ZnS Superlatticeâ Nanostructures by X

Article pubs.acs.org/JPCC

Routes to Probe Strain in “ZnO/ZnS Superlattice” Nanostructures by X‑ray Diffraction Qiong Gao, Jing Wen, Xin Liu, Lili Wu, Hong Gao,* and Xitian Zhang* Key Laboratory for Photonic and Electronic Bandgap Materials, Ministry of Education, School of Physics and Electronic Engineering, Harbin Normal University, Harbin 150025, P. R. China ABSTRACT: “ZnO/ZnS superlattice” nanostructures were synthesized via a chemical vapor deposition process. The lattice mismatch between ZnO and ZnS induced defects within the thin superlattice as well as deformations at the interface (junction), which could result in the appearance of strain. X-ray diffraction (XRD) is sensitive to very small changes of lattice parameters. The lattice constants of ZnO and ZnS for the “ZnO/ZnS superlattice” nanostructures and strains were obtained, respectively, on the basis of the XRD pattern. These data are consistent with the observation of high-resolution transmission electron microscopy images.

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residual strains in the films and surface layers. The XRD measurement procedures are phase-specific, noncontact, and nondestructive, which can determine the full strain/stress tensor of each crystalline phase existing in the specimen. Furthermore, much relevant information, such as the strain gradient, crystallographic texture, the size of diffracting domains, and the content of crystalline defects,26 can be obtained based on the diffraction lines. The traditional residual strain measurement by XRD is the sin2 ψ method.27 The strain tensor can be obtained from the shift of diffraction lines for some selected ψ angles. This method is suitable for the random distributed polycrystalline samples in which the biaxial strain model has been used. The biaxial strain model28 has been widely used to study the in-plane strains at the film/substrate and heterostructures interfaces.29 It can be decomposed into a sum of a uniaxial and a hydrostatic strain component, both of them being important tunable parameters in the strain-induced band gap engineering and having significant effects on the band structures.30−33 For the textured or single crystalline-like films, the needed diffraction peaks are difficult to observe in the standard Bragg−Brentano geometry, so many other modified sin2 ψ methods and the grazing-incidence XRD techniques have been developed to overcome these problems.34−37 If the triaxial strains or the strain gradients along the surface normal present in the samples, the relationship between the strain along the diffraction direction εφψ and sin2 ψ will violate the linear variation, and the biaxial strain model may fail to describe these situations, such as the observed oscillatory εφψ−sin2 ψ curve caused by the crystallographic texture and the curvature-

INTRODUCTION Recently, the quasi one-dimensional heterostructures,1,2 core/ shell nanostructures,3,4 and superlattice structures5 with a tunable dimension and structure complexity are regarded as building blocks for future nanoscale devices. These structures have the possibility of tuning their chemical, electronic, and optical properties at a wider range6−9 and performing diverse functionalities within a single nanostructure.10,11 They have a wide range of applications including flat panel displays, sensors, lasers, transducers, and photovoltaic devices.12−16 Significant progress has been made in the synthesis of various axial,6 radial,17 and branched nanoheterostructures.18 Among II−VI semiconductors, ZnO and ZnS have drawn immense interest because of their potential use in numerous electronic and optical devices. The electronic structures and optical properties of these ZnS/ZnO nanoheterostructures exhibit some amazing properties.19,20 The presence of residual strains is a common phenomenon in the majority of multilayer thin film structures and heterostructures, which can influence the physical properties of these structures significantly.21−24 In the nanoheterostructures, it is well-known that the intrinsic strains termed as interlayer are mainly caused by the mismatch of the lattice parameters of two different materials at the contacts, which are similar to the characteristics of thin film structures at the film/ substrate interface. Actually, many experimental results show that the mismatch strain and the strain relaxation are the main factors to induce the formation of nanoheterostructures and nanosuperlattices.25,6 Therefore, finding out the sources of the residual strains in the nanoheterostructures and measuring their magnitudes are important research topics in this area. Among the many methods available for the strain analysis, X-ray diffraction analysis (XRD) is widely used to determine the © 2013 American Chemical Society

