Letter pubs.acs.org/NanoLett
Quantitative Reconstructions of 3D Chemical Nanostructures in Nanowires P. Rueda-Fonseca,†,‡,§ E. Robin,†,§ E. Bellet-Amalric,†,§ M. Lopez-Haro,†,§,∥ M. Den Hertog,†,‡ Y. Genuist,†,‡ R. André,†,‡ A. Artioli,†,‡ S. Tatarenko,†,‡ D. Ferrand,†,‡ and J. Cibert*,†,‡ †
Université Grenoble Alpes, F-38000 Grenoble, France CNRS, Institut NEEL, F-38000 Grenoble, France § CEA, INAC, F-38000 Grenoble, France ∥ FEI Company, P.O. Box 80066, KA 5600 Eindhoven, The Netherlands ‡
S Supporting Information *
ABSTRACT: Energy dispersive X-ray spectrometry is used to extract a quantitative 3D composition profile of heterostructured nanowires. The analysis of hypermaps recorded along a limited number of projections, with a preliminary calibration of the signal associated with each element, is compared to the intensity profiles calculated for a model structure with successive shells of circular, elliptic, or faceted cross sections. This discrete tomographic technique is applied to II−VI nanowires grown by molecular beam epitaxy, incorporating ZnTe and CdTe and their alloys with Mn and Mg, with typical size down to a few nanometers and Mn or Mg content as low as 10%. KEYWORDS: energy dispersive X-ray spectrometry, nanowires, core−shell nanowires, quantum dots, electron microscopy.
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technique of choice for the quantitative study of nanometersized objects. In all cases, an electron beam is sent through the nanostructure, and the scattered electrons (for HAADF, GPA or EELS) or the X-ray emission (for EDX) excited over the whole trajectory through the material are recorded. Images are formed by scanning the incident beam across the structures in the plane perpendicular to the electron beam, but each pixel results from an average along the beam direction. A more complete analysis is needed if the goal is to obtain the full 3D composition profile. This is the objective of a tomographic reconstruction,14 which involves recording the signal projected along different azimuths at different positions and running a specific software to deduce the local properties. The resolution achieved directly depends on the number of projections accumulated around the tilt axis (described by the so-called Crowther criterion), and the precision on the counting statistic of each of them. Recent EDX tomography studies tried to minimize the number of projections,15,16 yet 14−15 projections are used and sophisticated procedures must be applied to cope with the low signal-to-noise ratio of each spectrum. In the present Letter, we show that a detailed information can be obtained from a limited number of projections, an important aspect in the case of NWs that are easily damaged by
he realization of structured nanowires strongly widens the range of semiconductor nanostructures and material assemblies that can be designed and fabricated. The simplest cases are core−shell nanowires (NWs) and dots embedded in a NW, but multishell NWs1 and multidots structuresstarting with artificial molecules, that is, two interacting dotsare rapidly envisioned. Such structures are expected to find applications in nanophotonics - from light emitting diodes in the visible and UV range to single photon emitters,2 energy harvesting (photovoltaic devices, piezoelectric systems,3 etc.), and various types of sensors or nanoelectronic devices. In all cases, the properties of a NW strongly depend on the chemical profile that has been realized, so that precise characterization tools have to be developed and applied to a single NW, in order to establish a correlation with the electric or optical properties of the same NW. One attractive method, developed in recent years, is atom probe tomography.4 In principle, direct information may be obtained on the composition profiles of NWs.5,6 It however requires a delicate preparation of the sample and may be challenging when applied to semiconductors. The most widely used techniques are based on transmission electron microscopy, such as high-angle annular dark-field (HAADF) microscopy,7 geometric phase analysis (GPA),8−10 and electron energy loss spectroscopy (EELS).11 More recently, significant technical improvements in the sensitivity and the quantitative character of energy-dispersive X-ray spectrometry (EDX)12,13 make it a © XXXX American Chemical Society
Received: November 4, 2015 Revised: January 19, 2016
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DOI: 10.1021/acs.nanolett.5b04489 Nano Lett. XXXX, XXX, XXX−XXX
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Figure 1. TEM or SEM images and element maps of O, Cd, Zn and Mg in (a) sample S1 (ZnTe NW with a long CdTe dot), and (b) sample S2 (ZnTe NW with a ZnMgTe shell and a short CdMnTe QD). (a) Left: high angle annular dark field (HAADF) image and EDX map of the whole NW at tilt 0°. Right: each hypermap was recorded at a different angle of tilt around the NW axis (−75°, − 45°, + 45° and +62° with respect to the initial position of the NW. (b) From left to right, SEM image and element maps of Zn, Cd, O, and Mg at different positions and scales, as indicated. The green rectangles indicate the line scans shown in Figure 3 (in each case, the scan is performed across the width of the NW and averaged over the width of the rectangle).
