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Determination of Polarization-Fields Across Polytype Interfaces in InAs Nanopillars Luying Li,* Zhaofeng Gan, Martha R. McCartney, Hanshuang Liang, Hongbin Yu, Wan-Jian Yin, Yanfa Yan, Yihua Gao, Jianbo Wang,* and David J. Smith* Heterocrystalline polytype structures have been intensively studied in recent years as novel types of superlattices. These polytype superlattices consist of chemically identical but structurally different materials, which match well at their interfaces.[1] Thus, the common problem of compositional changes associated with interfaces composed of chemically inequivalent materials can be avoided. The basic polytype structures for III–V and II–VI compounds are zincblende (ZB) with cubic stacking in the [111] direction, and wurtzite (WZ) with hexagonal stacking in the [0001] direction. The controlled growth of polytypic and twinning superlattices, which is rare in related bulk crystals, has been realized in single nanowires (NWs) by varying the NW diameter and growth temperature,[2] and by the addition of dopants.[3,4] The polytype superlattices would act as barriers for electron transport, leading to charge accumulation in certain regions due either to band offsets at the polytype interfaces,[5,6] or spontaneous polarization in the polytype regions with asymmetrical structures.[7,8] In this study, charge
Dr. L. Li, Prof. Y. Gao Center for Nanoscale Characterization and Devices Wuhan National Laboratory for Optoelectronics Huazhong University of Science and Technology Wuhan, 430074, China E-mail: [email protected] Dr. L. Li, Z. Gan, Prof. M. R. McCartney, Prof. D. J. Smith Department of Physics Arizona State University Tempe, Arizona, 85287–1504, USA E-mail: [email protected] H. Liang, Prof. H. Yu School of Electrical Computer, and Energy Engineering Arizona State University Tempe, Arizona, 85287–5706, USA Dr. W.-J. Yin, Prof. Y. Yan Department of Physics and Astronomy The University of Toledo Toledo, Ohio, 43606, USA Prof. Y. Gao School of Physics Huazhong University of Science and Technology Wuhan, 430074, China Prof. J. Wang School of Physics and Technology Center for Electron Microscopy and MOE Key Laboratory of Artificial Micro- and Nano-Structures Wuhan University Wuhan, 430072, China E-mail: [email protected]
DOI: 10.1002/adma.201304021
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distribution due to polarization fields within polytype superlattices is demonstrated at the nanometer scale using off-axis electron holography, and the determination of local spontaneous polarization in WZ crystals at atomic resolution is realized based on probe-corrected high-angle annular-dark-field (HAADF) images. Figure 1a is a transmission electron micrograph showing an InAs nanopillar, where the parallel dark lines indicate changes of stacking order along the growth direction. The area in the ¯ blue box in Figure 1a, which is projected along the 110 zone axis, is shown at higher magnification in Figure 1b, and the layer stacking is visible along the direction. A region with greater stacking disorder is clearly visible, and labeled here as the ‘polytype’ region. Conversely, the region labeled as ZB does not show any structural change along the stacking direction. The interfaces are indicated here by yellow dashed lines. The same region of the nanopillar shown in Figure 1b, was then characterized using off-axis electron holography. The reconstructed phase image of a typical hologram is shown in Figure 1c. The region outlined in the black box was used for phase-shift profiling, and the results are shown in Figure 1d. The thickness profile of the same region (red triangles) is flat across the entire region, but the phase shifts (blue disks) are higher in the polytype region relative to the ZB region. This difference could be considered as an indication of electrons and holes being distributed differently in the separate regions since there is no obvious indication of diffraction contrast in the image. Moreover, the phase shifts are linearly decreasing in the ZB region and show fluctuations within the polytype region, which could be considered as equivalent to multiple WZ quantum wells embedded in a ZB matrix. While the type-II band alignment between WZ and ZB polytype structures might lead to selective confinement of electrons to ZB-rich regions and holes to WZ-rich regions[9] (the conduction band offset at the WZ/ZB interface is ΔEc = 86 meV for bulk InAs, and the valence band offset is ΔEv = 46 meV),[10] spontaneous polarization in the WZ region could result in sawtooth-like potentials across the WZ/ZB polytype superlattices, which are linearly increasing in WZ regions and decreasing in ZB regions.[7,11] Thus, the phase-shift profile obtained here is likely to be the collective result of band offsets and spontaneous polarization. The phase profile can be converted to potential using the expression: φ = CE (VMIP + VSP) t, where CE = 0.00728 rad (V nm)−1 for an accelerating voltage of 200 kV, φ is the phase shift, t is the projected thickness, VMIP is the mean inner potential (MIP) of the material, and VSP is the electrostatic potential related to the spontaneous polarization. The thicknesses can be obtained from the corresponding reconstructed amplitude image assuming an inelastic mean free path (MFP) of 57 nm
