1. Introduction

The optical properties of semiconductor quantum dots (SC QDs) can be tailored by control of their size, shape and material composition. This ability is a result of quantum confinement effects, which strongly determine the density of states and hence QDs optical features [1, 2]. Over the last decade, significant advances in the field of nanoparticle synthesis has enabled fabrication of increasingly complex nanoparticles (NPs) such as various core/shell heterostructures [3,4], anisotropically shaped or branched nanoparticles containing different semiconducting materials [5–8] metal oxide - semiconducting quantum rods (QR) [9], and semiconductor-metal nanocrystal heterostructures [10, 11]. The production of such composite NPs that also retain quantum confinement makes these materials interesting in nonlinear optics.

Second-harmonic generation (SHG) from single dot-shaped CdTe/CdS core-shell QDs was recently observed by the authors using a two-photon scanning microscopy technique (TPSM) [12]. The strong second-order nonlinearity of the CdTe core with a large nonlinear coefficient d₁₄ of up to 200 pmV⁻¹ and its non-centrosymmetric, tetrahedral zinc-blende crystalline lattice [13, 14] allowed for downsizing QDs to 10–15 nm diameter, while maintaining a strong second-harmonic (SH) emission, in the range of 10⁵cts/s from a single QD. This was achieved with standard 100 fs pulses of near infrared (NIR) Ti-Sapphire laser light at 80 MHz repetition rate. The observed SH emission is polarization-sensitive, tunable and photo-stable out of the one-photon resonance [12]. It shows reduced photobleaching under strong excitation intensity, which is known as a main limitation of many organic fluorophores [15,16], and eliminated emission intermittency (’blinking’) as is commonly observed for luminescent QDs [17, 18]. These semiconducting QDs widen the range of applications of other nonlinearly active inorganic nanoparticles [19–23], especially for high spatial resolution in optical near-field probing or biological applications, such as nanolabeling.

The state-of-the-art techniques in developments of complex nanoscale objects provide the possibility of engineering the nonlinear properties of these structures. These properties would reflect the combination of tensorial optical responses from different materials as well as the precise structural engineering of hybrid heterostructures, obtained by applying different symmetries together:

Herein we propose an ’artificial’ nanosource for the controlled character of the nonlinear scattering from single hybrid SC QD, where the nonlinear emission is controlled through the choice of QD materials and geometrical parameters. As a proof-of-principle experiment we consider a rod-on-dot (RD) quantum confined heterostructure made of two semiconducting materials: CdTe and CdS- each having a different crystalline structure (zinc blende corresponding to the 4̄3 m and wurtzite 6mm point group symmetry, respectively), nonlinear susceptibility tensor and spatial geometry (QD and quantum rod (QR), respectively):

Our idea, based on the pointwise additive model of coupled SHG fields, is confirmed by the experimental findings, allowing for accurate extraction of the three-dimensional orientation of a single RD QD heterostructure as well as the CdS QR length

2. Materials and methods

2.1. Characterization of RD QD heterostructures

One-pot synthesis of rod-on-dot CdTe/CdS hybrids was conducted via modified standard procedures [26]. 60mg tetradecyl phosphonic acid (PCI synthesis) and 13 mg Cadmium oxide were added to 5mL octadecene (ODE) and heated up to 260°C under an Argon atmosphere, until full dissolution of the Cadmium oxide. At this point, 0.013 g of elemental Tellurium in 2ml trioctylphosphine (TOP) was swiftly injected into the flask and the temperature was lowered to 210°C. After several minutes the temperature was raised to 250°C and alternate injections of 0.1M Cadmium oleate in ODE and 0.1M TOP:Te, separated by 10 minutes, were performed. When the size of the QDs reached 6 nm, the TOP:Te was replaced by elemental Sulfur dissolved in a 1:1 mixture of ODE and TOP. Three consecutive injections were performed at increasing temperatures starting from 210°C and ending at 250°C. Following this, emission had shifted from 708 nm to 713 nm. At this stage, a more reactive sulfur precursor was used (0.1M Bis(trimethylsilyl)sulfide in ODE). Injections were carried out at temperatures varying from 180°C to 230°C. During these injections, the emission slowly red-shifted until reaching a final value of 720nm. The absorption and emission curves of both the CdTe cores and the final CdTe/CdS hybrids are given in Fig. 1.

