Shell


Mar 12, 2013 - Alessandro Minotto , Francesco Todescato , Ilaria Fortunati , Raffaella Signorini , Jacek J. Jasieniak , and Renato Bozio. The Journal ...
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Article pubs.acs.org/JPCC

Stranski−Krastanov Shell Growth in ZnTe/CdSe Core/Shell Nanocrystals Zhong-Jie Jiang and David F. Kelley* University of California, Merced, 5200 North Lake Road, Merced, California 95343, United States S Supporting Information *

ABSTRACT: ZnTe/CdSe core/shell nanoparticles are synthesized in noncoordinating solvents at different temperatures. The experimental results show that CdSe shell deposition at 215 °C on spherical ZnTe core particles is analogous to StranskiKranstanov growth of 2D epitaxial films. The shell thickness inhomogeneity is determined by measuring the inhomogeneity in interfacial hole transfer rates to an adsorbed hole acceptor, phenothiazine. We find that the first approximately three layers of CdSe are deposited uniformly and that subsequent layers produce a rough shell surface. The origin of the shell thickness inhomogeneity is investigated. ZnTe and CdSe have very close to the same lattice constants, and the interface therefore has very little lattice strain. However, cation interdiffusion changes the radial composition profile of the ZnTe-CdSe interface, leading to a large amount of lattice strain. The extent of cation interdiffusion and hence the surface morphology can be controlled by varying the deposition temperature and the subsequent annealing time and temperature. The particle spectroscopy and the shell thickness inhomogeneity are consistent with calculations based on an elastic continuum model with a cation interdiffusion constant of 1.3 × 10−2 nm2 min−1 in the ZnTe/CdSe particles at 250 °C. The comparison of the energetics involved in S−K growth of thin films and nanocrystal shells is discussed.



INTRODUCTION Colloidally synthesized semiconductor nanocrystals (NCs) are promising light-harvesting components in photovoltaic devices.1−4 Their broad absorption spectra, size-tunable optical properties, and large absorption coefficients make them particularly attractive as candidates to utilize the full solar spectrum.5−7 Despite these properties, the stability of core-only NCs remains an issue because semiconductor NCs can undergo photoinduced degradation of their optical properties.8−10 To address this problem, the NCs are often epitaxially coated with different semiconductor materials to form a core/shell structure, isolating the NC cores from the external environment.11−13 Shell deposition not only improves the stability of the NCs against photodegradation11,13,14 but also passivates surface traps, enhancing the photoluminescence (PL) quantum yields.13,15,16 A fundamental question regarding the dynamics of these core/shell NCs is the effect of the shell coating on interfacial electron and hole transfer rates. Because the shell can insulate one or both photogenerated carriers in the core, it is expected to slow the rate of charge transfer of the core confined carriers across the core/shell interface. This can decrease the © 2013 American Chemical Society

efficiency of photovoltaic devices because the utilization of the photogenerated excitons depends on the charge transfer rate. Lian et al.17 have shown that the rate of core-confined charge transfer depends on the thickness of the shell, showing an exponential decease with the shell thickness. This has also been demonstrated by calculation of the charge density at the surface of core/shell NCs.18 Because of this strong dependence on shell thickness, interfacial charge-transfer dynamics critically depend on the uniformity of the shell. It is generally assumed that the shells of nominally spherical core/shell semiconductor NCs grow in a layer-by-layer fashion and are therefore of very uniform thickness. However, several studies have shown that this is not always the case, and the morphology often depends on core and shell materials and the shell growth conditions. In general, several different growth modes can be observed. The usual growth modes are layer-bylayer (Frank−van der Merwe, F−M), layer-by-layer up to a Received: January 9, 2013 Revised: March 7, 2013 Published: March 12, 2013 6826

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V−W growth. In this case, the formation of isolated islands directly on the substrate is followed by their growth and eventual coalescence, leading to an extremely rough surface. In the very common case that there is an intermediate lattice mismatch, epitaxial growth proceeds via the S−K model, in which the formation of a uniformly strained film (the wetting layer) up to the critical thickness of monolayers is followed by the growth of 3D islands on the top of the uniform film. Consequently, the surface of films that grow in the S−K mode are rougher than those that grow in F−M mode but smoother than those that grow in V−W mode. One could imagine that with the relatively low temperatures at which colloidal core/shell NCs are grown, the shell thickness heterogeneity could be a result of either kinetic or thermodynamic effects. If the shell growth was completely controlled by the kinetics of monomer diffusion, the surface morphology would be described by a simple mechanism in which shell monomers react with the surface of the growing particle and are subsequently immobile. We present results below that indicate that this is not the case in the ZnTe/CdSe system at the temperatures and with the solution chemistry used in colloidal synthesis. The surface morphology depends on the thermal history of the particles and is therefore inconsistent with this sort of a simple kinetic model. We therefore focus on thermodynamic rather than kinetic mechanisms. The similarity to epitaxial film growth suggests that the roughness of the core/ shell NCs will depend on the lattice mismatch between the core and shell materials. Our recently published work appears at first glance to contradict this expectation.18 These studies were performed on ZnTe/CdSe NCs and measure the extent of surface roughness by an indirect but very sensitive method. ZnTe cores with a CdSe shell form “type-II” nanoparticles in which photogenerated holes are confined to the particle cores. These holes can tunnel through the shell to adsorbed hole acceptors. Hole transfer quenches the luminescence, giving a spectroscopic method of measuring the hole-tunneling dynamics. These dynamics critically depend on the shell thickness, and the shell thickness distribution can be inferred from time-resolved spectroscopic results. The results show that the particles exhibit a significant shell thickness inhomogeneity.18 The combination of TEM images and hole-transfer kinetics establishes that the average shell thickness varies little from particle to particle and that the shell thickness inhomogeneity is present on each particle. This occurs even though bulk ZnTe and CdSe are reported to have a very small lattice mismatch (∼0.3%).33−35 These results raise questions regarding the cause of the shell thickness inhomogeneity in colloidally synthesized core/shell NCs in general, particularly when there is a small lattice mismatch. Although the extent of the shell thickness inhomogeneity was measured and characterized, the factors determining the extent of inhomogeneity have not been previously investigated. The origin of the shell thickness inhomogeneity in ZnTe/ CdSe NCs is addressed in this article. The experimental results show that under the usual shell deposition conditions it is the lattice mismatch that causes the shell roughness. Although pure ZnTe and CdSe have a small lattice mismatch, rapid cation but slow anion interdiffusion creates a core/shell boundary that is best described as a (Zn,Cd)Te−(Cd,Zn)Se junction. As such, there is a large lattice mismatch across the Te−Se interface of these particles. Because the cation interdiffusion rate depends on the temperature, the extent of the lattice strain and hence