Received: January 9, 2013 Revised: June 12, 2013 Published: June 17, 2013 14247

dx.doi.org/10.1021/jp4002737 | J. Phys. Chem. C 2013, 117, 14247−14253

The Journal of Physical Chemistry C

Article

Figure 1. (a) SEM image for the “ZnO/ZnS superlattice” nanostructures; scale bar: 2 μm. (b) High magnification SEM image; scale bar: 400 nm. Inset shows a 3-fold symmetry structure; scale bar: 200 nm.

dependent εφψ−sin2 ψ curve resulting from the strain gradients normal to the surface. Many mathematical analysis methods have been developed to quantify and classify these inhomogeneous strains within the sample.27,38,39 For a thorough review of strain/stress analysis by XRD, we refer to the works by I. C. Noyan et al.40 and U. Welzel et al.41 In this paper, the “ZnO/ZnS superlattice” nanostructures were successfully synthesized for the first time. Combined with high-resolution transmission electron microscopy (HRTEM) data, the lattice strain in the “ZnO/ZnS superlattice” nanostructures was investigated by XRD. In this nanoheterostructure multilayer system, the thickness of different ZnO or ZnS layers is not a constant, so the residual strains at different interfaces between ZnO and ZnS are not uniform, which results in the inhomogeneous strain distributions in the sample. We employ a triaxial strain model to quantify the averaged in-plane and axial strains within the diffraction volume. An artificial triclinic distortion model is introduced to simulate the XRD data. The simulated pattern is consistent with the experimental results.

tendency to curl. Figure 1b is a magnified SEM image of the nanostructures, revealing that the three blades intersect at a common axis along their entire length. The angle between the two blades is ∼120°. The cross-section of the common axis for the nanostructures is an equilateral triangle. The blades are decorated by a large number of branch architectures. The branches have a length of about 300−500 nm and taper toward the tip. The composition of the nanostructures was first examined by using EDX attached to the SEM. The EDS spectrum demonstrates the existence of elements Zn, O, and S (not shown). In the experiment, straight nanostructures could also be synthesized (not shown), when the molar ratio of ZnO and ZnS powders was changed into 1:1. The experimental results indicate that the molar ratio of ZnO and ZnS powders determines the observed morphology. Recently, there are many reports about controlled fabrication by changing reaction conditions. For example, the shapes of the In2O3 nanospirals were controlled by the vapor concentrations within the system;42 the wall thickness of nanotubes was tuned by simply modifying the reaction time; 43 and the size of SnO 2 nanocrystals was modified by changing reaction temperature.44 XRD is a primary technique to probe the relationships among structure, composition, and strain. XRD pattern of the as-synthesized nanostructures is shown in Figure 2a, which contains two sets of diffraction peaks. They are indexed as wurtzite ZnO (JCPDS: 80-0074) and wurtzite ZnS (JCPDS: 75-1547), respectively. No impurities were detected. However, it should be noted that all peaks appear to have a slight shift (about ±0.1°) and obvious broadening in comparison with the standard pattern, revealing that there is strain in the lattice. The typical three strong peaks for (21̅1̅0), (0002), and (21̅1̅3) of ZnO and ZnS are enlarged, as shown in Figure 2b. The fwhm’s (full width half-maximum) of (21̅1̅0) and (21̅1̅3) peaks for ZnS are 0.5° and 0.6°, respectively. However, the (0002) peak clearly occurs to split. The fwhm’s of (21̅1̅0), (0002), and (21̅1̅3) peaks for ZnO are 0.4°, 0.5°, and 0.5°, respectively. These fwhm’s are much larger than those (0.2°) for the pure ZnO nanostructure. On the basis of the above data gathered, their mechanism of broadening and shifting for the XRD peaks could become an interesting issue. Hence, (21̅1̅0), (0002), and (21̅1̅3) peaks of ZnO and ZnS were decomposed into two peaks, respectively, as shown in Figure 2b. There are two sets of diffraction peaks in the XRD patterns for ZnO and ZnS, respectively. One (labeled by the blue curve) of them is located at the standard peak position, while another set (labeled by the green curve) for ZnO deviates by about −0.2° from the standard peak position and for ZnS deviates by about 0.2°.

