TY - JOUR
AU - Yang,, Jun-Mo
AB - Abstract Recent years have seen a great deal of progress in the development of transmission electron microscopy-based techniques for strain measurement. Dark-field electron holography (DFEH) is a new technique offering configuration of the off-axis principle. Using this technique with medium magnification (Holo-M), we carried out strain measurements in nanoscale-triangular SiGe/(001) Si with (004), (2−20) and (−111) diffraction spots. The reconstruction of holograms and interpretation of strain maps in term of strain precision were discussed and the strain distributions in the SiGe/(001) Si patterns were visualized. Based on linear anisotropic elastic theory for strain simulation, the simulated results obtained by the finite element method compared with the experimental results acquired by DFEH. The strain values were found to be 0.9–1.0%, 1.1–1.2% and 1.0–1.1%, for the (004), (2−20) and (−111) diffracted beams, respectively, and the strain precisions were determined to be ~2.1 × 10−3, 3.2 × 10−3 and 9.1 × 10−3 for the corresponding diffraction spots. As a result, DFEH is highlighted as a powerful technique for strain measurement, offering high-strain precision, high-spatial resolution and a large field of view. strain mapping, dark-field electron holography (DFEH), SiGe, finite element method (FEM), simulation Introduction Knowledge about strain is widely used in the semiconductor industry to improve the performance of electronic devices because of the associated enhancement in carrier mobility [1–3]. Management of strain dramatically increases the mobility of carriers (electrons or holes [4]), leading to significantly enhanced performances in semiconductor devices. In order to better understand and improve the properties of these devices, it is important to have accurate information about strain fields and process-induced strain [4,5]. Many different methods are used to measure strain in semiconductors. X-ray diffraction [6] and micro-Raman spectroscopy [7] are very well-established techniques that now can be used to map strain at the micron scale with spatial resolution approaching tens of nanometers. At smaller scales, transmission electron microscopy (TEM) has been used to provide information about strain in semiconductor devices. The TEM approach is based on techniques such as convergent beam electron diffraction CBED [8–10], nano beam electron diffraction NBED [11–13], high-resolution transmission electron microscopy (HRTEM) with geometric phase analysis (GPA) [14,15] and dark-field electron holography (DFEH) [16–19]. Béché et al. [18] discussed TEM techniques for strain measurement at nanoscale. CBED is very useful for strain analysis, and has the best strain precision among all methods of measurement [20]. However, CBED can sometimes be too sensitive to foil-bending in the highly strained areas of typical devices [2,10] and cannot combine the necessary spatial resolution, precision and field of view. NBED can provide strain maps, but the amount of data obtained will strongly limit the size of the map and the analysis process will be very time-consuming [12]. HRTEM is an easy method that includes the image processing technique of GPA, which can measure local strains. However, because of the relatively high magnification necessary to image at atomic scale, the field of view is limited [2,10,12]. Recently, Hytch et al. [16] reported DFEH, as an alternative method for measuring strain. This new technique has emerged as a powerful tool for mapping strain at nanoscale by measuring the geometric phase of a diffracted beam [17]. Based on off-axis electron holography with medium magnification, DFEH uses an electron biprism to overlap a strained region of the device with an unstrained region in Si. By selecting a specific diffracted beam with an objective aperture to obtain a dark-field hologram, the difference in the lattice constant of the strained and unstrained regions can be measured and the change of lattice constant can be mapped out through data processing [17,18,21,22]. This DFEH technique has been applied to the study of a variety of semiconductor nanostructures, ranging from a single layer to multilayers with thin and thick layers [5,17,18]. However, for strain measurements and simulations, those strain analyses were restricted to the strain distributions in SiGe patterns at nanoscale. In the work reported in this paper, we determined the strain distributions in nm-scale triangular SiGe patterns for (004), (2−20) and (−111) diffraction spots using DFEH with medium magnification mode. The effects of sample preparation and geometry on the initial stress and strain were considered