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Auger and Carrier Trapping Dynamics in Core/Shell Quantum Dots Having Sharp and Alloyed Interfaces Gary A. Beane, Ke Gong, and David F. Kelley ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.6b00370 • Publication Date (Web): 19 Feb 2016 Downloaded from http://pubs.acs.org on February 23, 2016

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Auger and Carrier Trapping Dynamics in Core/Shell Quantum Dots Having Sharp and Alloyed Interfaces. Gary A. Beane, Ke Gong‡ and David F. Kelley* Chemistry and Chemical Biology, University of California Merced, 5200 North Lake Road, Merced, CA 95343

Abstract. The role of interface sharpness in controlling the excited state dynamics in CdSe/ZnSe core/shell particles is examined here. Particles composed of CdSe/ZnSe with 2.4 – 4.0 nm diameter cores and approximately 4 monolayer shells are synthesized at relatively low temperature, ensuring a sharp core-shell interface. Subsequent annealing results in cadmium and zinc interdiffusion, softening the interface. TEM imaging and absorption spectra reveal that annealing results in no change in the particle sizes. Annealing results in a 5 - 10 nm blue shift in the absorption spectrum, which is compared to calculated spectral shifts to characterize the extent of metal interdiffusion.

The one- and two-photon dynamics are measured using time-resolved

absorption spectroscopy. We find that biexcitons undergo biexponential decays, with fast and slow decay times differing by about an order of magnitude. The relative magnitudes of the fast and slow components depend on the sharpness of the core-shell interface, with larger fast component amplitudes associated with a sharp core-shell interface. The slow component is assigned to Auger recombination of band edge carriers and the fast decay component to Auger recombination of holes that are trapped in defects produced by lattice strain. Annealing of these particles softens the core-shell interface and thereby reduces the amount of lattice strain and diminishes the magnitude of the fast decay component. The time constant of the slow biexciton Auger recombination component changes only slightly upon softening of the coreshell interface.

Keywords: Auger recombination, biexciton, lattice strain, trapping, carrier recombination.

‡

Present address: Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637

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Core/shell semiconductor nanocrystals (quantum dots, QDs) exhibit different, and often superior, optical properties compared to single component particles of either the core or shell materials. The core/shell optical properties are determined by a combination of overall particle morphology, band offsets and the lattice mismatch. In the case of spherical QDs, band offsets determine spatial extent of electron and hole wavefunctions. Core/shell particles can often be categorized as type-I or type-II. Type-I QDs have band offsets such that both the electron and hole are largely confined to the particle core. CdSe/ZnS and CdSe/ZnSe fall into this category.1 In contrast, type-II particles have either the electron or the hole confined to the core, and the other carrier largely confined to the shell. CdTe/CdSe is an example of this band alignment.2 An intermediate case are the “quasi-type-II” QDs, in which one carrier is confined to the core and the other is delocalized throughout the particle. CdSe/CdS is the most common example here.3 Any mismatch between the core and shell lattice constants results in lattice strain which can have large effects on the optical properties of core/shell QDs.4 The magnitude of the lattice strain energy depends on the core size, shell thickness and the extent of the lattice parameter mismatch. The typical situation (for example, CdSe/ZnSe or CdSe/CdS) is that the shell has a smaller lattice parameter than the core.

This results in the core being under isotropic

compression and the shell under radial compression and tangential tension. The total strain energy is given by the product of the stress and the strain, integrated over the entire core/shell particle. Lattice strain energies increase with both core size and shell thickness. These energies can be quite large, comparable to the energies involved in chemical bonds, and can therefore affect shell morphology. CdS has a lattice parameter that is about 3.9% smaller than CdSe.1 Despite this modest amount of lattice mismatch, CdSe/CdS QDs can have sufficiently high lattice strain energies to result in the formation of defects and/or irregular shell growth.5-7 The parameter that is characteristic of the amount of strain needed to produce defects is the strain energy density – the amount of strain per core surface area.

Recent studies indicate that

CdSe/CdS particles having strain energy densities above 0.59 eV/nm2 are thermodynamically unstable with respect to formation of defects or shell irregularities.7 These studies have also shown that lower temperature syntheses can produce metastable CdSe/CdS particles having lattice strain energies up to about 0.85 eV/nm2. Above that value, the strain is relieved by defect formation even if the shell is deposited at low temperatures. This limits the shell thickness that can be coherently deposited for any specified core diameter, assuming that the core/shell interface is sharp. The lattice mismatch in CdSe/ZnSe is about 6.6%, which is about 70% larger than in CdSe/CdS. The lattice strain energy scales as the square of the lattice mismatch and we expect that a coherent core-shell interface in CdSe/ZnSe QDs will have very large lattice strain energies.8, 9 ZnSe has similar elastic properties as CdS and the strain limits are likely to be about the same for the two shell materials.10 The conclusion is that even for the smallest cores, a 2 ACS Paragon Plus Environment

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CdSe/ZnSe particle having a sharp core/shell interface has a sufficiently large amount of lattice strain energy that the strain is relieved by defect formation. Thus, lattice strain plays a much larger role in CdSe particles having a ZnSe (compared to CdS) shell and results in larger lattice mismatch effects. We have also recently shown that in the case of CdSe/CdS QDs, the defects formed by the release of lattice strain can act as hole traps.7 One can anticipate a similar result for CdSe/ZnSe QDs, and that these traps will play a major role in the photophysics. One structural property of core/shell QDs that has recently received considerable attention is the sharpness of the core-shell interface.11-15 The core-shell transition can occur discontinuously (a ‘hard’ interface) or can be a graded, alloyed transition, occurring over several unit cells (a ‘soft’ interface). Particles having hard or soft interfaces can have different optical and dynamical properties for several different reasons.