critical thickness and islands thereafter (Stranski−Krastanov, S−K), and island growth (Volmer−Weber, V−W).19,20 An extreme example of the colloidal shell growth being controlled by the deposition chemistry and conditions is the growth of CdSe on CdTe. In this case, crystal structure and ligand effects result in either spherical core/shell or tetrahedral core/tetrapod particles.21 CdTe grows as spherical zincblende cores and CdSe shells grow as either a spherical zincblende shell or as thermodynamically preferred22 wurtzite rods. Similarly, the solution-phase growth of a CdSe shell on CdTe nanowires23 and growth of CdSe on ZnSe24 do not show layer-by-layer growth but rather island growth, even at submonolayer thicknesses. In the case of the solution-phase synthesis of CdS/CdSe, CdSe/CdS, and CdSe/ZnTe core/shell nanowires, shell growth can occur through either S−K or V−W island growth.25 In the inverse system of what is reported here, S−K growth of ZnTe on CdSe nanowires has been reported.25 The deposition reaction initially gives wetting layers; however, beyond a critical shell thickness, nucleation of randomly oriented NCs results in a polycrystalline coat. Shell thickness inhomogeneity in approximately spherical core/shell NCs has also been demonstrated in other recently published work.18,26,27 No obvious patterns emerge from the above studies, indicating that several factors influence the shell morphology of colloidally grown core/shell NCs. The growth of several monolayers of a shell material on a colloidal nanoparticle is analogous to the well-developed techniques for the growth of 2D epitaxial films on atomically flat semiconductor surfaces. In general, epitaxial films are not of uniform thickness and are often characterized by rough surfaces due to island growth.19,28,29 Following deposition at relatively high temperatures, the substrates/films are in a metastable thermodynamic equilibrium, with the actual equilibrium state corresponding to alloy formation. There are three relevant thermodynamic considerations in this metastable regime. First, surface roughness increases the total surface area and therefore increases the enthalpy associated with dangling surface bonds. Second, depending on the core and shell materials, increased surface roughness may decrease the strain energy associated with the core/shell lattice mismatch. Third, a very uniform surface has a low entropy and may therefore be thermodynamically unfavorable at high temperatures. The relative magnitudes of these quantities determine the surface morphology that will be observed.20,28−31 Coherent epitaxial film growth requires the coating material to adopt the in-plane lattice parameters of the immediately underlying substrate, which results in strain of both the film and substrate. The strain energy can be very large, and it is generally proposed that the film roughness depends on the relative magnitudes of the surface energy and strain energy terms. Entropy terms are smaller and involved in determining the temperature dependence of size and structure of the surface features.28,32 The magnitude of the strain energy increases with the number of film layers that grow coherently on the substrate. At the critical thickness, the increasing strain cannot be maintained and will be released through the formation of crystal defects or by island growth upon further film deposition. The critical thickness depends on the lattice mismatch, surface energy, and the elastic parameters of the two materials and characterizes the difference between F−M, S−K, and V−W growth.19,20 Materials with a low lattice mismatch favor the 2D FM growth, in which the deposited material forms a relatively smooth wetting film. Materials with a large lattice mismatch have a critical thickness of zero monolayers and adopt the 3D 6827

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Figure 1. (A) PTZ concentration-dependent absorption and PL spectra of ZnTe/CdSe nanocrystals having a 2.6 nm ZnTe core and a 0.9 nm CdSe shell. The CdSe shells are grown at 215 °C. (B) PTZ concentration-dependent PL kinetics of the same particles as in panel A. The dots are the experimental results, and the solid curves are the corresponding fittings, calculated by assuming a uniform shell thickness, eq 1. The PTZ concentrations are given in the Figures. 3

the surface morphology can be controlled by the shell deposition temperature and subsequent annealing.

I(t ) = I(0) ∑ P⟨m⟩(m) exp(−mkt ) ∑ (Ai exp(−t /τi))



m

i=1

(1)

RESULTS AND DISCUSSION The ZnTe/CdSe core/shell NCs are synthesized using variations of the method described in our recently published work,18 which involves the formation of the ZnTe core NCs by a high-temperature pyrolysis method and the subsequent deposition of the CdSe shell via a method similar to the successive ion layer adsorption and reaction (SILAR).16,36 Details of the syntheses and experimental methods are given in the Supporting Information, and TEM characterization of the particle sizes, shell thicknesses, and the variability of these quantities are given in a previous publication.18 ZnTe/CdSe NCs exhibit a type-II behavior, with ZnTe and CdSe having the conduction and valence band edges favoring the localization of the photoinduced holes in the ZnTe core and the electrons in the CdSe shell.18,35 These particles show high PL quantum yields with emission peaks that are tunable by both the size of the core and the thickness of shell.18,35 The luminescence can be quenched by adsorbed hole acceptors, such as phenothiazine (PTZ). Time-resolved PL quenching experiments give a distribution of PL decay times from which a distribution of hole-transfer rates can be inferred. The distribution of shell thicknesses is inferred from these dynamics.18 Spectral and quenching results for the case of a 2.6 nm diameter ZnTe core with a relatively thin, ∼0.90 nm CdSe shell (about three CdSe layers) deposited at low temperature (215 °C) are shown in Figure 1A. PTZ exhibits a strong absorption at ∼320 nm but otherwise does not change the absorption spectrum. There is also no shift in the PL spectrum, just a decrease in intensity with increasing PTZ concentration. The corresponding PL decays are shown in Figure 1B and are far more nonexponential in the presence of PTZ than for the bare particle. This is because there is a distribution of numbers of acceptors on each particle. The concentration-dependent PL decays can be calculated with the assumptions that the number of adsorbed acceptors follows a Poisson distribution and that all PTZs have the same chargetransfer coupling; that is, the surface is of uniform thickness. The accuracy of the fit to the experimental data is the measure of validity of the assumption that the shell is of uniform thickness. Specifically, we take