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EXPERIMENTAL METHODS The “ZnO/ZnS superlattice” nanostructures were synthesized by a thermal evaporation method. The mixture (molar ratio: 4:1) of the ZnO (analytically pure) and ZnS (fluorescently pure) powders was put into one end of an alumina boat. The Au thin film with a thickness of 2 nm was coated on Si(100) substrates by sputtering and then placed downstream of the precursor. Prior to heating, high-purity Ar (99.995%) was introduced into the tube with a constant flowing rate of 150 sccm as carrier gas. The furnace was heated to 1250 °C and maintained for about 30 min. Finally, the furnace was naturally cooled down. The as-synthesized products were characterized by field emission scanning electron microscopy (FE-SEM S4800 Hitachi Japan), HRTEM (Philips Tecnai 20), and energydispersive X-ray spectroscopy (EDS) equipped in the TEM. Their crystal structure was determined by powder XRD (Japan D/max-2600/pc), using the Cu Kα radiation of wavelength λ = 1.5418 Å. The step and integral time is 0.02° and 5 s, respectively.

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RESULTS AND DISCUSSION The general morphologies of the as-synthesized nanostructures are shown in Figure 1. As can be seen from the lowmagnification SEM image (Figure 1a), a dense carpet of nanostructures, having a typical length of tens of micrometers, covers the substrate. Some of the nanostructures have a natural 14248



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[211̅ 0̅ ] zone axis. The spacing between the adjacent lattice fringes at different areas is measured to be about 0.26 and 0.31 nm, respectively. The former belongs to the d-spacing of the (0002) planes for ZnO. The latter belongs to ZnS. From the HRTEM image, the quasi one-dimensional nanostructure is composed of alternating ZnO and ZnS along its length or [0001] growth direction, which is called “ZnO/ZnS superlattice” nanostructures, although the lattice fringes are not very clear due to the existence of dislocations and other defects. The relationship between the two nanostructures is (0001)ZnO// (0001)ZnS. Figure 3b shows a corresponding fast Fourier transform image. To study the atomic composition of the “ZnO/ZnS superlattice” nanostructures, an EDS line scan was conducted. Figure 3c shows the EDS line profiles of the “ZnO/ ZnS superlattice” nanostructures along their growth direction. The peak of element O and the valley of element S seem to appear at the same position, further confirming that the ZnO and ZnS alternatively grow along the [0001] direction. However, the thickness of each segment ZnO or ZnS is not uniform. It is estimated to be in the range of about 5−15 nm. The thickness is classified into two kinds from the statistical perspective: a thin layer (a few nanometers) and a so-called thick layer (larger than 10 nm). We conclude that (i) the periodicity for the “ZnO/ZnS superlattice” nanostructures is not regular; (ii) the shifting and broadening of the XRD peaks could be attributed to the lattice strain within the nanostructures; and (iii) the defects inside the nanostructure and dislocations at the interface could be mainly due to the lattice mismatch between ZnO and ZnS. To better investigate the nature of the defects here, the HRTEM and the corresponding Fourier transform images are further analyzed. The resultant lattice fringe images of Figure 3d and 3e, which are obtained by only inversely Fourier transforming the (0002)/(0002̅) and (011̅0)/(01̅10) pairs of diffraction spots in Figure 3b, respectively, reveal that (i) the (0002) planes are perfect except the presence of a few edge dislocations and that (ii) the (011̅0) planes show distortion or discontinuity. In special, the area between the two yellow dashed lines, which covers the heterojunction of ZnS/ZnO, shows a lot of defects. The a-axis lattice constant is 0.325 nm for wurtzite ZnO (JCPDS: 80-0074) and 0.384 nm for wurtzite ZnS (JCPDS: 75-1547), which results in a lattice mismatch of 14.9%. In such a case, the lattice mismatch between ZnO and ZnS could result in many dangling bonds or dislocations at the interface. A possible schematic model is constructed by using the Materials Studio software for (21̅1̅0) of the “ZnO/ZnS superlattices”, as shown in Figure 3f. As shown in Figure 2, the splitting of the three strong diffraction peaks for ZnO and ZnS indicates that the values of strains in different interfaces between ZnO and ZnS are different, which result in the inhomogeneous strain distributions in the sample. It is obvious from the morphology of the materials that the biaxial and the uniaxial tension/compression along the [0001] direction are the primary two types of deformation. The structures still maintain hexagonal symmetry in the epitaxial intergrowth direction because the 3-fold symmetry is conserved. A simple model can be assumed in which the substance is constituted by ZnO and ZnS with different thicknesses. It is possible that the differences of the thicknesses of the ZnO and ZnS layers could lead to the bimodal distribution of lattice constants a and c for the sample. The peak splitting could be attributed to two types of reflections that come from the nearly undistorted thick layers