One reason is that a soft

interface partially mitigates the effects of lattice mismatch. A soft interface will have less lattice strain energy. Calculations (detailed below) indicate that softening the core-shell interface can reduce the lattice strain energy by at least a factor of two and this can significantly reduce the defect density at the interface. The absence of carrier traps greatly improves the luminescence properties of these QDs. Most syntheses of QDs having very high PL QYs involve annealing of core/shell particles, which softens the core/shell interface, reducing the density of strain-induced defects.16

These calculations also suggest that a completely coherent CdSe/ZnSe core-shell

interface is possible only for the smallest cores (< 3 nm diameter) and only if the interface is alloyed. Another important aspect of QD photophysics is the dynamics of carrier Auger recombination.

Electron-hole recombination through an Auger mechanism involves a

radiationless process where the electron-hole energy is transferred to an additional electron or hole. As such, Auger processes occur only in charged particles or following the absorption of two photons to produce a biexciton. Auger dynamics are also thought to determine the excited state lifetimes of both negatively and positively charged QDs. Following photon absorption, charged QDs have two holes and one electron or two electrons and one hole and are referred to as positive or negative “trions”.17 Auger process are also thought to greatly reduce the excited state lifetime and therefore QY of charged particles and thereby account for the fluorescence intermittency observed in single particle studies.15 Although a biexciton can result in excitation of either an electron or hole, trion lifetimes indicate that the hole excitation is the dominant process.18 The rates of Auger process in biexcitons and trions are strongly size dependent.19-21 Although the magnitudes of the rates vary with the material, it is generally accepted that Auger relaxation rates of single component QDs at least approximately follow a volume scaling dependence.19, 22, 23 This volume scaling seems to be a near-universal aspect of Auger processes in many types of QDs.24 The observed size dependence of QD Auger rates is in part due to momentum considerations. The basic idea is the following:11, 25 Auger relaxation occurs with three or four particles (electrons and holes) all of which are at the zone center, and therefore 3 ACS Paragon Plus Environment

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have nominally zero momentum. Following radiationless recombination of an electron hole pair, the final state has a single, highly excited electron or hole. Associated with this excited particle is a large amount of linear momentum. The result of this change in overall total momentum is that the Auger process is momentum forbidden.

However, quantum

confinement can somewhat relax this momentum constraint in semiconductor QDs. Spatial confinement introduces higher momentum components into the electron and hole wavefunctions, facilitating overlap with the final, highly excited electron or hole state. This is a simple Uncertainty Principle consideration. The important point is that it is the rapid spatial variation and hence the localized nature of the electron or hole wavefunction that relaxes the momentum forbidden aspect of the Auger process. It has recently been suggested that the presence of a soft core-shell interface affects the rates of Auger processes in core/shell particles.11, 13, 25-28 Theoretical and experimental studies have suggested that the extent to which Auger relaxation is momentum forbidden depends on the sharpness of the core/shell interface in this type of QD. A soft or alloyed core/shell interface diminishes the extent to which the sharp radial edge of the electron or hole wavefunction contributes to the high momentum components and can thereby slow the Auger process. Several theoretical studies indicate that the Auger rates should be strongly non-monotonic with particle size, resulting from minima in the momentum-space wavefunctions.11, 20, 25, 26 However, when smoothed out from size inhomogenieties of the QD ensemble, close to volume dependence of the Auger time is predicted. In this paper we suggest that trapping and Auger dynamics are not independent. This builds on the observation that multicarrier recombination dynamics in type-II QDs are remarkably insensitive to the details of the hole wavefunction.22 Holes trapped at the core-shell interface are highly localized and therefore possess high momentum components. Being at the core-shell interface, they are in close spatial proximity and can electrodynamically couple to carriers at the band edge. Such trapped holes can therefore be involved in Auger processes with other carriers. The presence of high momentum components relaxes the momentum conservation constraints and thereby makes these processes very fast, much faster than those involving just band edge carriers. A simple back-of-the-envelope calculation shows that the spatial confinement associated with hole trapping can be a large effect.

For momentum

conservation constraints to be relaxed, the hole wavefunction must be sufficiently confined to have momentum components comparable to the momentum of a free hole at the bandgap energy. Consider the case of a 3.0 nm diameter CdSe particle having a bandgap energy of 2.3 eV. Assuming a hole effective mass of 0.44 of the free electron mass, this energy corresponds to a momentum of 5.4 x 10-25 kg m/s. The corresponding wavevector is 5.1 nm-1, which gives a wavelength of about 1.2 nm. A trapped hole localized to one unit cell has a dimension of 0.61 nm, which is about ½ of the above excited hole wavelength. The resulting momentum overlap between the trapped and energetic holes is very high. The same conclusion comes directly out 4 ACS Paragon Plus Environment

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of a simple Uncertainty Principle calculation, σp σx = ħ/2. If the σp is taken to be the hot hole momentum then σx is calculated to be about 1Å. Thus, if the spatial extent of the wavefunction is taken to be ± 2σx, (about 4Å) then this roughly corresponds to the size of a unit cell. In either calculation, the conclusion is that trapping of the hole essentially removes the momentumforbidden aspect of the Auger process. As a result, trapped holes at the core-shell interface may dominate the Auger processes that control the biexciton recombination process. Throughout the reported studies what has been lacking are definitive experimental studies of the trapping dynamics and the Auger rates in a series of core/shell particles in which the only thing that is changed is the interface sharpness. This paper examines the dynamical effects of well-characterized hard and soft core-shell interfaces in several sizes of CdSe/ZnSe QDs.

The trapping and Auger dynamics are studied using transient absorption (TA)

spectroscopy to examine bleach recovery kinetics as a function of excitation intensity.

Bleach

recovery kinetics of the 1S-1S and 1P-1P transitions give the time dependence of the 1S and 1P conduction band populations following excitation with one or more photons. In the present studies, CdSe/ZnSe particles are initially synthesized with sharp core/shell interfaces. These particles are then annealed, resulting in cadmium and zinc interdiffusion, softening the interface. Throughout the annealing process the total size and overall particle composition remain constant; the only thing that changes is the sharpness of the core-shell interface. Femtosecond transient absorption measurements then give the biexciton dynamics as a function of the radial composition profile. Results and Discussion 1. Particle characterization – radial composition profile (RCP). A crucial consideration in these studies is the determination of the RCP of the assynthesized particles and how the RCP changes as annealing proceeds. Annealing results in interfacial alloying, bringing some of the larger band gap shell material into what was originally the core.