where Ai and τi are the magnitude and the lifetime of the ith decay component in the absence of hole acceptors, k is the charge transfer to an individual adsorbed PTZ, and P⟨m⟩(m) is a Poisson distribution, P⟨m⟩ (m) = (m/m!)e−. The concentration-dependent average number of PTZs is given by a Langmuir isotherm: ⟨m⟩ = N

K ads[PTZ] 1 + K ads[PTZ]

(2)

where N is the number of PTZ binding sites on the particle, N = (1/2)ANC/AcdSe, ANC is the particle surface area, and ACdSe is the area of a CdSe unit, ∼(0.31 nm)2. This assumes that half of the particle has sites that adsorb PTZ. In the low concentration limit, only a small fraction of the sites are occupied and the model is sensitive to only the product of N and the PTZ adsorption equilibrium constant, Kads. In the present case, the decay curves are fit with a k value of 0.50 ns−1 and 1.3 PTZs per particle at the highest concentration. The results reported here are close to the low concentration limit, and it is simply the product of N and Kads that determines the average number of adsorbed PTZ molecules per particle. This product and the value of k are the only adjustable parameters of the model. Decay curves calculated from eq 1 are shown in Figure 1B, and a very good fit is obtained. The hole-tunneling rate is very sensitive to the shell thickness (see below), and this indicates that to a good approximation the shell has uniform thickness. The PL decay results for 2.6 nm ZnTe cores coated with a 1.2 nm thick CdSe shell deposited at 215 °C are shown in Figure 2. Deposition of a thicker CdSe shell results in more complicated quenching dynamics. The observed PL decays are more nonexponential but only somewhat slower than those obtained with the thinner shell. The small decrease in the extent of quenching is, at first look, somewhat surprising. Hole transfer occurs by tunneling through the CdSe shell, and the tunneling rates are a strong function of shell thickness. Wavefunction calculations indicate that this is an exponential dependence, 6828

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Equation 4 is evaluated with a Monte Carlo distribution of values of the hole quenching rate, kq. Each value of kq is given by

kq =

∑ mnkn n

where mn is the (randomly selected) number of the quenchers on the part of the particle having n monolayers and kn is the hole-quenching rate for an acceptor adsorbed on the shell having a local thickness of n monolayers. The hole-quenching rates are taken to have an exponential dependence on shell thickness, as given by eq 3. Values of mn are sampled independently from a Poisson distribution, P⟨m⟩(m) = (m/ m!)e− for all m = mn having an average of . As in the case of a uniform thickness shell (eq 2), the averages of these n distributions are given by a Langmuir isotherm

Figure 2. PL kinetics of ZnTe/CdSe NCs with different PTZ concentrations. These NCs have a 2.6 nm ZnTe core and a 1.2 nm CdSe shell deposited at 215 °C. The PTZ concentrations are given in the Figure. The solid curves are the corresponding fitting of the experimental results using the eq 1 (slower decaying color curves) and curves calculated assuming S−K growth of islands on three smooth shell monolayers (black curves).

kn = k 0e−βnd

⟨mn⟩ = N (n)

where N(n) is the number of the adsorption sites at a shell thickness of n monolayers. The magnitudes of N(n) are proportional to the fraction of the particle surface area having a shell thickness of n layers. Thus, specification of the N(n) distribution is how the distribution of shell thicknesses comes into the model. In the present case, we take the thicker shells to have an S−K growth model. This is approximated by taking the distribution of shell thickness to correspond to a three monolayer thick wetting layer, with a subsequent layer deposited into a Poisson distribution of thicknesses. Specifically

(3)

where d is the thickness of the monolayer (∼0.31 nm for a single CdSe layer), n is the number of monolayers, β is a constant, and k0 = 28.5 ns−1. The value of β is a measure of the extent to which the hole can tunnel through the CdSe shell and is evaluated from the calculated hole wave function density at the surface of the NCs.18 These calculations are described in the Supporting Information and give β = 5.4 nm−1. This value is also consistent with studies on similar systems.17 Thus, the addition of an additional 0.31 nm thick shell layer is expected to dramatically slow the quenching by a factor of ∼5.3. However, comparison of Figures 1 and 2 shows a much less dramatic quenching decrease. We suggest that these results can be understood in terms of CdSe shell deposition at this temperature, giving S−K type growth with a critical thickness of about three monolayers. With this growth pattern, the thicker shell has a distribution of thicknesses; that is, the thicker shell is considerably rougher. An extension of the model underlying eq 1 allows calculation of the PL quenching kinetics for a surface in which subsequent CdSe layers result in island formation rather than smooth layers. Determining the surface morphology requires fitting the time-resolved PL results to a model that includes both an assumed shell thickness distribution and the distribution of numbers of hole acceptor. In all cases, the number of adsorbed acceptors is taken to be a Poisson distribution. Island growth is modeled by taking the thickness distribution to be three smooth layers, followed by a Poisson distribution of thicknesses in the subsequent layers. This is a crude model of island growth but captures the essential feature that the subsequent layers consist of various sizes of islands with large gaps between them. As such, this model says nothing about the size or morphology of the islands. The accuracy of the fit to the experimental data is the measure of how well the assumed thickness distribution describes the core/shell particles. By analogy to eq 1, we take

N (n + n′) =

i=1

(n − n′)n 1 (ANC /A CdSe) tot exp(− (ntot − n′)) 2 n!