essentially due to the flux impinging onto the sidewalls of the NW.10 • Sample S1 involves pure ZnTe NWs with pure CdTe insertions. The CdTe insertion is obtained using Cd and Te cells with a large angle with respect to the NW axis (tan α = 0.65 for Te and tan α = 0.85 for Cd). As a result of a long insertion with a large lattice mismatch (6%), most of the NWs are kinked and we will show that their cross section is far from circular. Our objective is to show that recording a limited number of projections around a single tilt axis is enough to give quite precise information. • Sample S2 comprises an additional (Zn,Mg)Te outer shell. The insertion was realized with a CdTe cell having tan α = 0.21 and for a total flux toward the substrate that was half that of S1; hence, the flux on the sidewalls was ∼6 times smaller than for S1. A Mn beam was added to the CdTe flux and calibrated using reflection high energy electron diffraction (RHEED) oscillations on a test substrate so that the Mn flux was ∼10% the Cd or Te flux. Our objective here is to assess to what extend it is possible to determine compositions in the % range, and the purity and abruptness of a QD with nanometer size. Denoting y the electron beam direction (Figure 2), x and z two perpendicular directions for the scan (z being the NW axis), and under the experimental conditions described in the Methods section, the EDX signal obtained on element i in an object made of a semiconductor with the zincblende (or wurtzite) structure is Ii(x,z) = I0N0σi∫ ξi(x,y,z)dy, where N0 is the density of cation sites (inverse of the unit cell volume) and ξi(x,y,z) is the local composition (for instance, ξ in CdξZn1−ξTe). The cross sections σi are deduced from the ζ factors usually defined in EDX spectrometry,18 as σi = ζi/mi, where mi is the mass of atom i. The most useful characteristic value is then
the electron beam. Such a technique, known as discrete tomography, was applied to 3D atomic imaging of nanoparticles using a single projection in HAADF STEM,17 the additional information in this case being the crystallographic structure. To obtain such a detailed chemical information, we rely on two ingredients, the combination of which allows us to efficiently limit the number of projections, thus keeping a good signal-to-noise ratio, a good sensitivity to dilute chemical species and a good spatial resolution: • A preliminary calibration of the so-called ζ factors (see below), which allows us to quantitatively determine the effective thickness corresponding to each element along the direction of the incident electron beam, and thus to obtain a quantitative information not only along the directions perpendicular to a projection, but also along its direction. • An a priori knowledge of the symmetry of the nanostructure. Indeed, a single EDX projection is enough if the angular dependence of the composition is known, for instance, if the distribution is circular. The reliability and the accuracy of the reconstruction can even be checked thanks to the calibration of the ζ factors. More generally, using as few as two projections gives the essential information if assumptions can be done on the distribution. We give two examples of such an EDX analysis, obtained on NWs made of II−VI semiconductors (tellurides of Zn, Cd, Mg and Mn) with core−shell, multishell and dot-in-NW configurations. The results are discussed in terms of growth conditions (lateral vs axial growth, kinking, deviation from circular symmetry, facets) and their consequences on the composition distribution (purity of a QD, abruptness of the interfaces, incorporation of impurities) and on the electronic properties. Two samples incorporating a CdTe-based insertion in a micrometer-long ZnTe-based NW are analyzed, see Figure 1. They have been grown by molecular beam epitaxy using a gold catalyst. The crystal structure is zincblende, and at the rather low growth temperature used (350°), lateral growth is significant. Moreover, the growth of the CdTe insertion is
ti(x , z) =
∫ ξi(x , y , z)dy =
Ii(x , z) I0N0σi
(1)
which is an effective thickness. A thorough calibration of these ζ factors and of the incident intensity I0,13 using the very same B
DOI: 10.1021/acs.nanolett.5b04489 Nano Lett. XXXX, XXX, XXX−XXX