This increases the band gap in the region of the highest electron and hole

wavefunction amplitudes and therefore produces a blue shift in the energy of the lowest exciton.

These spectral changes can be accurately measured and compared to calculated

spectral shifts. It is through this comparison that accurate RCPs at any stage of annealing can be determined. CdSe particle are synthesized using procedures discussed in the Methods section. A typical absorption spectrum of CdSe cores is shown in figure 1. The core sizes are determined from a well-established sizing curve,29 and in this case the cores have a diameter of 4.0 nm. In the present discussion, we focus on these CdSe cores with approximately 5 monolayer ZnSe shells. Similar static spectroscopic results have been obtained with core sizes ranging from 2.4 to 4.0 nm. Absorption spectra of the CdSe/ZnSe core/shell particles at various stages of shell growth are shown in figure 1. 5 ACS Paragon Plus Environment

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582 -- 591

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Figure 1: A) Absorption spectra of 4.0 nm CdSe cores during the growth of the 5 monolayer shell. The insert shows the lowest exciton region. B) Absorption spectra of core/shell QDs during in-situ annealing at 260 °C. The lowest energy exciton shifts to the blue as annealing proceeds. Shell deposition shifts the absorption maximum by 9 nm, from 582 to 591 nm. It also increases the ratio of absorbances at 350 nm and the exciton maximum from 3.5 to 15.6. Over this range of absorption maxima the lowest exciton absorption cross section is known to increase by a factor of 1.10,30 and one can calculate the 350 nm absorption cross sections using bulk optical constants. Using these values and the known 350 nm CdSe and ZnSe optical constants,31, 32 a ZnSe shell thickness of 1.56 nm is calculated. This is consistent with the five SILAR cycles of shell growth.

This shell thickness was chosen as a compromise between competing

considerations: If the shell is too thin then essentially all of the shell material diffuses into the core and the soft core-shell interface is lost. Alternatively, due to increased lattice strain, very thick shells are difficult to deposit without excessive defects resulting in very low PL quantum yields. Thus, the 4 – 5 monolayer shells used here are readily synthesized with high quality and permit wide variation of the interface sharpness. This spectral shifts shown in figure 1 can be understood in terms of empirically corrected effective mass approximation (EMA) energy and wavefunction calculations (described below). These calculations are sensitive to the extent of lattice strain induced core compression. We find that agreement between experimental and calculated core/shell exciton energies requires that the core compression resulting from lattice mismatch is largely relieved by defect formation.

Specifically, to obtain the experimentally observed core/shell exciton

wavelength, the core pressure must be about 33% of that calculated for a coherent core-shell interface. This results in a loss of about 90% of the lattice strain energy. The partial release of


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core compression upon defect formation is consistent with what was observed upon strain release in CdSe/CdS QDs.6 These core/shell particles have been annealed at 260 °C and spectra of eight aliquots taken at 10 minute intervals were obtained. Several of these spectra presented in figure 1, showing that the absorption maxima shift to the blue as annealing proceeds. This blue shift can be quantitatively understood in terms of cadmium and zinc radial diffusion and empirically corrected effective mass calculations, as discussed below. It is important to note that annealing changes only the RCP. TEM images (see the Supporting Information) show that annealing has no measureable effect on the overall particle size or size distribution. There are no reactants in the annealing solution, so the absence of any change in size indicates that the overall particle composition also remains constant. Modeling of the spectral shift upon annealing requires the calculation of the RCP, the electron and hole potentials, and finally the electron and hole wavefunctions and the exciton energies. The RCP is calculated by solving the spherically symmetric radial diffusion equation.2 The initial condition is that there is a sharp boundary in an assumed spherical particle. We then have that the radially and temporally dependent composition, C(r,t), is described by:

dC ( r , t ) 1 d2 equation 1. = D∇ 2 C ( r , t ) = D ( r C (r , t ) ) dt r dr 2 For the case of ZnSe on CdSe, C(r,t) is the fraction of the alloy that is cadmium, and varies from 1 to 0. Initially, C(r,0) is given by a step function.

C (r ,0) = 1 0 < r < rc = 0 rc < r < R where rc is the core radius and R is the total (core plus shell) radius. The time dependence of C(r,t) gives the extent of diffusion as annealing proceeds.

Solving equation 1 and hence

obtaining C(r,t) is straight-forward, but depends on the boundary conditions. In the present case, no mass transfer occurs across the outer surface of the shell and Neumann boundary conditions are appropriate; we specify that

∂C (r, t ) = 0 . To satisfy this boundary condition ∂r R

and be a solution to equation 1, C(r,t) is expanded in a basis set of the spherical Bessel functions, j0(znr/R), where zn is the n’th zero of the j1 (and the n’th zero of j0’).33 These functions have the correct behavior at r = 0 and zero derivatives at r/R = 1. Thus, expanding C(r,0) in the j0(znr/R) basis ensures that the derivative at the surface is zero. We have that ∇ 2

(∑

n

)

Bn (t ) j0 ( zn r / R ) =

1 ∂ D

(∑

n

Bn ( t ) j0 ( zn r / R ) ∂t

),

with the Bn coefficients given by R

Bn (0) = ∫ r 2dr C ( r,0) j0 ( zn r / R)

equation 2

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The above expression may be solved for the Bi and gives

 − D zi2  Bi ( t ) = Bi (0) exp  t 2  R 

equation 3

with Bi(0) given by equation 2. Due to the small amount of diffusion that occurs upon shell deposition the initial condition corresponds to a small but finite value of t in equation 3. The above calculations can be applied to CdSe/ZnSe core/shell particles to calculate the RCP at any stage of annealing. The only adjustable parameter in this calculation is the diffusion coefficient, D, as discussed below. Following calculation of the RCP, the radially-dependent valence and conduction band potential are easily calculated. The CdSe/ZnSe QDs are type-I, with bulk material valence and conduction band offsets of 0.20 and 0.64 eV, respectively. In the alloyed interfacial region these potentials are taken to vary linearly with composition.