Figure 2. (a) XRD pattern of the “ZnO/ZnS superlattice” nanostructures (up part) and standard peaks (down part) of ZnO and ZnS. (b) The three strong peaks for ZnO and ZnS are fitted, respectively. Blue curves represent standard ZnO and ZnS peak positions. Green curves represent another set of ZnO and ZnS diffraction peaks deviated from the standard peak position due to the strain in the superlattice. (c) The simulated and magnified XRD patterns of diffraction peaks around main wurtzite triplets of ZnO and ZnS.

For getting the detailed structural information, the assynthesized nanostructures were characterized by HRTEM and EDS. Figure 3a shows a typical HRTEM image taken along the 14249



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Figure 3. (a) Typical HRTEM image of the “ZnO/ZnS superlattice” nanostructures; scale bar: 5 nm. (b) The corresponding fast Fourier transformation image. (c) The EDS line profiles of the “ZnO/ZnS superlattice” nanostructures along their growth direction. (d) (e) The lattice fringe images obtained by only inversely Fourier transforming the (0002)/(0002̅) and (011̅0)/(01̅10) pairs of diffraction spots in part b, respectively. (f) The possible atomic simulated models for the “ZnO/ZnS superlattices”.

Under the assumption that the deformations make the space symmetry of the structure unchanged, the in-plane and axial strains can be expresses as a − a0 εxx̅ = εyy̅ = a0 (1)

and strongly distorted thin layers, which could not be observed for the homogeneous system in terms of layer thicknesses. On the basis of the HRTEM observation, it is found that all of the observed layers are very thin, with the thicknesses in the range of 5−15 nm. We deduce that the distortion at the interface between the two materials could lead to the local overall distortion in the thin layers. It is generally accepted that the local microstrains could broaden the diffraction profiles from the statistical perspective. The microstrains in the thin layers exhibit some macrostrain properties in some special directions due to the lattice mismatch and the alternative thin layered structure of ZnO and ZnS. The resultant effect is that some macrostresses act on them. On the basis of the above analysis, we employ a triaxial strain model to give a quantitative description of the averaged strains existing in the distorted thin layers with respect to the nearly undistorted thick layers for the same sample.

εzz̅ =

c − c0 c0

(2)

where a, c and a0, c0 are the lattice constants of the thin and thick layers, respectively. There is no traditional proportional relationship between εx̅ x and εz̅ z because they are the averaged values of the biaxial and uniaxial strains existing in the different layers. The calculated results based on the values of interplanar distance d100 and d002 and the hkl-dependent strains are listed in Tables 1 and 2, respectively. Positive and negative values of strains represent tensile and compressive strains, respectively. We can conclude that: (i) ZnS is under the compressive strain 14250



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Table 1. Calculated Cell Parameters and Triaxial Strain Values of ZnO and ZnS sample ZnO ZnS

thin layer thick layer thin layer thick layer

a (Å)

c (Å)

εxx (%)

εzz (%)

3.27 3.25 3.79 3.82

5.25 5.22 6.23 6.28

0.62

0.57

−0.79

−0.80

Table 2. Calculated Strain (ε) in the Direction Parallel to the Normal to {HKIL} Planes for ZnO and ZnS HKIL

εZnO

εZnS

[21̅1̅0] [0002] [21̅1̅3]

0.25 0.40 0.24

−0.46 −0.38 −0.31

⎛π ⎞ cos⎜ + Δα⎟ = −Δα ⎝2 ⎠

(5)