where n′ is the critical number of smooth wetting layers and ntot is the equivalent total number of layers deposited. In this case, n′ = 3 and ntot = 4. Decay curves calculated from both eqs 1 and 4 are shown in Figure 2. Good fits with the experimental results are obtained only with the curves calculated from eq 4. The difference between the experimental results and the curves calculated from eq 1 shows the extent to which this experiment is sensitive to the surface morphology. We note that the Kads values in eq 4 needed to fit these results are larger than those in the case of the flat surface, eq 2 and Figure 1. We assign the differences to a combination of the larger surface area associated with a rough surface and increased binding at surface irregularities, such as step edges. We have not tried to quantitatively analyze how the Kads values vary with surface morphology because this adsorption constant and total surface areas are difficult to separate. The above results indicate that at this deposition temperature the first three shell layers are smooth and subsequent layers are not. Deposition of smooth layers minimizes the surface energy of the system, but to the extent that there is a core−shell lattice mismatch, results in considerable lattice strain energy. Each additional smooth layer further increases the lattice strain energy of the particle, and after about three layers the lattice strain becomes too large to support this type of shell growth. The result is that further deposition results in islands (modeled by a Poisson distribution of further shell layer thicknesses) that increase the surface energy but adds little to the lattice strain. Although ZnTe and CdSe have nearly identical lattice constants, we suggest that the core−shell lattice strain is produced as a result of cation interdiffusion. This creates a

3

I(t ) = I(0) ∑ (Ai exp( −t /τi)) exp(−kqt )

K ads[PTZ] 1 + K ads[PTZ]

(4) 6829

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Figure 3. (A) Absorption and PL spectra of nanocrystals with a 2.6 nm ZnTe core and a 1.2 nm CdSe shell deposited at 215 °C as a function of annealing time at 250 °C. Annealing times are indicated in the Figure. (B) PTZ concentration-dependent PL decay kinetics of these particles annealed at 250 °C for 40 min. The PTZ concentrations are indicated in the Figure. Also shown are curves calculated from eq 4.

observed in the case of comparable particles having a thinner shell (Figure 1). This indicates that the minimum shell thickness is considerably less than that in the case of smooth, three-layer shells and implies that annealing makes the shells rougher. Consistent with this observation, comparison with Figure 2 shows that the annealed particles undergo faster and more complete quenching than the unannealed particles. The decays in Figure 3 can also be fit to the model given by eq 4, except in this case there is no wetting layer, n′ = 0. The model underlying eq 4 is appropriate because annealing changes the anion radial composition profile very little, and the β value remains essentially constant. The fits are quite good, indicating that the shell thicknesses are far from uniform and can be modeled as a Poisson distribution of shell thicknesses. The lack of a wetting layer indicates that the shell becomes rougher, approximating V−W type shell growth, as annealing proceeds. Essentially identical quenching and PL decays are obtained if the same shell thickness is deposited at 240 °C. In either case, subsequent annealing at a temperature too low to cause significant cation diffusion (215 °C) has no effect on either the extent of quenching or the PL decays. These results indicate that the shell morphology depends only on shell thickness and the extent of cation interdiffusion. As annealing and hence cation diffusion proceed, the extent of lattice mismatch increases. In response, the wetting layer becomes thinner and the shell surface becomes rougher, minimizing the lattice strain energy at the expense of increased surface energy. This observation has an important implication: the shell morphology is in an equilibrium, determined by a combination of lattice strain and surface energies. Annealing or changes in the deposition temperature cause interdiffusion, but for a given lattice mismatch, the temperature does not significantly change the morphology. This is consistent with the idea that the entropy plays only a secondary role in determining the critical thickness.28,32 It is of interest to compare these results to those obtained for the planar, epitaxial growth of II−VI semiconductor thin films. The critical thickness observed for the film growth of CdSe on ZnSe is about 2.1 to 3.0 ML.37−40 The CdSe−ZnSe lattice mismatch is significantly larger (7.2%) than that obtained by cation diffusion in the present case. Despite the smaller lattice strain, in the present case, the critical thickness (0−3 ML, depending on the extent of annealing) is comparable to or less than that value. Growth of ZnTe on CdTe gives a lattice

radial composition profile that may be described as ZnTe− Zn,CdTe−Cd,ZnSe−CdSe, and the lattice mismatch at the tellurium−selenium interface is the primary source of lattice strain. One could imagine that cation interdiffusion could also alter the valence band potential and hence the hole density at the particle surface. This would alter the quenching dynamics by an electronic, rather than a structural effect. This has been taken into account in the calculated hole wave functions, and we find that it is a very small effect. Hole wave function calculations show that β values change <10% as the Zn−Cd profile changes from very sharp to almost flat. The reason that the β value is almost independent of the cation composition is that the valence band potentials of both CdxZn(1−x)Te and CdxZn(1−x)Se are almost independent of x. Thus, cation interdiffusion changes the valence band offset very little. (These potentials are given in the Supporting Information.) As a result, the extent to which the hole is confined in the particle core is determined by the sharpness of the Te−Se interface. Very little anion interdiffusion occurs at 215 °C, and this interface is quite sharp. These considerations suggest that the extent of lattice strain depends only on the extent of cation interdiffusion. Solid-state diffusion has a high activation barrier and proceeds rapidly only at the highest temperatures. High-temperature annealing of the particles or simply depositing the shell at a higher temperature is therefore predicted to result in further cation interdiffusion and hence greater lattice strain. However, the finite solubility of CdSe monomers can result in particle etching and ripening during the annealing process. The ripening rate increases rapidly with temperature, and there is a narrow temperature range, 240−250 °C, at which cation interdiffusion occurs at a reasonable rate (tens of minutes) with negligible ripening. Some particle etching can occur at this temperature and is suppressed by the addition of a very small amount of the Zn precursor (<1 monolayer). The effects of 40 min of annealing at 250 °C on the absorption and PL spectra and the quenching decay curves are shown in Figure 3. These particles have core diameters of 2.6 nm and shell thicknesses of 1.2 nm, comparable to those in Figure 2. The absorption and PL spectra shift to the red as a result of changes in quantum confinement and optical band-bowing effects. These shifts can be quantitatively understood in terms of wave function calculations, as discussed below. The decay curves exhibit components that are considerably faster than 6830