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continued by an inner shell down to the bottom of the NW. Sample S2, with a shorter CdTe inclusion, shows a more symmetrical, regular morphology. In this sample, the (Zn,Cd) Te inner shell is evidenced only at the bottom of the NW. The (Zn,Mg)Te shell is visible. Figure 3 displays selected atomic % profiles extracted from the hypermaps of Figure 1. One easily recognizes the characteristic profiles of a compact NW (Te) or a compact core (Cd or Mn across the QD), and those of a hollow shell (O, Mg; Cd below the QD in sample S1). When considering the low concentration values (for instance, Cd at 15 atom % in the QD of sample S1 and at 4 atom % in the QD of sample S2) one must keep in mind that (1) the Cd content is referred to all elements, anions and cations and that (2) the electron beam propagates through the ZnTe shell in front of the CdTe QD and behind and the signal is accumulated over the whole electron beam path. These averaged atom % should not be assimilated to local compositions. Recovering the ξi(x,y,z) distributions from the experimental ti(x,z) signal may appear as relatively straightforward if the NW displays circular symmetry: then ti(x,z) is the Abel transform of ξi(x,y,z) (or ξi(r,z) in cylindrical coordinates), and an integral formula exists for the inverse Abel transform.19 However, a numerical calculation of the integral is tricky. A few pairs of Abel transforms are known20 and may serve as a basis. The Abel transform of a Gaussian function is a Gaussian function, and generalized pairs have been proposed in order to represent rings.19 Another possible set of distributions is formed by uniform disks of various diameter d and uniform composition ξi: the Abel transform is a semiellipse of width d and height tmax i = ξid. For the sake of simplicity, this is our choice in the present study. Cases where the NW deviates from circular symmetry are more difficult to handle. In the fitting procedure, a first extension is to use off-centered elliptical contributions in the place of well-centered disks (we will address the problem of facets later on). A single projection cannot detect a shift of one component along the direction of the electron beam, and a second projection is needed, roughly perpendicular to the first one. As the ζ factors have been calibrated, we can decide from
Figure 2. Schematic view of an EDX measurement and corresponding signal from a NW.
setup and standards of known thickness and composition, makes these effective thicknesses fully quantitative: for instance, t(x,z) = ∑iti (x,z), where the sum runs over all cations (or anions), is the local thickness of the NW. In the case of a core− shell NW with pure semiconductors, say CdTe−ZnTe, tCd(x,z) is the local core thickness, and tCd(x,z) + tZn(x,z) is the local NW thickness. And ti(x,z)/t(x,z) is the content in atom i averaged along the y direction, ⟨ξi(x,z)⟩. Usually, the EDX data are reported for one direction y, either as atomic % profiles (i.e., ti(x,z)/∑iti(x,z), where the sum runs over all elements), or as element maps deduced from the ti(x,z) contours with well chosen thresholds. A tomographic reconstruction would be achieved by measuring ti(x,z) for all directions y, and calculating ξi(x,y,z) from the experimental data (i.e., calculating the inverse Radon transform of the measured signal). Here, we will first present selected data for our two NWs, in the form of element maps and average concentration profiles, then come back to the ti(x,z) data to propose model distributions ξi(x,y,z). Figure 1 display element maps of sample S1 and sample S2, respectively. An oxide layer is clearly revealed at the surface of the NWs. Sample S1 exhibits a strong contrast between the bottom part, which is quite symmetrical, and the top part which is strongly kinked and distorted above the CdTe inclusion. The CdTe insertion is elongated, with a cone shape, and it is
Figure 3. (a) Sample S1, Zn, Cd, O and Te relative composition (atomic % of the cation + anion content, averaged over the local thickness), along the line scan across the QD insertion at tilt = +45° (see Figure 1a). (b) Sample S1, Cd relative composition along the 3 line scans of Figure 1a at tilt = −45°, across the CdTe dot (top), below the dot and at the bottom of the NW (bottom). (c) Sample S2, Cd, Mn, and Mg relative composition along the line scans of Figure 1b across the dot for Cd and Mn, and below the dot for Mg. The symbols are the experimental data (the data outside the NW are set to zero), solid lines are the calculated values. C
