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Direct Optical Mapping of Anisotropic Stresses in Nanowires using TO Phonons Splitting Maria Vanessa Balois, Norihiko Hayazawa, Alvarado Tarun, Satoshi Kawata, Manfred Reiche, and Oussama Moutanabbir Nano Lett., Just Accepted Manuscript • DOI: 10.1021/nl500891f • Publication Date (Web): 27 May 2014 Downloaded from http://pubs.acs.org on May 30, 2014
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Direct Optical Mapping of Anisotropic Stresses in Nanowires using TO Phonons Splitting
Maria Vanessa Balois,1, b) Norihiko Hayazawa,1, b), a) Alvarado Tarun,1 Satoshi Kawata,1, c) Manfred Reiche,2 and Oussama Moutanabbir3,1, a)
1
Near-field Nanophotonics Research Team, RIKEN, The Institute of Physical and Chemical Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
2
Max Planck Institute of Microstructure Physics, Weinberg 2, Halle (Saale), 06120 Germany
3
Département de Génie Physique, École Polytechnique de Montréal, Montréal, C.P. 6079, Succ. Centre-Ville, Montréal, Québec, H3C 3A7 Canada
Strain engineering is ubiquitous in design and fabrication of innovative, highperformance electronic, optoelectronic, and photovoltaic devices.
The increasing
importance of strain-engineered nanoscale materials has raised significant challenges at both fabrication and characterization levels. Raman Scattering Spectroscopy (RSS) is one of the most straightforward techniques that have been broadly utilized to estimate the strain in semiconductors.
However, this technique is incapable of
measuring the individual components of stress thus only providing the average values of the in-plane strain. This inherit limitation severely diminishes the importance of RSS analysis and makes it ineffective in the predominant case of nanostructures and devices with nonuniform distribution of strain. Herein, we circumvent this major limitation and demonstrate for the first time the application of RSS to simultaneously probe the two local stress in-plane components in individual ultrathin silicon nanowires based on the imaging of the splitting of the two forbidden transverse optical phonons.
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KEYWORDS:
polarized-Raman,
TO
phonon,
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strained
silicon,
nanowire,
nanomembranes, stress anisotropy
-------------------------------------------------a)
Authors to whom correspondence should be addressed; electronic mail:
[email protected]; [email protected] b)
Department of Electronic Chemistry, Graduate School of Science and Engineering,
Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama, Kanagawa 226-8502 Japan c)
Also at: Department of Precision Science & Technology and Applied Physics,
Osaka University, Suita, Osaka 565-0871, Japan.
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Strain engineering has been a powerful strategy in fabrication and processing of a variety of electronic, optoelectronic, and photovoltaic devices.1-8 To implement these technologies, several processes have been proposed to generate strain in semiconductors in order to improve and control their physical properties by exploiting the influence of strain on the bandgap structure. The increasing importance of this strain-induced bandgap engineering in nanoscale materials has raised significant challenges at both fabrication and characterization levels. The latter in particular has sparked a surge of interest in developing a variety of spectroscopic and microscopic techniques to precisely probe strain and stress in ultra small semiconductor devices and structures.9-19 Lattice interaction with electrons and photons (from infrared to xray) is at the core of the techniques currently employed to probe strain and stress in nanoscale semiconductor structures and devices. Each of these techniques suffers, however, a number of limitations such as being invasive or insensitive to all strain components, or having a limited spatial resolution.
Transmission electron
microscopy-based techniques, including among others holographic interferometry9 and nanobeam electron beam diffraction,10 provide the ultimate spatial resolution in mapping stress, but they are invasive as they require a special sample preparation. This involves cutting the materials and thinning it down to ~100-500 nm, which can induce partial stress relaxation in addition to possible lattice local distortion during the analysis. X-ray-based techniques have immensely benefited from the availability of high-brilliance X-ray sources in the 3rd generation synchrotron sources or free electron lasers leading to development of lensless coherent imaging and nanodiffraction techniques.11-16 These techniques have recently succeeded in mapping the stress in sub-micrometer structures and devices.11-16 One such example of an effective X-ray-based technique was the use of X-ray nanodiffraction combined with
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finite element modeling to probe the local stress in single quantum dot-based devices.16 However, they are still not yet ready for routine analyses because of the need for synchrotron facilities besides requiring special sample preparation to eliminate the background signal from the underlying substrate. Up to date, RSS is still broadly utilized as a very straightforward and timeeffective technique to evaluate the stress states in semiconductors. Nevertheless, the major drawback limiting the use of this technique is its incapacity to discriminate between stress components thus only providing an average value.19 In fact, under the standard backscattering configuration, the incident and the scattered light are normal to the sample surface and thus the electric fields of the incident and scattered radiations are parallel to the sample surface. For cubic crystal structures with (001)surface orientation, Raman scattering selection rule imposes the sole excitation of the longitudinal optical (LO) phonon regardless of the incident and the scattered light polarizations.20 Therefore, only the stress-induced frequency shift of the LO phonon is detected. It is, however, noteworthy that this limitation is not inherent to RSS technique, but it is actually a result of the used scattering geometry.18,21 In a cubic crystal, in addition to LO phonon, there are two transverse optical phonon modes TO1 and TO2. All three phonon modes must be measured in order to obtain a precise analysis of stress states as illustrated in Figs. 1a – 1c. In the absence of strain (Fig. 1a), only a single triply degenerated phonon mode can be detected. However, in the case of a bi-isotropic in-plane strain (εxx = εyy), the original single phonon mode will split into two (Fig. 1b): the singlet LO and the doublet TO. This latter will split further into the two aforementioned singlet TO1 and TO2 phonon modes when the strain bi-isotropy is lost as it is the case for a nanowire under an anisotropic strain (εxx ≠ εyy). It is theoretically possible to detect all three phonon modes either when the
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incident or scattered electric fields are not strictly parallel to the sample surface or when the sample surface is not (001)-oriented.21,22 Herein, we focus our study on the technologically important (001)-oriented strained silicon.
Although the standard
backscattering configuration does not allow to probe directions other than z, we demonstrate that the use of high numerical aperture (NA) objectives circumvents this limitation and makes possible the observation of directions at a certain angle range around the z direction on a sub-micrometer scale.23,24 Moreover, our methodology also involves the effect that, when the polarized beam is focused by the high NA lens, the polarization condition at the tight focus becomes complex and exhibits different polarization components from the initial incident light. This behavior can no longer be neglected, as it is the case when low NA objectives are used. The Raman scattering intensity, I, associated with the excitation and the collection of light in micro-Raman analysis is dependent on the polarization vector of the incident (ei) and the scattered (es) light:25 I ∝ ∑ e sT R j ei , where Rj is the Raman 2
j
polarizability tensor for the jth active phonon mode and ei and es are the incident and scattered electric field unit vectors, respectively. The superscript T denotes transpose of the scattered electric field vector. Let us consider the standard case where, the edges of the nanowire are aligned along the direction. The Si Raman tensors expressed in the crystal axes (x, y, z) are transformed to the sample coordinate axes (x’, y’, z’) defined in Figure 1d. Typically, the Raman intensity is often calculated on the simplified Raman signal collection efficiency (ei and es) based on x’- or y’polarization. The z’- polarization is ignored for backscattering configuration, whereas the x’- and y’- polarizations are set either to unity or zero (undetectable) depending on the analyzer setting. However it was found that when the NA of the objective lens is
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sufficiently high (i.e NA>1.0), the z’- component becomes sufficiently strong which makes it possible to detect the TO phonon.18,26 Moreover, the intensity of depolarized (y’-component) light at the focus also increases and becomes comparable to the z’component for linearly x’-polarized incident light.