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mismatch of ∼6% and a critical thickness of five layers.41 Complete cation diffusion in the present case gives a core/shell particle that is essentially a Cd,ZnTe core and a Cd,ZnSe shell, having a comparable lattice mismatch, ∼7%. However, the annealed particles correspond to V−W growth, h = 0. We conclude that in all cases the colloidal particles show comparable or smaller critical thicknesses, despite having less lattice mismatch than that observed in the analogous case of epitaxially deposited thin films. In both the growth of flat thin films and colloidal shells, the fundamental considerations determining the critical thickness are the same: the relative magnitudes of surface and lattice strain energies. Differences in these quantities comparing films and colloidal particles are determined by two considerations: first, ligation greatly reduces the surface energy, and second, core compression reduces the strain energy compared with a flat substrate. It is the relative magnitudes of the surface and strain energies that determine the critical thickness − island formation occurs when the energetic cost of lattice strain energy exceeds that of producing the increased surface area associated with the islands. Growth of epitaxial films is done under vacuum conditions − there are no surface bound ligands and hence there is a very large energy associated with increased surface area of islands. In contrast, the colloidally grown particles are ligated with strongly binding ligands, such as octadecyl amine and trioctyl phosphine, which greatly reduce the surface energy of the shell. Surface energies of flat facets are a factor of ∼2 lower because of ligation.42−44 The energy reduction for step edges and corners (where there are fewer bonds within the material and multiple bonds with ligands are formed) has not been systematically calculated but must be a larger factor. Small islands have many such surfaces, resulting in a large difference in the ligated versus unligated surface energies. This is the fundamental reason why rough surfaces are formed in lattice mismatched core/shell particles. Given this consideration, for there to be a wetting layer under any circumstances there must also be a large reduction in the shell lattice strain energy. It is the balance of these effects that controls the wetting layer and island formation in core/shell NCs. The magnitude of the areal lattice strain energy densities (lattice strain energy per unit area of the shell or film) can be understood in terms of the stresses and strains calculated from an elastic continuum model, discussed next.

eters (which are assumed to vary linearly with composition). Interaction with the adjacent hypothetical shells gives each of these shells a radial pressure gradient. In this finite element calculation, the radially dependent displacements, stresses, and strains are then obtained by diagonalizing the matrix that results from imposing continuity at the interfaces of the hypothetical shells and the boundary condition that the pressure is zero at the particle surface. The shells are taken to be sufficiently thin that further discretization does not change the calculated results. The strain energy density is then given by E=(σrεr + σθεθ + σφεφ)/2, where the σr, σθ, σφ and εr, εθ, εφ are the stress and strain radial, θ, and φ components, respectively. The calculations of the radial compositions, elastic continuum stresses and strains, and the electron and hole wave functions are described in detail in the Supporting Information. An important input parameter into these calculations is the temperature-dependent cation diffusion constant, which determines how the radial composition profile changes with annealing time. This parameter is assessed by comparison of the experimental annealing-dependent lowest exciton energies with calculated values. In these calculations, electron and hole quantum confinement and interaction energies are obtained using an effective mass approximation with valence and conduction band potentials that include effects of variable cation and anion composition, lattice strain, and optical bandbowing in the alloys. The calculated exciton energies are therefore a function of the cation and anion composition profiles and hence the diffusion coefficients. Agreement with the experimental results is obtained with a cation interdiffusion constant of 1.3 × 10−2 nm2/min at 250 °C and an anion diffusion constant that is a factor of 15 smaller. The anion diffusion constant is taken from previous studies on CdTe/ CdSe.21 Because the cation diffusion is so much faster, the calculations are insensitive to the exact value of the anion diffusion constant. The calculated changes in PL peak energy are shown in Figure 4 and are compared with experimental values.



COMPARISON WITH CALCULATIONS The lattice strains that cause the different shell morphologies in ZnTe/CdSe core/shell particles can be understood in terms of cation diffusion and elastic continuum calculations. Diffusion is described by a continuum, radially symmetric diffusion equation dC(r , t ) 1 d ⎛ dC(r , t ) ⎞ = D∇2 C(r , t ) = D 2 ⎜r 2 ⎟ dt dr ⎠ r dr ⎝

Figure 4. Experimental (dots) and calculated (solid curve) PL maxima of ZnTe/CdSe core/shell NCs (1.3 nm cores, 1.18 nm thick shells) synthesized at 215 °C and annealed at 250 °C for the different times.

This equation is solved by expanding the initial radially dependent concentration in a Fourier−Bessel series, with each term having its own relaxation time, as described in the Supporting Information. This gives the time-dependent radial composition profile for both the anions and cations. The elastic stresses and strains are then described using elastic continuum theory.45 Specifically, the particle is considered to be a large number of hypothetical concentric shells, each having its previously determined composition and hence elastic param-

Excellent agreement is obtained except for a slight discrepancy in the initial stages of annealing, <10 min. This discrepancy is due to very slight particle growth resulting from the presence of starting material needed to inhibit particle etching. With these diffusion constants, the anion composition profile changes relatively little, whereas the cation composition profile changes dramatically as annealing, as shown in Figure 5. 6831

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Figure 5. (A) Calculated cation composition profile as a function of the annealing time at 250 °C for particles having a nominal 1.3 nm core and a 1.18 nm thick shell. The cation diffusion constant is taken to be 1.3 × 10−2 nm2 min−1. The anion composition profile changes little upon annealing. (B) Calculated lattice strain energy densities (energy per unit volume) for the same particles (solid curves) following different annealing times as indicated. Calculated results are also shown for hypothetical particles having similar elastic constants and a sharp core/shell interface with 3 and 4% lattice mismatches (dotted curves).

