CdSe Type-II Nanostructures: Morphology

Article pubs.acs.org/JPCC

Spectroscopy of CdTe/CdSe Type-II Nanostructures: Morphology, Lattice Mismatch, and Band-Bowing Effects Xichen Cai,† Hoda Mirafzal,† Kennedy Nguyen, Valerie Leppert, and David F. Kelley* University of California, Merced 5200 N. Lake Road, Merced, California 95344, United States S Supporting Information *

ABSTRACT: We compare the spectroscopy of two different morphologies of CdTe/CdSe type-II nanocrystals. Core/ tetrapod and spherical core/shell particles are grown from identical CdTe cores, and both morphologies exhibit type-II spectroscopic behavior. The two morphologies show very different oscillator strengths for the lowest (luminescent) transition; the core/tetrapod particles exhibit larger oscillator strengths for the same amount of spectral shift. A model is presented that explains this difference and accurately predicts emission wavelengths and relative oscillator strengths for the spherical particles. This model uses an elastic continuum treatment to consider strain induced by lattice mismatch at the core/shell interface. The CdTe−CdSe lattice mismatch results in a calculated core pressure of about 2.9 GPa for the particles with the thickest shells. This pressure causes a change in the CdTe conduction band energy of about 0.24 eV and a change in the CdTe lattice parameter of 2.3%. The change in the lattice parameter is also seen in XRD spectra and HRTEM lattice fringe images. Because of the different morphology, core compression is essentially absent in the core/tetrapod particles. The model also considers radial interdiffusion of the selenium and tellurium. Particle annealing results in an alloyed region at the core−shell interface, and the radial composition profile can be calculated from a diffusion treatment. Partial alloying causes the luminescence to shift further to the red, which may be quantitatively understood in terms of calculated radial composition profiles and the known optical band-bowing parameters of CdTe−CdSe alloys.

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INTRODUCTION Quantum dots (QDs) formed by II and VI elements such as CdSe, CdTe, CdS, etc. have been extensively studied in the last two decades. Heterostructures of the II−VI semiconductors can exhibit type-II behavior, in which photoexcitation produces a charge-separated electron−hole pair. The spectroscopic manifestation of type-II energetics is the observation of a low energy charge transfer band having low oscillator strength. CdTe and CdSe particles can be grown under similar conditions, and growth of type-II nanostructures is easily accomplished.1−10 CdTe conduction and valence band energies (about 3.9 and 5.4 eV below vacuum) are higher than those of CdSe (about 4.2 and 5.95 eV below vacuum) by 0.30 and 0.54 eV, respectively, and the band gap energy of CdTe (∼1.5 eV) is smaller than that of CdSe (∼1.74 eV).11 Thus, in a CdTe/CdSe core/shell particle, the hole localizes in the CdTe core and the electron localizes in the CdSe shell. The CdTe/CdSe band offsets are quite large resulting in obvious type-II spectroscopic behavior. There are several reports of the spectroscopy and exciton dynamics of CdTe/CdSe core/ shell particles.1−4,12−19 The energy and intensity of the charge transfer band in type-II particles depends on several aspects of the particle, specifically the core and shell materials, the size and shape of the core, and the thickness and shape of the shell. The spectroscopy of core/shell particles can also be affected by lattice mismatch and alloying effects.20−24 In the case of spherical particles, if the lattice parameter of the core is greater than that of the © 2012 American Chemical Society

shell, then the lattice mismatch results in the core being under very large (several gigapascals) hydrostatic pressure from the shell.20,25,26 Despite the fact that these are very large effects and can dominate the particle spectroscopy, there have been no reports comparing measurements with quantitative theoretical modeling of morphology, lattice mismatch, and alloying effects on CdTe/CdSe nanoparticle spectroscopy. The qualitative spectroscopy of CdTe/CdSe type-II particles is not very complicated. The lowest energy absorption of the CdTe core particles is the 1Se−1Sh3/2 exciton transition. As a CdSe shell is grown on a CdTe particle, the lowest exciton transition shifts to lower energies and loses oscillator strength, indicating hole localization in the core and increasing electron localization in the shell. The energy and oscillator strength of the lowest exciton transition are of central concern in the spectroscopy of these particles. The transition energies are easy to determine from the luminescence maximum. Oscillator strengths can be determined from either absorption intensities or from radiative lifetimes. Radiative lifetimes are notoriously difficult to measure accurately. The reason is that nanoparticles are typically inhomogeneous with respect to the extent of nonradiative relaxation.27 As a result, ensemble measurements of the luminescence decays are not single exponentials, and the longest observed decay Received: November 25, 2011 Published: March 7, 2012 8118