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ensure supercell periodicity.[7,11] Assuming EWZ = –EZB, and taking εr = 15 for InAs,[16] the absolute value of spontaneous polarization present in the WZ region is calculated to be psp = 0.0166 ± 0.0021 C m−2, where the error Δpsp is estimated through error propagation from the errors in potential measurement ΔV = ± 0.103 V and the pixel size Δz = ± 0.257 nm. Pure ZB InAs NWs and WZ NWs with small ZB segments are reported to have significantly distinct subthreshold characteristics, which are attributed to spontaneous polarization charges at the WZ/ZB interfaces, so that a polarization charge density of ≥1013 cm−2 is obtained.[8] The polarization charge density σ can be converted to spontaneous polarization Psp using: Psp = –σ. Thus, the spontaneous polarization for WZ-InAs should be ≥ 0.0160 C m−2, which is close to the measured holography value as well as being comparable to other hexagonal materials.[17] The spontaneous polarization is related to structures without any inversion center, and dipoles are formed by displacements of charged ions inside the crystal unit cell. The Figure 1. a) TEM image of InAs nanopillar, where the parallel dark lines indicate the existence of stacking disorder along the growth direction; b) HREM image of the region framed in characterization of spontaneous polariza¯ ] direction. The ZB and polytype regions are labeled, and the yellow (a) projected along the [ 110 tion in ferroelectric thin films was reported dashed lines show the boundaries of these regions; c) Phase image of the same region shown using the negative spherical-aberration in (b) as reconstructed from electron hologram. The area used for phase shift and thickness (Cs) imaging technique in an aberrationline profiles are indicated by the black box; d) While the thickness profile (red triangles) is flat corrected TEM.[18] Through careful measureacross the entire region, the phase shifts (blue disks) are higher with some fluctuations in the ment of the displacements of charged ions, polytype region, decreasing linearly in the ZB region. The blue line is a linear fit to phase shifts 180° domain walls that intersected regions in the ZB region. of reversed spontaneous polarizations were verified, and the variations of spontaneous polarization along the interface normal were also obtained.[18,19] for InAs.[12] The MFP for InAs is calculated through linear Similar studies on ferroelectric heterointerfaces and nanocrysextrapolation of the experimental values for AlAs (77 nm) and tals,[20–23] as well as transition-metal oxide interfaces,[24–26] have GaAs (67 nm) since the MFP values should be linearly propor[ 13 ] been carried out by scanning transmission electron microscopy tional to the average atomic numbers. Only VSP would con(STEM) using probe-corrected HAADF imaging. The aberratribute to the electrostatic field as a slope of the electrostatic tion-corrected HREM with negative Cs is sensitive to elements potential profile since the MIP is constant for any specific strucof low atomic number, whereas probe-corrected STEM HAADF ture. Thus, EZB can be calculated based on a linear fit (blue line) imaging requires no post-processing and is applicable to comof the experimental phase shift data, as shown in Figure 1d: paratively thick specimens. In our sample, all of the elements EZB = 0.0626 V nm−1. are easily visible in HAADF; the WZ/ZB heterocrystalline According to the Supercell approach, the spontaneous polarisuperlattices exist only in InAs nanostructures as opposed to zation of the WZ structure could be obtained using:[14,15] bulk crystals, and the projected thicknesses are normally of sev∂ VWZ ∂ VZB eral tens of nanometers (the thickness of the region studied by − ps p = − g 0g r E = − g 0g r (1) ∂z ∂z electron holography is ∼70 nm), which is too thick for atomic where E WZ = − ∂ V∂zWZ and E ZB = − ∂ V∂zZB correspond to the elecresolution with HREM. Thus, probe-corrected STEM HAADF tric fields in the WZ and ZB regions, respectively. For our speimaging is the better choice here for observation. cific case, only the electric field in the ZB region is obtainable Figure 2a is a probe-corrected STEM HAADF image of a since the existing WZ regions are not wide enough to allow region including ZB structures as well as stacking disorder reliable measurements of the corresponding electric field. Howalong the growth direction within the same nanopillar ever, the non-zero spontaneous polarization in the WZ regions used for electron holography characterization. The shear distorwould lead to opposite polarization charges with equal charge tions in the image induced by imperfections in the STEM scandensity at the opposite {0001} faces of the WZ/ZB polytype ning system andthe CCD camera are removed according to the ¯ superlattices, and the resulting EWZ should be close to –EZB to ZB structure in 110 projection, and the high frequency noise
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Figure 2. a) Probe-corrected HAADF image of the same InAs nanopillar used for electron holography characterization, including multiple stacking disorder. Three regions of WZ structure are highlighted by yellow background. The white dashed circle indicates individual tetrahedra within the WZ structure. b) and c) are sketches of ZB and WZ unit cells, where the [111]ZB is parallel to [0001]WZ. d) Model of individual tetrahedra, the displacement of charged ions inside the tetrahedra can be calculated based on the projected atomic positions on z axis.