for interpretation of the strain distribution in the triangular SiGe grown on a (001) Si substrate. Based on linear anisotropic elastic theory for strain simulation, we also employed the finite element method (FEM) with COMSOL Multiphysics modeling software. This incorporated pattern parameters, elastic and compositional properties of the SiGe and Si patterns in order to obtain the strain distributions in the triangular SiGe. Subsequently, using the high-resolution X-ray diffraction (HRXRD) results as reference measurements, we assessed the strain distributions in the nm-scale triangular SiGe patterns with DFEH, and compared them to the simulated results. This included a method for phase reconstruction and interpretation of the strain maps that could help other microscopists use this technique with medium magnification mode. Methods The Si1–xGex pattern samples with nominal Ge fraction x = 0.07 and thickness of ~18 nm for the SiGe top and ~9 nm for the SiGe side were grown on (001) Si substrate using chemical vapor deposition. TEM samples were prepared using focused ion-beam as reported by Javon et al. [22] and Li et al. [23], following a dedicated procedure aimed at improving the uniformity of the sample thickness while reducing sample bending. As Hÿtch et al. [24] mentioned, the sample thickness needs to be of uniform thickness; typically, this thickness should be about half the extinction distance of the diffracted beam of interest. For silicon and silicon germanium at 200 kV, samples were prepared to a thickness of ~120 nm, which could be used for all the usual cases. This preparation involved several steps. (i) After face-to-face gluing of the two pieces of the wafer, the substrate part of one piece was removed by tripod polishing in plan-view configuration. (ii) The small sample containing the feature of interest was then cut free and made ready to be lifted out. Subsequently, an in-situ lift-out process was used to carefully position the TEM sample on a carrier, which is glued to a modified TEM grid. (iii) A layer of carbon was evaporated onto both surfaces of the specimen to prevent electrostatic charging during the electron beam irradiation. DFEH was carried out on a 200 kV FE-TEM (JEM-ARM200F) microscope equipped with a biprism and a 2 k × 2 k CCD camera (US1000). For the microscope used, the illumination system consists of two condenser lenses (CL1 and CL2). The imaging system consisted of one lens coupled with a biprism, which was placed near the first image plane of the selected area aperture. With DFEH technique in medium magnification mode (HOLO-M), the available magnification range was between 100 k and 300 k, which is suitable for holography measurement of our samples. For observations, the size the electron beam was determined by decreasing the convergent angle, with the condenser lens aperture at 50 μm. The angle of beam scattering is controlled by the objective lens aperture (20 μm). To acquire dark-field holograms, the specimen was oriented under two-beam conditions close to the [110] zone axis, to obtain (004), (220) and (111) diffraction spots. As for conventional off-axis holography, holograms were acquired in elliptical illumination conditions to preserve the spatial coherence perpendicular to the biprism. Holograms were recorded with a biprism voltage of 30 V. The interference fringe spacing was measured (0.33 nm). The width of the biprism was 34 nm and the fringe of visibility was around 18% for a 15 s exposure. The holograms were analyzed using the HoloDark plug-in installed in the DigitalMicrograph (Gatan, Inc. Pleasanton, CA (USA)). The spatial resolution for strain measurement was determined by the radius of the mask used for holographic reconstruction, and was fixed to 1.5 nm. With the DFEH technique, in order to obtain the strain maps, two initial and overlapping waves are produced by applying a positive voltage of 30 V to the electron biprism. The intensity distribution of an electron hologram can be defined [25] as: I(r⃗)=ASi2+AROI2(r⃗)+2μASiAROI(r⃗)cos[∆∅(r⃗)+2π(q⃗c+∆⃗g(r⃗))r⃗] where r⃗ is the position vector in the recorded image. ASi and AROI are the amplitudes of the waves diffracted by the silicon substrate and the region of interest (SiGe). Here, Δ∅(r⃗)=∅Si−∅SiGe(r)⃗ is the phase difference between the two diffracted waves, μ is the contrast and qc is the carrier frequency, and Δ⃗g(r⃗)=g⃗Si-g⃗SiGe(r⃗) is the difference of the reciprocal lattice vectors that characterize the crystal structure in the two regions. The phase information can be separated into four contributions [24]: ∅=∅E+∅M+∅C+∅G where subscripts E, M, C and G refer respectively to the electrostatic, magnetic, crystalline