dx.doi.org/10.1021/jp301374u | J. Phys. Chem. C 2012, 116, 8118−8127

The Journal of Physical Chemistry C

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components may or may not correspond to the radiative lifetime. The overall extent of nonradiative decay can be assessed from luminescence quantum yield measurements, but when much of the decay is nonradiative, there remains ambiguity in determining the radiative rate. For this reason, the comparison of oscillator strengths based on integrated absorption intensities of the lowest exciton (charge transfer) band are generally more reliable. In this paper we report the synthesis of highly luminescent CdTe/CdSe type-II particles with different shell thickness. Two types of CdTe/CdSe morphologies are studied: particles having a spherical CdTe core with a spherical CdSe shell (core/shells) and particles having the same spherical CdTe cores with CdSe tetrapod arms (core/tetrapods). We measure the luminescence wavelengths and the integrated absorption intensities of the lowest exciton band for both types of particles. These studies address how the energy and oscillator strength of the lowest exciton transition depend on particle size and morphology. The core/shell and core/tetrapod morphologies exhibit significantly different spectroscopic properties. We suggest this is a manifestation of lattice mismatch effects. The basic idea is that a coherent (aligned lattice) interface across the mismatched lattices results in hydrostatic compression of the CdTe core. Core compression raises the CdTe conduction band level and therefore further localizes the electron in the CdSe shell.20,28 This decreases the extent of electron/hole overlap and hence decreases the oscillator strength lowest energy transition. The experimental results can be quantitatively understood in terms of an elastic continuum model that determines the radially dependent conduction band potential. This potential is used in subsequent effective mass approximation wave function calculations. We also model the effects of radial interdiffusion of the core and shell materials in the

spherical particles. The extent of diffusion and hence alloy formation can be controlled by particle annealing. The alloyed region exhibits spectroscopic properties that do not depend linearly with compositionCd(Te, Se) alloys exhibits “optical bandbowing”.29,30 As a result, the spectroscopic properties also depend on the sharpness of the CdTe−CdSe interface. There are numerous reports in the literature of the qualitative aspects of the type-II spectroscopic behavior of CdTe−CdSe particles.9,12,14,16,17 However, to the best of our knowledge, quantitative modeling of the factors that control the spectroscopy of these particles has not been reported. In the present paper, the effects of the lattice mismatch and band-bowing are quantitatively modeled in terms of known properties of the bulk materials.

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RESULTS AND DISCUSSION Particle Characterization and Spectroscopy. CdTe/ CdSe core/shell nanoparticles have been synthesized with the shell thicknesses to about 1.9 nm, as determined by TEM images and shown in Figure 1. UV−visible absorption and emission spectra are shown in Figure 2. With increasing CdSe shell thickness, the lowest energy absorption band shifts to longer wavelengths and loses intensity. Similar behavior is observed for the luminescence spectra. The dependence of the luminescence maximum wavelength on particle size is shown in Figure 3. Core/tetrapod and spherical core/shell particles are synthesized from the essentially identical CdTe cores. In the core/ tetrapod case, the CdSe “shell” is grown in an ODPA-rich chemical environment, which is known to promote the growth of wurtzite CdSe nanorods.27,31,32 The (111) facets of a zincblende crystal are identical to the wurtzite (0001) facets. Wurtzite CdSe therefore grows primarily along the (111) facets of the zincblende CdTe

Figure 1. TEM images of (a) CdTe core (∼3.5 nm) and CdTe/CdSe shell particles with shell thickness of (b) 0.3 nm and (c) 1.7 nm. The scale bars are 20 nm.

Figure 2. Absorption spectra normalized at 345 nm (left panel) and emission spectra (right panel) of core/shell particles following successive injections of CdSe precursors. The progressively longer wavelength spectra correspond to 3.5 nm CdTe cores and core/shell particles with total diameters (in nm) as indicated. 8119



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results in this way facilitates comparison of the different morphologies. The comparison in Figure 6 indicates that at comparable luminescence wavelengths, the oscillator strengths of the lowest energy exciton in the core/shell particles are less than in the case of the core/tetrapod particles. We suggest that this difference is largely due to compression of the CdTe core by the CdSe shell, resulting from the lattice mismatch of the two materials. A coherent interface across the mismatched lattices results in hydrostatic compression of the CdTe core and the CdSe shell being under a radially dependent pressure and tangential tension. Core compression effects on the spectroscopy are qualitatively easy to understand: compression raises the CdTe conduction band level and therefore further localizes the electron in the CdSe shell.20,28 This decreases the extent of electron/hole overlap and therefore the oscillator strength while having a much smaller effect on the electron energy. The difference between the two morphologies comes about because the core/tetrapods have CdSe growth primarily along the (111) faces and the CdSe does not initially encapsulate the core particle. The tetrapod shell therefore results in very little core compression. The spectral shifts and relative oscillator strengths of the spherical core/shell particles can be quantitatively understood in terms of the energies and wave functions calculated using an effective mass approximation. The core/shell particles have a well-defined, simple (spherical) morphology, which facilitates quantitative calculation of the spectroscopic properties. The more complicated morphology of the core/tetrapod particles makes calculation of their spectroscopic properties far more problematic, and detailed calculations will not be presented here. The calculations on the spherical particles include the effects of lattice mismatch compression and band-bowing. The radially dependent composition varies with annealing and can be calculated from a simple diffusion treatment. The radially dependent strain (and hence the change in lattice parameter) is calculated from an elastic continuum model. The variation of the conduction band potential with pressure is well-known for bulk CdTe and CdSe, and these data, along with the intrinsic CdTe/ CdSe conduction band offset, can be used to calculate the conduction band potential in the core/shell particle.20,28 The valence band potential can be calculated from the radial composition profile and the known CdTe−CdSe band-bowing parameter. Electron and hole energies and wave functions are then determined from the conduction and valence band potentials. Comparison of calculated lattice parameters with values determined from XRD spectra and HRTEM images provides additional checks on the elastic continuum calculations. In what follows we discuss the elastic continuum and radial diffusion calculations and the subsequent wave function calculations. The calculated energetics and wave function overlaps are related to the absorption intensities and compared with experimental results. Compression Strain. CdTe and CdSe have different lattice parameters, and this lattice mismatch causes strain at the core/ shell interface. The CdSe lattice parameter is about 6.6% smaller than that of CdTe.11,34 This mismatch results in a radially dependent pressure which may be calculated using elastic continuum theory. The radially dependent pressure is calculated in terms of the radial displacements. The spherical core/shell problem is set up for a finite shell with inner radius rc and outer radius R, and the inner and outer pressures are denoted as PC and PR, respectively, as depicted in Figure 7.

