NANO LETTERS
Wave Function Engineering in Elongated Semiconductor Nanocrystals with Heterogeneous Carrier Confinement
2005 Vol. 5, No. 10 2044-2049
J. Mu1 ller, J. M. Lupton,* P. G. Lagoudakis, F. Schindler, R. Koeppe, A. L. Rogach, and J. Feldmann Photonics and Optoelectronics Group, Physics Department and CeNS, Ludwig-Maximilians-UniVersita¨t Mu¨nchen, Amalienstrasse 54, 80799 Munich, Germany
D. V. Talapin and H. Weller Institute of Physical Chemistry, UniVersity of Hamburg, Grindelallee 117, 20146 Hamburg, Germany Received August 12, 2005
ABSTRACT We explore two routes to wave function engineering in elongated colloidal CdSe/CdS quantum dots, providing deep insight into the intrinsic physics of these low-dimensional heterostructures. Varying the aspect ratio of the nanoparticle allows control over the electron−hole overlap (radiative rate), and external electric fields manipulate the interaction between the delocalized electron and the localized hole. In agreement with theory, this leads to an exceptional size dependent quantum confined Stark effect with field induced intensity modulations, opening applications as electrically switchable single photon sources.
The manipulation of electronic wave function confinement in different dimensions, particularly in semiconductor nanostructures, often provides the framework for testing new physical phenomena.1-3 In contrast to well-defined quantum structures grown epitaxially,1-2 strongly reduced dimensionality comes naturally to synthetic systems such as colloids3 or π-conjugated molecules.4 On the down side, these materials often suffer from the drawback of substantial size heterogeneity in the ensemble and considerable temporal fluctuations such as blinking and spectral diffusion on the single nanoparticle level.5 Here, we demonstrate that controlled manipulation of the single particle wave function in colloidal semiconductor nanocrystals (NCs) provides unprecedented access to the intrinsic physics of these lowdimensional systems. Wave function engineering has previously been investigated theoretically and experimentally in spherical NCs by alternate growth of different shell materials leading to localization of charge carriers at specific distances from the core.6,7 We show that the combination of heterostructure material growth and physical shape control opens the possibility of independently tuning the electron and hole wave function distribution inside a NC. By strongly confining the hole yet maintaining a highly deformable * Corresponding author: tel, +49-89-2180-3356; fax, +49-89-21803441; e-mail,
[email protected]. 10.1021/nl051596x CCC: $30.25 Published on Web 08/30/2005
© 2005 American Chemical Society
electron wave function, a new region of field effects can be probed. This provides a route to enhancing the electric field response through the quantum-confined Stark effect (QCSE)8-10 as well as aiding the development of a truly microscopic understanding of excited-state configurations. Accurate shape control and the elimination of heterogeneity and polydispersity averaging in single nanoparticle measurements allow direct comparison with theory, demonstrating that individual colloidal quantum dots (QDs) can provide highly versatile semiconductor test beds for quantum engineering while maintaining the appealing growth and processing properties of solution-based materials. We recently introduced a novel class of NCs consisting of two different materials grown with a strongly asymmetric shape.11,12 This heterostructure facilitates electron penetration into the elongated CdS shell whereas the hole is confined inside the spherical CdSe core, which is preferentially situated at one end of the wurtzite structure.11,12 The choice of synthetic conditions allows a direct control of the nanoparticle aspect ratio (AR), enabling a tuning between three- and two-dimensional confinement.11 Elongated NCs are thus interesting systems for studying manifestations of the interplay between carrier delocalization and photon emission such as radiative rates as well as the dependence on external electrostatic perturbations. In contrast to spherical
Figure 1. Engineering of the wave function overlap in CdSe/CdS nanocrystals by shape control. (a) Band diagram and calculated electronic wave functions (light gray, CdSe; dark gray, CdS). (b) Fluorescence decay of elongated NCs for two different aspect ratios (ARs): 4.0 (black) and 1.6 (gray). (c) Radiative recombination rate as a function of AR (black squares). The lines indicate the calculated squared electron-hole wave function overlap integral for three different conduction band offsets ∆e.