This ignores optical band-bowing

effects, which are small for II-VI alloys having the same chalcogenide. These potentials also ignore compression effects, which can be quite significant. There is a relatively large lattice mismatch and for this core size and shell thickness, the calculated strain energies are much greater than the maximum strain energy allowing coherent shell growth for CdSe/CdS QDs. We have shown that strain energies of this magnitude are largely relieved by shell defect formation, which also greatly reduces the extent of core compression.6 As a result, the strain energies in this case are also expected to be relieved by defect formation. To the extent that the core compression remains constant, the calculated annealing spectral shift will be independent of core pressure effects, and this is the approximation we make. With these approximations, the radially-dependent conduction and valence band potentials are also shown in figure 2. The electron and hole wavefunctions can be calculated using an EMA method with these potentials. These calculations follow those detailed in references 2 and 34, in which the wavefunction is expanded in a basis set of the spherical Bessel functions. This approach gives continuity of the wavefunction and of probability current without explicitly considering the core-shell boundary conditions. It therefore easily generalizes to the case of a diffuse core-shell interface. EMA calculations are known to predict larger quantum confinement effects than what is observed.

These errors are minimized by considering the electron and hole moving in

potentials having finite barriers at the particle surface. However, even with finite barriers, EMA calculations typically over-predict the extent of quantum confinement, and the extent of these errors increases with increasing quantum confinement energy. The fundamental problem is −1

 ∂2 E  that the effective mass is defined as m* = h 2  2  , and the plot of E versus k is not quadratic at  ∂k  the larger quantum confinement energies of the smaller particles.35, 36 The obvious solution to this problem is to empirically correct the effective masses as a function of quantum confinement


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energy, as was done in reference 34. We have previously shown that the corrected CdSe electron effective mass may be given by, 2 me* ( corrected ) = me* ( bulk ) ( 0.36773 + 2.756434 x10−4 EQC − 8.3105x10−9 EQC ) , where EQC is the electron

plus hole quantum confinement energy. The correction factor to the electron effective mass is calculated in a way that is self-consistent with the calculated quantum confinement energies. Throughout these calculations, the electron-hole coulombic interaction is treated as a perturbation. This empirical correction is chosen so that the EMA calculations very accurately reproduce the known CdSe sizing curve for particles having exciton wavelengths of 500 – 650 nm.29 The same approach (using the same correction expression) is used to give the exciton energy and the electron and hole wavefunctions for CdSe/ZnSe core/shell particles having radially dependent conduction and valence band potentials. From these calculations the lowest exciton wavelength can be calculated as a function of the extent of annealing, Dt in equation 3. Comparing calculated and experimental exciton wavelengths permits evaluation of the diffusion constant, D, and hence calculation of the RCP as annealing proceeds. Using the spectra in figure 1, the calculated initial and 70 minute RCPs are obtained and shown in figure 2. The corresponding valence and conduction band potentials and electron and hole energy levels are also shown in figure 2.

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Figure 2. A) Plots of the RCP before (solid curve) and after (dotted curve) 70 minutes of annealing. B) Conduction (black) and valence (red) band potentials with respect to CdSe for CdSe/ZnSe particles before (solid curve) and following (dashed curve) 70 minutes of annealing. The solid and dashed horizontal lines indicate the electron (black) and hole (red) quantum confinement energies before and after annealing, respectively. The initial RCP shows that prior to annealing the core-shell interface is quite sharp: the 80% and 20% cadmium compositions are separated by about 0.20 nm, which is less than the dimensions 9 ACS Paragon Plus Environment

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of a single unit cell.

Following 70 min of annealing, the interface defined this way has

broadened to 0.67 nm, about two Cd(Se,S) layers. It is important to note that although the interface is dramatically changed, the total size and overall composition of these QDs is unchanged by annealing. One crucial check for internal consistency of these calculations is that the value of the radial diffusion coefficient (equation 1) needed to fit the observed spectral shift should be independent of the extent of annealing.

Otherwise stated, the extent of annealing is

characterized by the quantity Dt, and a plot of Dt should increase linearly with time. Such a plot is shown in figure 3 on a sample (3.54 nm core, 4.5 monolayer shell) that was annealed for 200 minutes. The behavior is linear within experimental error, indicating that the diffusion that occurs during annealing is well described by the simple radial diffusion model, equations 1 – 3. The diffusion coefficient is strongly temperature dependent, and in this case is about 4.04 x 10-4 nm2/min. 0.12 0.10

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0.06 0.04 0.02 0.00 0

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Figure 3. Plot of the extent of annealing, Dt, (as determined from the absorption spectra) as a function of annealing time. Also shown is a linear fit to the values of Dt versus time. 2. Dynamical results: large particles. Excitation intensity dependent TA results (1S-1S exciton bleach recovery kinetics) for 4.0 nm core with 5 monolayer shell particles (figure 1) having hard and soft interfaces (0 and 70 min annealing) are shown in figure 4. We note that the magnitude of the bleach signal is very close to what is expected based on power density considerations. The QD concentration in the TA experiments is set such that the sample absorbances at the excitation (387 nm) and first exciton wavelengths are about 1.0 and 0.10, respectively.