Thus, contributions from the
depolarized light can no longer be ignored in the analysis of the scattered Raman signal. The configuration z ( x ' y') z is an example for this case in polarized RSS. To accurately describe the scattering process involving illumination and collection by a high NA lens, the ei cannot be assumed to be constant across the focal volume. Considering all these non-negligible effects, the intensity of the Raman mode can then be rewritten as:18
2π
Ii = I0 ∑ ∫ 0 i
E scaX (θ , φ, η ) θ max ∫ 0 R(α, β, γ ) EscaY (θ, φ, η ) EscaZ (θ , φ, η )
T
2
E ' x × R • R (α, β, γ ) E ' sinθ dθ dφ y i E ' z
(1)
where, I0 is the incident intensity, η is the angle setting of the analyzer with respect to the x’ – axis, and θ and φ are the polar and azimuthal angles, respectively. E’x, E’y, E scaX (θ , φ, η ) and E’z are the component of the incident electric field. E (θ , φ, η ) scaY EscaZ (θ , φ, η )
is the
scattered electric field derived from the objective lens transfer matrix, which describes the radiation dipole collection efficiency of a high NA objective lens (see Supporting Information Section II). In this work, η is equal to 1. Ri is the Raman tensor in the crystal coordinate (x, y, z) system, which can be transformed into the sample coordinate (x’, y’, z’) system using the Euler rotation matrix, R(α,β,γ).
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integration is done over the solid angle, sinθ dθ dφ, and is confined only to the collection cone for the scattered light. Figure 1d shows the experimental configuration used in this work.
Two
coordinate systems are defined, namely the crystal and the sample coordinates, represented as x, y, z and x’, y’, z’, respectively. The edge of the nanowire is aligned along the direction. Linearly polarized light from a 532 nm laser is set parallel to the nanowire long axis (x’ – axis). The beam is expanded and focused onto the nanowires using a high NA oil-immersion objective lens (NA = 1.49, ×100). The diameter of the laser spot is ~436 nm at the surface, which is smaller than the spacing between nanowires (~500 nm) to insure that only one nanowire is exposed to the laser during the analysis. The surface of the ε-Si is directly immersed in oil.
The
backscattered Raman signal is collected by the same objective lens and then passes through an edge filter which blocks the Rayleigh signal in order to detect the backscattered Raman signal.
This signal then proceeds to an analyzer, which
determines which phonon mode is detected, depending on the configuration. In all measurements discussed in this manuscript, the configuration described by Porto’s notation z ( x ' y') z is used. In this polarization configuration, TO phonon modes are predominantly detected, particularly in the case of nanowires (see Supporting Information Section I and Fig. S2).
To extract the TO phonon peaks, double
Lorentzian fitting was used, as shown in Figs. 2a – 2c, based on the results of the simulation suggesting that the detected signal consists only of TO1 and TO2 (negligible LO intensity) with equal intensity due to symmetry of the nanowire with respect to its orientation in the sample coordinate system. This observation was supported by numerical simulations, wherein the TO/LO ratio was computed for
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varying nanowire widths (see Supporting Information Section II, Fig. S2b and S2c) using the same z ( x ' y') z polarization configuration as that in experiment. From the simulations, it was found that the TO/LO ratios for the 80 nm, 50 nm and 30 nm nanowires are 23.56, 54.89 and 84.57, respectively. These values are very large as compared to the TO/LO ratio for the nanomembrane, which is 0.94 (see Supporting Information Fig. S2b). This means that for nanowires, the LO contribution is very small to the point that it is negligible. In contrast, previous work based on z ( x ' x ') z in Porto’s notation predominantly detects only LO phonon mode27. To verify the validity of the numerical simulations, experiments were made on strained nanomembranes under both z ( x ' x ') z and z ( x ' y') z configurations and are summarized in the Supporting Information (Fig. S3). The analyzed light then enters a spectrometer (grating = 1800 g mm-1, focal length = 500 mm, slit width = 100 µm) equipped with a thermo-electronically cooled charge coupled device (CCD) camera (1340 × 400 pixels, 20 µm/pixel). The nanowire array samples were mounted on an x’-y’ translation stage. 3.5 µm x 2.75 µm areas were scanned with a 25 nm step while being illuminated by the focused laser beam. A Raman spectrum was recorded at each step using an exposure time of 5 s and an incident laser power of 2 mW at the sample. Appropriate incident power was used to eliminate laser heating that may affect the detected Raman shift. It should be noted that in order to keep the high NA focus precisely on the nanowire, autofocusing28 was utilized for all the measurements.
Figure 1e shows a scanning electron microscope (SEM) image of strained silicon nanowire arrays investigated in this study (see optical image in Supporting Information Fig. S1a). Each nanowire is 30 nm or 80 nm in width and 1 µm in length.
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Similarly, nanowires of 50 nm in width were also investigated.
The arrays of
nanowires were obtained by patterning a biaxially tensile strained 15 nm-thick silicon (ε-Si) nanomembrane directly on oxide synthesized by epitaxy and ion-cut processes.18,29 To suppress the background from the underlying Si substrate in Raman signals, a Ge layer was inserted between the oxide layer and the handle substrate. Thus, only the nanowire Si-Si intrinsic mode is detected (Supporting Information Figs. S1b and S1c). Figures 2a – 2c show the experimentally obtained Raman spectra at the center of the nanowire for 80 nm, 50 nm and 30 nm widths, respectively. These spectra were obtained under TO-active configuration wherein the contributions from the LO peak are negligible as supported by numerical simulations (see Section II of Supporting Information). The red vertical lines in Fig. 2a indicate the TO1 (515.96 cm-1) and the TO2 (517.71 cm-1) Raman shift peak for the 80 nm width nanowire. The difference between the two peaks is ∆ωTO_80 =1.75 cm-1. This difference in the TO peaks is related to the strain anisotropy in the nanowire as illustrated in Fig. 1c. Similarly, for the 50 nm nanowire, the blue vertical lines in Fig. 2b indicate the TO1 Raman shift peak at 515.84 cm-1 and the TO2 Raman shift peak at 517.75 cm-1. The difference between the two peaks is ∆ωTO_50 = 1.91 cm-1 and is found to be slightly higher than that of 1.75 cm-1 for the 80 nm-wide nanowire. Figure 2c shows the Raman spectra from the 30 nm-wide nanowire. The signal is relatively weaker than the Raman spectra obtained from the 80 nm and 50 nm nanowires due to the smaller volume probed as compared to the wider nanowires. The green vertical lines denote the TO1 (515.6 cm-1) and TO2 (518.32 cm-1) Raman shift peak. The splitting is more apparent at this width and the difference between the two peaks is ∆ωTO_30 = 2.72 cm1
. This indicates that the difference in the TO peaks tend to increase with smaller
widths of the nanowire. Note that this is the first experimental demonstration of TO1
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and TO2 splitting in (001)-oriented silicon. The observed behavior is summarized in Fig. 2d displaying the TO1 and TO2 Raman shift peak as a function of the nanowire width. As a reference, the Raman peak of the nanomembrane is also shown in this figure. Based on the experiment on the unpatterned strained silicon nanomembrane, which can be considered as an infinitely wide nanowire, the extracted TO phonon frequency ωTO_∞ = 516.26 cm-1 (see Section III of Supporting Information). We see a slight increase in the TO1 peak position (within a ±0.5 cm-1 range) as the nanowire width increases. In contrast, the TO2 Raman peak decreases with increasing nanowire width. Besides, TO2 was also found to have a higher slope compared to TO1, which suggest that TO2 is more sensitive to the changes in the nanowire dimension. For both TO1 and TO2, the evolution of the peak positions as the nanowire width increases exhibits a linear but opposite trend. It is also worth mentioning that the TO1 and TO2 peaks converge at 516.26 cm-1, which corresponds to the Raman peak of the nanomembrane (i.e., a nanowire with an infinite width). These results agree very well with theoretical predictions shown in Fig. 1b, where the detected TO is doubly degenerate for the nanomembrane. As illustrated above, this degeneracy is lifted in the case of the nanowire. From the linear trends, one can extrapolate that at a width of 155 nm the structure is sufficiently broad to possibly preserve the bi-isotropic character at the center, similar to the original nanomembrane.
