Letter pubs.acs.org/NanoLett
Plastic and Elastic Strain Fields in GaAs/Si Core−Shell Nanowires Sònia Conesa-Boj,† Francesca Boioli,∥,⊥ Eleonora Russo-Averchi,† Sylvain Dunand,‡ Martin Heiss,† Daniel Rüffer,† Nicolas Wyrsch,‡ Christophe Ballif,‡,§ Leo Miglio,∥ and Anna Fontcuberta i Morral†,* †
Laboratoire des Matériaux Semiconducteurs (LMSC)and ‡Institute of Microengineering (IMT), Photovoltaics and Thin Film Electronics Laboratory, École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland § Centre Suisse d’Electronique et de Microtechnique (CSEM) PV-Center, 2000 Neuchâtel, Switzerland ∥ L-NESS and Department of Materials Science, University of Milano-Bicocca, 20125 Milano, Italy S Supporting Information *
ABSTRACT: Thanks to their unique morphology, nanowires have enabled integration of materials in a way that was not possible before with thin film technology. In turn, this opens new avenues for applications in the areas of energy harvesting, electronics, and optoelectronics. This is particularly true for axial heterostructures, while core−shell systems are limited by the appearance of strain-induced dislocations. Even more challenging is the detection and understanding of these defects. We combine geometrical phase analysis with finite element strain simulations to quantify and determine the origin of the lattice distortion in core− shell nanowire structures. Such combination provides a powerful insight in the origin and characteristics of edge dislocations in such systems and quantifies their impact with the strain field map. We apply the method to heterostructures presenting single and mixed crystalline phase. Mixing crystalline phases along a nanowire turns out to be beneficial for reducing strain in mismatched core−shell structures. KEYWORDS: Nanowires, GaAs, Si, molecular beam epitaxy (MBE), plasma enhanced chemical vapor deposition (PECVD), geometrical phase analysis (GPA) and finite element strain simulations
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A key issue for characterizing and understanding defects in core−shell structures is their three-dimensional and nanoscale character. The techniques currently used for the characterization of strain in nanowires include X-ray diffraction,27 photoluminescence,28 and photoreflectance.29 Unfortunately, these are rather indirect techniques that average over nanowire ensembles. Another strategy is based on high-resolution transmission electron microscopy (HRTEM) on individual nanowires. In some cases, dislocations have been characterized by performing detailed analysis of high-resolution TEM on cross sections,16 which provides local information on the structure of the nanowire. A related approach is provided by convergent beam electron diffraction (CBED). This technique has been used to determine the strain field in individual nanowires,30 in thin film structures,31 and in integrated circuit components.32 A drawback of this method is that the information is acquired on a point-by-point basis, which makes it cumbersome to obtain a global measurement of the strain distribution along the whole nanowire.33 Recently, the combination of high-resolution transmission electron microscopy (HRTEM) and geometric phase analysis
emiconductor nanowires have offered many new opportunities both in fundamental science1 and in technology in the form of improvements and new concepts in electronics,2,3 optoelectronics,4 sensors,5 thermoelectrics,6 and solar cells.7−11 Many of these new avenues originate from their small foot-print and large aspect ratio. As an example, the reduced cross-section area has enabled the fabrication of highly mismatched sharp axial heterostructures, otherwise impossible in the thin film form.12−14 In principle, the small diameter of nanowires should also enable a more effective strain relaxation in core−shell structures with respect to planar thin films, thereby also opening new perspectives in combinations of materials and functional devices. Still, one of the great challenges for the viability of core−shell heterostructures is to understand the plastic strain relaxation mechanism generated in the core−shell system. The nature and the geometry of the dislocations originated in such core−shell systems leading to relieve strain has been demonstrated that depends on the material system.15,16 It has been proposed that mismatched core−shell nanowires may result in highly strained structures,17,18,16 which could relax by forming misfit dislocations.19−22 As misfit dislocations are responsible for the degradation of the functional properties in semiconductors,23,24 there have been many efforts toward the reduction of dislocation and structural defects in the fabrication of mismatched heterostructures.25,26 © 2014 American Chemical Society
Received: December 14, 2013 Revised: January 30, 2014 Published: February 24, 2014 1859
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Figure 1. (a) Bright-field TEM image of a GaAs nanowire after deposition of Si shell. The inset corresponds to the Fourier Transform exhibiting the Bragg reflections coming from both materials. (b) High-resolution TEM image of the region marked by square in (a).