QDs,5 our elongated NCs facilitate the electric field effect on the electronic wave function due to the increased delocalization volume and simultaneously reduce the random influence of surface charges.12 Magnitudes of the QCSE scatter widely in spherical NCs, an effect which has previously been attributed to the presence of a permanent dipole moment of variable amplitude.5,13,14 Introducing shape control to the QCSE allows us to correlate shape and orientation directly with the observed QCSE magnitudes. To date the QCSE has only been investigated in zerodimensional QDs of either colloidal or epitaxial origin, which have a comparatively small spatial volume and a symmetric spatial carrier confinement of electrons and holes,5,15-19 making them particularly sensitive to the effect of randomly distributed surface charges.5 As meandering surface charges yield a unique signature in spectral diffusion once the nanoparticle symmetry is broken,12 we expect our elongated Nano Lett., Vol. 5, No. 10, 2005
NCs to provide an excellent intermediate between threedimensional (QDs)5 and one-dimensional (quantum wells)8-10 strong confinement to explore the QCSE. Very recently, Rothenberg et al. studied the effect of electric fields on the emission of single bare CdSe nanorods and observed fieldinduced intensity modulations along with spectral shifts.20 By trapping the hole in CdSe, we are able to simplify the physical problem of field effects in one dimension and apply a quantum mechanical description of the effect. This reveals that intensity modulations are a result of changes in radiative and not in nonradiative rates. Controlling shell growth along the wurtzite c-axis allows a tuning of AR from 1.6 (almost spherical) to 4.11 A band diagram of the structures is given in Figure 1a. Compared to bare CdSe nanorods21 these asymmetric heterostructure NCs should exhibit a substantial difference in the level of confinement of electrons and holes, which controls the exciton lifetime. Figure 1b shows the fluorescence decay for NCs of AR 1.6 and 4, respectively, dispersed in toluene solution. The emission rate decreases strongly with increasing AR. Although the decay is nonexponential, we can approximate the radiative rate τrad-1 ) Q/τPL by simply extracting the 1/e fluorescence time (τPL) and taking into account the photoluminescence (PL) quantum yield Q, which was previously reported in ref 11. Although this choice of τPL is not strictly accurate, it provides greater physical consistency than achievable with multi- or even stretched exponential treatment of the data. We note that the functionality of the decay curves is similar in all cases so that a choice of τPL as e-1, 10-1, 10-2, or 10-3 of the initial intensity does not change the dependence on aspect ratio. The radiative decay rate τrad-1, shown in Figure 1c, decreases by a factor of 5 with increasing AR, supporting the picture of a delocalized electron recombining with a hole localized on the CdSe core. Figure 1a illustrates the computed wave functions. To unravel the interplay between geometrical shape, emission energy, and wave function overlap, the electronic states of the NCs are modeled using a semiempirical iterative approach and an isotropic effective mass approximation. The Coulombic electron-hole interaction, which analytical calculations have shown to account for ∼20% of the confinement energy in spherical particles,22 is incorporated into our numerical model by an effective potential Ve,h
( (
) )
p2π2 r + Vh(b) r + Vext(b) r Φe(b) r ) EeΦe(b) r ∆ + Vcb(b) 2me*(b) r (1) p2π2 r + Ve(b) r - Vext(b) r Φh(b) r ) EhΦh(b) r ∆ + Vvb(b) 2mh*(b) r (2)
where Vvb and Vcb are the valence and conduction band potentials, respectively, and Vext indicates an external potential due to an applied electric field, which is initially set to zero. The first term in the two equations corresponds to the kinetic energy with an effective mass m* depending on the local material (mh*(CdSe) ) 0.45; me*(CdSe) ) 0.13; mh*(CdS) ) 0.7; me*(CdS) ) 0.26,7). The second term 2045
represents the valence and conduction band energies, and the third one constitutes the electron-hole interaction mediated through an effective potential. The wave functions were solved iteratively using a finite element method with a sequential optimization of Ve,h following the Hartree selfconsistent potential approach.23 Excellent agreement to within 5% is found between our calculation and prior analytical estimates of the correlation energy in spherical NCs.22 Due to a valence band offset of 0.78 eV between the two materials, the hole is confined in the core for all ARs. Although the band gaps of CdSe and CdS are well-known (1.68 and 2.46 eV, respectively24), the values for the conduction band offset ∆e scatter widely throughout the literature from -0.3 to 0.3 eV.24-26 The lines in Figure 1c indicate the squared wave function overlap integral (which governs the radiative rate8-10) for three different conduction band offsets. An offset of only 0.1 eV leads to strong localization of the electron inside the core. |〈φh|φe〉|2 consequently varies by only 15% with AR, far below the experimental result. In contrast, for ∆e ) -0.1 eV the electron quickly delocalizes into the shell for moderate ARs, decreasing |〈φh|φe〉|2 by over a factor of 20. A conduction band offset of ∆e ) 0 eV allows the wave function overlap to decrease within the same range as the measured radiative rate. ∆e ) 0 eV lies within the range of reported values24-26 and will be used for subsequent calculations as it satisfactorily reproduces both transition energies (not shown) and rates (Figure 1c). A core radius of 2 nm (consistent with electron microscopy11) provides the best agreement between experiment and theory. Naturally, the model constitutes only the simplest conceivable approximation to the electronic states and neglects static effects due to the crystal anisotropy and internal fields. As we are primarily interested in the influence of physical shape, we feel confident in disregarding these potential perturbations. Increasing the NC volume and thereby decreasing the confinement of the electron will make the electron wave function more sensitive to external perturbations such as electric fields. The magnitude of the Stark shift in quantum wells depends strongly on the well width.9 For narrow wells the spatial separation of the charge carriers is insufficient to allow an electric field to induce a pronounced change in the energy levels, whereas larger widths enable efficient separation of charge carriers. This leads to an increased QCSE at the expense of reduced overall quantum confinement. In NCs with three-dimensional strong confinement it has, however, not previously been possible to quantify the influence of the external field perturbation and the resulting Stark shifts on the actual single particle waVe functions. Prior descriptions of the QCSE in QDs followed a semiclassical formalism.5,15,17-19 Strong confinement of only one of the two constituents of the exciton should simplify deductions concerning the effect of applied electric fields. Furthermore, this new approach facilitates quantitative investigation of QCSE magnitudes in colloidal nanostructures and introduces the novel aspect of geometrical anisotropy. To do this, the spectroscopy has to be carried out on single NCs5,15 so as to minimize the influence of inhomogeneous spectral broaden2046
Figure 2. QCSE in the single particle emission at 5 K. (a) Normalized emission spectra of a single NC in an external electric field showing a strong QCSE. The solid line corresponds to a model calculation assuming that the NC lies parallel to the external field. The insets schematically indicate the band structure in the presence of an external field of negative and positive sign, respectively. (b) Single NC exhibiting a weak QCSE of up to 5 meV. The model calculation under the assumption of the electric field vector being perpendicular to the NC long axis is superimposed.