The particles have an effective


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diameter (defined as the diameter of CdSe particles having the same exciton wavelength) of 4.2 nm and therefore an exciton extinction coefficient29 of 2.8 x 105 L mol-1cm-1. This gives an extinction coefficient at 387 nm that is about a factor of 10 greater (see figure 1), or about 2.8 x 106 L mol-1 cm-1. The QD concentration is about 0.4 μM and the result is that throughout the irradiated volume of the 1.0 cm path length cell, about 4.8% of the particles are excited. This calculation predicts that at the lowest power, the exciton bleach should be about 5 x 10-3, which is consistent with what is shown in figure 4. With this beam diameter and extinction coefficient, excitation pulse energies less than about 0.2 μJ preclude the possibility of significant multiphoton processes and biexciton formation. 40

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Figure 4. (A, B) Bleach recovery kinetics for hard and soft interface particles (as indicated) having a 4.0 nm core and a 5 monolayer shell, taken at the power levels of 0.12 (black) and 0.7 (red) μJ/pulse. Also shown are fits to the low power kinetics having a 21% (soft interface) and 36% (hard interface), 415 ps decay component (blue curves). (C, D) High minus scaled low power kinetics for the soft and hard interface particles. The hard interface results are fit to a 11 ACS Paragon Plus Environment

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biexponential decay having 19 ps (41%) and 240 ps (59%) components and the soft interface results are fit to a biexponential decay having 21 ps (17%) and 190 ps (83%) components (red curves). Also shown in C) are calculated curves corresponding to the same decay times and fast:slow component amplitude ratios of 47:53 and 35:65 (thinner blue curves). The comparison of these curves with the experimental results shows that the fast:slow amplitude ratios can be determined quite accurately. The full data range of TA traces C) and D) are given in the Supporting Information. The low power kinetics for both hard and soft interface particles (figures 4A and 4B) show a small amplitude approximately 415 ps decay component and no evidence of faster decays. We note that this decay time is about a factor of two longer than the longest biexciton times discussed below. As such, much of this decay may be due to trion Auger decay, brought about by surface charging and single photon absorption.37 However, these core/shell particles are highly strained. In an earlier paper we showed that for CdSe/CdS particles that have lattice strain energies greater than 0.59 eV/nm2 strain release results in hole trap states.7 In the present case, a coherent core/shell interface is calculated to have a strain energy density of 1.27 eV/nm2, which is more than twice the maximum that an equilibrium coherent interface can maintain in CdSe/CdS particles. This could result in several different types of carrier recombination centers. It is therefore quite possible that several different types of nonradiative processes contribute to the observed low power decays. As such, no definitive assignment of the low power transient can be made. The high power kinetics correspond to 0.7 μJ/pulse, also focused to a 1.45 mm spot size. To accurately assess of the fraction of particles that absorb 0, 1, 2, etc., photons, attenuation of the excitation beam through the sample must be considered.

This results in a Poisson

distribution with the average being position dependent. Overall average values are obtained by integration of the absorption probabilities over the 1 cm cell pathlength. In the present case about 24% of the particles are excited, with 3.8% absorbing two photons and 0.7% absorbing three or more photons. Biexciton Auger recombination times are obtained by scaling the low power kinetics to match the higher power kinetics at the longest times and subtracting the result from the high power kinetics. The 1P-1P transition (508 nm) also shows a small bleach in the TA spectra, which can be assigned to triexciton formation. This bleach recovers on the 10 ps timescale. However, triexciton dynamics have a smaller effect on the 1S-1S transition38 and at the power densities used in these studies, very little of the 1S-1S high minus scaled low power difference signal is due to absorption of three or more photons. The high minus scaled low power kinetics for the hard and soft interface particles are shown in figures 4C and 4D. The hard interface particles show a biexponential decay, having 19 ps (41%) and 240 ps (59%) components. Upon softening of the interface, the decay times change very little, giving 21 and 190 ps components. However, the relative amplitude of the slow component significantly 12 ACS Paragon Plus Environment

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increases to 83%, with 17% in the fast component. The signal to noise ratios in the high minus scaled low power kinetics are high, about 75. The large separation of the fast and slow time constants along with this high S/N ratio facilitates quite accurate determination of the fast to slow component amplitude ratio.

Curves calculated having the same decay times and

amplitude ratios 25% larger or smaller are shown in figure 4C and are clearly outside of the experimental data. Thus, the large change in fast to slow amplitude ratios that occurs upon annealing (more than a factor of 3) is well outside of the experimental uncertainty. We suggest these results can be understood in terms of the model depicted in figure 5. - conduction e e band

- conduction e e band

fast

slow

h+ h+ valence

+ h+ interface h localized valence

band

band

Figure 5.

Left panel:

trap

Mechanism for slow, bandedge Auger relaxation.

Center panel:

Mechanism for fast, trapped hole Auger relaxation. Right panel: Schematic of band edge (blue) and trapped (red) wavefunctions in position (top) and momentum (bottom) space.

The

momentum of the hot hole is indicated as p* and the schematic shows that the trapped hole has a much larger amplitude at this momentum. In this model, two types of biexciton Auger recombinations can occur. First, the usual biexciton Auger process in which both holes are in the valence band (left panel of figure 5). Momentum constraints limit the rate of this process and it is relatively slow, with the slow component of the biexciton decay (approximately 200 ps) assigned to this process. Second, strain-induced defects at the core-shell interface can result in localized hole traps, and these localized holes can also be involved in Auger recombination with conduction band electrons (center panel of figure 5). A bleach recovery TA experiment measures only the conduction band populations and is therefore insensitive to the hole trapping dynamics.38 However, the trapped holes have very small effective volumes and therefore largely relax the momentum constraints controlling subsequent Auger processes, as depicted in the right panel of figure 5. Holes trapped at the core-shell interface also have considerable overlap with the conduction band electrons which 13 ACS Paragon Plus Environment