and geometric contributions. Here, we assume that the electrostatic, magnetic and crystalline phases are constant over the field of view, so that ∂∅E,M,C/∂r=0 ⁠. The geometric phase can be defined as the extra phase term induced by a translation u = ux + uy + uz of the reference crystal [21,24]: ∅G=−2πg⋅u(r) In the reconstruction process, the hologram is analyzed utilizing the Fast Fourier Transform (FFT) given by [25]: FT{I(r⃗)}={δ(q⃗)+FT[A2(r⃗)]}+μ⋅δ(q⃗−q⃗c)⨂FT[A(r⃗)exp(i∅(r⃗))]+μ⋅δ(q⃗+q⃗c)⨂FT[A(r⃗)exp(−i∅(r⃗))] where the first term corresponds to the center band. This represents essentially the conventional image; it contains both elastically and inelastically scattered electrons, and both linear and nonlinear terms. However, it does not contain the image phase ∅(r⃗) and hence is not of further interest here. The second and third terms contain the phase and amplitude of the wave. These two terms are called sidebands and they are complex conjugate terms one from each other. One of these two sidebands of the FFT is spatially filtered, and its inverse FFT can be computed to recover the phase and amplitude of the wave. During the inverse Fourier transformation of sideband information, the parameters used for the phase reconstruction (referred to as the aperture size) need to be carefully controlled. Generally, the aperture radius was set to reach a position from 1/3 to 1/2 of the distance between the maximums of the center band and the sideband. HRXRD with ω-2θ scans along the growth direction is generally used to analyze the material composition, crystalline orientations and precise lattice constant measurements. These provide information about lattice mismatch between the SiGe and the Si substrate. Therefore, HRXRD ω-2θ scans were also used in strain calculations for the SiGe samples. With this method, the modular design of the hybrid 2-bounce Ge (220) monochromators used, allowed users to insert different optical elements easily. Symmetric (004) and (220) spectra were collected so that the XRD results obtained could be used as reference measurements; these results were compared with the DFEH results. In this study, the strain ε along the growth direction induced by lattice mismatch was calculated using the following equation: ε = (aSiGe–aSi)/aSi, where aSiGe and aSi correspond to the lattice constant of the SiGe region and the Si substrate [26]. For this paper, the FEM was used to model a 3D model of the nanoscale-triangular SiGe pattern in COMSOL Multiphysics 5.0 (COMSOL, Inc. Burlington, MA (USA)). Based on linear anisotropic elastic theory, strains were simulated in the nanoscale-triangular SiGe pattern. Domains of different chemical composition were distinguished by their elastic coefficients and lattice parameters, which were evaluated by applying Vegard's law. The geometry of the model was based on the bright-field images of the observed structures. In our model, we have taken into account the geometric periodicity of the SiGe pattern, which is considered infinite using a periodic boundary condition. With respect to the Si substrate, we define the coordinate system as x//[1−10], y//[110] and z//[001], where the y-axis corresponds to the electron beam direction (zone axis) and the z-direction is the direction normal to the surface of the substrate (direction of growth). In the z-direction, the lower boundary of the Si substrate was constrained and the upper surface treated as a free surface. Simulations were carried out for a 120-nm thick sample with four free surfaces, corresponding to the TEM samples. It should be noted that SiGe patterns were compressed in the in-plane direction and stretched in the growth direction by Poisson's effect. For the Young's modulus and Poisson's ratio of a standard (100) Si wafer, E and ν depend on the direction; those are ESi[110] = 169 GPa and νSi[110] = 0.06 while ESi[001] = 130 GPa and νSi[001] = 0.28, as reported in the literature [26–31]. The elastic stiffness constants defined for the cubic system of Si where x, y and z are orthogonal {001} directions are C11 = 165.6 GPa, C12 = 63.9 GPa and C44 = 79.5 GPa. The SiGe is treated as an elastically isotropic material having the following Young's modulus and Poisson's ratio: ESiGe = 159 GPa, νSiGe = 0.27. To calculate the strain, the stiffness had to be rotated by 45° around the [001] direction. Results and discussion As shown in Fig. 1a–d, SiGe nm-scale triangular patterns have a top SiGe layer with thickness of ∼18 nm, and a SiGe side with thickness of ∼9 nm. Figure 1a shows the TEM image of the SiGe patterns, which indicates the biprism positions. The biprism position was adjusted parallel to the x-axis direction