Figure 3. Experimental values of the luminescence wavelength (open squares) taken from Figure 2b as a function of particle diameter for spherical core/shell particles. Calculated values are shown with the dotted line. The data points correspond to CdTe cores and core/shell particles synthesized with 1, 3, 5, 7, 9, and 11 injections of CdSe shell precursors. TEM images of the particles and histograms of the size distributions are given in the Supporting Information.

core particles, resulting in tetrapods;33 see Figure 4. However, Figure 4 shows that the tetrapods are not perfect. In some cases the particles have only two or three arms. Furthermore, as the arms are

Figure 4. TEM image of CdTe/CdSe core/tetrapod heterostructures following 12 injections of CdSe precursors.

grown further, the bases of the tetrapod arms are larger than the original CdTe core particles and taper toward the ends. The core/ tetrapod absorption and emission spectra are shown in Figure 5. Although the spectra of the core/shell and core/tetrapod particles both show the transition from simple cores to type-II spectra, there are significant differences in the spectra. The most obvious difference is that for a given amount of red shift of the absorption spectra, the intensity of the lowest exciton band is considerably less for the core/shell particles compared to the core/tetrapods. This can be quantified by a comparison of the integrated absorbances of the lowest exciton band for spectra normalized in the ultraviolet, as shown in Figure 6. The integrated absorbances are obtained from the spectra plotted on a wavelength (rather than energy) scale and normalized to the 345 nm absorbance. The lowest energy transition is fit to a Gaussian, and the area of the Gaussian is then plotted against the wavelength of the luminescence maximum. Plotting the 8120



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Figure 5. Absorption spectra normalized at 345 nm (left panel) and emission spectra (right panel) of core/tetrapod particles following the indicated number of successive injections of CdSe precursors. These spectra are analogous to those in Figure 2, except shell was deposited under wurtzite growth conditions.

CdTe39 and 0.37 for CdSe.40 The change in band gap with pressure for CdTe is quite large, 87.3 meV/GPa.20,28,41 Combining these values, we get that for a hydrostatic (isotropic) pressure, ΔEcb = P × 704 cm−1/GPa (CdTe). For a sharp core−shell interface between materials having the same elastic parameters, the core pressure is given by42 P=

ε2K (1 − 2ν) (3d + 3d2 + d3) 1−ν (1 + d)3

(1)

where d is ratio of the shell thickness to the core radius. Evaluation of this expression using CdSe−CdTe averaged elastic parameters gives a very approximate value of the interior pressure. For the nanoparticles studied here, the thickest shells are on the order of the core radius, d ∼ 1.0. In this case we calculate a core pressure of about 2.5 GPa and a core conduction band shift of 1750 cm−1. This simple calculation shows that these are large values and that compression effects significantly alter the particle spectroscopy. The more general problem is one in which the composition profile changes gradually at a diffuse core−shell interface. In this case the particle is considered to be a large number of concentric shells, each having a slightly different composition, with the composition profile calculated from a diffusion treatment, discussed below. The lattice constant and elastic parameters are taken to scale linearly with composition. This treatment

Figure 6. Plots of normalized integrated (wavelength) absorbances of the core/shell (solid squares) and core/tetrapod (black circles) particles. Also shown is a plot of S2λ2/V1/2 versus λ calculated with (dotted curve) and without (solid curve) compression considered in the calculation.

For a coherent core−shell interface, the interior pressures depend on the particle dimensions, the extent of lattice mismatch (ε = 0.066 for the CdTe/CdSe interface11,34), and the elastic properties of the materials. The elastic properties are expressed in terms of the bulk modulus, defined as K = (∂P)/(∂ln V), and Poisson’s ratio, ν. K has values of 42.4 GPa for CdTe and 53 GPa for CdSe,35−38 and Poisson’s ratio is about 0.33 for

Figure 7. Schematic of the parameters used in the elastic continuum model calculations (left panel). Plots of the calculated radial pressure profile (solid curve) and the relative lattice mismatch (open circles) for a 3.4 nm CdTe core with a 1.7 nm thick CdSe shell (right panel). 8121



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With the appropriate values for the pressure-dependent conduction band shifts, the conduction band energy profile is given by

results in a simple matrix expression for the radial pressure profile (2)