Figure 6. (A) Calculated areal strain energy densities (energy per unit of core surface area) for different lattice mismatches compared with the calculated ZnTe/CdSe nanoparticles as a function of annealing time. Also shown are the values for 3 and 4% lattice mismatches on a planar surface. (B) Calculated strain areal energy densities assuming a 4% lattice mismatch for different core sizes as a function of shell thickness.

This causes lattice strain at the relatively sharp Te−Se interface. From the calculated composition profiles, radially dependent lattice parameters and lattice strain energy densities are calculated and shown in Figure 5B. For comparison, calculated strain-energy densities for hypothetical core/shell particles having the same sizes and elastic constants and lattice mismatches of 3 and 4% are also shown. The strain-energy profiles of the hypothetical sharp interface particles have a somewhat different radial dependence than in the case where the lattice mismatch results from cation diffusion. However, the overall magnitude of the initial (prior to annealing) lattice strain energy is comparable to the sharp interface at 3 to 4% lattice mismatch. These calculations give the total lattice strain energy for the unannealed particles as 1.45 GPa nm3 compared with 1.05 and 1.87 GPa nm3 for the hypothetical 3 and 4% mismatched particles, respectively. The areal strain energy density (lattice strain energy per core surface area) varies with annealing time, as shown in Figure 6A. The strain energy initially increases as annealing produces a larger lattice mismatch. It reaches a maximum after ∼50 min, then decreases as a result of essentially complete cation diffusion (maximizing lattice strain), followed by slower anion diffusion, which reduces it.

These strain energies can be compared with those obtained for flat, thin films. The areal strain energy density for a flat thin film is given by46 E = 3K((1 − 2ν)/(1 − ν))hf 2, where h is the film thickness, f is the fractional lattice mismatch, K is the bulk modulus, and ν is the Poisson ratio. Areal strain energy densities are calculated as a function of the core radius and shell thickness and are shown in Figure 6B. These calculations assume a 4% lattice mismatch (f = 0.04) and the same bulk modulus and Poisson ratio as ZnTe. For a shell thickness of 1.18 nm, this calculation gives a planar surface energy density of 0.144 GPa nm, which is a factor of 3.3 larger than that of a core radius of 1.3 nm. The reduction in areal energy density occurs as a result of core compression, which is absent in the case of a flat film. It is also of interest to note that the limiting behaviors of the flat film and core/shell particle are completely different. Upon deposition of a thin film, the lattice parameter of an infinite, flat substrate is unchanged. The film must simply accommodate this lattice parameter. As a result, the strain energy increases linearly with film thickness. At some thickness, the strain energy will become sufficiently large that defects or islands will be formed. Very different behavior is seen for core/ shell particles. As the shell becomes thicker, the core is further compressed (assuming the shell lattice parameter is less than that of the core). The extent of the strain at the shell surface 6832

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The Journal of Physical Chemistry C decreases as the shell becomes thicker; see Figure 5B. The above considerations result in the a leveling off of the strain energy with increased shell thickness, as shown in Figure 6A. The limiting strain energy is determined by the core and shell elastic parameters and lattice mismatch. For sufficiently small lattice mismatches, this energy may not exceed that required to produce islands or defects. As a result, very thick, uniform shells can be grown on NC cores,47 whereas analogous flat films would be thermodynamically unstable.



REFERENCES

(1) Loef, R.; Houtepen, A. J.; Talgorn, E.; Schoonman, J.; Goossens, A. Study of Electronic Defects in CdSe Quantum Dots and Their Involvement in Quantum Dot Solar Cells. Nano Lett. 2009, 9, 856− 859. (2) Choi, J. J.; Lim, Y.-F.; Santiago-Berrios, M. B.; Oh, M.; Hyun, B.R.; Sun, L.; Bartnik, A. C.; Goedhart, A.; Malliaras, G. G.; Abruña, H. D.; Wise, F. W.; Hanrath, T. PbSe Nanocrystal Excitonic Solar Cells. Nano Lett. 2009, 9, 3749−3755. (3) Pan, Z.; Zhang, H.; Cheng, K.; Hou, Y.; Hua, J.; Zhong, X. Highly Efficient Inverted Type-I CdS/CdSe Core/Shell Structure QDSensitized Solar Cells. ACS Nano 2012, 6, 3982−3991. (4) Jung, J.-Y.; Zhou, K.; Bang, J. H.; Lee, J.-H. Improved Photovoltaic Performance of Si Nanowire Solar Cells Integrated with ZnSe Quantum Dots. J. Phys. Chem. C 2012, 116, 12409−12414. (5) Kim, J. Y.; B.Choi, S.; Noh, J. H.; Noh, S. H.; Lee, S.; Noh, T. H.; Frank, A. J.; Hong, K. S. Synthesis of CdSe-TiO2 Nanocomposites and Their Applications to TiO2 Sensitized Solar Cells. Langmuir 2009, 25, 5348−5351. (6) Laghumavarapu, R. B.; Moscho, A.; Khoshakhlagh, A.; El-Emawy, M.; Lester, L. F.; Huffaker, D. L. GaSb/GaAs Type II Quantum Dot Solar Cells for Enhanced Infrared Spectral Response. Appl. Phys. Lett. 2007, 90, 173125(1−3). (7) Fu, H.; Tsang, S.-W. Infrared Colloidal Lead Chalcogenide Nanocrystals: Synthesis, Properties, And Photovoltaic Applications. Nanoscale 2012, 4, 2187−2201. (8) Peng, X.; Schlamp, M. C.; Kadavanich, A. V.; Alivisatos, A. P. Epitaxial Growth of Highly Luminescent CdSe/CdS Core/Shell Nanocrystals with Photostability and Electronic Accessibility. J. Am. Chem. Soc. 1997, 119, 7019−7029. (9) Spanhel, L.; Haase, M.; Weller, H.; Henglein, A. Photochemistry of Colloidal Semiconductors. 20. Surface Modification and Stability of Strong Luminescing CdS Particles. J. Am. Chem. Soc. 1987, 109, 5649− 5655. (10) Katari, J. E. B.; Colvin, V. L.; Alivisatos, A. P. X-ray Photoelectron Spectroscopy of CdSe Nanocrystals with Applications to Studies of the Nanocrystal Surface. J. Phys. Chem. 1994, 98, 4109− 4117. (11) Sambur, J. B.; Parkinson, B. A. Communication CdSe/ZnS Core/Shell Quantum Dot Sensitization of Low Index TiO2 Single Crystal Surfaces. J. Am. Chem. Soc. 2010, 132, 2130−2131. (12) Talapin, D. V.; Mekis, I.; Gotzinger, S.; Kornowski, A.; Benson, O.; Weller, H. CdSe/CdS/ZnS and CdSe/ZnSe/ZnS Core-Shell-Shell Nanocrystals. J. Phys. Chem. B 2004, 108, 18826−18831. (13) Nazzal, A. Y.; Wang, X.; Qu, L.; Yu, W.; Wang, Y.; Peng, X.; Xiao, M. Environmental Effects on Photoluminescence of Highly Luminescent CdSe and CdSe/ZnS Core/Shell Nanocrystals in Polymer Thin Films. J. Phys. Chem. B 2004, 108, 5507. (14) Hines, M. A.; Guyot-Sionnest, P. Synthesis and Characterization of Strongly Luminescent ZnS-Capped CdSe Nanocrystals. J. Phys. Chem. 1996, 100, 468. (15) Mora-Sero, I.; Gimenez, S.; Fabregat-Santiago, F.; Gomez, R.; Shen, Q.; Toyoda, T.; Bisquert, J. Recombination in Quantum Dot Sensitized Solar Cells. Acc. Chem. Res. 2009, 42, 1848−1857. (16) Li, J. J.; A.Wang, Y.; W.Guo; Keay, J. C.; Mishima, T. D.; Johnson, M. B.; Peng, X. Large-Scale Synthesis of Nearly Monodisperse CdSe/CdS Core/Shell Nanocrystals Using Air-Stable Reagents via Successive Ion Layer Adsorption and Reaction. J. Am. Chem. Soc. 2003, 125, 12567. (17) Zhu, H.; Song, N.; Lian, T. Controlling Charge Separation and Recombination Rates in CdSe/ZnS Type I Core−Shell Quantum Dots by Shell Thicknesses. J. Am. Chem. Soc. 2010, 132, 15038−15045.