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as the main contribution to the axial growth at the tip of a micrometer-long NW is due to the lateral flux impinging onto the NW sidewalls,10 the length of the CdTe insertion is large. This induces a noticeable kinking, resulting in a non circular character of the profiles. In our model, we had to introduce tilted, off-centered ellipses; this is partly ascribed to shadowing effects. Sample S2 features a much shorter CdTe inclusion, in agreement with our use of a CdTe cell, which makes a small angle with the NW axis. Another consequence is a reduced lateral growth of CdTe evidenced by the EDX study. With this sample, which embeds a small CdTe inclusion in a rather thick NW (8 nm vs 100 nm in diameter at the level of the dot), the present analysis is close to its limit. Nevertheless, we clearly detect the presence of Mn inside the dot, with a composition about Cd0.9Mn0.1Te, which agrees with the flux ratio (from the CdTe and Mn cell that are positioned symmetrically with respect to the NW axis, hence with the same angle of incidence). The presence of Mn was confirmed by the observation of a sizable giant Zeeman effect in the photoluminescence spectra recorded on the very same NW (not shown). Actually, such an analysis of EDX spectrometry provides us with a fairly good knowledge of the quantum dot profile, and a good basis for the interpretation of magnetooptical spectroscopic data.21 The presence of Mg is also evidenced, in spite of the low sensitivity of EDX spectrometry (at 200 kV) to such a light element. The crystal structure of NWs gives rise to strongly anisotropic growth rates and results in faceted sidewalls and core−shell interfaces. The edges between two facets are usually rounded so that narrow structures are reasonably well described by circular or elliptical cross sections. This is the case of the CdTe quantum dots in the present study. Facetting is however clearly observed on the bigger structures, and for instance (Figure 5) on the plot of t(x,z), which gives the local thickness
the intensity of the measured signal whether elliptical contributions have to be introduced. Note also that ellipses with different values of the ellipticity and corresponding orientation, such as the Lissajous curves x = cos(θ), y = cos(θ − θ0) with different values of the dephasing θ0, results in the same apparent widths but different intensities and are easily discriminated thanks to this calibration. The number of useful components is dictated by the signal-to-noise ratio. For sample S1, we used four projections, and we generally introduced five elliptical components that were easily distinguished and assessed with a precision better than 3 nm in size and position and a few % in composition. The solid lines in Figure 3 have been calculated with the decompositions shown in Figure 4. The criterion was a correct
Figure 4. Model composition. Left: sample S1, with the schematic longitudinal profile, and the actual cross sections used to fit the experimental data at the positions indicated by dashed lines; at the level of the CdTe quantum dot, the compositions are, from the center to the outside, pure CdTe, Cd 0.70 Zn 0.30 Te, Cd 0.32 Zn 0.68 Te, Cd0.14Zn0.86Te, then partial oxides mainly of Zn; at the bottom of the NW, the compositions are pure ZnTe, Cd 0.44 Zn 0.56 Te, Cd0.08Zn0.92Te, oxides. Right: Sample S2, at the level of the dot (CdTe core with 10% Mn, pure ZnTe shell, Zn0.91Mg0.09Te and Zn0.84Mg0.16Te shells, partial oxides) and at the base of the NW (pure ZnTe core, very dilute Cd0.02Zn0.98Te and Zn0.99Mg0.01Te, partial oxides with Zn and Mg). The inset gives the composition color code and the scale common to all cross sections.
fit for all elements and all projections shown in Figure 1; in Figure 3, we show only characteristic examples. An example of the whole procedure is given in the Supporting Information. In both samples, the CdTe dot features a fairly circular profile, with a 6 nm diameter in sample S1 and 8 nm in sample S2. This corresponds to the size of the contact between the tip of the NW and a gold nanoparticle having the shape of an almost full sphere, as discussed in ref 10. This core is made of pure or almost pure CdTe, with no Cd−Zn interdiffusion detected in these measurements. In sample S1grown with the Cd and Te cells, which make a large angle with respect to the NW axisa significant lateral growth is detected both at the level of the dot (with a progressive decay from CdTe to ZnTe over a characteristic length about 5 nm) and at the bottom of the NW (formation of an inner shell with a rather strong Cd−Zn mixing). In addition,
Figure 5. Local thickness t(x,z) (black squares) and Cd average concentration (red triangles) across the basis of sample S1, at the position given in Figure 1, and tilt +45° and −45°. Solid lines are calculated from the cross section shown on the right side.