DP = ε

Ecb(r ) = C(r )(Ecb(CdTe) + (εrr + εθθ + εϕϕ)3.70 eV)

where D is a tridiagonal matrix containing the elastic parameters and ε is the lattice mismatch vector. This is solved for P, giving the radially dependent pressure for any radial composition profile. The derivation and solution of eq 2 is discussed in the Supporting Information. The lattice mismatch and pressure profiles for a 1.7 nm thick CdSe shell on a 3.4 nm diameter CdTe core following a small amount of radial diffusion (discussed below) are shown in Figure 7. The core pressure is calculated to be 2.8 GPa, in reasonable agreement with the estimate obtained from eq 1. The core is under isotropic pressure, making it easy to calculate the conduction band shift from the pressure. Calculation of the shell conduction band potential is complicated by the anisotropic nature of the strain; it is under radial pressure and tangential tension, and it is the net volume change that determines the shift in the conduction band energy. The volume dependence of the band gap is given by α = −dEg/dln V with values of α being 3.70 and 2.28 eV for CdTe and CdSe, respectively. The radial and tangential components of the fractional lattice parameter change are given by the strain tensor. Hence, the conduction band energy shift is more generally given by ΔE = α(εrr + εθθ + εϕϕ), where εrr, εθθ, and εφφ are the radial, theta, and phi components of the strain tensor, respectively. Radially dependent εrr, εθθ, and εφφ values are calculated from the pressures and elastic constants, as discussed in the Supporting Information. This calculation requires having the radial composition profile, which is discussed next. The valence band energies are taken to be unaffected by deformation. Diffusion at the Core−Shell Interfacial Boundary. Annealing the particles results in radial diffusion which softens the sharp core/shell boundary.22,43 In a spherical particle, this can be modeled as one-dimensional radial diffusion. The initial condition is that there is an infinitely sharp boundary; that is, the composition function, C(r, t), is a step function. For the case of a CdSe shell on a CdTe core, C(r, t) is taken to be the fraction of the alloy that is Te. In the absence of diffusion we have that

+ (1 − C(r ))(Ecb(CdSe) + (εrr + εθθ + εϕϕ) 2.28 eV)

The valence band energy has a nonlinear dependence on composition due to “optical band-bowing”. The valence band energy depends on the composition of a CdTex/CdSe(1−x) alloy as follows E vb(x) = xE vb(CdTe) + (1 − x)E vb(CdSe) + bx(1 − x)

where b is the band-bowing constant and has an experimental value of about 1.27 eV for CdTe/CdSe.21 Thus the valence band potential is given by E vb(r ) = C(r )E vb(CdTe) + (1 − C(r ))E vb(CdSe) + bC(r )(1 − C(r ))

(6)

Equations 5 and 6 define the radial potentials for calculating the electron and hole wave functions. Electron and Hole Wave Functions. The electron and hole wave functions can be calculated once the radially dependent potentials are determined. The Schrödinger equation for the core/shell particles has a position-dependent mass, which results in a non-Hermitian kinetic energy operator. However, the SWE may be written as follows44 ⎛ ℏ2 ⎞ ⎜⎜ − ⎟⎟((1/m*(r ))∇2 Ψ + ∇(1/m*(r ))·∇Ψ) + V (r )Ψ = E Ψ ⎝ 2 ⎠ (7)

In the present calculations the effective mass is taken to be a linear function of the composition m*(r ) = m*core + (m*shell − m*core )C(r )

where C(r) is the same composition function as specified above. The lowest electron S wave function is expanded in a set of zeroth order spherical Bessel functions.

C(r , 0) = 1 0 < r < rc = 0 rc < r < R

Ψ=

The time dependence of C(r, t) is described by the diffusion equation. With spherically symmetric particles dC(r , t ) 1 d ⎛ dC(r , t ) ⎞ ⎟ = D∇2 C(r , t ) = D 2 ⎜r 2 dt dr ⎠ r dr ⎝

(5)

∑ A nj0 (k nr)

(8)

n

Unlike the case in which the mass is position independent, substitution of this wave function into eq 7 generates offdiagonal kinetic energy matrix elements. The An coefficients in eq 8 are obtained by diagonalizing the sum of the kinetic and potential energy operators. Specifically

(3)

Solving eq 3 and hence obtaining C(r, t) is straightforward, and the solution with the appropriate boundary conditions is given in the Supporting Information. We get that

V ( i , j) =

⎛ −Dz 2 ⎞ ⎤ ⎡ R 2 C(r , t ) = ∑ ⎢ ρ dρ j0 (z i ρ/R )C(ρ , 0)⎥ exp⎜⎜ 2 i t ⎟⎟ j0(z ir /R ) ⎦ ⎣ 0 ⎝ R ⎠ i

∫

T (i , j) =

(4)

where j0 is a spherical Bessel function and zn is the nth zero of j0′. For any given annealing time, this composition profile can be denoted as C(r) and used in the calculation of the radial profiles of the pressure, ρ(r), and the strains, εrr, εθθ, and εφφ.