ing and the random nanoparticle orientation. To apply electric fields to a single NC, a strongly diluted solution of NCs in polystyrene was spin cast from toluene onto interdigitated Al finger electrodes (height 50 nm, spacing 8 µm), providing randomly oriented single NCs with an average separation of 5 µm. The sample was mounted in a coldfinger He cryostat and cooled to 5 K. Nonresonant illumination with a continuous wave Ar+ laser in a dark field configuration (457.9 nm) allowed PL collection with an epifluorescence microscope (NA: 0.55).12 The normalized and averaged PL spectra of a single elongated NC exposed to a repeatedly cycled electric field are shown in Figure 2a in dependence of field. The nanoparticle exhibits a strong QCSE (∼80 meV at 600 kV/ cm, or ∼50 times the zero-field line width) and displays line broadening, which varies approximately as the square root of the energetic shift.5 The LO phonon satellite of CdSe at 27 meV also increases from 0.2 to 1 relative intensity with respect to the zero-phonon line with electric field, in agreement with prior reports on spherical NCs.5 As the sign of the voltage changes from negative to positive the emission becomes virtually independent of electric field. This is a direct manifestation of the spatially asymmetric band structure of the NC. Application of a field to the NC excited state dipole results in more substantial electron penetration into the CdS shell and a considerable red shift. The second case Nano Lett., Vol. 5, No. 10, 2005
is illustrated in Figure 2b, where the emission of the NC shifts near symmetrically by only 5 meV. These two effects are accurately reproduced quantitatively using the numerical model (solid line) by adding an additional external electric potential. As the orientation of the NC long axis with respect to the field is not preset, the orientation constitutes the only free parameter in modeling the data. Whereas substantial electron penetration into the CdS shell can occur for the case of parallel orientation, orthogonal orientation to the field barely modifies the transition energy as the hole cannot penetrate the shell as illustrated in the sketch in Figure 2a. The higher dielectric constant of the NC compared to the matrix introduces an effective dielectric screening, which reduces the field inside the NC by a factor of ∼4 (i.e., the ratio of dielectric constants NC ≈ 9.5 and Matrix ≈ 2.5). The quantitative agreement between experiment and theory demonstrates that Stark spectroscopy can be used as a tool to provide insight into the electronic wave function distributions and the nanoparticle geometry. A QCSE should also occur orthogonally to the long axis, in analogy to spherical NCs.5 This is expected to result in a small but symmetrical Stark shift as demonstrated in Figure 2b. In this case the maximal Stark shift is reduced to 5 meV, comparable to the case for spherical NCs.5 The calculations also provide an estimate for the influence of the correlation energy in dependence of the electric field. Whereas this is estimated as 20% of the confinement energy in spherical particles,22 we find that it is reduced to 9% in the nanorods. Separation of the carrier wave functions at a field of 600 kV/cm lowers the correlation energy to 0.1%, pushing the carriers together at an equally strong field raises the contribution to 28%. Spectral diffusion and jumping plays a major role in this class of QDs5,12-14 and is also observed during the application of external electric fields. Surface charge can lead to the formation of a permanent dipole moment on the NC,27 which changes a weak quadratic QCSE into a strong linear one.5 Alternatively, surface charges can shield the exciton from the external field.5 Redistribution of surface charge is driven by the excess photon energy pumped into the system and occurs in the absence of discrete PL switching (i.e., ionization) events.12-14 To minimize the influence of spectral diffusion, low excitation powers (