Looking at the
difference between TO1 and TO2 Raman shift peaks for each nanowire width, we see that ∆ωTO_30 > ∆ωTO_50 > ∆ωTO_80. The increase in the splitting between the TO1 and TO2 is due to the narrowing of the width of the nanowires and is a manifestation of the increase in the anisotropy as the nanowire width decreases. To the best of our knowledge, this is the first demonstration of TO mode splitting. Figures 3a – 3c display the TO1 and TO2 Raman shift images of the 80 nm, 50 10
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nm, and 30 nm nanowires, respectively.
These images were obtained through
filtering based on the integrated intensity in order to identify the nanowires (see Supporting Information Fig. S4 for the intensity profile). This visualization of the fitted Raman shifts validates further the numerical simulations and demonstrates the successful detection of both TO1 and TO2 phonons. To examine the behavior of these modes along a nanowire, Figure 3d exhibits the profiles of the LO, TO1 and TO2 phonon frequencies along the x’ – axis of the nanowire. Each profile is averaged over 10 different measurements of single nanowires. The nanomembrane is used as a reference indicating the initial Raman shifts of LO and TO phonon modes prior to patterning, which are 514.97 cm-1 and 516.26 cm-1, respectively (Supporting Information Fig. S3). The LO peaks at each position of the nanowires were obtained via single Lorentzian fitting in the LO – active z ( x ' x ') z polarization setting (see Section V of Supporting Information). It can be seen that for the Raman shifts, TO2 > LO > TO1. This behavior reflects the case of anisotropic strain illustrated in Fig. 1c. For TO1, the Raman shift does not vary much as the nanowire width decreases. TO2, on the other hand, exhibits an increase in the Raman shift as the width decreases. For both cases, the Raman shift around the center of the nanowire ( x’ – position: 200 nm to 800 nm) is relatively constant and increases towards the edges. Based on the obtained TO1 and TO2 Raman shifts – ∆ωTO1 and ∆ωTO2, respectively – the stress along the length (σ’xx) and along the width (σ’yy) can now be directly evaluated using:30
∆ωTO1 ( x ') = −2.88σ ' xx ( x ') − 0.54σ ' yy ( x ')
(2)
∆ωTO2 ( x ') = −0.54σ ' xx ( x ') − 2.88σ ' yy ( x ')
(3)
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where the numerical values were derived using the phonon deformation potentials (PDPs) reported in Ref. 31 and the elastic compliance tensor reported in Ref. 32. Substituting the two TO modes’ frequencies from Fig. 3 to equations (2) and (3), σ’xx and σ’yy along the nanowires are determined as shown in Fig. 4a. Interestingly, this demonstrates that stress in-plane components can be resolved using RSS in backscattering configuration. The general trend is that the stress is higher at the center of the nanowire and decreases as it approaches the edges of the nanowire. Interestingly, and against the prevalent belief that patterning induces strain relaxation in all directions,33,34 we observe that the stress along the nanowire axis, σ’xx, is higher than that of the original stress in the nanomembrane before patterning, which is around 1.2 GPa. However, the stress decreases significantly along y’-direction, σ’yy. The strong contraction along the smallest dimension is attributed to a higher free surface to volume ratio along y’-direction. Fig. 4a also provides strong evidence that this contraction in the y’-direction is accompanied by a stretch along the x’-direction as expected from the Poisson effect. This lattice expansion translates into an increase in the stress along this direction. This subtle but important observation cannot be achieved based on the sole detection of LO phonons. Therefore, it is of paramount importance to detect both TO1 and TO2 to precisely characterize the stress distribution in nanowires and other nanoscale systems with anisotropic stresses. In order to probe the behavior of the stress anisotropy, Fig. 4b exhibits the anisotropy ratio σ’xx / σ’yy as a function of the nanowire width. Expectedly, the narrower the width, the higher is the anisotropy ratio. Interestingly, the anisotropy appears to be more significant at the edge of the nanowire where the contraction along the shortest dimension is more pronounced. This heterogeneous distribution of stress in nanowires and its sensitivity to the nanowire width are very important for the design and fabrication of strained 12
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silicon-based devices as the electrical, optical and mechanical properties of the nanowire depend on them. Using a high NA lens and polarized Raman spectroscopy, we have realized the detection of TO phonons, which is essential for a more comprehensive characterization of stress in nanostructures such as nanowires. Based on numerical simulations, we were able to infer that the LO contribution in the Raman signal is negligible and the detected signal is mainly composed of TO1 and TO2. Based on the measured Raman signals from strained silicon nanowires, TO mode splitting is observed for the first time. The splitting between the modes becomes larger as the nanowire width becomes smaller therefore showing higher anisotropic stress relaxation for narrower nanowires. From Raman shift imaging of the TO1 and TO2 modes, the stress profiles in single nanowires are directly obtained and it was seen that the stress along the x’ – axis is higher than the stress of the nanomembranes as a result of the strong lattice contraction along the shortest dimension. Through the detection of the two TO modes, a more detailed stress analysis can be made which will provide a better understanding of the interplay between stress and basic properties and performance of strained semiconductors based nanoscale materials and devices.