that was used to measure the (004) and (−111) holograms. The other perpendicular to the x-axis was used to obtain the (2−20) hologram. As can be seen in Fig. 1b, at medium magnification (200 k), the TEM image shows high contrast between the Si region and the SiGe one, and the electron diffraction pattern inset indicates the spots for strain measurements. Here, we defined the coordinate system as x//[1−10], y//[110] and z//[001], where the y-axis corresponds to the electron beam direction (zone axis), the z-direction is the direction normal to the surface of the Si substrate. In Fig. 1c, the atomic model for the [110] projection of the SiGe patterns points out the arrangement of Si and Ge atoms in the Si and SiGe regions. When SiGe was grown on a Si substrate, lattice expansions could occur in the SiGe regions along the z- and x-directions. Figure 1d shows the model image for simulation used in the COMSOL Multiphysics modeling software. Fig. 1. Open in new tabDownload slide (a) TEM image showing the biprism positions. (b) TEM image with high contrast between the Si region and the SiGe one and the electron diffraction pattern (inset) for strain measurements. (c) Atomic model of the arrangement of atoms in the Si and SiGe regions along the [110] zone axis. (d) Model image for simulation. Fig. 1. Open in new tabDownload slide (a) TEM image showing the biprism positions. (b) TEM image with high contrast between the Si region and the SiGe one and the electron diffraction pattern (inset) for strain measurements. (c) Atomic model of the arrangement of atoms in the Si and SiGe regions along the [110] zone axis. (d) Model image for simulation. Figure 2a and b exhibits HRXRD ω-2θ scans. Based on the HRXRD measurement, it was possible to accurately determine the SiGe thickness t and the Ge concentration x. In Fig. 2a and b, it can be seen that the XRD spectra obtained at the symmetric (004) reflection of the top SiGe and the (2−20) reflection of the SiGe side, respectively. Using this method, the interplanar distances of Si and SiGe were evaluated and found to be 1.358 and 1.368 Å, respectively, for the (004) spot, and 1.920 and 1.935 Å, respectively, for the (2−20) spot. Considering in-plane and out-of-plane strains in the nm-scale triangular SiGe pattern, as Boureau et al. [32] reported, with layer below the critical thickness, the material retains the initial lattice parameter of pure Si in the plane parallel to the surface during the growth process, there is no plastic relaxation [33]. This means that the lattice expansion can only occur in the nm-scale triangular SiGe pattern along the z-direction for the top SiGe region and in the x-direction for the SiGe side. Therefore, the strain along those two directions can be determined by the c and a parameters, respectively. For the (004) spot, the c value was estimated to be ~5.472 Å, and the a value was evaluated and found to be 5.474 Å. As described in a previous section, the strain induced by the mismatch in lattice spacing between two regions is given by ε = (aSiGe – aSi)/aSi, where the lattice constant of Si is 5.431 Å. The strain values were calculated and found to be 0.75% and 0.79% for the (004) and (2−20) spots, respectively. These two values were considered important components comparable to the values obtained using DFEH. Fig. 2. Open in new tabDownload slide HRXRD ω-2θ scan for the SiGe pattern sample: (a) symmetric (004) reflection of the top SiGe and (b) the (2−20) reflection of the SiGe side. Fig. 2. Open in new tabDownload slide HRXRD ω-2θ scan for the SiGe pattern sample: (a) symmetric (004) reflection of the top SiGe and (b) the (2−20) reflection of the SiGe side. To interpret the simulated results, we studied in terms of initial strains and initial stresses for modeling the mechanics of the system. We developed 3D FEM-based models considering the full anisotropy of the system and materials. Vergard's law was adopted to determine the mechanical properties and lattice mismatch stress of the triangular SiGe pattern. The lattice parameter aSiGe of the Ge mole fraction x in the Si1–xGex can be given by the following equation: aSiGe = (1 – x)aSi + xaGe, where the lattice constant of Si is 5.431 Å and the lattice constant of Ge is 5.657 Å. According to Vergard's law, the lattice constant of SiGe was estimated and found to be ~5.45 Å. The strain induced by the lattice mismatch was calculated and found to be 0.35%. This is called the initial strain. The initial stress σ can be calculated using the constitutive elastic equation: σ = εE/(1 – ν), where E is Young's modulus, ν is Poisson's ratio, and σ and ε refer to the stress and strain, respectively. The elastic modulus