 

Fig. 1 (a) Absorption and (b) emission curves for the CdTe cores (dashed lines) and the CdTe/CdS hybrid structures (solid lines). The CdTe/CdS absorption curve is vertically shifted for clarity.

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The QD geometrical features were investigated using transmission electron microscopy (TEM) (Fig. 2a) and by atomic force microscopy (AFM) (Fig. 2b, 2c). Size determination is quite important since SHG is expected to scale as the squared volume of the scatterer, making it especially critical when applied to complex structures composed of at least two different types of materials requiring a strong necessity for dimension characterization for further SHG studies. The size of spherical CdTe cores was determined from the absorption spectrum during their growth to 5.9 nm [26]. For the case of geometrically complex structures, such as RD QDs, dimensions are best obtained directly from the TEM images. The size distribution of forty isolated RD QDs, directly obtained from the TEM images, is shown in the histograms in Figure 2d–f. Size dispersion varies in a range between 5.7 – 6.2 nm diameter of the CdTe core (consistent with the optical measurements), and 2.4 – 3.6 nm diameter of the CdS rod. The length of the CdS rod is dispersed over a wider range, from 6.0 – 16.0 nm, with a mean value of 11.0 nm.

 

Fig. 2 a) TEM image of the rod-on-dot quantum heterostructures; CdTe cores and CdS rods are clearly distinguishable. b – c) AFM topographical and phase scans (obtained with a tapping mode (TM)) of a single and well isolated RD QD immersed within a ≈ 30 nm thick PMMA host-matrix. d – f) TEM based histograms of the effective size distribution, characterizing the CdTe core and CdS rod dimensions.

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The complexity of the RD QDs leads to several implications, arising from a new geometry and new physical features of such-formed hybrid NPs. This consequently impacts on described SHG studies. Indeed, analysis of the SHG polarization dependency requires a precise definition of the mutual orientations of the CdTe cubic zinc-blende lattice, which belongs to the 4̄3m point group symmetry, with respect to that of the CdS rod structure. In this particular case, synthesis conditions of RD QDs imposed growth of the CdS rod into the hexagonal wurtzite form, corresponding to a 6mm point group symmetry. To describe the relative lattice orientations of the two crystal structures at the interface we used the convention described in the literature [27–29]. The epitaxial relationships are therefore characterized by the [011̄0] axis of CdS oriented parallel to the [112̄] axis of CdTe, and the CdS [0001] axis oriented parallel to the [111] axis of CdTe, which means that the 6-fold axis of symmetry (parallel to [0001]) is oriented along the rod’s growth direction. This orientation comes from the epitaxial constraint compatibility of the zinc-blende +/ −(111) and wurtzite +/ −(0001) facets at the interface [6, 28]. For two different materials such as CdTe and CdS, it minimizes the mismatch between two lattices down to 9.8% [30]. Thus, the rotation angle of the CdS rod around its [0001] axis relative to the CdTe is fixed.

2.2. Sample preparation

A dilute sample containing CdTe/CdS hybrid RD QDs was prepared following a similar procedures to that described in Ref. [12], and previously used for single dot studies. Before deposition, prepared colloidal solution of RD QDs in anisole (2.0 mg per 5 mL of the solvent) was sonicated for 1 hour to avoid aggregation. In order to obtain ≈ 30nm thick poly(methyl methacrylate) (PMMA) host-matrix layer (MicroChem 4% 495K in anisole, diluted to 2% MW), measured with a DEKTAK 3ST surface profiler, prepared solution containing RD QDs was spin coated (4000 rpm, 1000 acc., 45 s) on glass cover slips (#1, cleaned before with oxygen plasma) and held at 180°C for 1 min. The quality of the sample was checked by taking several AFM scans (Veeco, Nanoscope V) using tapping mode to confirm the presence of well dispersed monocrystals. The characteristic shape of the rod and the core are distinguishable in Figure 2b–c, despite the presence of the PMMA host-matrix layer.