of the NW and thus reflects the sidewall facets. Note that the shape of t(x,z) is observed also on the HAADF profile, but the calibration of the EDX signal (actually, of the ζ factors) makes the EDX determination of t(x,z) fully quantitative. As an example, sample S1 features an hexagonal cross section at its basis, in agreement with a NW axis along the ⟨111⟩ axis of the zincblende structure, and (112) sidewall facets. Note that D
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QUANTAX-800 software from BRUKER for background correction and deconvolution to extract the contributions of the L lines of Te, Cd, Au, and K lines of Zn, Mg, and O. The absorption correctionfor the typical size of the NWswas estimated to be negligible for Te, Zn, Cd, and Mn and less than 10% for O and Mg. The cross sections for each element (σi in eq 1) are deduced from the ζ factors directly measured on our equipment at the same operating conditions using reference samples of known composition and thickness,13 as σi = ζi/mi, where mi is the mass of atom i.
although the values of concentrations agree reasonably with those from the previous model with elliptical cross sections, the inclusion of facets ensures a better fit of the thicker structures: this is clearly seen on the total thickness t(x) (black symbols in Figure 5), which features straight segments. Such a dependence cannot be reproduced if we assume an elliptical profile, which results in an ellipse-like dependence t(x); we obtain a good fit (solid line) by assuming the hexagonal cross section shown in the right part of Figure 5. The improvement is more subtle for the inner structures: the Cd profile at the bottom of the NW and tilt −45° (red triangles) exhibits small structures at −10 nm and +10 nm (green arrows in Figure 5), which could not be reproduced with the elliptical cross section (Figure 3b) but are expected for the hexagonal cross section (Figure 5). Note that the composition of the inner shell is about the same in the two models (44% and 40% Cd). A full comparison, with a critical analysis in terms of resolution, sensitivity, and precision in the compositions, is shown in the Supporting Information. At the CdTe insertion, this NW is kinked toward the ⟨112⟩ axis: the same analysis reveals a rectangular cross section, with perpendicular (111) and (110) facets, as shown in the title figure. In conclusion, the morphology and chemical composition of CdTe QDs and Cd1−xMnxTe QDs (Mn concentration of few %) embedded in core−shell ZnTe/ZnMgTe NWs has been explored using a 3D reconstruction method which exploits discrete EDX tomography. The analysis is based on an initial calibration of the absolute EDX yield and a calculation of the EDX signal related to each element assuming a radial composition profile of the NW, which is compared to the experimental signal measured for a limited number of projections. Local compositions down to 10% Mn and less are accessible, and it is thus possible to obtain quantitatively the composition of a (Cd,Mn)Te diluted magnetic alloy in a quantum dot, or of a (Zn,Mg)Te shell, or the absence of contamination of a core (or quantum dot) by the surrounding shell. Size characteristics are obtained such as the diameter of a core in the few-nanometer range, the extension of a core−shell interface due to interdiffusion or segregation, or the presence of a spurious shell due to lateral growth. The presence of facets in the built-in interfaces, related to the crystal structure, is also clearly evidenced.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.5b04489. Procedure for quantitative 3D EDX reconstruction. (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Present Address
(M.L.-H.) Departamento de Ciencias de los Materiales e ́ Ingenieriá Metalúrgica y Quimica Inorgánica, Facultad de Ciencias, Universidad de Cádiz, Campus Rio San Pedro, Puerto Real, 11510 Cadiz, Spain. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was performed in the joint CNRS-CEA group “Nanophysique & Semiconducteurs”, the team “Laboratory of Material Study by Advanced Microscopy”, and the team “Materials, Radiations, Structure”. We acknowledge funding by the French National Research Agency (project “Magwires”, ANR-11-BS10-013, and project COSMOS, ANR-12-JS100002). We thank all the members of the Magwires project for many discussions.
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METHODS Sample Growth. The details of the conditions used for the sample preparation and the growth of nanowires have been reported previously.10,22,23 The growth was achieved by molecular beam epitaxy with (i) a low growth temperature (350 °C) kept constant during the growth of the whole heterostructure (QD and shell); (ii) a solid Au catalyst particle indicating that the NW growth takes place in the vapor−solid− solid mode; (iii) a growth in homoepitaxy over a ZnTe buffer layer. Quite different growth conditions have been reported24 by Wojnar et al. EDX. We used EDX spectrometry coupled to a FEI Tecnai Osiris S/TEM equipped with four Silicon Drift Detectors and operated at 200 kV. The NWs were removed mechanically from the as-grown samples and deposited on a holey carboncoated copper grid (sample S1) or on a patterned Si3N4/Si substrate which allows a preliminary study by cathodoluminescence and magneto-photoluminescence. The EDX signal is an hypermap where each pixel corresponds to the X-ray emission of atoms along the electron beam. We used the
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