and Poisson's ratio of the Si1–xGex alloy is obtained by linear interpolation of pure silicon and Ge bulk materials [27]. The initial stresses in the SiGe were found by adjusting the computed strains to fit the experimentally measured ones. Therefore, the variables put in the models include the initial stresses and the initial strains of the triangular SiGe pattern. Figure 3a–d shows the strain results along the [001] direction (the z-direction) obtained by the DFEH technique, and the simulation for the (004) diffracted beam. In Fig. 3a, the dark-field hologram presents the biprism position of the top SiGe pattern, and the inset is the (004) two-beam condition used for holography measurement and simulation of strain. Figure 3b exhibits the strain map in the [001] direction from the dark-field hologram using Holodark. Figure 3c is the strain map obtained by COMSOL Multiphysics. In Fig. 3d, the strain profiles were extracted from strain maps along the z-direction in the boxes in (b) and (c), with red and black lines corresponding to experimental and simulated results, respectively. In comparing the experimental and the simulated results, we used the terms of the strain value and the depth of strain distributions in the top SiGe layer of the pattern sample. Using the X-ray results as reference measurement for the symmetric (004) reflection, the experimental and the simulated strain values almost fit, and were found to be around 0.9–1.0%. This is greater than the strain value (0.75%) obtained by the XRD method. The depth of the strain distribution along the z-direction was estimated and found to be ∼18 nm, which corresponds to the maximum thickness of the top SiGe layer of the pattern sample. We expect that the strain values from the experimental results measured using DFEH, and the simulated ones obtained using FEM in COMSOL Multiphysics, were equal to the strain value from the XRD results. This is called the bulk strain value. However, there can be slight differences in the strain values. In explanation, as mentioned before, considering the effects of the specimen preparation process and the geometry of the specimen on strain values and strain distributions, the strain value at the surface is greater, and is relative to the bending of the lattice planes. Depending on the variation in thickness during the sample-preparation process, especially for the nm-scale triangular SiGe pattern, pattern bending is inevitable. In general, DFEH can be sensitive to pattern bending in the highly strained areas as was mentioned in Béché et al. [18]. Based on simulation models, the initial stress and initial strain induced by the lattice mismatch can be used in the models to fit the experimentally measured strains. In addition, there is a high-strain level with a value of ~1.4% at the SiGe–Si interface. In other words, a lot of noise is present at the interface due to phase discontinuities. The strain precision known as strain sensitivity corresponds to the standard deviation of strain level within a region of reference [18]. For the estimation of the precision, the strain precision was estimated to 2.1 × 10−3 from the unstrained Si substrate. Fig. 3. Open in new tabDownload slide (a) Dark-field hologram for the (004) diffracted beam. Inset shows the two-beam condition. (b) Strain map in the [100] direction from dark-field hologram using HoloDark. (c) Simulated strain map produced using COMSOL Multiphysics. (d) The extracted strain profile (red line) from the region indicated by the box in (b) compared with the simulated strain profile (black line) extracted from the region indicated by the box in (c). Fig. 3. Open in new tabDownload slide (a) Dark-field hologram for the (004) diffracted beam. Inset shows the two-beam condition. (b) Strain map in the [100] direction from dark-field hologram using HoloDark. (c) Simulated strain map produced using COMSOL Multiphysics. (d) The extracted strain profile (red line) from the region indicated by the box in (b) compared with the simulated strain profile (black line) extracted from the region indicated by the box in (c). Using the same approaches, Fig. 4a–d shows the strain results along the [1−10] direction (the x-direction) obtained for the (2−20) diffracted beam. The dark-field hologram at the (2−20) diffraction spot, with an electron bias voltage of 30 V, is illustrated in Fig. 4a and the inset indicates the (220) two-beam condition. The strain map is displayed in Fig. 4b where the red color indicates the positive strain value in the SiGe region. This means that the lattice expansion could occur in the x-direction parallel to the references [1−10]. Figure 4c shows the strain map obtained