⎛π ⎞ Δβ 2 sin⎜ + Δβ ⎟ = 1 − ⎝2 ⎠ 2

(6)

⎛π ⎞ cos⎜ + Δβ ⎟ = −Δβ ⎝2 ⎠

(7)

⎛2 ⎞ 1 3 cos⎜ π + Δγ ⎟ = − − Δγ ⎝3 ⎠ 2 2

(8)

⎛2 ⎞ Δγ 3 sin⎜ π + Δγ ⎟ = − ⎝3 ⎠ 2 2

(9)

So, eq 1 can be rewritten as 1 2 dHKL

and (ii) ZnO is under the tensile strain. Figure 4 is a schematic stress diagram of the local “ZnO/ZnS superlattice” nanostructures. The blue and orange arrows indicate the stress direction of ZnS and ZnO, respectively. For a more accurate quantitative analysis of the XRD pattern of the strained multilayer system, we introduce an artificial triclinic distortion model to quantify the ranges of variation for the in-plane and axial strains at the different interfaces of the two materials. The inverse square of the interlayer spacing can be written as 1 1 = 2 [H2b2c 2 sin 2 α + K 2a 2c 2 sin 2 β 2 dHKL V 2 2 2

2

2 ⎡ ⎛1 ⎛ 3 ⎞ Δγ ⎞ 3 2 +Lab⎜ − Δγ ⎟ ⎟ + 2KLa bc ⎢Δβ ⎜ + ⎝ 2 ⎠ 2 ⎠ 2 ⎣ ⎝2 2 2 2

⎤ ⎡ ⎛1 ⎤ ⎞ 3 + Δα ⎥ + 2LHab2c ⎢Δα⎜ + Δγ ⎟ + Δβ ⎥ ⎠ 2 ⎦ ⎣ ⎝2 ⎦ ⎛ ⎞⎤ 1 3 + 2HKabc 2⎜ΔαΔβ + + Δγ ⎟⎥ ⎝ ⎠⎥⎦ 2 2

+ L a b sin γ + 2KLa bc(cos β cos γ − cos α)

Δα = −[8 3 m2 − 4 3 m1m3 − 2 3 m2m3 +

+ 2LHab2c(cos γ cos α − cos β) + 2HKabc 2

/[3( −4 + m32)]

(3)

where V is the cell volume. a, b, c, α, β, and γ are cell parameters. H, K, and L are Miler indexes. When an infinitesimal deformation in the hexagonal structure occurs, the above trigonometric function could be written as sin(π/2 + Δα), cos(π/2 + Δα), sin(π/2 + Δβ), cos(π/2 + Δβ), sin(π2/3 + Δγ), and cos(π2/3 + Δγ). Their first-order Taylor series expansion can be written as ⎛π ⎞ Δα 2 sin⎜ + Δα⎟ = 1 − ⎝2 ⎠ 2

(10)

Solving eq 10 by ignoring the high-order terms of Δα, Δβ, and Δγ, we can obtain

2

(cos α cos β − cos γ )]

2 2 ⎡ ⎛ Δβ 2 ⎞ Δα 2 ⎞ 1 ⎢ 2 2 2⎛ 2 2 2 = 2 H b c ⎜1 − ⎟ ⎟ + K a c ⎜1 − 2 ⎠ 2 ⎠ ⎝ V ⎢⎣ ⎝

Δβ = −[8 3 m1 − 2 3 m1m3 − 4 3 m2m3 +

3 m2m32] (12)

m 1 + 3 3 3

(13)

V

(

d010c 1 −

(4)

(11)

/[3( −4 + m32)] Δγ = −

a=

3 m1m32]

β2 2

)

(14)

Figure 4. Schematic stress diagram of the local “ZnO/ZnS superlattice” nanostructures. Yellow arrows represent the ZnO lattice to be under the tensile status. Blue arrows represent the ZnS lattice to be under the compressive status. 14251



b=

V

(

d100c 1 −

c=

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α2 2

)

d010

(15)

V

2d002

(

Province (ZD201112), and Institution of Higher Education, Doctoral Fund Jointly Funded Project (20112329110001), and the Graduate Students’ Scientific Research Innovation Project of Heilongjiang Province (YJSCX2012-186HLJ).