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16. Hrauda, N.; Zhang, J.; Wintersberger, E.; Etzelstorfer, T.; Mandl, B.; Stangl, J.; Carbone, D.; Holý, V.; Jovanović, V.; Biasotto, C.; Nanver, L. K.; Moers, J.; Grützmacher, D.; Bauer, G. Nano Lett. 2011, 11, 2875-2880. 17. Huber, A.J.; Ziegler, A.; Köck, T.; Hillenbrand, R. Nature Nanotech. 2009, 4, 153-157. 18. Tarun, A.; Hayazawa, N.; Ishitobi, H.; Kawata, S.; Reiche, M.; Moutanabbir, O. Nano Lett. 2011, 11, 4780-4788. 19. De Wolf, I. Semicond. Sci. Technol. 1996, 11, 139-154. 20. Loudon, R. Adv. Phys. 1964, 13, 423-482. 21. Ossikovski, R.; Nguyen, Q.; Picardi, G.; Schreiber, J. J. Appl. Phys. 2008, 103, 093525. 22. Mizoguchi, K.; Nakashima, S. J. Appl. Phys. 1989, 65, 2583-2590. 23. Bonera, E.; Fanciulli, M.; Batchelder, D.N. J. Appl. Phys. 2003, 94, 2729-2740. 24. Poborchii, V.; Tada, T.; Usuda, K.; Kanayama, T. Appl. Phys. Lett. 2010, 97, 041915. 25. De Wolf, I.; Maes, H. E.; Jones, S.K. J. Appl. Phys. 1996, 79, 7148-7156. 26. Kosemura, D.; Ogura, A. Appl. Phys. Lett. 2010, 96, 212106. 27. Tarun, A.; Hayazawa, N.; Balois, M. V.; Kawata, S.; Reiche, M.; Moutanabbir, O.; New J. Phys. 2013, 15, 053042. 28. Hayazawa, N.; Furusawa, K.; Kawata, S. Nanotechnology 2012, 23, 465203. 29. Moutanabbir, O.; Reiche, M.; Hähnel, A.; Erfurth, W.; Gösele, U.; Motohashi, M.; Tarun, A.; Hayazawa, N.; Kawata, S. Nanotechnology 2010, 21, 134013. 30. Kosemura, D.; Tomita, M.; Usuda, K.; Ogura, A. Jpn. J. Appl. Phys. 2012, 51, 02BA03. 31. Anastassakis, E.; Cantanero, A.; Cardona, M. Phys. Rev. B 1990, 41, 7529-7535. 32. Brantley, W. A. J. Appl. Phys. 1973, 44, 534-535. 33. Jain, S. C.; Dietrich, B.; Richter, H.; Atkinson, A.; Harker, A. H. Phys. Rev. B 1995, 52, 6247-6253. 34. Ma, F.; Zhang, T.W.; Xu, K.W.; Chu, P.K. Appl. Phys. Lett. 2011, 98, 191907.
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Supporting Information Available Additional information. This material is avialable free of charge via Internet at http://pubs.acs.org.
Notes The authors declare no competing financial interest.
Acknowledgements N.H. gratefully acknowledges financial support from a Grant-in-Aid for Young Scientist (A) No. 21686007 from The Ministry of Education, Culture, Sports, Science and Technology.
O.M. acknowledges funding from NSERC-Canada (Discovery
Grants) and Canada Research Chair.
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Figure Captions Figure 1 | Phonon mode splitting for various types of induced strain. a, In the absence of strain, the detected phonon frequency is triply degenerate consisting of the LO and TO phonon modes. b, In the case of a bi-isotropic strain (nanomembrane), the triply degenerate mode is split into two: singlet LO and doublet TO. c, When anisotropic strain is present, the doublet TO is further split into two singlet TO phonon modes resulting to three phonon modes in total: one singlet LO and two singlet TO. d, Schematic of the excitation beam (λ = 532 nm) and sample orientation with respect to the crystal axes (x,y,z) and sample axes (x’,y’,z’). The nanowire x’ and y’ axes are rotated around the z = z’ axis by 45˚ with respect to the crystal x and y axes. e, SEM images of the arrays of strained silicon nanowires. The scale bar denotes 1 µm. The nanowires are 1 µm long and have a width of 30, 50, or 80 nm. Figure 2 | TO phonon mode splitting in (001)-oriented strained silicon nanowires. Raman spectra from the center of the nanowire with widths of a, 80 nm, b, 50 nm and c, 30 nm. Each Raman spectrum represents averaged data from 10 nanowires. The black hollow circles represent the actual experimental data, while the solid curves represents the fitted data. For fitting, the background signal was subtracted and it was assumed that the intensities of TO1 and TO2 are equal due to symmetry. Splitting becomes more evident as the nanowire becomes narrower. To further support the idea that splitting is indeed occurring, the spectral width (∆υ) of the experimental data was determined. They are ∆υ80 = 5.38 cm-1, ∆υ50 = 5.46 cm-1, and ∆υ30 = 5.93 cm-1, for 80 nm, 50 nm and 30 nm nanowire widths, respectively. Spectral width broadening occurs as the nanowire width decreases, which coincides with the increase of the splitting between the TO phonon peaks. d, The Raman shift of each nanowire is plotted with the degenerated phonon frequency (=516.26 cm-1) of the unpatterned nanomembrane corresponding to infinity width (see Supporting Information Fig. S3b). Figure 3 | Raman Shift imaging of strained silicon nanowire arrays. The TO1 and TO2 Raman shift derived from the double Lorentzian fitting were used to visualize the Raman distribution for a, 80 nm, b, 50 nm, and c, 30 nm width nanowires. The areas without any nanowires present were set to be black to improve the contrast of the image (see also the corresponding Raman intensity image in Supporting Information 17
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Fig. S4). The scale bar is equivalent to 1 µm. The edges of the nanowires are rounded as compared to the SEM image shown in Fig. 1e. This is due to the convolution of the edge of the nanowire and the focus spot, which is probing the nanowire. d, The LO, TO1 and TO2 Raman shifts along the x’ – axis of a nanowire is plotted and compared to those of the nanomembrane (LO: 514.97 cm-1, TO: 516.26 cm-1) (See Supporting Information Fig. S3). These data were averaged from 10 nanowires for each set. Figure 4 | Stress and anisotropy in nanowires of varying width. a, The stress in the x’ – axis, σ’xx, and y’ – axis, σ’yy, along the x’ – direction of a nanowire for varying width, as compared to the stress in a nanomembrane (1.2 GPa). The circular, square and triangular markers are the computed stresses for the 80 nm, 50 nm and 30 nm nanowire widths, respectively. The solid lines are the corresponding fitting from the computed stresses. b, The behavior of the anisotropy ratio as a function of the width both at the center and at the edge of nanowires.
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M.V. Balois, et. al. Figure 1
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M.V. Balois, et. al. Figure 2
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M.V. Balois, et. al. Figure 3
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M.V. Balois, et. al. Figure 4
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Communication
Direct Optical Mapping of Anisotropic Stresses in Nanowires using TO Phonons Splitting Maria Vanessa Balois, Norihiko Hayazawa, Alvarado Tarun, Satoshi Kawata, Manfred Reiche, and Oussama Moutanabbir Nano Lett., Just Accepted Manuscript • DOI: 10.1021/nl500891f • Publication Date (Web): 27 May 2014 Downloaded from http://pubs.acs.org on May 30, 2014
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Direct Optical Mapping of Anisotropic Stresses in Nanowires using TO Phonons Splitting
Maria Vanessa Balois,1, b) Norihiko Hayazawa,1, b), a) Alvarado Tarun,1 Satoshi Kawata,1, c) Manfred Reiche,2 and Oussama Moutanabbir3,1, a)
1
Near-field Nanophotonics Research Team, RIKEN, The Institute of Physical and Chemical Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
2
Max Planck Institute of Microstructure Physics, Weinberg 2, Halle (Saale), 06120 Germany
3
Département de Génie Physique, École Polytechnique de Montréal, Montréal, C.P. 6079, Succ. Centre-Ville, Montréal, Québec, H3C 3A7 Canada
Strain engineering is ubiquitous in design and fabrication of innovative, highperformance electronic, optoelectronic, and photovoltaic devices.
The increasing
importance of strain-engineered nanoscale materials has raised significant challenges at both fabrication and characterization levels. Raman Scattering Spectroscopy (RSS) is one of the most straightforward techniques that have been broadly utilized to estimate the strain in semiconductors.