using the FEM method in the COMSOL Multiphysics modeling software 5.0. It has been observed that the strain distributions illustrated in Fig. 4d are quite uniform and smooth along the x-direction on the whole SiGe side for both the experimental and the simulated results. From the assumption described previously in the simulation, the experimental and simulated results are in very good agreement in terms of the strain value and the depth of the strain distributions. The strain values were estimated to be ~1.1–1.2% for the experimental and the simulated results. The depths of the strain distributions were calculated and found to be ∼9 nm, corresponding to the thickness of the SiGe side. In comparison with reference measurements, both the experimental and simulated strain values are greater than the bulk strain value (0.79%). To interpret this phenomena, it was decided to use the same approach to an explanation as mentioned in the analyses for the (004) diffracted beam. In this case, the strain precision was determined to be up to 3.2 × 10−3 from the substrate region. Fig. 4. Open in new tabDownload slide (a) Dark-field hologram using the (2−20) diffracted beam and the two-beam condition (inset). (b) Strain map along the [1−10] direction from dark-field hologram using HoloDark. (c) Simulated strain map produced by COMSOL Multiphysics. (d) The experimental strain profile (red line) compared with the simulated strain profile (black line). Fig. 4. Open in new tabDownload slide (a) Dark-field hologram using the (2−20) diffracted beam and the two-beam condition (inset). (b) Strain map along the [1−10] direction from dark-field hologram using HoloDark. (c) Simulated strain map produced by COMSOL Multiphysics. (d) The experimental strain profile (red line) compared with the simulated strain profile (black line). To assess more information in terms of the strain values and the depth of strain distributions from the experiment and the simulation, but without using the XRD results as reference measurements (these can be seen in Fig. 5a–d), we analyzed the strain results for the (−111) spot along the [001] direction. Figure 5b and c displays the strain maps obtained using the DFEH technique and the FEM method, respectively. From the strain profiles, as illustrated in Fig. 5d, the strain values were estimated and found to be 1.0–1.1% (both experimental and simulated). The depth of the strain distribution was ~18 nm, corresponding to the maximum thickness of the top SiGe layer of the pattern sample. As can be seen in Fig. 5d, the strain distributions are clearly uniform and smooth over the whole SiGe area. We recognize that there is very good agreement for the strain value and the depth of strain distribution between the experimental and simulated results. For the measurement of precision, the strain precision evaluated from the Si substrate was found to be 9.1 × 10−3. This value is the highest in all the cases. This difference may come from different two-beam conditions that reduced the quality of the hologram acquired on the part of sample. Reducing the phase sensitivity significantly influences the strain precision. Fig. 5. Open in new tabDownload slide (a) Dark-field hologram from the (−111) diffracted beam. (b) Strain map in the [001] direction from dark-field hologram using HoloDark. (c) Simulated strain map obtained using COMSOL Multiphysics. (d) Comparison between the experimental strain profile (red line) and the simulated strain profile (black line). Fig. 5. Open in new tabDownload slide (a) Dark-field hologram from the (−111) diffracted beam. (b) Strain map in the [001] direction from dark-field hologram using HoloDark. (c) Simulated strain map obtained using COMSOL Multiphysics. (d) Comparison between the experimental strain profile (red line) and the simulated strain profile (black line). Concluding remarks The DFEH technique can provide strain measurement with high precision, high-spatial resolution and a large field of view. However, this method demands more effort in terms of alignment and requires a stable microscope. DFEH requires perfectly parallel sides since the phase is sensitive to variation in thickness of the samples. Using this technique with medium magnification mode, and with alignment for optimal conditions for observation as described previously, we analyzed successfully the strain results in the nm-scale triangular SiGe pattern. The experimental results were compared with the simulated results obtained using COMSOL Multiphysics for (004), (2−20) and (−111) diffraction beams. The strain distributions are quite uniform and smooth for all spots over the whole SiGe sample, with high-strain precision (<9.1 × 