Figure 2. (a) High-resolution TEM image of the GaAs/Si core−shell nanowire. (b,c) Phase image corresponding to the (11̅1) Bragg spot and a line scan quantification crossing the phase shift indicated by the arrow in the map of (b), respectively. (d) εzz strain field map, where a tensile region crossing the nanowire diameter is clearly visible (red line). (e) Line scan performed a cross the tensile line. (f) Schematic drawing showing the tensile line crossing the diameter and limited in the ranges by edge dislocations.
(GPA)34 has been shown to be a promising tool in quantifying lattice distortion and strain field measurements on a wide range of systems, such as Al/Si nanocluster,35 Germanium nanowires on Si(111) substrate,36 crack-tip in silicon,37 Si/Ge,38 GaN/ InGaN,39 and GaN/AlN40 axial and radial heterostructures nanowires, respectively. To the best of our knowledge, this technique has not been applied to the lattice displacements, or strain fields, on highly mismatch core−shell nanowires. In addition, while significant theoretical predictions about misfit strain relaxation mechanism in core−shell nanowires exist, few quantitative analyses have been performed.16,41−44 In this work, the combination of HRTEM and GPA has been applied to the evaluation of the strain field relaxation map in GaAs/Si core−shell nanowires. Two different crystalline core− shell structures have been explored, one consisting in pure zincblende (ZB) and the other composed by a wurtzite/zinc-blende (W/ZB) heterostructure. Understanding the strain release in these systems is an important milestone toward the use of GaAs/Si heterostructures in realistic nanodevices. A particularly relevant example is provided by the indirect band gap of Si, which under compressive strain in GaAs nanowires could result into a quasi-direct energy band gap thus becoming promising candidates for high efficiency solar cells and light emission materials.45 The combination of GPA with finite element
method (FEM) strain simulations is extremely powerful, for it allows us to identify the origin and the geometry of edge dislocations in core−shell nanowire systems and determine the strain field in the system. We begin by analyzing our core−shell structures by HRTEM, calculating the phase image to determine the displacement field in the structure. Figure 1a shows a representative bright-field HRTEM image of GaAs/Si core−shell nanowire at a low magnification. The total diameter of the nanowire is 74 nm. The inset of Figure 1a shows the fast Fourier transform (FFT) of the marked area. We observe Bragg reflections arising from both GaAs and Si, marked by arrows. The reflections are separated, indicating that both Si and GaAs are relaxed in their equilibrium lattice constant. In Figure 1b, we show a higher magnification of the marked region in Figure 1a, observed in a [110]ZB zone axis. A shell of around 4 nm is observed by the different contrast in the micrograph. The surface of the Si-shell displays more roughness than the core underneath, probably due to strain relief associated with misfit dislocations, as previously shown in Ge/Si core−shell structures.42 The latter is a good reference system, because the GaAs/Si exhibit an equivalent lattice mismatch. We now turn to the calculation of the phase and displacement fields.46 This is obtained by relating the lattice 1860
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Burgers vector b = a/3[111̅ ], as described in ref 48. This configuration is sketched in Figure 3a by the dashed blue line.