∫0

Rf 2

r dr V (r ) j0(i πr /R f ) j0(j πr /R f )

π2ℏ2 2m0R f 2

∫0

Rf 2 r dr (1/m*(r )) j0(i πr /R f ) j0(j πr /R f )

and T1(i , j) = 8122

ℏ2 2m 0

∫0

Rf 2 r dr j0(j πr /R f ) d(1/m*(r ))/dr d(j0 (i πr /R f ))/dr



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where m0 is the electron mass and Rf is a radius large enough to account for the electron wave function outside of the particle. This is the radius at which the wave function has fallen to essentially zero, typically 1−2 nm larger than the particle radius. The integrals are performed numerically, and the eigenvalues and eigenvectors of the matrix V + T + T1 give the energies and An coefficients of the wave functions. This approach gives continuity of the wave function 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. This approach gives the independent electron and hole wave functions. Electron−hole attraction is then considered by first-order perturbation theory in the basis set of the above-defined functions. Comparison of Experiment with Calculations. The elastic continuum model predicts that coherent addition of a thick CdSe shell puts the CdTe core under considerable hydrostatic pressure, on the order of 2.9 GPa. This has both crystallographic and spectroscopic manifestations. The crystallographic result is that the CdTe core shows a volume reduction of 7.1%. Thus, the CdTe lattice parameter is predicted to be reduced by 2.3% from 0.648 to 0.633 nm. Similarly, coherent growth results in a 4.3% increase in the CdSe lattice parameter at the interface, with that value decreasing through the shell. XRD spectra, shown in Figure 8, confirm a reduction in CdTe

core and shell lattices. XRD and HRTEM literature values and analyses are detailed in the Supporting Information. The 0.36 nm spacing is obtained from the entire CdTe/CdSe core/ shell particle. It is therefore a weighted average that is slightly less than the 0.366 nm value calculated for the CdTe core. These results also indicate that the shell lattice is coherent with that of the core. If the core/shell structure was incoherent, then there would be many discontinuities at the core−shell interface, with each material having its usual bulk lattice parameters. All nanoparticles observed using HRTEM showed continuous lattice fringes. For comparison, Figure 9B shows a representative image of a core/tetrapod particle. The tetrapod arms show (002) planes with a d-spacing of 0.350 nm, consistent with that of bulk wurtzite CdSe. It is of interest to compare compression in these core/shell particles to that reported for CdTe/ZnSe core/shell particles.20 Despite the larger lattice mismatch (14.4%) and a high density of stacking faults, coherent growth is also reported for CdTe/ ZnSe particles. In this case, XRD and HRTEM results indicate a core lattice compression of 5.1% for a 1.9 nm CdTe core and a 1.8 nm thick ZnSe shell. The extent of core compression can be calculated from eq 2, using the literature elastic parameters cited in ref 20. For this size of spherical core and shell thickness, solution of eq 2 gives a core pressure of 6.4 GPa and a lattice constant compression of 5.2%, in quantitative agreement with the experimental value reported in ref 20. Thus, for both the CdTe/CdSe results presented above and the CdTe/ZnSe results in ref 20, the elastic continuum model gives agreement with the observed lattice parameters. Returning to the spherical CdTe/CdSe particles, with the above calculated radial composition and strain profiles, it is possible to calculate the radially dependent potentials of the conduction and valence bands given in eqs 5 and 6, which permits calculation of the electron and hole energies and wave functions. The calculation for the as-synthesized (no annealing) particles assumes that only a very slight amount of core−shell interdiffusion occurs during the shell growth reaction. The role of core−shell interdiffusion is further discussed in the context of particle annealing, below. In this case, we assume a radial diffusion coefficient of 3.5 × 10−5 nm2 min−1 (see eqs 3 and 4) at the shell growth temperature of 230 °C. Band gap energies for constant-diameter (3.5 nm) cores and different shell thicknesses are calculated and plotted versus total particle diameter in Figure 3. Quantitative agreement is obtained for all but the largest particles. The reaction slows as the shell gets thicker, and we suspect that much more core−shell interdiffusion occurs at the end of the synthesis, causing this discrepancy. Relative oscillator strengths can be calculated from the electron and hole wave functions. The variation of the lowest energy exciton oscillator strength with particle size has been studied for several types of semiconductor nanocrystals. The case of singlematerial particles is simpler than the type-II particles considered here and has been studied more extensively.45,46 For singlecomponent particles, the oscillator strength per particle is size independent, for sufficiently small particles.46−48 At much larger particle sizes, the oscillator strength in the lowest exciton transition increases with the particle volume. Alternatively stated, ignoring the fine structure, the relative fraction of the oscillator strength in the lowest exciton absorption increases as the particle size is decreased in the strongly quantum-confined regime. An early, but very physically insightful treatment explaining this behavior was presented by Brus.49 The basic argument is that the oscillator strength depends on the number of oscillators that

Figure 8. XRD patterns for CdTe cores, CdTe/CdSe core/shells, and CdTe/CdSe tetrapods. CdTe cores exhibit zincblende CdTe peaks, while CdTe/CdSe tetrapods exhibit wurtzite CdSe peaks (wurtzite CdSe tetrapod arms comprise ∼80% of sample volume). CdTe/CdSe core/shells exhibit zincblende (111), (220), and (311) peaks with lattice spacing between that for zincblende CdTe and zincblende CdSe, consistent with a coherent core/shell morphology.