(

d100 1 −

3 2 α2 2

−

γ 2

■

1/2

)

1/2

β2 2

1/2

) (1 − )

(1) Wu, D. P.; Jiang, Y.; Yuan, Y. F.; Wu, J. S.; Jiang, K. ZnO−ZnS Heterostructures with Enhanced Optical and Photocatalytic Properties. J. Nanopart. Res. 2011, 13, 2875−2886. (2) Cheng, C. W.; Liu, B.; Yang, H. Y.; Zhou, W. W.; Sun, L.; Chen, R.; Yu, S. F.; Zhan, J. X.; Gong, H.; Sun, H. D.; Fan, H. J. Hierarchical Assembly of ZnO Nanostructures on SnO2 Backbone Nanowires: Low-Temperature Hydrothermal Preparation and Optical Properties. ACS Nano 2009, 3, 3069−3076. (3) Cao, F. F.; Deng, J. W.; Xin, S.; Ji, H. X.; Schmidt, O. G.; Wan, L. J.; Guo, Y. G. Cu-Si Nanocable Arrays as High-Rate Anode Materials for Lithium-Ion Batteries. Adv. Mater. 2011, 23, 4415−4420. (4) Wang, K.; Chen, J. J.; Zeng, Z. M.; Tarr, J.; Zhou, W. L.; Zhang, Y.; Yan, Y. F.; Jiang, C. S.; Pern, J.; Mascarenhas, A. Synthesis and Photovoltaic Effect of Vertically Aligned ZnO/ZnS Core/Shell Nanowire Arrays. Appl. Phys. Lett. 2010, 96, 123105(1−3). (5) Sun, Y.; Cui, H.; Gong, L.; Chen, J.; She, J. C.; Ma, Y. M.; Shen, P. K.; Wang, C. X. Carbon-in-Al4C3 Nanowire Superstructures for Field Emitters. ACS Nano 2011, 5, 932−941. (6) Robinson, R. D.; Sadtler, B.; Demchenko, D. O.; Erdonmez, C. K.; Wang, L. W.; Alivisatos, A. P. Spontaneous Superlattice Formation in Nanorods Through Partial Cation Exchange. Science 2007, 317, 355−358. (7) Fang, X. S.; Bando, Y.; Gautam, U. K.; Zhai, T. Y.; Gradecak, S.; Golberg, D. Heterostructures and Superlattices in One-Dimensional Nanoscale Semiconductors. J. Mater. Chem. 2009, 19, 5683−5689. (8) Jiang, Z.; Qing, Q.; Xie, P.; Gao, R. X.; Lieber, C. M. Kinked p-n Junction Nanowire Probes for High Spatial Resolution Sensing and Intracellular Recording. Nano Lett. 2012, 12, 1711−1716. (9) Kempa, T. J.; Cahoon, J. F.; Kim, S. K.; Day, R. W.; Bell, D. C.; Park, H. G.; Lieber, C. M. Coaxial Multishell Nanowires with HighQuality Electronic Interfaces and Tunable Optical Cavities for Ultrathin Photovoltaics. Proc. Natl. Acad. Sci. U.S.A. 2012, 109, 1407−1412. (10) He, R. R.; Law, M.; Fan, R.; Kim, F.; Yang, P. D. Functional Bimorph Composite Nanotapes. Nano Lett. 2002, 2, 1109−1112. (11) Law, M.; Zhang, X. F.; Yu, R.; Kuykendall, T.; Yang, P. D. Thermally Driven Interfacial Dynamics of Metal/Oxide Bilayer Nanoribbons. Small 2005, 1, 858−865. (12) Fang, X. S.; Wu, L. M.; Hu, L. F. ZnS Nanostructure Arrays: A Developing Material Star. Adv. Mater. 2011, 23, 585−598. (13) Fang, X. S.; Zhai, T. Y.; Gautam, U. K.; Li, L.; Wu, L. M.; Bando, Y.; Golberg, D. ZnS Nanostructures: From Synthesis to Applications. Prog. Mater. Sci. 2011, 56, 175−287. (14) Gullapalli, H.; Vemuru, V. S. M.; Kumar, A.; Botello-Mendez, A.; Vajtai, R.; Terrones, M.; Nagarajaiah, S.; Ajayan, P. M. Flexible Piezoelectric ZnO-Paper Nanocomposite Strain Sensor. Small 2010, 6, 1641−1646. (15) Zhou, W. B.; Baneyx, F. Aqueous, Protein-Driven Synthesis of Transition Metal-Doped ZnS Immuno-Quantum Dots. ACS Nano 2011, 5, 8013−8018. (16) Fang, X. S.; Bando, Y.; Liao, M. Y.; Gautam, U. K.; Zhi, C. Y.; Dierre, B.; Liu, B. D.; Zhai, T. Y.; Sekiguchi, T.; Koide, Y. SingleCrystalline ZnS Nanobelts as Ultraviolet-Light Sensors. Adv. Mater. 2009, 21, 2034−2039. (17) Sun, X. H.; Sham, T. K.; Rosenberg, R. A.; Shenoy, G. K. OneDimensional Silicon-Cadmium Selenide Heterostructures. J. Phys. Chem. C 2007, 111, 8475−8482. (18) Gao, J.; Lebedev, O. I.; Turner, S.; Li, Y. F.; Lu, Y. H.; Feng, Y. P.; Boullay, P.; Prellier, W.; Tendeloo, G. V.; Wu, T. Phase Selection Enabled Formation of Abrupt Axial Heterojunctions in Branched Oxide Nanowires. Nano Lett. 2012, 12, 275−280.