is filtered using the annular mask tool in Digital Micrograph. For each pair of atomic dumbbells visible in this image, the bright spot should correspond to In3+ (ZIn = 49) and the dark spot to As3− (ZAs = 33). It is clear that the dumbbell polarity is maintained across the polytypic interfaces, similar to cases reported elsewhere for ZnSe, ZnTe, GaAs, ZnO, and GaN-AlN NWs.[7,27] Three regions with local stacking sequences following the WZ structure are highlighted by yellow background, as indicated in Figure 2a. The unit cells for ZB and WZ structures are sketched in Figures 2b and 2c, respectively. The stacking is ABCABC… for cubic ZB along the [111] direction, and ABAB… for hexagonal WZ along the [0001] direction, which are parallel to each other when WZ/ZB heterocrystalline interfaces are formed. The letters A, B, C correspond to a bilayer consisting of one layer with group III atoms and one layer with group V atoms. The tetrahedral bonding for ZB structure is centrosymmetric, with no displacement between different charged ions. The WZ structure, on the other hand, tends to stretch atomic spacings along the c axis and reduce the atomic distances in planes perpendicular to the c axis relative to those in ZB structure.[28] Thus, centrosymmetry is lost for tetrahedral bonds in
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the WZ structure. One of the WZ tetrahedra projected along ¯ the 2110 direction is shown in Figure 2d, which corresponds to the region within the white dashed circle in Figure 2a. The displacement δ between columns of In3+ and As3− could be calculated as a difference vector between each In3+ and the center of mass of its four nearest neighbors of As3− using: δ = 3(z3 –z2) – (z2 – z1), where the z axis is defined in Figure 2d as pointing to the right. Historically, probe instability has been a problem with the STEM. Thus, the most common imaging defects found in HAADF images including scan noise, specimen drift and probe wobbling were corrected using the Jitterbug software.[29] However, it was found that the resulting STEM-HAADF images were almost unchanged from the originals and so no corrections needed to be made, which indicates that it was initially of high stability. A least-squares fit to each of the atomiccolumn positions using two-dimensional Gaussian profiles is then carried out using MacTempas software, and the locations are obtained as coordinates: (x, z). Since the z coordinate is the only parameter related to the displacement of charged ions along the c axis, the contrast maxima positions parallel to the heterocrystalline interfaces are averaged over the vertical
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√ √ ageom,p = aZB 2 and c geom,p = aZB p 3
(2)
where p is 2 for WZ structure. In this way, the lattice parameter for ZB structure is geometrically converted to equivalent WZ
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width of the figure, which helps to lower the level of random noise. The pure ZB region framed within the red box in Figure 2a, is treated with the crystallographic image processing tool in MacTempas software. This tool involves applying the Hanning mask to the Fast Fourier Transform (FFT) of the corresponding area of interest, and selecting two consecutive reflections, which define the reciprocal space. The phases and amplitudes are then extracted from the FFT, and a new image can be created with the imposed symmetry. In this way, the displacements of atoms from their ideal positions in the image due to random noise can be averaged. Figure 3a shows the resulting processed image, where the red crosses are overlapped to indicate the actual atomic-column positions obtained through the peakfinding algorithm. The atoms are found to be perfectly aligned in the vertical direction. The value of displacement δ within the tetrahedra is calculated over the whole image, which appears periodically to be 0 or 1 pixel (1 pixel = 0.0148 nm). Considering the residual random noise and the limitations imposed by the finite pixel size, tetrahedra with ZB structure should be centrosymmetric without any spontaneous polarization. The displacement δ is calculated for all of the highlighted WZ regions in Figure 2a. The value is negative everywhere, which means that the tetrahedral bond along the c axis is always longer than the other off-axis bonds, resulting in a dipole moment pointing to the right, as shown in Figure 2d. Thus, there should be positive polarization charges accumulated at the WZ/ZB interface, and negative polarization charges at the ZB/WZ interface, which would result in linearly decreasing phase shifts across the ZB region, as was the case measured by electron holography. The empirical rule of Chelikowsky and Philips states that those WZ structures which are unstable compared to the corresponding ZB structures should have c/a ratios greater than ideal, while this ratio should be less than ideal for stable WZ structures.[30] While the WZ structure is comparatively unstable for InAs,[31] the c/a ratio for WZ structure is considered to be slightly larger than that calculated geometrically from the cubic bulk lattice constant. The lattice parameters of ZB-InAs and WZ-InAs are carefully measured in Figure 2a with the atomic positions obtained from the peaking finding algorithm overlapped. The average value of the lattice parameter aZB obtained for ZB-InAs is calibrated according to the generally accepted cubic bulk lattice constant for InAs (aZB = 6.058 Å)[32] to correct for the slight magnification deviation of the microscope. The measurements are carried out perpendicular to the ZB/WZ interface (red and blue triangles) and as well as parallel to the interface (red and blue squares), and the results are presented in Figure 3b. The error bar is estimated to be ∼0.1 Å considering the finite pixel size of the experimental STEM-HAADF image and the accuracy of the peak-finding algorithm. The lattice parameters of WZ structures obtained only through geometric conversion from their corresponding ZB structures are related to aZB and the hexagonality of different polytypes p by:[28]
Figure 3. a) Probe-corrected HAADF image obtained by treating the ZB region framed by the red box in Figure 2(a) with the crystallographic image processing tool in MacTempas software. The red crosses are overlapped to indicate the exact atomic-column positions. b) Measurements of lattice parameters perpendicular (red and blue triangles) as well as parallel (red and blue squares) to the ZB/WZ interface. The error bar of ∼0.1 Å are included considering the finite pixel size of the experimental STEM-HAADF image and the accuracy of the peak-finding algorithm. c) The blue squares represent the measured values of local spontaneous polarization for those tetrahedral bonds in the highlighted WZ regions, with the largest and smallest values labeled by red and green dashed circles. The horizontal widths of the red and green squares at the top indicate the largest and smallest tetrahedral bonds along c axis. The blue line is the spontaneous polarization averaged over all of the individual data points. The error bar of ∼0.0085 C m−2 is obtained through propagation of errors in measurements of atomic displacements and the lattice parameters of WZ structure.