lattice parameter. CdTe/CdSe core/shell samples exhibit a zincblende diffraction pattern with lattice spacings intermediate between CdTe and CdSe, consistent with a strained coherent core/shell morphology. The d-spacing value for the (111) planes in the CdTe/CdSe core/shell particles is calculated to be 0.36 nm from the XRD results, compared to bulk values of 0.374 nm for CdTe and 0.351 nm for CdSe. Figure 9A shows a representative HRTEM image of a single CdTe/CdSe core/shell particle with ⟨110⟩ zincblende zone axis orientation with spherical morphology. Clearly visible in the single particle image are continuous (111) planes with d-spacing 0.359 nm, consistent with XRD results and indicating alignment of the 8123



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Figure 9. (A) HRTEM image of a zincblende core/shell particle with ⟨110⟩ zone axis orientation showing spherical morphology. Lattice fringes of the (111) planes at 0.359 nm are indicated, intermediate between (111) plane spacings for zincblende CdTe and CdSe. (B) HRTEM image of a core/tetrapod particle showing the spacing of the (002) lattice planes.

above the band edge that quantum confinement effects are unimportant.19,47 However, the validity of this assumption has not been experimentally demonstrated for type-II particles, and simple energetic considerations suggest that when there is a large valence band offset, it is not correct. Consider the present case of a CdTe with a CdSe shell. In the simplest approximation, the relative amounts of energy that photoexcitation puts in the electron and hole scale like the inverse of each particle’s effective mass. The CdTe electron and hole effective masses are 0.10 and 0.40 in units of the electron mass, respectively.50,51 CdTe has a 1.5 eV band gap, and 3.6 eV (345 nm) excitation puts about 1.68 and 0.42 eV in the electron and hole, respectively. However, the CdSe valence band is at a potential 0.54 eV further positive than that of CdTe. This is greater than the hole energy following 3.6 eV excitation, and we conclude that the initially produced hole is largely confined to the CdTe core. Furthermore, if the shell is sufficiently thin, then CdSe localized excitons also cannot be formed. Thus, deposition of a thin CdSe shell results in essentially no increase in the effective volume. These energetic considerations indicate that how the 3.6 eV extinction coefficient scales with the shell thickness is somewhat complicated and a simple linear scaling with total volume does not apply to the thin shell limit. Because of these uncertainties, we treat this scaling empirically. We find that reasonable overall agreement with the experimental results is obtained with an assumption that is intermediate between the two extreme possibilities, specifically, that the 345 nm absorbance scales as V1/2. With this assumption, plots of S2λ2/V1/2 can be compared to experimental plots of the (wavelength) integrated absorbance, shown in Figure 6. We emphasize that this scaling with the volume is purely empirical and is not the main point to be made here. The important point is made by comparison of the core/ shell and core/tetrapod experimental results and the calculated curves in Figure 6. This comparison shows that the differences between the calculated curves obtained with and without lattice mismatch compression correspond reasonably well to the experimental differences between the core/shell and core/tetrapod particles. This difference is independent of any assumptions regarding how the UV absorbance scales with particle volume, and normalization to 345 nm simply provides a way to compare the spectra. Agreement of the calculated and experimental intensities is consistent with the hypothesis that the spectral differences between the core/shell and core/tetrapod particles are

contribute to the lowest exciton transition times the fraction of the oscillator strength that goes into that transition. The number of oscillators is proportional to the number of unit cells and scales with the particle volume. The fraction of the oscillator strength in the lowest exciton transition is proportional to its volume in momentum space. As the particle gets smaller so do the electron and hole wave functions, so the Fourier transforms (momentum space representations) of these functions get larger. Thus, the volume in momentum space scales with the inverse of the particle volume. The net effect is that in the strongly quantum-confined limit, the product of these two terms is size independent. This is, of course, consistent with the simple argument that in this limit, exciton formation is a one-electron transition and the oscillator strength is determined by the magnitude of the intrinsic dipole moment operator. The situation is somewhat more complicated in type-II particles. In this case, the shell thickness determines the extent of electron−hole overlap and the exciton energy, both of which affect the oscillator strength. The measurable quantities are the integrated absorption coefficient and the radiative lifetime. In this paper we will focus on the integrated absorption coefficient. This quantity can be related to the oscillator strength when there is complete electron−hole overlap. The electron−hole overlap integral is defined as S = ∫ 0∞r2 dr ΨeΨh and is related to the integrated absorption coefficient by

∫ ε(ω)dω = ∫ (ε(λ)/λ2)dλ = S2f0 where f 0 is the lowest exciton transition oscillator strength when the electron and hole wave functions completely overlap. The main difficulty in comparing the experimental integrated absorption intensities with calculated values of S2 is that absolute particle concentrations are not known. The absorption spectra presented in Figures 2 and 5 are simply normalized to an absorbance at a wavelength far to the blue of the excitonic features, in this case, 345 nm. The central question regarding the use of this type of normalized spectra is how the 345 nm absorption intensity varies with particle size. Two extreme assumptions could be made: that the absorbance scales linearly with particle volume or that the absorbance is independent of particle volume. The former assumption is commonly made for type-I (and in some cases type-II) semiconductor nanoparticles and is justified by the fact that near-UV excitation generates a electron−hole pair with both carriers having sufficient energy 8124