10−3). With the XRD results as reference measurements, it can be seen that there is good agreement between the experimental and the simulated values of strain and depth of strain distributions, compared with the bulk strain value and thicknesses of the SiGe top and SiGe side in the SiGe pattern sample. The results demonstrate that the DFEH is a very versatile technique for measuring strain in semiconductor devices. Funding The Technology Innovation Program, [10048393], Core Technology Development of Measurement and Analysis Techniques for the Promotion of Nanotechnology Commercialization, funded by the Ministry of Trade, Industry, and Energy (MOTIE, Korea). References 1 Cooper D , Denneulin T , Bernier N , Béché A ( 2016 ) Strain mapping of semiconductor specimen with nm-scale resolution in a transmission electron microscope . Micron 80 : 145 – 165 . Google Scholar Crossref Search ADS PubMed WorldCat 2 Hue F , Hytch M , Houdellier F , Snoeck E , Claverie A ( 2008 ) Strain mapping in MOSFETS by high-resolution electron holography . Mat. Sci. Eng. B 154–155 : 221 – 224 . Google Scholar Crossref Search ADS WorldCat 3 Armigliato A , Balboni B , Carnevale G P , Pavia G , Piccalo D , Frabboni S , Benedetti A , Cullis A G ( 2003 ) Application of convergent beam electron diffraction to two-dimensional strain mapping in silicon devices . Appl. Phys. Lett. 82 : 2172 . Google Scholar Crossref Search ADS WorldCat 4 Lee M L , Fitzgerald E A , Bulsara M T , Currie M T , Lochtefeld A ( 2005 ) Strained Si, SiGe, and Ge channels for high-mobility metal-oxide-semiconductor field-effect transistors . J. Appl. Phys. 97 : 011101 . Google Scholar Crossref Search ADS WorldCat 5 Hoang V V , Cho Y J , Yoo J H , Yang J-M , Choi S H , Jung W D , Choi Y H , Hong S-K ( 2015 ) 2D strain measurement in sub-10 nm SiGe layer with dark-field electron holography . Curr. Appl. Phys. 15 : 1529 – 1533 . Google Scholar Crossref Search ADS WorldCat 6 Miao J , Charalambous P , Kirz J , Sayre D ( 1999 ) Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens . Nature 400 : 342 – 344 . Google Scholar Crossref Search ADS WorldCat 7 Senez V , Armigliato A , de Wolf I , Carnevale G , Balboni R , Frabboni S , Benedetti A ( 2003 ) Strain determination in silicon microstructures by convergent beam electron diffraction, process simulation and micro-Raman spectroscopy . J. Appl. Phys. 94 : 5574 . Google Scholar Crossref Search ADS WorldCat 8 Armigliato A , Balboni R , Frabboni S ( 2005 ) Improving spatial resolution of convergent beam electron diffraction strain maps in silicon microstructures . Appl. Phys. Lett. 86 : 063508 . Google Scholar Crossref Search ADS WorldCat 9 Armigliato A , Spessot A , Balboni R , Benedetti A , Carnevale G , Frabboni S , Mastracchio G , Pavia G ( 2006 ) Convergent beam electron diffraction investigation of strain induced by Ti self-aligned silicides in shallow trench Si isolation structures . J. Appl. Phys. 99 : 064504 . Google Scholar Crossref Search ADS WorldCat 10 Zhang P , Istratov A A , Weber E R , Kisielowski C , He H , Nelson C , Spence J C H ( 2006 ) Direct strain measurement in a 65 nm node strained silicon transistor by convergent-beam electron diffraction . Appl. Phys. Lett. 89 : 161907 . Google Scholar Crossref Search ADS WorldCat 11 Usuda K , Numata T , Takagi S ( 2005 ) Strain evaluation of strained-Si layers on SiGe by the nano-beam electron diffraction (NBD) method . Mater. Sci. Semicond. Process 8 : 155 – 159 . Google Scholar Crossref Search ADS WorldCat 12 Usuda K , Numata T , Irisawa T , Hirashita N , Takagi S ( 2005 ) Strain characterization in SOI and strained-Si on SGOI MOSFET channel using nano-beam electron diffraction (NBD) . Mater. Sci. Eng. B 124–125 : 143 – 147 . Google Scholar Crossref Search ADS WorldCat 13 Béché A , Rouvière J L , Clément L , Hartmann J M ( 2009 ) Improved precision in strain measurement using nano beam electron diffraction . Appl. Phys. Lett. 95 : 123114 . Google Scholar Crossref Search ADS WorldCat 14 Vajargah S H , Couillard M , Cui K , Tavakoli S G , Robinson B , Kleiman R N , Preston J S , Botton G A ( 2011 ) Strain relief and AlSb buffer layer morphology in GaSb heteroepitaxial films grown on Si as revealed by high-angle annular dark-field scanning transmission electron microscopy . Appl. Phys. Lett. 98 : 082113 . Google Scholar Crossref Search ADS WorldCat 15 Guerrero E , Galindo P L , Yanez A , Pizarro J , Guerrero-Lebrero M P , Molina S I ( 2009 ) Accuracy assessment of strain mapping from Z-contrast images of strained nanostructures . Appl. Phys. Lett. 95 : 143126 . Google Scholar Crossref Search ADS WorldCat 16 Hytch M , Houdellier F , Hue F , Snoeck E ( 2008 ) Nanoscale holographic