However, this technique is incapable of
measuring the individual components of stress thus only providing the average values of the in-plane strain. This inherit limitation severely diminishes the importance of RSS analysis and makes it ineffective in the predominant case of nanostructures and devices with nonuniform distribution of strain. Herein, we circumvent this major limitation and demonstrate for the first time the application of RSS to simultaneously probe the two local stress in-plane components in individual ultrathin silicon nanowires based on the imaging of the splitting of the two forbidden transverse optical phonons.
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KEYWORDS:
polarized-Raman,
TO
phonon,
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strained
silicon,
nanowire,
nanomembranes, stress anisotropy
-------------------------------------------------a)
Authors to whom correspondence should be addressed; electronic mail:
[email protected]; [email protected] b)
Department of Electronic Chemistry, Graduate School of Science and Engineering,
Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama, Kanagawa 226-8502 Japan c)
Also at: Department of Precision Science & Technology and Applied Physics,
Osaka University, Suita, Osaka 565-0871, Japan.
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Strain engineering has been a powerful strategy in fabrication and processing of a variety of electronic, optoelectronic, and photovoltaic devices.1-8 To implement these technologies, several processes have been proposed to generate strain in semiconductors in order to improve and control their physical properties by exploiting the influence of strain on the bandgap structure. The increasing importance of this strain-induced bandgap engineering in nanoscale materials has raised significant challenges at both fabrication and characterization levels. The latter in particular has sparked a surge of interest in developing a variety of spectroscopic and microscopic techniques to precisely probe strain and stress in ultra small semiconductor devices and structures.9-19 Lattice interaction with electrons and photons (from infrared to xray) is at the core of the techniques currently employed to probe strain and stress in nanoscale semiconductor structures and devices. Each of these techniques suffers, however, a number of limitations such as being invasive or insensitive to all strain components, or having a limited spatial resolution.
Transmission electron
microscopy-based techniques, including among others holographic interferometry9 and nanobeam electron beam diffraction,10 provide the ultimate spatial resolution in mapping stress, but they are invasive as they require a special sample preparation. This involves cutting the materials and thinning it down to ~100-500 nm, which can induce partial stress relaxation in addition to possible lattice local distortion during the analysis. X-ray-based techniques have immensely benefited from the availability of high-brilliance X-ray sources in the 3rd generation synchrotron sources or free electron lasers leading to development of lensless coherent imaging and nanodiffraction techniques.11-16 These techniques have recently succeeded in mapping the stress in sub-micrometer structures and devices.11-16 One such example of an effective X-ray-based technique was the use of X-ray nanodiffraction combined with
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finite element modeling to probe the local stress in single quantum dot-based devices.16 However, they are still not yet ready for routine analyses because of the need for synchrotron facilities besides requiring special sample preparation to eliminate the background signal from the underlying substrate. Up to date, RSS is still broadly utilized as a very straightforward and timeeffective technique to evaluate the stress states in semiconductors. Nevertheless, the major drawback limiting the use of this technique is its incapacity to discriminate between stress components thus only providing an average value.19 In fact, under the standard backscattering configuration, the incident and the scattered light are normal to the sample surface and thus the electric fields of the incident and scattered radiations are parallel to the sample surface. For cubic crystal structures with (001)surface orientation, Raman scattering selection rule imposes the sole excitation of the longitudinal optical (LO) phonon regardless of the incident and the scattered light polarizations.20 Therefore, only the stress-induced frequency shift of the LO phonon is detected. It is, however, noteworthy that this limitation is not inherent to RSS technique, but it is actually a result of the used scattering geometry.18,21 In a cubic crystal, in addition to LO phonon, there are two transverse optical phonon modes TO1 and TO2. All three phonon modes must be measured in order to obtain a precise analysis of stress states as illustrated in Figs. 1a – 1c. In the absence of strain (Fig. 1a), only a single triply degenerated phonon mode can be detected. However, in the case of a bi-isotropic in-plane strain (εxx = εyy), the original single phonon mode will split into two (Fig. 1b): the singlet LO and the doublet TO. This latter will split further into the two aforementioned singlet TO1 and TO2 phonon modes when the strain bi-isotropy is lost as it is the case for a nanowire under an anisotropic strain (εxx ≠ εyy). It is theoretically possible to detect all three phonon modes either when the
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incident or scattered electric fields are not strictly parallel to the sample surface or when the sample surface is not (001)-oriented.21,22 Herein, we focus our study on the technologically important (001)-oriented strained silicon.
Although the standard
backscattering configuration does not allow to probe directions other than z, we demonstrate that the use of high numerical aperture (NA) objectives circumvents this limitation and makes possible the observation of directions at a certain angle range around the z direction on a sub-micrometer scale.23,24 Moreover, our methodology also involves the effect that, when the polarized beam is focused by the high NA lens, the polarization condition at the tight focus becomes complex and exhibits different polarization components from the initial incident light. This behavior can no longer be neglected, as it is the case when low NA objectives are used. The Raman scattering intensity, I, associated with the excitation and the collection of light in micro-Raman analysis is dependent on the polarization vector of the incident (ei) and the scattered (es) light:25 I ∝ ∑ e sT R j ei , where Rj is the Raman 2
j
polarizability tensor for the jth active phonon mode and ei and es are the incident and scattered electric field unit vectors, respectively. The superscript T denotes transpose of the scattered electric field vector. Let us consider the standard case where, the edges of the nanowire are aligned along the direction. The Si Raman tensors expressed in the crystal axes (x, y, z) are transformed to the sample coordinate axes (x’, y’, z’) defined in Figure 1d. Typically, the Raman intensity is often calculated on the simplified Raman signal collection efficiency (ei and es) based on x’- or y’polarization. The z’- polarization is ignored for backscattering configuration, whereas the x’- and y’- polarizations are set either to unity or zero (undetectable) depending on the analyzer setting. However it was found that when the NA of the objective lens is
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sufficiently high (i.e NA>1.0), the z’- component becomes sufficiently strong which makes it possible to detect the TO phonon.18,26 Moreover, the intensity of depolarized (y’-component) light at the focus also increases and becomes comparable to the z’component for linearly x’-polarized incident light.
Thus, contributions from the
depolarized light can no longer be ignored in the analysis of the scattered Raman signal. The configuration z ( x ' y') z is an example for this case in polarized RSS. To accurately describe the scattering process involving illumination and collection by a high NA lens, the ei cannot be assumed to be constant across the focal volume. Considering all these non-negligible effects, the intensity of the Raman mode can then be rewritten as:18
2π
Ii = I0 ∑ ∫ 0 i
E scaX (θ , φ, η ) θ max ∫ 0 R(α, β, γ ) EscaY (θ, φ, η ) EscaZ (θ , φ, η )
T
2
E ' x × R • R (α, β, γ ) E ' sinθ dθ dφ y i E ' z
(1)
where, I0 is the incident intensity, η is the angle setting of the analyzer with respect to the x’ – axis, and θ and φ are the polar and azimuthal angles, respectively. E’x, E’y, E scaX (θ , φ, η ) and E’z are the component of the incident electric field. E (θ , φ, η ) scaY EscaZ (θ , φ, η )
is the
scattered electric field derived from the objective lens transfer matrix, which describes the radiation dipole collection efficiency of a high NA objective lens (see Supporting Information Section II). In this work, η is equal to 1. Ri is the Raman tensor in the crystal coordinate (x, y, z) system, which can be transformed into the sample coordinate (x’, y’, z’) system using the Euler rotation matrix, R(α,β,γ).