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Figure 10. (left panel) Plots of experimental (large open circles) emission maximum wavelengths as a function of annealing time at 250 °C. Also shown are calculated curves of the band gap assuming a band-bowing parameter of 1.27 eV (solid squares) and 0.0 eV (open squares). (right panel) Plots of the calculated composition profile prior to annealing (solid) and following 120 min of annealing (dotted).

indicates that the simple diffusion model accurately describes the composition profile.

largely due to core compression effects. These results are also consistent with the XRD and HRTEM results discussed above and with the literature results on CdTe/ZnSe particles. We conclude that the elastic continuum model correctly gives the extent to which the CdSe shell compresses the CdTe core as determined by the change in lattice parameter and the morphology dependence of the core conduction band energy. Particle Annealing and Diffusion. Annealing of core/ shell particles results in diffusion and a softening of the core− shell interface.22,43 The alloy region produced at the interface has optical properties that do not vary linearly with alloy composition, the so-called optical band-bowing effect, described in eq 6. The deviation from linearity is quite large, and optical band-bowing can result in significant spectral shifts. In the present case, we find that the luminescence wavelength dramatically increases as annealing proceeds and an alloy region is formed; see Figure 10. This spectral shift can be understood in terms of optical band-bowing affecting the valence band and the loss of core− shell pressure affecting the conduction band. The radial composition profile can be calculated from eq 4 as a function of the annealing time. The only adjustable parameter in this calculation is the diffusion constant, which simply scales with the time axis. In this calculation, the diffusion constant is taken to be 8.7 × 10−4 nm2 min−1 at the annealing temperature of 250 °C. The diffusion coefficient at this temperature is about a factor of 15 larger than at the shell growth temperature of 230 °C. We note that this change in diffusion coefficient with temperature indicates an activation energy of about 3.1 eV, which is roughly consistent with the known activation energy for CdSe selfdiffusion.52,53 At the longest annealing times, a significant fraction of the particle consists of a CdTe−CdSe alloy, as shown in Figure 10. Subsequent calculation of the electron and hole wave functions gives the band gap energy, which is compared with the experimental results in Figure 10. A calculated curve that assumes no band-bowing is shown for comparison. In the absence of band-bowing, core−shell interdiffusion shifts the spectrum to the blue, opposite of what is observed experimentally. Annealing also somewhat diminishes the core pressure caused by the lattice mismatch. However, in terms of the calculated luminescence wavelength of alloyed particles, the band-bowing effect is much larger than that of core compression. Figure 10 shows that when the literature value of the band-bowing parameter is used, quantitative agreement with the experimental results is obtained. This

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CONCLUSIONS Several conclusions may be drawn from the results presented here. 1 High quality CdTe/CdSe core/shell and core/tetrapod particles are grown using modified literature methods. Identical spherical CdTe cores are grown in both syntheses, with the shell morphology determined by the subsequent chemistry. The lattice mismatch between CdTe and CdSe (6.6%) results in hydrostatic compression of the CdTe cores in the case of the core/shell particles. The core pressure and resulting changes in lattice parameters are calculated using an elastic continuum model and the known elastic constants of CdTe and CdSe. The calculated core pressure for the particles with the thickest shells is 2.9 GPa, resulting in a decrease in the lattice parameter of 2.3%. This is consistent with measured lattice fringe spacings obtained from HRTEM images. 2 The elastic continuum model can be applied to existing literature data on CdTe/ZnSe core/shell particles. In that case, diffraction experiments indicate 5.1% compression, in quantitative agreement with the calculated values. 3 The spectra of the core/shell particles has significantly less intensity in the lowest exciton (charge transfer) band than in the case of the core/tetrapod particles. This difference may be quantitatively understood in terms of the overlap of calculated electron and hole wave functions. Core compression caused by the core−shell lattice mismatch further raises the CdTe conduction band, further localizing the electron in the CdSe core. This decreases the wave function overlap and lowers oscillator strength of the charge transfer band. The core/tetrapod particles have CdSe growth selectively along the (111) facets and therefore little core compression, accounting for the spectral differences between the two morphologies. 4 Annealing of the core/shell particles results in radial diffusion, softening of the core−shell composition interface, and producing a radially symmetric alloy region. The radial composition profiles depend on the annealing time and are calculated from a diffusion equation. The valence band energies of CdTe−CdSe alloys vary nonlinearly with the alloy composition, a phenomenon known 8125



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as “band-bowing”. Using the calculated composition profiles and the known band-bowing coefficient, these effects can be incorporated into the calculations of the electron and hole wave functions and energies. This results in quantitative agreement with the experimentally measured luminescence maxima.