2.3. Nonlinear scanning polarization microscopy

The nonlinear optical response was measured with the same TPSM setup, equipped with Nikon Eclipse TE2000-U inverted confocal microscope, that was previously used to study SH emitting spherical CdTe/CdS core/shell QDs [12]. NPs were excited with a Spectra-Physics Mai-Tai HP Ti-Sapphire oscillator, emitting 100 fs pulses at a repetition rate of 80 MHz. SHG photons were detected in the epi-direction via a high numerical aperture oil-immersion objective (Nikon X100 PA IR, NA = 1.4), and well separated spectrally from the NIR excitation beam (dichroic mirror with a cutoff wavelength at 700 nm), as well as from eventual two-photon excited luminescence (TPEL) by a set of BG38-39 band-pass filters and short-pass Semrock SP561 filter. Polarization analysis was achieved by precise rotation of the achromatic half-wave plate in the excitation optical path. In the detection channel, the SHG signal was decomposed into x and y polarization components by a polarizing beam splitter, and detected by two silicon avalanche photodiodes (APDs, Perkin-Elmer SPCM-AQR-14) working in the photon counting regime. The emission spectrum was obtained with an Oriel Multispec 7740 spectrometer (160 nm narrow slit), equipped with an Andor Technology DV420-OE CCD camera. Measurements of the SHG excitation wavelength dependence were performed using APDs with an integration time of 1s, while the excitation wavelength was automatically tuned using the Mai-Tai scanning mode with a step of 1 nm/sec. The raw data was corrected by the laser output power and transmission characteristics of all optical components of the setup, as well as by the quantum efficiency of the APDs (see Supplementary Information for Ref. [12]).

3. Results and discussion

3.1. Theoretical model: SHG emission from RD heterostructure

In order to obtain the direct expression of the second-harmonic polarization response from a hybrid RD QD consisting of two different materials, we use a linear combination of components of the CdTe and the CdS second-order susceptibility tensors, assuming the contribution of each of them to be proportional to its volume in the whole structure: ${\chi }_{RD}^{\left(2\right)}\propto {\chi }_{CdTe}^{\left(2\right)}+V_{CdS}{V}_{CdTe}^{-1}{\chi }_{CdS}^{\left(2\right)}$. The volumes of the spherical CdTe core and of the cylindrical CdS rod are characterized by considering the shape of each part, and the size distribution including the diameter of the CdTe core assumed as D_CdTe = 6.0 nm and the diameter of the CdS rod D_CdS = 3.0 nm. The length of the rod is a variable, which has a strong impact on the total SHG response, as analyzed below. The contribution of SH fields generated from both materials into the total SHG field emitted by a single RD scatterer: $E_{\mathit{scat}}^{\mathit{SHG}}\propto \frac{{\partial }^2}{\partial t^2}{P}_{SHG}^{\left(2\right)}$ requires consideration of coupling and appearance of the interference effect occurring between SHG fields from both sources. Thus the SHG intensity $I_{\mathit{tot}}^{SHG}\propto {\left|E_{\mathit{scat}}^{\mathit{SHG}}\right|}^2$, resulting from a linear combination of the second-harmonic fields, can be expressed as:

This pointwise additive model, when applied separately to both x and y polarization components, allows for quantitative analysis of the SHG field terms described by Eq. (3) accounting for the total SHG field emitted by the whole hybrid crystalline structure. Figure 3 shows an example of such an analysis, conducted for one of the experimentally obtained results. The signal intensities are plotted as a function of the polarization angle of the pump relative to the laboratory x-axis for both x-polarized and y-polarized SH in the lab frame. We fit the relative orientation of the QD in the lab frame and the relative volume via the length of the rod, while other parameters (diameter of the CdTe core and width of the CdS rod) are kept fixed at the mean values obtained from TEM images.

 

Fig. 3 (a) Graphical illustration and (b) analytical analysis of the polarization response of decomposed total SHG field $E_{\mathit{scat}}^{\mathit{SHG}}$, calculated for a single RD QD (b). Polarization plots show contributions of the CdTe core, CdS rod and the interference term (positive and negative) into $I_{\mathit{tot}}^{\mathit{SHG}}$.