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facilitates Auger processes. We suggest that the result is that Auger processes involving these localized holes are much faster than with delocalized holes and the fast (approximately 20 ps) component is assigned to this process. In this mechanism, a specific particle either has an interfacial hole trap or it does not, which explains the separation of timescales between the fast and slow components. This is also consistent with the observation that biexciton Auger rates in CdSe/CdS particles are observed to be highly inhomogeneous.39 The sharp interface particles have more lattice strain and therefore a higher probability of having an interfacial defect that can act as a hole trap. The result is that the fraction of particles giving the fast Auger process decreases as the interface is softened. The fraction of particles having interfacial hole traps can be assessed from the relative amplitudes of the fast and slow Auger components. In the present case, this fraction decreases from 41% to 17% upon annealing, compare figures 4C and 4D. It is important to note that this proposed mechanism is different than one in which softening the core-shell interface reduces the Auger rate of band edge carriers. In the proposed mechanism the Auger rate of the band edge carriers has very little dependence on the nature of the coreshell interface. It is the fraction of particles having strain-induced defects that varies with the sharpness of the interface, and this controls the magnitudes of the fast and slow Auger components. 3. Dynamical results: mid-sized and small particles. Analogous studies have also been performed on mid-sized particles, having a 3.1 nm core and an approximately 4 monolayer thick shell, see Supporting Information. These particles have smaller photon cross sections and somewhat higher powers were used to obtain comparable magnitudes of the exciton bleach. In this case the particles were annealed at 260 °C for 140 min. Spectroscopic and dynamical studies were performed following 0, 10, and 140 minutes of annealing. The calculated RCPs are shown in figure 6.

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0.6 0.4

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Figure 6. A) Calculated RCPs for the mid-sized QDs following 0 (hard), 10 (intermediate) and 140 (soft) minutes of annealing, as indicated. B – D) Biexciton decay kinetics (high minus scaled low power) for the hard, intermediate and soft interface particles. Also shown are fit biexponential decay curves corresponding 8 ps and 85 ps decay components.

The slow

components are 11.5%, 28% and 51% of the total decay for the hard, intermediate and soft cases, respectively. As in the case of the larger particles, the initial RCP corresponds to a very sharp interface that becomes progressively softer as annealing proceeds. Following 140 minutes of annealing the 80% to 20% alloy interface is quite soft, having a thickness of about 3 (Cd,Zn)Se monolayers. Figure 6 also shows that the dynamics change very significantly as annealing proceeds. In all cases, the two-photon kinetics show a biexponential decay that can be accurately fit to 8 ps and 85 ps decay components. As annealing occurs the primary change is that the relative amplitude of the slow component increases at the expense of the fast component. This is a large effect, with the percentage of the slow component increasing by more than a factor 4 in the 140 min annealed case. The important point is that the Auger rates do not continuously change as annealing proceeds, rather, it is the amplitude ratio of fast and slow components that changes, which is consistent with the mechanism proposed in figure 5. Transient absorption and PL decay kinetics for 2.4 nm CdSe cores having 4 monolayer shells are shown in figure 7. The static and PL decays for hard (no annealing) and soft (final annealing) interface samples are given in the See Supporting Information.


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80

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20 15 10 5 0 -5 0

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Figure 7. Bleach recovery and PL decay (inserts) kinetic results for particles having a 2.40 nm core and 4 monolayer shell with (A) hard and (B) soft interfaces. Bleach recovery kinetics are obtained at the indicated pulse energies and the PL decay kinetics are obtained at very low power. Also shown in (B) is a curve fit to the low power kinetics having a 90 ps decay component. (C ) The high minus scaled low power kinetics for the soft interface particles are shown along with a fit curve corresponding to a 13 ps (48%) and 65 ps (52%) decays. Unlike the larger particles for which annealing makes only modest differences in the PL decays or quantum yields, annealing has a dramatic effect on the luminescence and transient absorption properties of the smaller particles. To understand these differences, one must consider the presence of both electron and hole traps, both of which can result from straininduced defects. Prior to annealing, the hard interface particles have a very low luminescence quantum yield and a very rapid PL decay. Annealing greatly increases the quantum yield and lengthens the PL decay. Similar results are seen in the hard interface bleach recovery kinetics. The low power kinetics can be fit to a biexponential decay having approximately 6 ps (60%) and 16 ACS Paragon Plus Environment

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50 ps (40%) decay components. In contrast, the soft interface particles show only a relatively small (40% of the total) 90 ps decay component and no faster decay components. These differences can be understood in terms of strain-induced electron trap formation. The initial particles are highly strained, having a calculated strain energy density (assuming a coherent core-shell interface) of 1.26 eV/nm2, well over the maximum of coherent shell growth of 0.59 eV/nm2. Annealing relieves much of the lattice strain. The calculated RCP for the annealed particles gives an equilibrium strain energy density of 0.57 eV/nm2, just below the maximum. Lattice strain considerations therefore indicate that the difference in the hard versus soft interface exciton dynamics is due to the presence of defects that act as electron traps only in the hard interface particles. Following these considerations, the larger core particles discussed above are calculated to have higher strain energies than the small particles and would also be expected to have a high density of electron trapping defects. However, fast decay components are absent in the low power large particle kinetics, see figure 4. This difference can be understood in terms of the energetics of the defects. Electron trapping defects would correspond to ‘dangling bonds’ from cadmium or zinc atoms. As such, these orbitals would have energies that are close to being independent of the particle size. However, the QD conduction band energy is very strongly size dependent. Comparing the particles with 4.0 nm and 2.4 nm cores, the conduction band is about 0.2 eV higher in the latter case. We suggest that the larger core particles probably do have a high density of defect states, but metal orbitals corresponding to these defects are at an energy that is above the conduction band, and as a result, cannot act as electron traps. Due to the higher conduction band energy in the smaller particles, these states are energetically accessible and rapid electron trapping occurs in the hard interface particles. Annealing greatly reduces the defect density in the smaller particles, and figure 7 shows that little or no fast component associated with electron trapping is present in the low power kinetics. The rapid PL quenching only in the smallest particles is consistent with the general observation that it is more difficult to synthesize very small CdSe particles that are highly luminescent. Due to the rapid electron trapping it is difficult to extract Auger times from the hard interface kinetics. Biexciton Auger times can be obtained from the soft interface bleach recovery kinetics. Using a procedure exactly analogous to that described for the larger particles, biexciton Auger times of approximately 13 ps (48%) and 65 ps (52%) are obtained. (Because of the smaller extinction coefficients, higher pulse energies are needed to achieve the same excitation probabilities.) As with the larger particles, the longer decay time is assigned to the Auger dynamics of band edge holes. The biexciton dynamics for all of the particles discussed above are summarized in table 1.