CONCLUSIONS The following conclusions can be drawn from the results and analysis presented above: (1) CdSe shells deposited on ZnTe cores at 215 °C exhibit a Stranski−Krastanov (S−K) growth morphology. This results from the lattice mismatch between the core and shell materials. Although there is only a small lattice mismatch between ZnTe and CdSe, cation interdiffusion creates a large lattice mismatch at the Te−Se interface. Thus, the core/shell NCs may be described as ZnTe−Zn,CdTe−Cd,ZnSe−CdSe or even Zn,CdTe−Cd,ZnSe in the case of a longer time of thermal annealing. (2) The extent of cation interdiffusion and hence core−shell lattice mismatch can be controlled by the shell deposition temperature, subsequent annealing, or both. At the low shelldeposition temperature, there is a relatively small lattice mismatch and CdSe shell deposition occurs via the S−K mode, initially favoring the formation of a relatively smooth surface. Further shell deposition produces a rough surface. At the high shell-deposition temperature, however, the significant interdiffusion produces a large lattice mismatch across the radial coordinate of the ZnTe/CdSe NCs, which leads to the W−Vtype mode of shell growth. (3) Colloidally grown particles have surface ligands that greatly reduce the surface energy compared with epitaxial films grown under vacuum conditions. Compression effects in core/ shell particles reduce the magnitude of the lattice strain energy. The reduction in surface energy is the dominant effect and results in colloidally grown shells having a smaller critical number of wetting layers compared with epitaxially grown films having similar lattice mismatches. (4) The results of the elastic continuum calculations corroborate the experimental observations. The calculations show that the magnitude of the radial lattice mismatch increases with increasing thermal annealing time. From a combination of calculations and spectroscopic results, a cation interdiffusion constant in the ZnTe/CdSe NCs of 1.3 × 10−2 nm2 min−1 at 250 °C is obtained. ASSOCIATED CONTENT

S Supporting Information *

A complete description of the syntheses, experimental methods and calculations are provided. This material is available free of charge via the Internet at http://pubs.acs.org.



ACKNOWLEDGMENTS

This work was supported by grants from the Department of Energy, grant no. DE-FG02-04ER15502 and grant no. DEFG02-13ER16371.







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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] Notes