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structures for the purpose of direct comparison. The average values of the measured lattice parameters for WZ structures are: aWZ = 4.269 Å, cWZ = 7.005 Å, and the average values obtained from geometric conversion of ZB parameters are: ageom,p = 4.284 Å, and cgeom,p = 6.996 Å. Thus, the actual WZ unit cell is slightly stretched along the c axis and contracted in the plane perpendicular to the c axis. The spontaneous polarization can be calculated based on the experimental lattice parameters of WZ structure, the atomic displacement δ, and the Born effective charge values of the ions. These effective charges for In3+ and As3− in the WZ structure are calculated using the Berry phase expression based on firstprinciples calculations implemented in VASP,[33–36] which are 2.80 for In3+ and −2.60 for As3− along the c axis. The calculated spontaneous polarization for the three WZ regions are shown in Figure 3c as blue squares, while the horizontal blue line is the spontaneous polarization averaged over all of the data points. The averaged value is Psp = 0.0245 C m−2, which is of the same order of magnitude as the value obtained from the electron holography analysis as well as from estimates based on published measurements. Moreover, the obtained Psp values are nowhere near constant across the WZ regions with the largest value of 0.0589 C m−2 (in red dashed circle) and the smallest value of 0.0089 C m−2 (in green dashed circle). The variations of Psp across the WZ regions are reasonable, for the reasons stated below. Polytypes with different stacking sequences have slightly different lattice parameters, and the corresponding distortions from their ZB counterparts are reported to increase linearly with hexagonality.[23] In our case, the WZ regions are sandwiched between other polytypes, and the lattice mismatch at the interfaces would introduce strain, which would penetrate through the WZ regions of only two unit cells in width, and further distort the tetrahedral bonds. The horizontal width of the red square in Figure 3c indicates the length of the local tetrahedral bond along the c axis, which is much larger than the others and leads to the abnormally large value of Psp. The green square, on the other hand, denotes the much smaller length of the local tetrahedral bond along the c axis, and thus the abnormally small value of Psp. For this reason, the individual Psp value is more meaningful than the average value since it reflects the local displacements within the tetrahedra at atomic resolution and their variations along the interface normal, which verifies the significance of probecorrected HAADF imaging for characterizing the spontaneous polarization close to the polytype heterocrystalline interfaces. In summary, polytype heterocrystalline structures within InAs nanopillars are characterized by multiple transmission electron microscopy techniques. The electric field related to spontaneous polarization within the ZB region is revealed at the nanometer scale using off-axis electron holography, and the measured value of spontaneous polarization for WZ-InAs is close to published results. Through probe-corrected HAADF imaging, local values of spontaneous polarization are determined with atomic resolution, and the corresponding value averaged over the entire set of data points is of the same order of magnitude as the electron holography measurements. Moreover, strain-induced variations of spontaneous polarization along the interface normal are calculated and possible explanations are provided. The polytype heterocrystalline superlattices described here are promising for future device applications, even though these segments with
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different polytype structures are normally of only a few nanometers in width. In addition, the probe-corrected HAADF imaging technique is shown to be capable of providing atomic column positions in both the cation and anion sub-lattices, allowing polarization effects to be determined at the level of a single atomically-defined defect based on analysis of the associated structural distortions. This improved knowledge and understanding of strain-induced variations of spontaneous polarization along the interface normal could provide valuable information for tailoring charge distribution in semiconductor nanostructures and, which will help to control this process better as well as opening new pathways for fabrication of future devices. With the advantages of controlled band structure engineering, novel electronic and optoelectronic behavior of polytypic homostructures within III–V semiconductor nanowires can be anticipated. The approach of atomic-scale polarization determination can also be used to study the influence of other types of interfaces on the physical properties of materials.
Experimental Section The InAs nanopillars with nominal Sb concentration of 10% were grown on nanopatterned substrates by metal-organic chemical vapor deposition (MOCVD) in the catalyst-free growth mode. It has been reported that the addition of a small amount of Sb to InAs NWs leads to a tunable structural change from perfect ZB to perfect WZ, via intermediate stacking faults and twinning superlattices.[3] The nanocrystals were deposited on copper grids with carbon support films for electron microscopy observation. High-resolution electron microscopy (HREM) imaging and off-axis electron holography were carried out using a Philips CM200-FEG transmission electron microscope (TEM) equipped with an electrostatic biprism and a 2.8 k × 2.6 k Gatan Orius SC200W chargecoupled-device camera. The sample was imaged in the diffraction mode with the diffraction lens turned off to achieve a larger field of view. The biprism voltage was set at 30 V, and the magnification was set at ∼120 kX. The probe-corrected HAADF imaging was performed using a JEOL ARM200F TEM (camera length: 6 cm, convergence angle: 20 mrad, collection angle: 90 ∼ 170 mrad). Both microscopes were operated at an accelerating voltage of 200 KV.
Acknowledgements This study was supported by National Natural Science Foundation of China (51371085, 11304106), MOE Doctoral Fund (20120142120059), the Fundamental Research Funds for the Central Universities (HUST: 2012QN107), SRF for ROCS, SEM, DOE Grant DE-FG02–04ER46168 (ASU), and the U. S. Army Research Office under contract/grant number W911NF-11–1–0530. Acquisition of the JEM-ARM200F at Arizona State University was supported by NSF Grant 0821796. J. Wang acknowledges support from 973 Program (2011CB933300), National Natural Science Foundation of China (51271134, 51071110, 40972044, J1210061), China MOE NCET Program (NCET-07–0640), MOE Doctoral Fund (20090141110059), and the Fundamental Research Funds for the Central Universities. The authors thank D. Huffaker for providing the sample, and L. Jones for sharing the Jitterbug tool used for image-distortion correction. The authors also acknowledge the use of facilities in the John M. Cowley Center for High Resolution Electron Microscopy at Arizona State University.