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Table 1. Biexciton decay times and amplitudes. Core diam. / 2.4 3.1 nm a Veff / nm3 14.5 21.9 interface hard soft hard intermed soft fast decay / ps 13 8 slow decay / ps 65 85 fast/slow 0.93 7.7 2.6 0.96 amplitude ratio b average decay 40.0 16.8 29.6 47.3 time / ps a defined as the volume of a CdSe QD having the same exciton energy b defined as (Aslow τslow + Afast τfast)/ (Aslow + Afast)

4.0 41.3 hard 19 240 0.69

soft 21 190 0.20

149

161

The slow components are consistent with approximate volume scaling of these Auger times. The small particles have an effective volume of about 14.5 nm3, which is a factor of 2.85 less that the large particles and a factor of 1.5 less than the mid-sized particles. This reasonably follows ratios of Auger times, 2.9 and 1.3 for the large and mid-sized particles, respectively. Although there is more uncertainty in the faster Auger times, these times do not appear to follow this simple volume scaling. Calculation of these Auger rates is complicated by the unknown extent of relaxation of the Auger momentum constraints and by possible inhomogenieties in the overlap of trapped holes with conduction band electrons. However, to the extent that hole excitation is the dominant process, the biexciton Auger time could be expected to scale as the product of the effective radii of the electron and each of the carriers,27 that is, τ xx ∝ Re Rh1 Rh 2 . The roughly order of magnitude faster Auger time observed with a trapped hole is then consistent with the spatial extent of the of the trapped hole being about an order of magnitude smaller in linear dimension than the particle core. This corresponds to about one unit cell, which is what one expects for a carrier trap. The fast to slow amplitude ratio results in table 1 show the most important result of this paper; alloying the core-shell interface greatly increases the relative amplitude of the slower Auger process. One can also define an average biexciton lifetime, ∞

τ ave = ∫ S (t ) dt S (0) , where S(t) is the biexciton population, and is taken to be the high minus 0

scaled low power signal. In the case where the decay can be described by a biexponential, we have that S (t ) = Af exp(−t / τ f ) + As exp(−t / τ s ) where Af and As are the amplitudes of the fast and slow components having decay times of τf and τs, respectively.

τ ave = ( Af τ f + Asτ s )

(A

f

In this case

+ As ) , and values of the average Auger time are given in table 1. In the

case of the intermediate sized (3.1 nm core) particles, this value increases by a factor of 2.8 upon annealing, despite the lack of significant change of either the fast or slow Auger times. It is of interest to compare the fast and slow decay components reported here to previously reported biexciton Auger times on different sizes of CdSe QDs, capped with organic 18 ACS Paragon Plus Environment

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ligands. Results taken from several papers by Klimov et al.23 have been compiled to give a volume scaling relation of τxx (ps) = const V (nm3) equation 4. with const = 1.5. Other results19 give a similar relation with const = 1.3. This is in reasonable agreement with results on smaller sized particles reported by Pandey and Guyot-Sionnest.22 We conclude that the existing data on CdSe particles gives biexciton Auger times described by equation 4, with const = 1.4 ± 0.1. With this relation, biexciton decay times of approximately 20, 31 and 58 ps are predicted for the small, mid-sized and large particles in table 1. In all three cases, the predicted values are between the fast and slow decay components. This suggest that CdSe QDs having only organic ligands on the surface may exhibit biexciton Auger dynamics involving both valence band and trapped holes. This is not a surprising conclusion; such particles typically have fairly low luminescence quantum yields as a result of rapid carrier trapping at surface states. As mentioned above, single particle results have been reported that indicate highly inhomogeneous biexciton Auger dynamics.39 However, we are aware of only one other set of studies that measure non-exponential biexciton decay kinetics in CdSe QDs. Sahu et al.40 use a transient coherence spectroscopic method (MUPPETS) and report a distribution of biexciton times, centered at 18 ps for 2.7 nm CdSe/ZnS QDs, having an exciton peak at 520 nm and an effective volume of 10.3 nm3. In a later paper these authors report that this distribution of biexciton lifetimes can be fit to a biexponential decay, S(t) = 0.635 exp(−t /6 ps) + 0.365 exp(−t /40 ps), having 6 and 40 ps lifetimes, for a weighted average of 18.4 ps.41 These values can be compared to annealed smallest particles discussed above, having an only slightly larger effective volume of 14.5 nm3, see table 1. Assuming volume scaling of both fast and slow components from the results in references, decay times of 8.5 and 56 ps are predicted for our smallest particles. The longer time is in good agreement with the 65 ps value in table 1. The short time component of the CdSe/ZnSe particles is significantly longer, presumably because of differences in the types of trap states in particles having different shell materials. Summary and Conclusions In this paper we have examined the role of lattice strain in the biexciton dynamics of core/shell QDs. The magnitude of the lattice strain energy determines the probability that the particle will have hole-trapping defects at the core-shell interface. We propose that holes trapped at these defects can be involved in Auger recombination with conduction band electrons. Thus two different types of biexciton Auger processes can occur; process involving only band edge holes and processes involving a trapped hole. Band edge holes have very low amplitude high momentum components and therefore their Auger processes are momentum forbidden and comparatively slow. Trapped holes are much more localized, giving them much larger high momentum components and therefore much faster Auger processes. The relative amounts of the slow and fast Auger processes are controlled by the amount of lattice strain, which is largely determined by the sharpness of the core-shell interface. A soft, alloyed 19 ACS Paragon Plus Environment