The authors declare no competing financial interest. 6833

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(18) Jiang, Z.-J.; Kelley, D. F. Effects of Inhomogeneous Shell Thickness in the Charge Transfer Dynamics of ZnTe/CdSe Nanocrystals. J. Phys. Chem. C 2012, 116, 12958−12968. (19) Shchukin, V. A.; Bimberg, D. Spontaneous Ordering of Nanostructures on Crystal Surfaces. Rev. Mod. Phys. 1999, 71, 1125−1171. (20) Barabási, A.-L. Thermodynamic and Kinetic Mechanisms in Self-Assembled Quantum Dot Formation. Mater. Sci. Eng., B 1999, 67, 23−30. (21) 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. (22) West, A. R. Basic Solid State Chemistry; Wiley: Chichester, U. K., 1988. (23) Liu, S.; Zhang, W.-H.; Li, C. Colloidal Synthesis and Characterization of CdSe/CdTe Core/Shell Nanowire Heterostructures. J. Cryst. Growth 2011, 336, 94. (24) Kurtz, E.; Don, B. D.; Schmidta, M.; Kalta, H.; Klingshirna, C.; Litvinovb, D.; Rosenauerb, A.; Gerthsenb, D. CdSe Quantum Islands in ZnSe: A New Approach. Solid Thin Films 2002, 412, 89. (25) Goebl, J. A.; Black, R. W.; Puthussery, J.; Giblin, J.; Kosel, T. H.; Kuno, M. Solution-Based II−VI Core/Shell Nanowire Heterostructures. J. Am. Chem. Soc. 2008, 130, 14822. (26) Yu, Z.; Guo, L.; Du, H.; Krauss, T.; Silcox, J. Shell Distribution on Colloidal CdSe/ZnS Quantum Dots. Nano Lett. 2005, 5, 565−570. (27) Sark, W. G. J. H. M. v.; Frederix, P. L. T. M.; Heuvel, D. J. V. d.; Gerritsen, H. C.; Bol, A. A.; Lingen, J. N. J. v.; Donega, C. d. M.; Meijerink, A. Photooxidation and Photobleaching of Single CdSe/ZnS Quantum Dots Probed by Room-Temperature Time-Resolved Spectroscopy. J. Phys. Chem. B 2001, 105, 8281. (28) Williams, R. S.; Medeiros-Rebeiro, G.; Kamins, T. I.; Ohlberg, D. A. A. Equilibrium Shape Diagram for Strained Ge Nanocrystals on Si(001). J. Phys. Chem. B 1998, 102, 9605−9609. (29) Williams, R. S.; Medeiros-Rebeiro, G.; Kamins, T. I.; Ohlberg, D. A. A. Chemical Thermodynamics of the Size and Shape of Strained Ge Nanocrystals Grown on Si(001). Acc. Chem. Res. 1999, 32, 425− 433. (30) Zhang, Y. W.; Srolovitz, D. J. Surface Instability and Evolution of Nonlinear Elastic Heteroepitaxial Thin-Film Structures. Phys. Rev. B 2004, 70, 041402(1−4). (31) Eisenberg, H. R.; Kandel, D. Formation, Ripening, And Stability of Epitaxially Strained Island Arrays. Phys. Rev. B 2005, 71, 115423(1− 9). (32) Daruka, I.; Barabási, A.-L. Dislocation-Free Island Formation in Heteroepitaxial Growth: A Study at Equilibrium. Phys. Rev. Lett. 1997, 79, 3708. (33) Simashkevich, A. V.; Tsiulyanu, R. L. Liquid-Phase Epitaxy of CdSe, ZnSe and ZnTe Layers. J. Cryst. Growth 1976, 35, 269−272. (34) Gashin, P. A.; Sherban, D. A.; Simashkevich, A. V. Radiative Recombination in ZnTe-CdSe and ZnSe-CdTe Heterojunctions. J. Lumin. 1977, 15, 109−113. (35) Xie, R.; Zhong, X.; Basché, T. Synthesis, Characterization, and Spectroscopy of Type-II Core/Shell Semiconductor Nanocrystals with ZnTe Cores. Adv. Mater. 2005, 17, 2741−2745. (36) Battaglia, D.; Peng, X. Formation of High Quality InP and InAs Nanocrystals in a Noncoordinating Solvent. Nano Lett. 2002, 2, 1027. (37) Strassburg, M.; Deniozou, T.; Hoffmann, A.; Heitz, R.; Pohl, U. W.; Bimberg, D.; Litvinov, D.; Rosenauer, A.; Gerthsen, D.; Schwedhelm, S.; Lischka, K.; Schikora, D. Coexistence of Planar and Three-Dimensional Quantum Dots in CdSe/ZnSe Structures. App. Phys. Lett. 2000, 76, 685. (38) Schikora, D.; Schwedhelm, S.; As, D. J.; Lischka, K.; Litvinov, D.; Rosenauer, A.; Gerthsen, D.; Strassburg, M.; Hoffmann, A.; Bimberg, D. Investigations on the Stranski−Krastanow Growth of CdSe Quantum Dots. Appl. Phys. Lett. 2000, 76, 418. (39) Robin, I.-C.; André, R.; Bougerol, C.; Aichele, T.; Tatarenkoa, S. Elastic and Surface Energies: Two Key Parameters for CdSe Quantum Dot Formation. Appl. Phys. Lett. 2006, 88, 233103.

(40) Flack, F.; Samarth, N.; Nikitin, V.; Crowell, P. A.; Shi, J.; Levy, J.; Awschalom, D. D. Near-Field Optical Spectroscopy of Localized Excitons in Strained CdSe Quantum Dots. Phys. Rev. B 1996, 54, R17312. (41) Cibert, J.; Gobil, Y.; Dang, L. S.; Tatarenko, S.; Feuillet, G.; Jouneau, P. H.; Saminadayar, K. Critical Thickness in Epitaxial CdTe/ ZnTe. Appl. Phys. Lett. 1990, 56, 292. (42) Manna, L.; Wang, L. W.; Cingolani, R.; Alivisatos, A. P. FirstPrinciples Modeling of Unpassivated and Surfactant-Passivated Bulk Facets of Wurtzite CdSe: A Model System for Studying the Anisotropic Growth of CdSe Nanocrystals. J. Phys. Chem. B 2005, 109, 6183−6192. (43) Csik, I.; Russo, S. P.; Mulvaney, P. Density Functional Study of Surface Passivation of Nonpolar Wurtzite CdSe Surfaces. J. Phys. Chem. C 2008, 112, 20413−20417. (44) Schapotschnikow, P.; Hommersom, B.; Vlugt, T. J. H. Adsorption and Binding of Ligands to CdSe Nanocrystals. J. Phys. Chem. C 2009, 113, 12690−12698. (45) Saada, A. S. Elasticity Theory and Applications; Permagon Press: New York, 1974. (46) Ayers, J. E., Mismatched Heteroepitaxial Growth and Strain Relaxation (Chapter 5). In Heteroepitaxy of Semiconductors Theory, Growth, and Characterization; CRC Press: Boca Raton, FL, 2007. (47) Guo, Y.; Marchuk, K.; Sampat, S.; Abraham, R.; Fang, N.; Malko, A. V.; Vela, J. Unique Challenges Accompany Thick-Shell CdSe/nCdS (n > 10) Nanocrystal Synthesis. J. Phys. Chem. C 2012, 116, 2791−2800.

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