measured using a Jobin−Yvon Fluorolog-3 spectrometer. The instrument consists of a xenon lamp/double monochromator excitation source and a CCD detector. The spectra are corrected for instrument response, using correction curves generated from the spectrum of an Optronix spectrally calibrated lamp. Quantum yields are determined by comparison of the nanoparticle spectra with the spectrum of Rhodamine 6G and Rhodamine 640 with the appropriate spectral calibration factors. Time-resolved luminescence measurements were obtained by time-correlated singlephoton counting (TCSPC), using a PicoQuant PMD 50CT SPAD detector and a Becker−Hickel SP-630 board. The light source was a cavity-bumped Ti:sapphire laser (Coherent Mira) operating at 410 nm with a 1 MHz repetition rate. In all cases, the fluorescence was focused through a 0.25 m monochromator with a 150 groove/mm grating and onto the detector. X-ray powder diffraction (XRD) spectra were collected for 12 h using a PANalytical X’Pert PRO diffractometer with cobalt source (Kα λ = 1.790 307 Å) scanned in θ−θ Bragg−Brentano mode with samples on a zero-background silicon sample holder. Transmission electron microscopy (TEM) images were obtained with a FEI Tecnai 12 transmission electron microscope with an accelerating voltage of 100 kV in the Electron Microscope Laboratory (EML), UC Berkeley, and HRTEM images were obtained with a JEOL-2010 TEM equipped with a LaB6 filament and operated at 200 kV in the Imaging and Microscopy Facility, UC Merced, and at the National Center for Electron Microscopy on a Philips CM200/FEG operated at 200 kV. Samples were prepared by placing a drop of solution on a transmission electron microscope copper grid with holey carbon film, and the fringe spacings on the HRTEM images were calibrated with a gold crystal standard.

EXPERIMENTAL SECTION Chemicals. Cadmium oxide (CdO, 99.5%), trioctylphosphine (TOP, 97%), trioctylphosphine oxide (TOPO, 90%), octadecene (ODE, 90%), and methanol (MeOH, 98%) were obtained from Aldrich. Selenium (99%), zinc oxide (ZnO, 99.9%), oleic acid (90%), and chloroform (CHCl3, 99.8%) were obtained from Alfa Aesar. Octadecylphosphonic acid (ODPA 99%) was obtained from PCI synthesis. ODPA was recrystallized from toluene before use. TOP and ODE were purified by vacuum distillation. TOPO was purified by repeated recrystallization (three times) from acetonitrile. All other chemicals were used as received. CdTe/CdSe Core/Shell Nanoparticles. These particles are synthesized using a modified method according to previous publications.6,27,54 The CdTe core synthesis, 0.1 mmol Te, 0.15 mL TOP, and 0.15 mmol ODPA are added in 1 mL of ODE solution under nitrogen atmosphere in a glovebox. The purpose of adding ODPA to the TOPTe is to inhibit particle growth. We find that this results in a more monodisperse particle size distribution. The mixture is heated to about 100 °C, giving a clear solution. The solution is kept warm before it is added into the Cd precursor solution. This solution is formed by dissolving 0.2 mmol of CdO and 0.8 mmol of oleic acid in 3 mL of ODE and heating to ∼300 °C in a 50 mL threeneck flask. The injection of Te precursor solution is carried out at 280 °C. Following 3 min of core growth, the shell precursors, 1 mmol of CdO mixed with 4 mmol OA in 9 mL of ODE and 0.9 mmol of Se mixed with 1.6 mL of TOP in 9 mL of ODE, are added dropwise alternatively according to the size of the desired particles. Growth occurs at 230 °C for 10 min after the shell precursor addition. The synthesis is carried out under a nitrogen atmosphere. Aliquots are taken at different time intervals and kept under a nitrogen atmosphere by bubbling nitrogen into the glass vessel. The final sample is washed by methanol:CHCl3 (1:1 v:v) mixture to remove unreacted reagents and redissolved in CHCl3 or toluene for optical measurements. CdTe/CdSe Core/Tetrapod Nanoparticles. These particles are synthesized using the same procedure as the CdTe cores. The cadmium precursor for the tetrapod shell is prepared by mixing of 1 mmol of CdO with 1.5 mmol of ODPA in 3.0 g of TOPO and heating the mixture until a clear solution is obtained under nitrogen atmosphere. The temperature is about ∼320 °C. The solution is cooled, 2 mL of ODE is added, and the temperature is kept at ∼200 °C. The selenium precursor for the shell is prepared by mixing 0.5 mmol of Se and 0.5 mmol of ODPA with 0.25 mL of TBP and 0.25 mL of TOP in 10 mL of ODE. At 260 °C all of the cadmium precursor solution is injected into the reaction flask containing the CdTe cores. After 10 min, 1 mL of the Se precursor solution is added dropwise to grow the shell. The particle is allowed to grow at 240 °C for 10 min, at which time after addition of 1 mL of the shell precursor, the procedure is repeated. The aliquots taken and sample treatments are the same as that for the core/shell preparation. Instrumentation. UV−visible absorption was measured using a Cary 50 spectrophotometer. Luminescence spectra were

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ASSOCIATED CONTENT

S Supporting Information *

Discussion of compression strain, diffusion of core−shell boundary, HRTEM and XRD analyses, and TEM images and size distribution. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions †

These authors contributed equally to this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research is supported by the National Science Foundation SOLAR Program under Grant No. CHE-0934615. HRTEM was performed at the National Center for Electron Microscopy, which is supported by the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. TEM and XRD were performed at the Imaging & Microscopy Facility (IMF) at UC Merced with helpful assistance from Michael Dunlap.

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CdSe Type-II Nanostructures: Morphology

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