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3.2. Theoretical model: SHG dependence on the CdS rod length

Detailed studies of the CdS rod length dependence give evidence of the significant contribution of this feature to the overall SHG response. The polarization pattern of the SHG emission from the zinc-blende-like CdTe core displays characteristic fourfold cloverleaf response [12], as expected from its octupolar 4̄3m symmetry [31, 32], progressively changing into a dominantly dipolar-like pattern as the CdS rod grows. Appearance of the rod leads to a progressive loss of additional maxima for each component, which is imposed by the dipolar 6mm symmetry of the hexagonal form of the CdS crystalline lattice. Thus the character of the SHG emission can be tuned between different symmetries by control over the geometrical features of the SC heterostructure. The pointwise additive model has been used to visualize the transformation of total SHG field dependence on the CdS rod length. In Fig. 4 we present calculations for a single RD QD for five cases: a CdTe core with approximately 6 nm diameter, RD QD with different lengths of the CdS rod: 4, 8, 13 nm (corresponding to the experimental data), and 20 nm, where the SHG emission pattern is aligned along the CdS rod [0001] axis, and without visible contribution of the CdTe core to SHG response. It is clear that the appearance of even a short CdS rod, e.g. 4 nm long, changes the SHG pattern in a drastic manner as compared to the fourfold cloverleaf response of the core. Further growth of the CdS rod significantly reduces the relative CdTe contribution, leading to approximately equal contributions of both materials for 8 nm long rod (which gives V_CdS ≈ 57nm³ versus V_CdTe ≈ 113nm³), while 13 nm long rods (V_CdS ≈ 92nm³) are enough for the dipolar character of the SHG polarization response to prevail over the octupolar core contribution. An overgrown 20 nm long rod completely transforms the SHG field into quasi dipolar-like.

 

Fig. 4 a) Rod-on-dot QD cross-sections illustrating growth of the CdS QR in a range from 4 – 20 nm on a 6 nm diameter CdTe core. b) Calculated polarization responses of the SHG emission, obtained for a single RD QD during progressive growth of its rod.

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Taking into account two facts, primarily that the number of emitted SHG photons is proportional to the volume squared of the emitter and, secondly, comparable nonlinearities of CdTe and CdS (here for CdTe we assume the low value of d₁₄ = 64.0pmV⁻¹) [13, 14], it appears that the interference term has a strong constructive or destructive contribution, and based on the model (expression (3)) it changes linearly with a linear growth of the CdS quantum rod.

3.3. Polarization analysis of the experimental results

One of the distinct advantages arising from the SHG process of nanoscale scatterers is undoubtedly its high sensitivity to the polarization of the incident optical electromagnetic field Ē^ω. This enables probing of the spatial orientation of the scatterer relative to the laboratory frame. Such experiments have been successfully conducted with both single-material inorganic and organic nanocrystals, where the SHG response was determined by the regular crystalline lattice (where it is relatively easy to process experimental polarization analysis from a theoretical model) [12, 19, 20, 33, 34].

Decomposition of the x and y components of the optical polarization components of the emitted SHG field is achieved as a function of the rotation angle of the incident electromagnetic field Ē^ω at the fundamental frequency ω. This model neglects depolarization and propagation effects due to the embedding dielectric host material [35]. The RD QDs response can thus be specified by a single P̄^2ω dipole oscillating at the 2ω frequency [13]:

Analysis of the experimental data obtained for three differently oriented RD QDs (Fig. 5a) show very high sensitivity of the polarization response with respect to the orientation of the ${\chi }_{RD}^{\left(2\right)}$ tensor, determined by the spatial position of the hybrid lattice. The excellent agreement between the fits (see Fig. 5b) and the raw data is firstly, proof of the single dot origin of the harmonic signal, ruling out the occurrence of complex crystalline multiple QD clusters or aggregates, thus opening possibilities for precise determination of the corresponding spatial orientation of both the CdTe core and CdS rod structures. The fit obtained for QD1 experimental result (first row of Fig. 5) has been used to illustrate decomposition of the total SHG field based on the pointwise additive model into contributions of each part of the heterostructure and the interference term, presented in Fig. 3. The impact of the different lengths of the CdS QR on the SHG polarization pattern (Fig. 4) corresponds to the same experimental result.