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interface greatly reduces the amount of lattice strain and hence the probability of having interfacial hole traps. We find that it is the removal of these hole traps that cause the average Auger time to dramatically increase with softening of the core-shell interface. While both the fast and slow Auger recombination process change very little with changing the interface, the net effect is that the average Auger decay time increases as a consequence of softening of the core-shell interface. Methods Chemicals. Cadmium oxide (CdO, 99.5%), octadecylamine (ODA, 90%), oleylamine (technical grade, 70%), octylamine (99%), zinc oxide (ZnO, 95%), trioctylphosphine oxide (TOPO, 90%), tributylphosphine (TBP, 97%), octadecene (ODE, 90%), hexane (99.8%), methanol (MeOH, 98%) were obtained from Aldrich. Selenium (Se, 99%), oleic acid (OA, 90%), and chloroform (CHCl3, 99.8%) were obtained from Alfa Aesar. ODA and TOPO were recrystallized from toluene before use. All other chemicals were used as received. Particle synthesis. CdSe particle cores are synthesized using a standard method based on the reaction of cadmium oleate or cadmium stearate with trioctylphosphine selenium in a solution of octadecene, trioctylphosphine oxide and octadecylamine.30 The core sizes are determined from a well-established sizing curve.29 Shell growth is by a modified SILAR method similar to that used by Acharya et al.42 The ZnSe shell deposition is at 220 °C using 0.15 M Zn-oleate and a selenium suspension (Se-SUS), with cycles of zinc and selenium deposition taking 10 and 5 minutes, respectively. Typically 4 – 5 ZnSe shells are deposited. Following shell deposition, the absorption spectra do not shift on the tens of minutes timescale at 220 °C. Several sizes of core/shell particles have been annealed at 260 °C for as much as 200 minutes. The final solution was extracted by hexane/methanol (volume ratio of ∼1:1) twice. The nonpolar phase containing the particles was separated and heated under vacuum to remove the residual hexane and methanol. The PL decays for all of the hard (no annealing) and soft (final annealing) interface samples are given in the Supporting Information. Optical measurements.

Excitation intensity dependent transient absorption results were

obtained with an apparatus described in reference 37. Samples were held in rapidly stirring 1 cm cuvettes having an absorbance at the excitation wavelength of about 0.7 - 1.0. In a typical low power experiment, the 0.12 μJ, 387 nm, 1 kHz excitation pulses are focused to a 1.45 mm spot size. Higher power experiments use between 0.7 and 6.0 μJ/pulse. The sample is probed with a white light continuum and the spectrum dispersed on a cooled CCD. Static luminescence spectra were measured on a Jobin-Yvon Fluorolog 3 using a CCD detector. Photoluminescence kinetics were obtained following excitation with very low intensity 410 nm pulses at 1 MHz from a cavity-dumped frequency-doubled Coherent MIRA laser. The luminescence was imaged through a 1/4 m monochromator with a 150 groove/mm grating onto a Micro Photon Devices PDM 50CT SPAD detector. Time-correlated photoncounting decays are accumulated using a Becker Hickle SPC-630 board. The overall temporal 20 ACS Paragon Plus Environment

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response function of the system is about 100 ps. Quantum yield measurements were made using the same samples as the time-resolved luminescence measurements. Corresponding Author *E-mail: [email protected] Supporting Information Available Optical measurement of different sized particles and TEM images are given in the Supporting Information. This information is available free of charge via the Internet at http://pubs.acs.org. Notes The authors declare no competing financial interest. Acknowledgement This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under award number DE-FG02-13ER16371. References 1. West, A. R., Basic Solid State Chemistry. Wiley Chichester, 1988. 2. Cai, X.; Mirafzal, H.; Nguyen, K.; Leppert, V.; Kelley, D. F., The Spectroscopy of CdTe/CdSe type-II Nanostructures: Morphology, Lattice Mismatch and Band-Bowing Effects. J. Phys. Chem. C 2012, 116, 8118 - 8127. 3. Pal, B. N.; Ghosh, Y.; Brovelli, S.; Laocharoensuk, R.; Klimov, V. I.; Hollingsworth, J. A.; Htoon, H., ‘Giant’ CdSe/CdS Core/Shell Nanocrystal Quantum Dots As Efficient Electroluminescent Materials: Strong Influence of Shell Thickness on Light-Emitting Diode Performance. Nano Lett. 2012, 12, 331–336. 4. Smith, A. M.; Mohs, A. M.; Nie, S., Tuning the Optical and Electronic Properties of Colloidal Nanocrystals by Lattice Strain. Nature Nanotechnology 2009, 4, 56 - 63. 5. Gong, K.; Kelley, D. F., A Predictive Model of Shell Morphology in CdSe/CdS Core/Shell Quantum Dots. J. Chem. Phys. 2014, 141, 194704 - 194712. 6. Gong, K.; Kelley, D. F., Lattice Strain Limit for Uniform Shell Deposition in Zincblende CdSe/CdS Quantum Dots. J. Phys. Chem. Lett. 2015, 6, 1559-1562. 7. Gong, K.; Beane, G.; Kelley, D. F., Strain Release in Metastable CdSe/CdS Quantum Dots. Chemical Physics, submitted. 8. Rockenberger, J.; Troger, L.; Rogach, A. L.; Tischer, M.; Grundmann, M.; Eychmuller, A.; Weller, H., The Contribution of Particle Core and Surface to Strain, Disorder and Vibrations in Thiol-Capped CdTe Nanocrystals. J. Chem. Phys. 1998, 108, (18), 7807-7815. 9. Ithurria, S.; Guyot-Sionnest, P.; Mahler, B.; Dubertret, B., Mn2+ as a Radial Pressure Gauge in Colloidal Core/Shell Nanocrystals. Phys. Rev. Lett. 2007, 99, 265501.


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TOC graphic



fast

slow

h+ h+ valence

+ h+ interface h localized valence

band

band

trap

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Auger and Carrier Trapping Dynamics in Core ... - ACS Publications

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