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integration is done over the solid angle, sinθ dθ dφ, and is confined only to the collection cone for the scattered light. Figure 1d shows the experimental configuration used in this work.
Two
coordinate systems are defined, namely the crystal and the sample coordinates, represented as x, y, z and x’, y’, z’, respectively. The edge of the nanowire is aligned along the direction. Linearly polarized light from a 532 nm laser is set parallel to the nanowire long axis (x’ – axis). The beam is expanded and focused onto the nanowires using a high NA oil-immersion objective lens (NA = 1.49, ×100). The diameter of the laser spot is ~436 nm at the surface, which is smaller than the spacing between nanowires (~500 nm) to insure that only one nanowire is exposed to the laser during the analysis. The surface of the ε-Si is directly immersed in oil.
The
backscattered Raman signal is collected by the same objective lens and then passes through an edge filter which blocks the Rayleigh signal in order to detect the backscattered Raman signal.
This signal then proceeds to an analyzer, which
determines which phonon mode is detected, depending on the configuration. In all measurements discussed in this manuscript, the configuration described by Porto’s notation z ( x ' y') z is used. In this polarization configuration, TO phonon modes are predominantly detected, particularly in the case of nanowires (see Supporting Information Section I and Fig. S2).
To extract the TO phonon peaks, double
Lorentzian fitting was used, as shown in Figs. 2a – 2c, based on the results of the simulation suggesting that the detected signal consists only of TO1 and TO2 (negligible LO intensity) with equal intensity due to symmetry of the nanowire with respect to its orientation in the sample coordinate system. This observation was supported by numerical simulations, wherein the TO/LO ratio was computed for
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varying nanowire widths (see Supporting Information Section II, Fig. S2b and S2c) using the same z ( x ' y') z polarization configuration as that in experiment. From the simulations, it was found that the TO/LO ratios for the 80 nm, 50 nm and 30 nm nanowires are 23.56, 54.89 and 84.57, respectively. These values are very large as compared to the TO/LO ratio for the nanomembrane, which is 0.94 (see Supporting Information Fig. S2b). This means that for nanowires, the LO contribution is very small to the point that it is negligible. In contrast, previous work based on z ( x ' x ') z in Porto’s notation predominantly detects only LO phonon mode27. To verify the validity of the numerical simulations, experiments were made on strained nanomembranes under both z ( x ' x ') z and z ( x ' y') z configurations and are summarized in the Supporting Information (Fig. S3). The analyzed light then enters a spectrometer (grating = 1800 g mm-1, focal length = 500 mm, slit width = 100 µm) equipped with a thermo-electronically cooled charge coupled device (CCD) camera (1340 × 400 pixels, 20 µm/pixel). The nanowire array samples were mounted on an x’-y’ translation stage. 3.5 µm x 2.75 µm areas were scanned with a 25 nm step while being illuminated by the focused laser beam. A Raman spectrum was recorded at each step using an exposure time of 5 s and an incident laser power of 2 mW at the sample. Appropriate incident power was used to eliminate laser heating that may affect the detected Raman shift. It should be noted that in order to keep the high NA focus precisely on the nanowire, autofocusing28 was utilized for all the measurements.
Figure 1e shows a scanning electron microscope (SEM) image of strained silicon nanowire arrays investigated in this study (see optical image in Supporting Information Fig. S1a). Each nanowire is 30 nm or 80 nm in width and 1 µm in length.
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Similarly, nanowires of 50 nm in width were also investigated.
The arrays of
nanowires were obtained by patterning a biaxially tensile strained 15 nm-thick silicon (ε-Si) nanomembrane directly on oxide synthesized by epitaxy and ion-cut processes.18,29 To suppress the background from the underlying Si substrate in Raman signals, a Ge layer was inserted between the oxide layer and the handle substrate. Thus, only the nanowire Si-Si intrinsic mode is detected (Supporting Information Figs. S1b and S1c). Figures 2a – 2c show the experimentally obtained Raman spectra at the center of the nanowire for 80 nm, 50 nm and 30 nm widths, respectively. These spectra were obtained under TO-active configuration wherein the contributions from the LO peak are negligible as supported by numerical simulations (see Section II of Supporting Information). The red vertical lines in Fig. 2a indicate the TO1 (515.96 cm-1) and the TO2 (517.71 cm-1) Raman shift peak for the 80 nm width nanowire. The difference between the two peaks is ∆ωTO_80 =1.75 cm-1. This difference in the TO peaks is related to the strain anisotropy in the nanowire as illustrated in Fig. 1c. Similarly, for the 50 nm nanowire, the blue vertical lines in Fig. 2b indicate the TO1 Raman shift peak at 515.84 cm-1 and the TO2 Raman shift peak at 517.75 cm-1. The difference between the two peaks is ∆ωTO_50 = 1.91 cm-1 and is found to be slightly higher than that of 1.75 cm-1 for the 80 nm-wide nanowire. Figure 2c shows the Raman spectra from the 30 nm-wide nanowire. The signal is relatively weaker than the Raman spectra obtained from the 80 nm and 50 nm nanowires due to the smaller volume probed as compared to the wider nanowires. The green vertical lines denote the TO1 (515.6 cm-1) and TO2 (518.32 cm-1) Raman shift peak. The splitting is more apparent at this width and the difference between the two peaks is ∆ωTO_30 = 2.72 cm1
. This indicates that the difference in the TO peaks tend to increase with smaller
widths of the nanowire. Note that this is the first experimental demonstration of TO1
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and TO2 splitting in (001)-oriented silicon. The observed behavior is summarized in Fig. 2d displaying the TO1 and TO2 Raman shift peak as a function of the nanowire width. As a reference, the Raman peak of the nanomembrane is also shown in this figure. Based on the experiment on the unpatterned strained silicon nanomembrane, which can be considered as an infinitely wide nanowire, the extracted TO phonon frequency ωTO_∞ = 516.26 cm-1 (see Section III of Supporting Information). We see a slight increase in the TO1 peak position (within a ±0.5 cm-1 range) as the nanowire width increases. In contrast, the TO2 Raman peak decreases with increasing nanowire width. Besides, TO2 was also found to have a higher slope compared to TO1, which suggest that TO2 is more sensitive to the changes in the nanowire dimension. For both TO1 and TO2, the evolution of the peak positions as the nanowire width increases exhibits a linear but opposite trend. It is also worth mentioning that the TO1 and TO2 peaks converge at 516.26 cm-1, which corresponds to the Raman peak of the nanomembrane (i.e., a nanowire with an infinite width). These results agree very well with theoretical predictions shown in Fig. 1b, where the detected TO is doubly degenerate for the nanomembrane. As illustrated above, this degeneracy is lifted in the case of the nanowire. From the linear trends, one can extrapolate that at a width of 155 nm the structure is sufficiently broad to possibly preserve the bi-isotropic character at the center, similar to the original nanomembrane.
Looking at the
difference between TO1 and TO2 Raman shift peaks for each nanowire width, we see that ∆ωTO_30 > ∆ωTO_50 > ∆ωTO_80. The increase in the splitting between the TO1 and TO2 is due to the narrowing of the width of the nanowires and is a manifestation of the increase in the anisotropy as the nanowire width decreases. To the best of our knowledge, this is the first demonstration of TO mode splitting. Figures 3a – 3c display the TO1 and TO2 Raman shift images of the 80 nm, 50 10
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nm, and 30 nm nanowires, respectively.
