electric fields via the attachment of specific ligand molecules.36 As a concluding remark, however, we would like to point out that, far from being detrimental, the presence of surface-trapped excitons can, in some cases, be desirable. Indeed it has recently been shown that trap emission from a range of emitting surface states can be combined to obtain white light emission in ultrasmall CdSe NCs.37 In these systems, the blue and green emission originating from specific ligand-induced traps effectively balances the red emission from the deep traps related to the presence of Se dangling bonds, creating a pure white spectrum. The substantially improved understanding of the mechanism responsible for surface localization of the charge carriers, provided by the present work, can therefore also enable trapping enhancement strategies, allowing a fuller exploitation of trap emission in optoelectronic devices. The reversibility of the trapping transition remains an open question. A thermally activated process was recently suggested by Mooney et al., 38 where core excitonic states are thermodynamically coupled to the surface states. In that work
the authors used the semiclassical Marcus−Jortner electron transfer (ET) theory to explain the observed temperature dependence of the surface PL. Their treatment explicitly assumed a microscopic reversibility of the trapping process, by including in the rate equations terms describing the depopulation of the trap state due to the backward ET reaction. In the language of molecular electron transfer theory, our work provides the first calculation of the exact form of the electronic coupling matrix element (HDA) that represents the pre-exponential factor in the Marcus−Jortner rate equation.39
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ASSOCIATED CONTENT
* Supporting Information S
AMT matrix elements calculated for transitions to hole traps at the core/shell interface of InAs/ZnSe NCs with Rcore = 20 Å. Theoretical population decay curves and best biexponential fits. AMT times and matrix elements calculated for transitions to selected impurity states. Impurity positions within the NC. This material is available free of charge via the Internet at http:// pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Author Contributions
Both authors contributed equally to this work. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS M.C. gratefully acknowledges financial support from the Royal Society under the URF scheme. F.M.G.C. was supported by the Campus de Excelencia Internacional of Universidad de Granada and by research project TEC2010-16211 funded by the Spanish Ministerio de Ciencia e Innovación.
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