fringes in the micrograph to the ones projected by a reference Bragg reflection peak. The phase shift is related to the displacement of lattice fringes by Pg( r ⃗) = −2πg ⃗ ·u ⃗( r ⃗)
(1)
where u⃗(r)⃗ is the local displacement with respect to the reference lattice, g.⃗ Figure 2a shows a HRTEM micrograph corresponding to a central region of the GaAs/Si core−shell nanowire shown in Figure 1a−d. The right upper part of the micrograph is chosen as the reference lattice spacing. The z, x reference frame is such that the z-direction corresponds to the (11̅1) direction, parallel to the nanowire growth axis. The xdirection is the (11̅ 2), perpendicular to the z-axis. We take the Bragg reflection g⃗ = (11̅1) in the power spectrum highlighted in the inset of Figure 2a to calculate the displacement fields. The result is a phase micrograph with respect to the reference, enabling us to locate and quantify any displacement. In the case of Figure 2b, we have looked at the displacement along the growth direction. The phase map obtained from the micrograph in Figure 2a is shown in Figure 2b. This phase image has values in radians in a range from −π to + π. In the central region of the map we observe a clear phase shift along the axis of the nanowire, limited by two edge dislocations identified by two points where the phase increases from 0 to 2π radians (being in the color range yellow and blue, respectively). By performing a profile line across this region (Figure 2c), we can quantify the phase shift, which is P(z) = 2.0 ± 0.1. Now we can calculate the corresponding displacement along the g⃗ = (11̅1) direction, using eq 1. We obtain a value of uz = 0.32 [111̅ ], which is about 1/3[11̅1]. This value is in good agreement to the projection of the Burgers vector along the axial direction which would occur by the insertion of one edge dislocation in the core−shell system. Such plastic relaxation along the axial direction was also predicted and observed in reference15 where a Ge/Si core− shell system was studied. By using in situ high-resolution TEM analysis they determine that extra (111) half-planes are induced by perfect dislocations that glide on {111} planes. However, in our case, we do not have such a kind of dislocations, most likely because of the different growth conditions of our GaAs/Si system, that is, a much lower Si growth temperature. In addition to one contribution to the strain relaxation longitudinal respect to the nanowire axis, the edge dislocations also produce a localized elastic distortion. The latter is correlated with the appearance of a strain field, which our particular analysis outlines. As detailed now, the strain field across a micrograph can be obtained from the phase maps. Figure 2d shows the axial εzz strain map, defined as εzz = ∂uz/∂z. In the same location of the phase change, we observe a tensile region as indicated by the red color code. A profile across the tensile region was taken to quantify the axial strain (Figure 2e), which turns out to be around 4%. For clarity, we have plotted in Figure 2f a scheme of the nanowire geometry, showing the tensile line (in red) crossing the nanowire facet, between the two edge dislocations in the neighboring facets. In order to obtain a global understanding of the localized strain fields observed experimentally, we have simulated the εzz strain map component for the GaAs/Si core−shell system. The stress field induced by a dislocation in the multifaceted nanowire is calculated by FE method, following ref 47. In particular, we have simulated the effects of an edge dislocation loop, lying in the (11̅1) plane at the core−shell interface with
Figure 3. (a) Sketch of the nanowire assuming an edge dislocation loop, lying in a (11̅1) plane at the core−shell interface with Burgers vector b = a/3[11̅1]. (b) Finite element εzz strain simulation map assuming an edge dislocation loop as sketched in (a).