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Received: August 9, 2013 Revised: September 14, 2013 Published online: November 4, 2013
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Determination of Polarization-Fields Across Polytype Interfaces in InAs Nanopillars Luying Li,* Zhaofeng Gan, Martha R. McCartney, Hanshuang Liang, Hongbin Yu, Wan-Jian Yin, Yanfa Yan, Yihua Gao, Jianbo Wang,* and David J. Smith* Heterocrystalline polytype structures have been intensively studied in recent years as novel types of superlattices. These polytype superlattices consist of chemically identical but structurally different materials, which match well at their interfaces.[1] Thus, the common problem of compositional changes associated with interfaces composed of chemically inequivalent materials can be avoided. The basic polytype structures for III–V and II–VI compounds are zincblende (ZB) with cubic stacking in the [111] direction, and wurtzite (WZ) with hexagonal stacking in the [0001] direction. The controlled growth of polytypic and twinning superlattices, which is rare in related bulk crystals, has been realized in single nanowires (NWs) by varying the NW diameter and growth temperature,[2] and by the addition of dopants.[3,4] The polytype superlattices would act as barriers for electron transport, leading to charge accumulation in certain regions due either to band offsets at the polytype interfaces,[5,6] or spontaneous polarization in the polytype regions with asymmetrical structures.[7,8] In this study, charge
Dr. L. Li, Prof. Y. Gao Center for Nanoscale Characterization and Devices Wuhan National Laboratory for Optoelectronics Huazhong University of Science and Technology Wuhan, 430074, China E-mail: [email protected] Dr. L. Li, Z. Gan, Prof. M. R. McCartney, Prof. D. J. Smith Department of Physics Arizona State University Tempe, Arizona, 85287–1504, USA E-mail: [email protected] H. Liang, Prof. H. Yu School of Electrical Computer, and Energy Engineering Arizona State University Tempe, Arizona, 85287–5706, USA Dr. W.-J. Yin, Prof. Y. Yan Department of Physics and Astronomy The University of Toledo Toledo, Ohio, 43606, USA Prof. Y. Gao School of Physics Huazhong University of Science and Technology Wuhan, 430074, China Prof. J. Wang School of Physics and Technology Center for Electron Microscopy and MOE Key Laboratory of Artificial Micro- and Nano-Structures Wuhan University Wuhan, 430072, China E-mail: [email protected]
DOI: 10.1002/adma.201304021
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distribution due to polarization fields within polytype superlattices is demonstrated at the nanometer scale using off-axis electron holography, and the determination of local spontaneous polarization in WZ crystals at atomic resolution is realized based on probe-corrected high-angle annular-dark-field (HAADF) images. Figure 1a is a transmission electron micrograph showing an InAs nanopillar, where the parallel dark lines indicate changes of stacking order along the growth direction. The area in the ¯ blue box in Figure 1a, which is projected along the 110 zone axis, is shown at higher magnification in Figure 1b, and the layer stacking is visible along the direction. A region with greater stacking disorder is clearly visible, and labeled here as the ‘polytype’ region. Conversely, the region labeled as ZB does not show any structural change along the stacking direction. The interfaces are indicated here by yellow dashed lines. The same region of the nanopillar shown in Figure 1b, was then characterized using off-axis electron holography. The reconstructed phase image of a typical hologram is shown in Figure 1c. The region outlined in the black box was used for phase-shift profiling, and the results are shown in Figure 1d. The thickness profile of the same region (red triangles) is flat across the entire region, but the phase shifts (blue disks) are higher in the polytype region relative to the ZB region. This difference could be considered as an indication of electrons and holes being distributed differently in the separate regions since there is no obvious indication of diffraction contrast in the image. Moreover, the phase shifts are linearly decreasing in the ZB region and show fluctuations within the polytype region, which could be considered as equivalent to multiple WZ quantum wells embedded in a ZB matrix. While the type-II band alignment between WZ and ZB polytype structures might lead to selective confinement of electrons to ZB-rich regions and holes to WZ-rich regions[9] (the conduction band offset at the WZ/ZB interface is ΔEc = 86 meV for bulk InAs, and the valence band offset is ΔEv = 46 meV),[10] spontaneous polarization in the WZ region could result in sawtooth-like potentials across the WZ/ZB polytype superlattices, which are linearly increasing in WZ regions and decreasing in ZB regions.[7,11] Thus, the phase-shift profile obtained here is likely to be the collective result of band offsets and spontaneous polarization. The phase profile can be converted to potential using the expression: φ = CE (VMIP + VSP) t, where CE = 0.00728 rad (V nm)−1 for an accelerating voltage of 200 kV, φ is the phase shift, t is the projected thickness, VMIP is the mean inner potential (MIP) of the material, and VSP is the electrostatic potential related to the spontaneous polarization. The thicknesses can be obtained from the corresponding reconstructed amplitude image assuming an inelastic mean free path (MFP) of 57 nm