(16)

where ⎛ 1 1 1 ⎞ m1 = ⎜ 2 − − 2 ⎟d002d100 2 4d002 d100 ⎠ ⎝ d101

(17)

⎛ 1 1 1 ⎞ ⎟d002d010 m2 = ⎜ 2 − − 2 2 4d002 d010 ⎠ ⎝ d011

(18)

⎛ 1 1 1 ⎞ m3 = ⎜ 2 − 2 − 2 ⎟d010d100 d010 d100 ⎠ ⎝ d110

(19)

⎛ 2π ⎞ V = abc sin⎜ + Δγ ⎟ ⎝ 3 ⎠ ⎤1/2 ⎡ ⎞ 2 2⎛ π ⎥ ⎢1 − sec ⎜ + Δγ ⎟sin Δα ⎝6 ⎠ ⎥ ⎢ ⎥ ⎢ − sin 2 Δβ tan 2⎛⎜ π + Δγ ⎞⎟− ⎥ ⎢ ⎝6 ⎠ ⎥ ⎢ ⎛π ⎞ ⎛π ⎞⎥ ⎢ ⎜ ⎟sin Δα sin Δβ tan⎜ ⎟ 2 sec γ γ + Δ + Δ ⎢ ⎝6 ⎠ ⎝6 ⎠⎥ ⎥ ⎢ 2 ⎦ ⎣ − sin Δβ

(20)

The lattice parameters of the triclinic distortion model can be calculated by substituting the values of dHKL obtained from the XRD data into the equations above. As shown in Figure 2c, the simulated XRD pattern based on the triclinic model is consistent with the experimental results if we require that the averaged values of εxx (εyy) and εzz in the thin and thick layers for ZnO varied no more than 0.42% and 0.46% and that for ZnS varied no more than 0.60% and 0.20%, which can give us an approximate result to describe the range of the values for the strains in different layers.

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CONCLUSIONS A novel layered “ZnO/ZnS superlattice” nanostructure was synthesized. XRD spectroscopy is a suitable technique that probes the strain in any semiconductor nanostructures, combined with fundamental theory calculation. The stains in the “ZnO/ZnS superlattice” nanostructure are qualitatively and quantitatively discussed, respectively, combined with TEM technology.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*Tel.: 86-451-8806-0629. Fax: 86-451-8806-0629. E-mail: [email protected]; [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was partially supported by the Natural Science Foundation of China (No. 51172058 and 11074060), the Key Project of Natural Science Foundation of Heilongjiang 14252



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