interferometry for strain measurements in electronic devices . Nature 453 : 1086 – 1089 . Google Scholar Crossref Search ADS PubMed WorldCat 17 Béché A , Rouvière J L , Barnes J P , Cooper D ( 2011 ) Dark-field electron holography for strain measurement . Ultramicroscopy 111 : 227 – 238 . Google Scholar Crossref Search ADS PubMed WorldCat 18 Béché A , Rouvière J L , Barnes J P , Cooper D ( 2013 ) Strain measurement at the nanoscale: comparison between convergent beam electron diffraction, nano-beam electron diffraction, high-resolution imaging and dark-field electron holography . Ultramicroscopy 131 : 10 – 23 . Google Scholar Crossref Search ADS PubMed WorldCat 19 Zhu J , Zhou Y K , Toh S L , Mai Z H , Lam J , Du A Y , Hua Y N , Rajgopal R ( 2012 ) TEM dark-field off-axis electron holography strain measurement on embedded-SiGe pMOSFETs and comparison with nano-beam diffraction strain measurement. In: 19th IEEE International Symposium on the Physical and Failure Analysis of Integrated Circuits (IPFA), pp 1 – 5 . 20 Rouvière J L , Sarigiannidou E ( 2005 ) Theoretical discussions on the geometrical phase analysis . Ultramicroscopy 106 : 1 – 17 . Google Scholar Crossref Search ADS PubMed WorldCat 21 Hÿtch M J , Snoeck E , Kilaas R ( 1998 ) Quantitative measurement of displacement and strain fields from HREM micrographs . Ultramicroscopy 74 : 131 – 146 . Google Scholar Crossref Search ADS WorldCat 22 Javon E , Lubk A , Cours R , Reboh S , Cherkashin N , Houdellier F , Gatel C , Hÿtch M J ( 2014 ) Dynamical effects in strain measurements by dark-field electron holography . Ultramicroscopy 147 : 70 – 85 . Google Scholar Crossref Search ADS PubMed WorldCat 23 Li J , Malis T , Dionne S ( 2006 ) Recent advances in FIB-TEM specimen preparation techniques . Mater. Charact. 57 : 64 – 70 . Google Scholar Crossref Search ADS WorldCat 24 Hÿtch M J , Houdellier F , Hüe F , Snoeck E ( 2011 ) Dark-field electron holography for the measurement of geometric phase . Ultramicroscopy 111 : 1328 – 1337 . Google Scholar Crossref Search ADS PubMed WorldCat 25 Lichte H , Lehmann M ( 2008 ) Electronholography: basics and applications . Rep. Prog. Phys. 71 : 016102 . Google Scholar Crossref Search ADS WorldCat 26 Bedell S W , Reznicek A , Fogel K , Ott J , Sadana D K ( 2006 ) Strain and lattice engineering for Ge FET devices . Mater. Sci. Semicond. Process 9 : 423 . Google Scholar Crossref Search ADS WorldCat 27 Lee C-C , Cheng H-C , Hsu H-W , Chen Z-H , Teng H-H , Liu C-H ( 2014 ) Mechanical property effects of Si1−xGex channel and stressed contact etching stop layer on nano-scaled n-type metal-oxide-semiconductor field effect transistors . Thin Solid Films 557 : 316 – 322 . Google Scholar Crossref Search ADS WorldCat 28 Wortman J J , Evens R A ( 1965 ) Young's modulus, shear modulus, and Poisson's ratio in silicon and germanium . J. Appl. Phys. 36 : 153 . Google Scholar Crossref Search ADS WorldCat 29 Hopcroft M A , Nix W D , Kenny T W ( 2010 ) What is the Young's modulus of silicon . J. Microelectromech. Syst. 19 : 229 . Google Scholar Crossref Search ADS WorldCat 30 Matoy K , Schönherr H , Detzel T , Schöberl T , Pippan R , Motz C , Dehm G ( 2009 ) A comparative micro-cantilever study of the mechanical behavior of silicon based passivation films . Thin Solid Films 518 : 247 . Google Scholar Crossref Search ADS WorldCat 31 Denneulin T , Cooper D , Rouviere J L ( 2014 ) Practical aspects of strain measurement in thin SiGe layers by (004) dark-field electron holography in Lorentz mode . Micron 62 : 52 – 65 . Google Scholar Crossref Search ADS PubMed WorldCat 32 Boureau V , Benoit D , Warot B , Hÿtch M , Claverie A ( 2015 ) Strain/composition interplay in thin SiGe layers on insulator processed by Ge condensation . Mater. Sci. Semicond. Process 42 : 251 – 254 . Google Scholar Crossref Search ADS WorldCat 33 Tezuka T , Nakaharai S , Moriyama Y , Hirashita N , Toyoda E , Numata T , Irisawa T , Usuda K , Sugiyama N , Mizuno T , Takagi S-I ( 2007 ) Strained SOI/SGOI dual-channel CMOS technology based on the Ge condensation technique . Semicond. Sci. Technol. 22 : S93 – S97 . Google Scholar Crossref Search ADS WorldCat © The Author 2016. Published by Oxford University Press on behalf of The Japanese Society of Microscopy. All rights reserved. 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TI - Strain mapping in a nanoscale-triangular SiGe pattern by dark-field electron holography with medium magnification mode
JF - Microscopy
DO - 10.1093/jmicro/dfw036
DA - 2016-12-01
UR - https://www.deepdyve.com/lp/oxford-university-press/strain-mapping-in-a-nanoscale-triangular-sige-pattern-by-dark-field-1IF8J4Zd80
SP - 499
VL - 65
IS - 6
DP - DeepDyve
ER -