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ensure supercell periodicity.[7,11] Assuming EWZ = –EZB, and taking εr = 15 for InAs,[16] the absolute value of spontaneous polarization present in the WZ region is calculated to be psp = 0.0166 ± 0.0021 C m−2, where the error Δpsp is estimated through error propagation from the errors in potential measurement ΔV = ± 0.103 V and the pixel size Δz = ± 0.257 nm. Pure ZB InAs NWs and WZ NWs with small ZB segments are reported to have significantly distinct subthreshold characteristics, which are attributed to spontaneous polarization charges at the WZ/ZB interfaces, so that a polarization charge density of ≥1013 cm−2 is obtained.[8] The polarization charge density σ can be converted to spontaneous polarization Psp using: Psp = –σ. Thus, the spontaneous polarization for WZ-InAs should be ≥ 0.0160 C m−2, which is close to the measured holography value as well as being comparable to other hexagonal materials.[17] The spontaneous polarization is related to structures without any inversion center, and dipoles are formed by displacements of charged ions inside the crystal unit cell. The Figure 1. a) TEM image of InAs nanopillar, where the parallel dark lines indicate the existence of stacking disorder along the growth direction; b) HREM image of the region framed in characterization of spontaneous polariza¯ ] direction. The ZB and polytype regions are labeled, and the yellow (a) projected along the [ 110 tion in ferroelectric thin films was reported dashed lines show the boundaries of these regions; c) Phase image of the same region shown using the negative spherical-aberration in (b) as reconstructed from electron hologram. The area used for phase shift and thickness (Cs) imaging technique in an aberrationline profiles are indicated by the black box; d) While the thickness profile (red triangles) is flat corrected TEM.[18] Through careful measureacross the entire region, the phase shifts (blue disks) are higher with some fluctuations in the ment of the displacements of charged ions, polytype region, decreasing linearly in the ZB region. The blue line is a linear fit to phase shifts 180° domain walls that intersected regions in the ZB region. of reversed spontaneous polarizations were verified, and the variations of spontaneous polarization along the interface normal were also obtained.[18,19] for InAs.[12] The MFP for InAs is calculated through linear Similar studies on ferroelectric heterointerfaces and nanocrysextrapolation of the experimental values for AlAs (77 nm) and tals,[20–23] as well as transition-metal oxide interfaces,[24–26] have GaAs (67 nm) since the MFP values should be linearly propor[ 13 ] been carried out by scanning transmission electron microscopy tional to the average atomic numbers. Only VSP would con(STEM) using probe-corrected HAADF imaging. The aberratribute to the electrostatic field as a slope of the electrostatic tion-corrected HREM with negative Cs is sensitive to elements potential profile since the MIP is constant for any specific strucof low atomic number, whereas probe-corrected STEM HAADF ture. Thus, EZB can be calculated based on a linear fit (blue line) imaging requires no post-processing and is applicable to comof the experimental phase shift data, as shown in Figure 1d: paratively thick specimens. In our sample, all of the elements EZB = 0.0626 V nm−1. are easily visible in HAADF; the WZ/ZB heterocrystalline According to the Supercell approach, the spontaneous polarisuperlattices exist only in InAs nanostructures as opposed to zation of the WZ structure could be obtained using:[14,15] bulk crystals, and the projected thicknesses are normally of sev∂ VWZ ∂ VZB eral tens of nanometers (the thickness of the region studied by − ps p = − g 0g r E = − g 0g r (1) ∂z ∂z electron holography is ∼70 nm), which is too thick for atomic where E WZ = − ∂ V∂zWZ and E ZB = − ∂ V∂zZB correspond to the elecresolution with HREM. Thus, probe-corrected STEM HAADF tric fields in the WZ and ZB regions, respectively. For our speimaging is the better choice here for observation. cific case, only the electric field in the ZB region is obtainable Figure 2a is a probe-corrected STEM HAADF image of a since the existing WZ regions are not wide enough to allow region including ZB structures as well as stacking disorder reliable measurements of the corresponding electric field. Howalong the growth direction within the same nanopillar ever, the non-zero spontaneous polarization in the WZ regions used for electron holography characterization. The shear distorwould lead to opposite polarization charges with equal charge tions in the image induced by imperfections in the STEM scandensity at the opposite {0001} faces of the WZ/ZB polytype ning system andthe CCD camera are removed according to the ¯ superlattices, and the resulting EWZ should be close to –EZB to ZB structure in 110 projection, and the high frequency noise
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Figure 2. a) Probe-corrected HAADF image of the same InAs nanopillar used for electron holography characterization, including multiple stacking disorder. Three regions of WZ structure are highlighted by yellow background. The white dashed circle indicates individual tetrahedra within the WZ structure. b) and c) are sketches of ZB and WZ unit cells, where the [111]ZB is parallel to [0001]WZ. d) Model of individual tetrahedra, the displacement of charged ions inside the tetrahedra can be calculated based on the projected atomic positions on z axis.