 

Fig. 5 a) Experimentally obtained polarization analysis of the SH emission observed for three RD QDs (QD 1–3). Open scattered points represent the raw data, while line traces show smoothed functions (SF). b) Calculated fits of the experimental data smoothed traces. c) 3D projections of RD QD crystalline lattices, characterizing the orientations of experimentally studied RD NPs by Euler sets of angles.

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In order to obtain their orientations we have taken into account the mutual relations between both lattices, and used the model described in previous subsections. Generated three-dimensional projections (Fig. 5c) of hybrid RD QD lattices corresponding to the orientations of experimentally scanned RD QDs, seen in the x,y,z laboratory frame, show the mutual positions of the CdTe and CdS lattices. It is clear that the orientation of the dipole is determined by the [0001] axis of CdS oriented along the QR. In each case, the out-of-plane deviation (described by the angle β between the CdS [0001] axis and the x, y plane) is lower than 45°, which to some extent was forced by the spin coating conditions resulted in ≈ 30nm thick PMMA host-matrix, where the RD QDs were expected to lie on the surface. However, our model can also efficiently support less frequently occuring NPs with vertically oriented rods.

3.4. Spectral dependence of the SHG: influence of the quantum confinement effect

An example of the diffraction limited and well-contrasted SHG spot obtained by scanning a single RD QD is shown in the inset of Fig. 6a (together with its orientation in reference to the laboratory axis). The full width half maximum (FWHM) of the observed spot is approximately 290 nm. Typically, scans were obtained with the excitation wavelength set at 890 nm and with an incident power of 3.0 mW, leading to a focused pulsed peak intensity of about 95GWcm⁻².

 

Fig. 6 a) SHG emission spectra, recorded with the same incident power of about 3.0 mW, at six different excitation wavelengths (intensities without correction, given in arbitrary units). The inset shows a diffraction limited scan of a single RD QD with respect to the laboratory axis frame. b) SHG quadratic dependency on the incident power of the excitation light, evidencing a two-photon process. The inset contains the same data plotted on a logarithmic scale. c) Photostability of the SHG signal scattering from a single RD QD, recorded as two polarization components along x (red trace) and y (blue trace), respectively.

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Examples of emission spectra recorded at various excitation frequencies between 850 – 950 nm and showing about 7 nm narrow line-width peaks of SHG, with a high signal-to-background ratio, are presented in Fig. 6a as uncorrected raw data traces in arbitrary units. SHG emission, however, even without correcting for the transmission of optical components is clearly dominant over the whole range of excitation. The second-order character of the SH emission is confirmed by the quadratic dependence on the incident power of the excitation laser light (Fig. 6b). Signals obtained from purely SHG emitting RD QDs (e.g. Fig. 6c) show a high degree of photo-stability, even when doubling the intensity of the excitation in comparison with the used excitation conditions. We observe, however, an inverse correlation between the intensity of two-photon luminescence from these QDs and their photostability. We believe that the reduced photo-stability of QDs exhibiting stronger band-edge luminescence is due to induced excited state absorption at the excitation frequency. For RD QDs exhibiting low luminescence quantum yield (studied in this work) the excited state population completely decays nonradiatively within the 12 ns time interval between consecutive excitation pulses, eliminating such possible effects.

As can be seen in Fig. 6c, under ’standard conditions’ (890 nm of excitation wavelength, with the polarization of the incident optical electric field oriented along the dipole moment of the single RD QD) we have observed approximately 7 · 10⁴cts/s SHG signal count rate, which is as strong as typical luminescence from bright QDs, despite the relatively low quantum efficiency of the APDs of ≈24% at 445 nm. Taking into account the transmission of the collection optics as well as the collection efficiencies, this corresponds to a SHG cross section of the order of 50GM. It is important to point out, that this count rate was obtained from hybrid RD QD with 12nm long rods, which corresponds to a volume of about 113nm³ for the CdTe core and 85nm³ for the CdS rod, such that the total volume was nearly 6 times less than that of spherical CdTe/CdS QDs (with a mean diameter about 13 nm) previously observed in single-dot studies [12]. In this particular case, however, excitation at 890 nm does not provide the highest possible SHG cross-section. The blue curve in Figure 7 shows that the optimal excitation wavelength at 925 nm instead of 890 nm (for this size of RD QD) would result in a nearly one and half times higher count rate of about 1.1 · 10⁵cts/s. SHG obtained with that excitation frequency would be also detected with higher efficiency by the Silicon-based APDs.