The strain field induced by edge dislocations running through the examined nanowire facet in the GaAs/Si core− shell system obtained from the FE calculations is depicted in Figure 3b. In agreement with the experimental results, we observe the presence of a tensile line (∼4%) crossing the diameter of the nanowire and limited by two of six edge dislocation segments (solid white lines in Figure 3a) composing the closed loop. This suggests that the two edge dislocations observed in the GPA image, see Figure 2d, are the fingerprint of edge dislocations traveling around the nanowire core at the GaAs/Si interface and that the localized tensile strain is induced by a looplike dislocation configuration. Although the geometry employed in the FE simulations is a simplification of the real dislocation microstructure, it allowed us to reproduce the essential features of the strain field observed experimentally and to identify the three-dimensional defect structure. This finding reveals the power of combining HRTEM/GPA with FE simulations. Finally, we discuss an alternative mechanism for strain reduction in nanowires. With this purpose, we consider Si/ GaAs core−shell structures exhibiting polytypism. In polytypic phases, not only the band structure changes but also the lattice constants.50 In principle, a mixture of crystalline phases per se might reduce the occurrence of dislocations. Additionally, if the polytypes exhibit opposite variation in the lattice constant, this might provide a path for dislocation-free strain reduction. We study a core−shell structure in which the GaAs core exhibits a mixture of wurtzite/zinc-blende, rather than being pure zincblende as shown above. Figure 4a shows a high-resolution TEM image, where the intensity contrast between the core and the surface reveal the existence of a Si shell. One can also observe contrast lines perpendicular to the nanowire axis, which correspond to the existence of polytypism in the nanowire, as detailed here below. High-resolution TEM of the square region marked with a blue square in Figure 4a is shown in Figure.4b. We observe an alternation between nanoscale regions of wurtzite and zinc-blende sections. The crystalline structure of the core and the shell are identical, indicating that the crystal structure of the core has been successfully transferred to the Si shell. Crystalline structure transfer of wurtzite was first 1861
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Figure 4. (a) Bright-field TEM image revealing the axial and radial silicon growth on a GaAs core, as well as the presence of the Si crystalline grains on the sidewalls of the core−shell system. (b,c) High-resolution TEM image of the region marked with a blue square in (a) and the corresponding Fourier transform in (c). (e,f) The strain components εzz and εxx in a given region of the wurtzite/zinc-blende core−shell system.
demonstrated in reference51 in the case of GaP-Si core shell nanowires. We have calculated the strain field map along the axial and perpendicular direction, z and x, respectively, taking as a reference the upper silicon wurtzite segment. To achieve this, we have selected the Bragg reflections corresponding to (11̅1)ZB∥(0001)W and (11̅00)W (Figure 4c). Figure 4d,e shows the strain components εzz and εxx in a given region of the wurtzite/zinc-blende core−shell system. For clarity, we have marked with white dashed lines the wurtzite and zincblende segments that were identified in the TEM image in Figure 4b. Compressive lines appear in blue, while tensile appear in red. Interestingly, we find compressive lines (∼2.5%) perpendicular to the growth direction in the region where a thin zinc-blende segment is sandwiched between thicker wurtzite segments. This means the thin zinc-blende section in the Si shell acquires a compression in the axial direction, while the adjacent segment in the core exhibits a compensating axial tension. As for the radial direction, one observes the complementary behavior as compared to the axial direction, the ratio being related to the Poisson coefficient. Indeed, this is precisely what the εxx strain map shows in Figure 4e. In short, axial and radial strain relaxation with nanoscale wurtzite/zincblende stacking in the Si shell is complementary to the one observed in the GaAs core and in each of the crystalline phases. Polytypism turns out to be an effective mechanism for the reduction of strain and appearance of dislocations in mismatched core−shell nanowires. This particular setting can be useful in applications where polytypism is advantageous such as the thermoelectric properties, as recently shown by the Linke’s group.52