is filtered using the annular mask tool in Digital Micrograph. For each pair of atomic dumbbells visible in this image, the bright spot should correspond to In3+ (ZIn = 49) and the dark spot to As3− (ZAs = 33). It is clear that the dumbbell polarity is maintained across the polytypic interfaces, similar to cases reported elsewhere for ZnSe, ZnTe, GaAs, ZnO, and GaN-AlN NWs.[7,27] Three regions with local stacking sequences following the WZ structure are highlighted by yellow background, as indicated in Figure 2a. The unit cells for ZB and WZ structures are sketched in Figures 2b and 2c, respectively. The stacking is ABCABC… for cubic ZB along the [111] direction, and ABAB… for hexagonal WZ along the [0001] direction, which are parallel to each other when WZ/ZB heterocrystalline interfaces are formed. The letters A, B, C correspond to a bilayer consisting of one layer with group III atoms and one layer with group V atoms. The tetrahedral bonding for ZB structure is centrosymmetric, with no displacement between different charged ions. The WZ structure, on the other hand, tends to stretch atomic spacings along the c axis and reduce the atomic distances in planes perpendicular to the c axis relative to those in ZB structure.[28] Thus, centrosymmetry is lost for tetrahedral bonds in
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the WZ structure. One of the WZ tetrahedra projected along ¯ the 2110 direction is shown in Figure 2d, which corresponds to the region within the white dashed circle in Figure 2a. The displacement δ between columns of In3+ and As3− could be calculated as a difference vector between each In3+ and the center of mass of its four nearest neighbors of As3− using: δ = 3(z3 –z2) – (z2 – z1), where the z axis is defined in Figure 2d as pointing to the right. Historically, probe instability has been a problem with the STEM. Thus, the most common imaging defects found in HAADF images including scan noise, specimen drift and probe wobbling were corrected using the Jitterbug software.[29] However, it was found that the resulting STEM-HAADF images were almost unchanged from the originals and so no corrections needed to be made, which indicates that it was initially of high stability. A least-squares fit to each of the atomiccolumn positions using two-dimensional Gaussian profiles is then carried out using MacTempas software, and the locations are obtained as coordinates: (x, z). Since the z coordinate is the only parameter related to the displacement of charged ions along the c axis, the contrast maxima positions parallel to the heterocrystalline interfaces are averaged over the vertical
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√ √ ageom,p = aZB 2 and c geom,p = aZB p 3
(2)
where p is 2 for WZ structure. In this way, the lattice parameter for ZB structure is geometrically converted to equivalent WZ
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width of the figure, which helps to lower the level of random noise. The pure ZB region framed within the red box in Figure 2a, is treated with the crystallographic image processing tool in MacTempas software. This tool involves applying the Hanning mask to the Fast Fourier Transform (FFT) of the corresponding area of interest, and selecting two consecutive reflections, which define the reciprocal space. The phases and amplitudes are then extracted from the FFT, and a new image can be created with the imposed symmetry. In this way, the displacements of atoms from their ideal positions in the image due to random noise can be averaged. Figure 3a shows the resulting processed image, where the red crosses are overlapped to indicate the actual atomic-column positions obtained through the peakfinding algorithm. The atoms are found to be perfectly aligned in the vertical direction. The value of displacement δ within the tetrahedra is calculated over the whole image, which appears periodically to be 0 or 1 pixel (1 pixel = 0.0148 nm). Considering the residual random noise and the limitations imposed by the finite pixel size, tetrahedra with ZB structure should be centrosymmetric without any spontaneous polarization. The displacement δ is calculated for all of the highlighted WZ regions in Figure 2a. The value is negative everywhere, which means that the tetrahedral bond along the c axis is always longer than the other off-axis bonds, resulting in a dipole moment pointing to the right, as shown in Figure 2d. Thus, there should be positive polarization charges accumulated at the WZ/ZB interface, and negative polarization charges at the ZB/WZ interface, which would result in linearly decreasing phase shifts across the ZB region, as was the case measured by electron holography. The empirical rule of Chelikowsky and Philips states that those WZ structures which are unstable compared to the corresponding ZB structures should have c/a ratios greater than ideal, while this ratio should be less than ideal for stable WZ structures.[30] While the WZ structure is comparatively unstable for InAs,[31] the c/a ratio for WZ structure is considered to be slightly larger than that calculated geometrically from the cubic bulk lattice constant. The lattice parameters of ZB-InAs and WZ-InAs are carefully measured in Figure 2a with the atomic positions obtained from the peaking finding algorithm overlapped. The average value of the lattice parameter aZB obtained for ZB-InAs is calibrated according to the generally accepted cubic bulk lattice constant for InAs (aZB = 6.058 Å)[32] to correct for the slight magnification deviation of the microscope. The measurements are carried out perpendicular to the ZB/WZ interface (red and blue triangles) and as well as parallel to the interface (red and blue squares), and the results are presented in Figure 3b. The error bar is estimated to be ∼0.1 Å considering the finite pixel size of the experimental STEM-HAADF image and the accuracy of the peak-finding algorithm. The lattice parameters of WZ structures obtained only through geometric conversion from their corresponding ZB structures are related to aZB and the hexagonality of different polytypes p by:[28]
Figure 3. a) Probe-corrected HAADF image obtained by treating the ZB region framed by the red box in Figure 2(a) with the crystallographic image processing tool in MacTempas software. The red crosses are overlapped to indicate the exact atomic-column positions. b) Measurements of lattice parameters perpendicular (red and blue triangles) as well as parallel (red and blue squares) to the ZB/WZ interface. The error bar of ∼0.1 Å are included considering the finite pixel size of the experimental STEM-HAADF image and the accuracy of the peak-finding algorithm. c) The blue squares represent the measured values of local spontaneous polarization for those tetrahedral bonds in the highlighted WZ regions, with the largest and smallest values labeled by red and green dashed circles. The horizontal widths of the red and green squares at the top indicate the largest and smallest tetrahedral bonds along c axis. The blue line is the spontaneous polarization averaged over all of the individual data points. The error bar of ∼0.0085 C m−2 is obtained through propagation of errors in measurements of atomic displacements and the lattice parameters of WZ structure.