 

Fig. 7 Excitation spectra showing the wavelength dependence of the SHG intensity observed from two different single RD QDs (red and blue traces). The open black scattered trace, placed for comparison, shows this dependency for spherical CdTe/CdS QDs, reported in Ref. [12]. All curves reflect changes of the SHG cross-section with respect to the quantum size confinement effect (cross-sections of QDs are scaled with a real ratio with respect to size differences).

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The SHG emission reflects an effective nonlinear coefficient ${\left({\chi }_{RD}^{\left(2\right)}\right)}_{\mathit{eff}}^{\mathit{2}}$ corresponding to the second-order nonlinear optical susceptibility squared, measured at a high level of the emission photostability in the range from 800 to 990 nm (no phase-matching requirement). The raw data was corrected for the excitation laser power, detector response and transmission of the various optical components [12]. This results in the curves presented in Fig. 7. The blue excitation spectrum trace corresponds to the typical sized RD QD. As can be expected from a system with a discrete energy level spectrum, it exhibits multiple peaks. As for previously studied spherical QDs (see the open black scattered trace) [12], there is an optimal excitation wavelength for SHG at about 925 nm. It is, nevertheless, significantly blue-shifted with respect to the peak positions for larger spherical CdTe/CdS QDs (970 nm) as could be expected due to the stronger carrier confinement regime in agreement with the larger band gap of the smaller QD. RD QDs which were identified as having a shorter CdS rod (thus having an increased confinement of the electron) exhibit, in accordance with this observation, an even further blue shift in the SHG excitation spectrum, as can be seen in the red trace. A more thorough evaluation of the χ⁽²⁾ excitation spectra is proposed in Ref. [12] and is currently under further study.

4. Conclusions

In summary, this work demonstrates a new approach for the engineering of the second-order nonlinearity of semiconducting hybrid rod-on-dot heterostructures at the single nanoparticle scale for efficient and photostable SHG emission. These hybrid nanoparticles exhibit extremely strong and stable emission (with size dependent optimal SHG cross-section) although their volume is reduced by at least a factor of five from the previous smallest SHG scattering probes. Moreover, it emphasizes the structural relationship between the CdTe core and CdS rod and contributions of their respective χ⁽²⁾ tensors on the SH field. The pointwise additive model allows for comprehensive simulation of the polarization response, showing quantitative contributions of the CdTe core and the CdS rod, as well as that of their interference term into the total SH emission. The high degree of agreement between the simulation and the experimentally observed results is not circumstantial and can be considered as evidence for the single crystalline nature of the investigated QD sample. It permits precise determination of the spatial orientation of the crystalline structure. It also shows that the hybrid system can be adequately decomposed into a sum of its constituents in the case of semiconductor-semiconductor hybrids. This simple result is not trivial and is even surprising since it does not hold for metal-semiconductor hybrid particles [10]. Still, coupling of the two semiconductor parts may affect the relative magnitude of the χ⁽²⁾ coefficient, and will be investigated in a future work. Simulation analysis show that the SHG response strongly depends on the CdS rod length and transforms from the four clover-leaf shape characteristic of the octupolar zinc-blende symmetry of the CdTe core into a typically dipolar response oriented along the CdS rod and imposed by the main polar axis of its hexagonal symmetry point group. The conceptual as well as practical possibility to fine tune at will the balance between dipolar and octupolar contributions by adequate stoichiometry-based molecular engineering considerations has already been demonstrated in the case of organo-metallic compounds for nonlinear optics (NLO) [36]. Extending such an approach from molecular to nanoscale and from organo-metallics to semiconducting materials requires a very different approach which is proposed and demonstrated here for the first time, to the best of our knowledge. Moreover, maintaining control over this delicate multipolar balance at the scale of nanolabels while minimizing the size of RD QDs paves the way towards very efficient and precise orientation monitoring in original bio-imaging applications.