In conclusion, controlling and understanding the formation of strain-induced defects is crucial in order for core−shell systems to be used as building blocks in nanodevices. Here we have applied a combination of high-resolution TEM, geometrical phase analysis, and finite element methods to determine and quantify the origin of the lattice distortion in highly lattice mismatched GaAs-Si core−shell nanowire structures. This approach provides a powerful insight into the origin and characteristics of defects such as edge dislocations in these systems. For instance, the three-dimensional FE simulation indicates that the tensile line observed in the twodimensional GPA measurement is the fingerprint for an edge dislocation loop traveling around the nanowire core at the GaAs/Si interface. Finally, our results suggest that mixing crystalline phases along the nanowire could play an important role in strain reduction in mismatched core−shell structures. Understanding the strain engineering and minimizing the number of defect nucleation in the core−shell structures is an important milestone toward the use of highly lattice mismatch core−shell nanowires heterostructures in realistic nanodevices. Even though our approach has been applied to the Si/GaAs system, the results exhibit a general character it can thus be extended to a broad range of semiconductors nanowires. Methods. Nanowire Growth. The nanowires were grown using a DCA P600 MBE machine. The GaAs nanowires were obtained under rotation at 7 rpm at a temperature of 634 °C under a flux of Ga equivalent to a planar growth rate of 0.323 A· s−1 and a V/III beam equivalent pressure ratio of 17. The GaAs nanowire samples were transferred to the plasma enhanced chemical vapor deposition (PECVD) chamber for the subsequent Si growth at 250 °C. The PECVD reactor operated 1862
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Notes
at radio frequency (RF at 70 MHz) power. As precursors gases we used silane (SiH4) (10 W, 15 sccm) and hydrogen (H2) (10 W, 100 sccm). Electron Microscopy. High-resolution images were obtained using a Philips/FEI CM300 transmission electron microscope equipped with a Schottky field emission gun (FEG) operating at 300 kV. Energy dispersive X-ray spectroscopy (EDX) was performed using a FEI Tecnai OSIRIS microscope operated at 200 kV using the Super-X (0.9 rad collection angle) detector and Bruker Esprit software. Geometrical phase analysis53 was used to measure the 2D strain field from each HRTEM image. Finite Element Strain Simulations. The strain field associated to a Frank-type partial dislocation was calculated by finite element (FE) method (by using the software COMSOL Multiphysics). In the numerical simulations, we have assumed as input a nanowire with a hexagonal base characterized by {110} side facets. The dislocation geometry that was considered consists in an edge dislocation loop, lying in a (11̅1) plane at the core−shell interface, with Burgers vector b = a/3[11̅1]. The problem of finding the strain field of a dislocation in the nanowire has been addressed by following the computational approach reported in ref 47, where the combined effect of elastic and plastic relaxation is tackled using elasticity theory suitably solved by FE methods. In particular, the analytical bulk solution of the dislocation strain field48,49,54 is used as initial condition in our simulations. The contribution to the total strain field induced by the free surfaces and by the interfaces is obtained by FE method that allows one to numerically solve the condition of mechanical equilibrium combined to the boundary conditions. This technique allowed us to take into account both the elastic strain field induced by the lattice mismatch f = 0.041 between Si and GaAs, the deformation field produced by the dislocation as well as the influences of the free surfaces. The numerical values of the core radius and the shell thickness have been taken to be 33 and 4 nm, respectively. In addition, isotropic elastic constants were assumed. In particular, we set ESi = 131 GPa, νSi = 0.27 and EGaAs = 120 GPa, νGaAs = 0.23, where ν is Poisson’s ratio and E is the Young modulus of Si and GaAs. The εzz strain map was calculated by integrating εzz along z, that is, the [110] direction, at each (x,y) position in the map. Critical Thickness in Zinc-Blende Core−Shell GaAs/Si Systems. The numerical values for the different parameters used for the model are the following: for the GaAs core (Si shell) we adopt a lattice parameter of 0.56533 nm (0.54310 nm); for the zinc blende elastic stiffness coefficients we use c11 = 119(160)GPa, c12 = 54(58)GPa, and c44 = 60(80)GPa. Finally, the stacking fault energy per unit area is γ = 45(55)mJ/ m2.
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The authors declare no competing financial interest.
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ACKNOWLEDGMENTS S.C.B. acknowledges funding from the Marie Heim-Vögtlin program project PMPDP2-139702. A.F.M. is grateful for funding through the ERC Starting Grant UpCon, ERANETRus “InCoSiN” and FP7 ITN “Nanoembrance”. N.W. acknowledges support from SNF.
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ASSOCIATED CONTENT
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Additional figures and information. This material is available free of charge via the Internet at http://pubs.acs.org.
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REFERENCES
AUTHOR INFORMATION
Corresponding Author
*E-mail: anna.fontcuberta-morral@epfl.ch. Present Address ⊥
Unité Matériaux et Transformations (UMET), Université Lille 1, 59655 Villeneuve d’Ascq, France. 1863
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