These images were obtained through
filtering based on the integrated intensity in order to identify the nanowires (see Supporting Information Fig. S4 for the intensity profile). This visualization of the fitted Raman shifts validates further the numerical simulations and demonstrates the successful detection of both TO1 and TO2 phonons. To examine the behavior of these modes along a nanowire, Figure 3d exhibits the profiles of the LO, TO1 and TO2 phonon frequencies along the x’ – axis of the nanowire. Each profile is averaged over 10 different measurements of single nanowires. The nanomembrane is used as a reference indicating the initial Raman shifts of LO and TO phonon modes prior to patterning, which are 514.97 cm-1 and 516.26 cm-1, respectively (Supporting Information Fig. S3). The LO peaks at each position of the nanowires were obtained via single Lorentzian fitting in the LO – active z ( x ' x ') z polarization setting (see Section V of Supporting Information). It can be seen that for the Raman shifts, TO2 > LO > TO1. This behavior reflects the case of anisotropic strain illustrated in Fig. 1c. For TO1, the Raman shift does not vary much as the nanowire width decreases. TO2, on the other hand, exhibits an increase in the Raman shift as the width decreases. For both cases, the Raman shift around the center of the nanowire ( x’ – position: 200 nm to 800 nm) is relatively constant and increases towards the edges. Based on the obtained TO1 and TO2 Raman shifts – ∆ωTO1 and ∆ωTO2, respectively – the stress along the length (σ’xx) and along the width (σ’yy) can now be directly evaluated using:30
∆ωTO1 ( x ') = −2.88σ ' xx ( x ') − 0.54σ ' yy ( x ')
(2)
∆ωTO2 ( x ') = −0.54σ ' xx ( x ') − 2.88σ ' yy ( x ')
(3)
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where the numerical values were derived using the phonon deformation potentials (PDPs) reported in Ref. 31 and the elastic compliance tensor reported in Ref. 32. Substituting the two TO modes’ frequencies from Fig. 3 to equations (2) and (3), σ’xx and σ’yy along the nanowires are determined as shown in Fig. 4a. Interestingly, this demonstrates that stress in-plane components can be resolved using RSS in backscattering configuration. The general trend is that the stress is higher at the center of the nanowire and decreases as it approaches the edges of the nanowire. Interestingly, and against the prevalent belief that patterning induces strain relaxation in all directions,33,34 we observe that the stress along the nanowire axis, σ’xx, is higher than that of the original stress in the nanomembrane before patterning, which is around 1.2 GPa. However, the stress decreases significantly along y’-direction, σ’yy. The strong contraction along the smallest dimension is attributed to a higher free surface to volume ratio along y’-direction. Fig. 4a also provides strong evidence that this contraction in the y’-direction is accompanied by a stretch along the x’-direction as expected from the Poisson effect. This lattice expansion translates into an increase in the stress along this direction. This subtle but important observation cannot be achieved based on the sole detection of LO phonons. Therefore, it is of paramount importance to detect both TO1 and TO2 to precisely characterize the stress distribution in nanowires and other nanoscale systems with anisotropic stresses. In order to probe the behavior of the stress anisotropy, Fig. 4b exhibits the anisotropy ratio σ’xx / σ’yy as a function of the nanowire width. Expectedly, the narrower the width, the higher is the anisotropy ratio. Interestingly, the anisotropy appears to be more significant at the edge of the nanowire where the contraction along the shortest dimension is more pronounced. This heterogeneous distribution of stress in nanowires and its sensitivity to the nanowire width are very important for the design and fabrication of strained 12
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silicon-based devices as the electrical, optical and mechanical properties of the nanowire depend on them. Using a high NA lens and polarized Raman spectroscopy, we have realized the detection of TO phonons, which is essential for a more comprehensive characterization of stress in nanostructures such as nanowires. Based on numerical simulations, we were able to infer that the LO contribution in the Raman signal is negligible and the detected signal is mainly composed of TO1 and TO2. Based on the measured Raman signals from strained silicon nanowires, TO mode splitting is observed for the first time. The splitting between the modes becomes larger as the nanowire width becomes smaller therefore showing higher anisotropic stress relaxation for narrower nanowires. From Raman shift imaging of the TO1 and TO2 modes, the stress profiles in single nanowires are directly obtained and it was seen that the stress along the x’ – axis is higher than the stress of the nanomembranes as a result of the strong lattice contraction along the shortest dimension. Through the detection of the two TO modes, a more detailed stress analysis can be made which will provide a better understanding of the interplay between stress and basic properties and performance of strained semiconductors based nanoscale materials and devices.
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References 1. Chu, M.; Sun, Y.; Aghoram, U.; Thompson, S. E. Annu. Rev. Mater. Res. 2009, 39, 203-229. 2. Hashemi, P.; Gomez, L.; Hoyt, J. L. IEEE Electron Device Lett. 2009, 30, 401-403. 3. Wu, Z.; Neaton, J. B.; Grossman, J. C. Nano Lett. 2009, 9, 2418-2422. 4. Jacobsen, R. S.; Andersen, K. N.; Borel, P. I.; Fage-Pedersen, J.; Frandsen, L. H.; Hansen, O.; Kristensen, M.; Lavrinenko, A. V.; Moulin, G.; Haiyan, O.; Peucheret, C.; Zsigri, B.; Bjarklev, A. Nature 2006, 441, 199-202. 5. Jain, J. R.; Hryciw, A.; Baer, T. M.; Miller, D. A. B.; Brongersma, M. L.; Howe, R. T. Nature Photon. 2012, 6, 398-405. 6. Süess, M. J.; Minamisawa, R. A.; Schiefler G.; Frigerio, J.; Chrastina, D.; Isella, G.; Spolenak, R.; Faist, J.; Sigg, H. Nature Photon. 2013, 7, 466-472. 7. Boucaud, P.; El Kurdi, M.; Sauvage, S.; de Kersauson, M.; Ghrib, A.; Checoury, X. Nature Photon. 2013, 7, 162. 8. Minamisawa, R.; Süess, M. J.; Spolenak, R.; Faist, J.; David, C.; Gobrecht, J.; Bourdelle, K. K.; Sigg, H. Nat. Commun. 2012, 3, 1096. 9. Hÿtch, M.; Houdellier, F.; Hüe, F.; Snoeck, E. Nature 2008, 453, 1086-1089. 10. Hähnel, A.; Reiche, M.; Moutanabbir, O.; Blumtritt, H.; Geisler, H.; Höntschel J.; Engelmann, H. J. Microsc. Microanal. 2012, 18, 229-240. 11. Newton, M. C.; Leake, S. J.; Harder, R.; Robinson, I. K. Nature Mat. 2010, 9, 120-124. 12. Holt, M.; Harder, R.; Winarski, R.; Rose, V. Annu. Rev. Mater. Res. 2013, 43, 183-211. 13. Godard, P.; Carbone, G.; Allain, M.; Mastropietro, F.; Chen, G.; Capello, L.; Diaz. A.; Metzger, T. H.; Stangl, J.; Chamard, V. Nat. Commun. 2011, 2, 568. 14. Xiong, G.; Moutanabbir, O.; Huang, X.; Paknejad, S. A.; Shi, X.; Reiche, M.; Robinson, I. K. Appl. Phys. Lett. 2011, 99, 114103. 15. Mastropietro, F.; Eymery, J.; Carbone, G.; Baudot, S.; Andrieu, F.; Favre-Nicolin, V. Phys. Rev. Lett. 2013, 111, 215502.