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structures for the purpose of direct comparison. The average values of the measured lattice parameters for WZ structures are: aWZ = 4.269 Å, cWZ = 7.005 Å, and the average values obtained from geometric conversion of ZB parameters are: ageom,p = 4.284 Å, and cgeom,p = 6.996 Å. Thus, the actual WZ unit cell is slightly stretched along the c axis and contracted in the plane perpendicular to the c axis. The spontaneous polarization can be calculated based on the experimental lattice parameters of WZ structure, the atomic displacement δ, and the Born effective charge values of the ions. These effective charges for In3+ and As3− in the WZ structure are calculated using the Berry phase expression based on firstprinciples calculations implemented in VASP,[33–36] which are 2.80 for In3+ and −2.60 for As3− along the c axis. The calculated spontaneous polarization for the three WZ regions are shown in Figure 3c as blue squares, while the horizontal blue line is the spontaneous polarization averaged over all of the data points. The averaged value is Psp = 0.0245 C m−2, which is of the same order of magnitude as the value obtained from the electron holography analysis as well as from estimates based on published measurements. Moreover, the obtained Psp values are nowhere near constant across the WZ regions with the largest value of 0.0589 C m−2 (in red dashed circle) and the smallest value of 0.0089 C m−2 (in green dashed circle). The variations of Psp across the WZ regions are reasonable, for the reasons stated below. Polytypes with different stacking sequences have slightly different lattice parameters, and the corresponding distortions from their ZB counterparts are reported to increase linearly with hexagonality.[23] In our case, the WZ regions are sandwiched between other polytypes, and the lattice mismatch at the interfaces would introduce strain, which would penetrate through the WZ regions of only two unit cells in width, and further distort the tetrahedral bonds. The horizontal width of the red square in Figure 3c indicates the length of the local tetrahedral bond along the c axis, which is much larger than the others and leads to the abnormally large value of Psp. The green square, on the other hand, denotes the much smaller length of the local tetrahedral bond along the c axis, and thus the abnormally small value of Psp. For this reason, the individual Psp value is more meaningful than the average value since it reflects the local displacements within the tetrahedra at atomic resolution and their variations along the interface normal, which verifies the significance of probecorrected HAADF imaging for characterizing the spontaneous polarization close to the polytype heterocrystalline interfaces. In summary, polytype heterocrystalline structures within InAs nanopillars are characterized by multiple transmission electron microscopy techniques. The electric field related to spontaneous polarization within the ZB region is revealed at the nanometer scale using off-axis electron holography, and the measured value of spontaneous polarization for WZ-InAs is close to published results. Through probe-corrected HAADF imaging, local values of spontaneous polarization are determined with atomic resolution, and the corresponding value averaged over the entire set of data points is of the same order of magnitude as the electron holography measurements. Moreover, strain-induced variations of spontaneous polarization along the interface normal are calculated and possible explanations are provided. The polytype heterocrystalline superlattices described here are promising for future device applications, even though these segments with
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different polytype structures are normally of only a few nanometers in width. In addition, the probe-corrected HAADF imaging technique is shown to be capable of providing atomic column positions in both the cation and anion sub-lattices, allowing polarization effects to be determined at the level of a single atomically-defined defect based on analysis of the associated structural distortions. This improved knowledge and understanding of strain-induced variations of spontaneous polarization along the interface normal could provide valuable information for tailoring charge distribution in semiconductor nanostructures and, which will help to control this process better as well as opening new pathways for fabrication of future devices. With the advantages of controlled band structure engineering, novel electronic and optoelectronic behavior of polytypic homostructures within III–V semiconductor nanowires can be anticipated. The approach of atomic-scale polarization determination can also be used to study the influence of other types of interfaces on the physical properties of materials.
Experimental Section The InAs nanopillars with nominal Sb concentration of 10% were grown on nanopatterned substrates by metal-organic chemical vapor deposition (MOCVD) in the catalyst-free growth mode. It has been reported that the addition of a small amount of Sb to InAs NWs leads to a tunable structural change from perfect ZB to perfect WZ, via intermediate stacking faults and twinning superlattices.[3] The nanocrystals were deposited on copper grids with carbon support films for electron microscopy observation. High-resolution electron microscopy (HREM) imaging and off-axis electron holography were carried out using a Philips CM200-FEG transmission electron microscope (TEM) equipped with an electrostatic biprism and a 2.8 k × 2.6 k Gatan Orius SC200W chargecoupled-device camera. The sample was imaged in the diffraction mode with the diffraction lens turned off to achieve a larger field of view. The biprism voltage was set at 30 V, and the magnification was set at ∼120 kX. The probe-corrected HAADF imaging was performed using a JEOL ARM200F TEM (camera length: 6 cm, convergence angle: 20 mrad, collection angle: 90 ∼ 170 mrad). Both microscopes were operated at an accelerating voltage of 200 KV.
Acknowledgements This study was supported by National Natural Science Foundation of China (51371085, 11304106), MOE Doctoral Fund (20120142120059), the Fundamental Research Funds for the Central Universities (HUST: 2012QN107), SRF for ROCS, SEM, DOE Grant DE-FG02–04ER46168 (ASU), and the U. S. Army Research Office under contract/grant number W911NF-11–1–0530. Acquisition of the JEM-ARM200F at Arizona State University was supported by NSF Grant 0821796. J. Wang acknowledges support from 973 Program (2011CB933300), National Natural Science Foundation of China (51271134, 51071110, 40972044, J1210061), China MOE NCET Program (NCET-07–0640), MOE Doctoral Fund (20090141110059), and the Fundamental Research Funds for the Central Universities. The authors thank D. Huffaker for providing the sample, and L. Jones for sharing the Jitterbug tool used for image-distortion correction. The authors also acknowledge the use of facilities in the John M. Cowley Center for High Resolution Electron Microscopy at Arizona State University.
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Received: August 9, 2013 Revised: September 14, 2013 Published online: November 4, 2013
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