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16. Hrauda, N.; Zhang, J.; Wintersberger, E.; Etzelstorfer, T.; Mandl, B.; Stangl, J.; Carbone, D.; Holý, V.; Jovanović, V.; Biasotto, C.; Nanver, L. K.; Moers, J.; Grützmacher, D.; Bauer, G. Nano Lett. 2011, 11, 2875-2880. 17. Huber, A.J.; Ziegler, A.; Köck, T.; Hillenbrand, R. Nature Nanotech. 2009, 4, 153-157. 18. Tarun, A.; Hayazawa, N.; Ishitobi, H.; Kawata, S.; Reiche, M.; Moutanabbir, O. Nano Lett. 2011, 11, 4780-4788. 19. De Wolf, I. Semicond. Sci. Technol. 1996, 11, 139-154. 20. Loudon, R. Adv. Phys. 1964, 13, 423-482. 21. Ossikovski, R.; Nguyen, Q.; Picardi, G.; Schreiber, J. J. Appl. Phys. 2008, 103, 093525. 22. Mizoguchi, K.; Nakashima, S. J. Appl. Phys. 1989, 65, 2583-2590. 23. Bonera, E.; Fanciulli, M.; Batchelder, D.N. J. Appl. Phys. 2003, 94, 2729-2740. 24. Poborchii, V.; Tada, T.; Usuda, K.; Kanayama, T. Appl. Phys. Lett. 2010, 97, 041915. 25. De Wolf, I.; Maes, H. E.; Jones, S.K. J. Appl. Phys. 1996, 79, 7148-7156. 26. Kosemura, D.; Ogura, A. Appl. Phys. Lett. 2010, 96, 212106. 27. Tarun, A.; Hayazawa, N.; Balois, M. V.; Kawata, S.; Reiche, M.; Moutanabbir, O.; New J. Phys. 2013, 15, 053042. 28. Hayazawa, N.; Furusawa, K.; Kawata, S. Nanotechnology 2012, 23, 465203. 29. Moutanabbir, O.; Reiche, M.; Hähnel, A.; Erfurth, W.; Gösele, U.; Motohashi, M.; Tarun, A.; Hayazawa, N.; Kawata, S. Nanotechnology 2010, 21, 134013. 30. Kosemura, D.; Tomita, M.; Usuda, K.; Ogura, A. Jpn. J. Appl. Phys. 2012, 51, 02BA03. 31. Anastassakis, E.; Cantanero, A.; Cardona, M. Phys. Rev. B 1990, 41, 7529-7535. 32. Brantley, W. A. J. Appl. Phys. 1973, 44, 534-535. 33. Jain, S. C.; Dietrich, B.; Richter, H.; Atkinson, A.; Harker, A. H. Phys. Rev. B 1995, 52, 6247-6253. 34. Ma, F.; Zhang, T.W.; Xu, K.W.; Chu, P.K. Appl. Phys. Lett. 2011, 98, 191907.
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Supporting Information Available Additional information. This material is avialable free of charge via Internet at http://pubs.acs.org.
Notes The authors declare no competing financial interest.
Acknowledgements N.H. gratefully acknowledges financial support from a Grant-in-Aid for Young Scientist (A) No. 21686007 from The Ministry of Education, Culture, Sports, Science and Technology.
O.M. acknowledges funding from NSERC-Canada (Discovery
Grants) and Canada Research Chair.
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Figure Captions Figure 1 | Phonon mode splitting for various types of induced strain. a, In the absence of strain, the detected phonon frequency is triply degenerate consisting of the LO and TO phonon modes. b, In the case of a bi-isotropic strain (nanomembrane), the triply degenerate mode is split into two: singlet LO and doublet TO. c, When anisotropic strain is present, the doublet TO is further split into two singlet TO phonon modes resulting to three phonon modes in total: one singlet LO and two singlet TO. d, Schematic of the excitation beam (λ = 532 nm) and sample orientation with respect to the crystal axes (x,y,z) and sample axes (x’,y’,z’). The nanowire x’ and y’ axes are rotated around the z = z’ axis by 45˚ with respect to the crystal x and y axes. e, SEM images of the arrays of strained silicon nanowires. The scale bar denotes 1 µm. The nanowires are 1 µm long and have a width of 30, 50, or 80 nm. Figure 2 | TO phonon mode splitting in (001)-oriented strained silicon nanowires. Raman spectra from the center of the nanowire with widths of a, 80 nm, b, 50 nm and c, 30 nm. Each Raman spectrum represents averaged data from 10 nanowires. The black hollow circles represent the actual experimental data, while the solid curves represents the fitted data. For fitting, the background signal was subtracted and it was assumed that the intensities of TO1 and TO2 are equal due to symmetry. Splitting becomes more evident as the nanowire becomes narrower. To further support the idea that splitting is indeed occurring, the spectral width (∆υ) of the experimental data was determined. They are ∆υ80 = 5.38 cm-1, ∆υ50 = 5.46 cm-1, and ∆υ30 = 5.93 cm-1, for 80 nm, 50 nm and 30 nm nanowire widths, respectively. Spectral width broadening occurs as the nanowire width decreases, which coincides with the increase of the splitting between the TO phonon peaks. d, The Raman shift of each nanowire is plotted with the degenerated phonon frequency (=516.26 cm-1) of the unpatterned nanomembrane corresponding to infinity width (see Supporting Information Fig. S3b). Figure 3 | Raman Shift imaging of strained silicon nanowire arrays. The TO1 and TO2 Raman shift derived from the double Lorentzian fitting were used to visualize the Raman distribution for a, 80 nm, b, 50 nm, and c, 30 nm width nanowires. The areas without any nanowires present were set to be black to improve the contrast of the image (see also the corresponding Raman intensity image in Supporting Information 17
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Fig. S4). The scale bar is equivalent to 1 µm. The edges of the nanowires are rounded as compared to the SEM image shown in Fig. 1e. This is due to the convolution of the edge of the nanowire and the focus spot, which is probing the nanowire. d, The LO, TO1 and TO2 Raman shifts along the x’ – axis of a nanowire is plotted and compared to those of the nanomembrane (LO: 514.97 cm-1, TO: 516.26 cm-1) (See Supporting Information Fig. S3). These data were averaged from 10 nanowires for each set. Figure 4 | Stress and anisotropy in nanowires of varying width. a, The stress in the x’ – axis, σ’xx, and y’ – axis, σ’yy, along the x’ – direction of a nanowire for varying width, as compared to the stress in a nanomembrane (1.2 GPa). The circular, square and triangular markers are the computed stresses for the 80 nm, 50 nm and 30 nm nanowire widths, respectively. The solid lines are the corresponding fitting from the computed stresses. b, The behavior of the anisotropy ratio as a function of the width both at the center and at the edge of nanowires.
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M.V. Balois, et. al. Figure 1
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M.V. Balois, et. al. Figure 2
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M.V. Balois, et. al. Figure 3
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M.V. Balois, et. al. Figure 4
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