 View Online  Export Citation CrossMark RESEARCH ARTICLE | JULY 18 2022 Off-axis Raman spectroscopy for nanoscale stress metrology Zoheb Khan ; Thomas Nuytten; Paola Favia; ... et. al Journal of Applied Physics 132, 035104 (2022) https://doi.org/10.1063/5.0100602 Articles You May Be Interested In Anisotropic stress in narrow sGe fin field-effect transistor channels measured using nano-focused Raman spectroscopy APL Mater (January 2018) Metrology of image placement AIP Conference Proceedings (November 1998) D ow nloaded from http://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/5.0100602/16510500/035104_1_online.pdf https://pubs.aip.org/aip/jap/article/132/3/035104/2837160/Off-axis-Raman-spectroscopy-for-nanoscale-stress https://pubs.aip.org/aip/jap/article/132/3/035104/2837160/Off-axis-Raman-spectroscopy-for-nanoscale-stress?pdfCoverIconEvent=cite https://pubs.aip.org/aip/jap/article/132/3/035104/2837160/Off-axis-Raman-spectroscopy-for-nanoscale-stress?pdfCoverIconEvent=crossmark javascript:; javascript:; javascript:; javascript:; https://doi.org/10.1063/5.0100602 https://pubs.aip.org/aip/apm/article/6/5/058501/1023620/Anisotropic-stress-in-narrow-sGe-fin-field-effect https://pubs.aip.org/aip/acp/article/449/1/513/975577/Metrology-of-image-placement https://servedbyadbutler.com/redirect.spark?MID=176720&plid=2071766&setID=592934&channelID=0&CID=757753&banID=521007412&PID=0&textadID=0&tc=1&adSize=1640x440&matches=%5B%22inurl%3A%5C%2Fjap%22%5D&mt=1685010423244691&spr=1&referrer=http%3A%2F%2Fpubs.aip.org%2Faip%2Fjap%2Farticle-pdf%2Fdoi%2F10.1063%2F5.0100602%2F16510500%2F035104_1_online.pdf&hc=52a7a12a2cef65380961d976cbb0739410f33e99&location= Off-axis Raman spectroscopy for nanoscale stress metrology Cite as: J. Appl. Phys. 132, 035104 (2022); doi: 10.1063/5.0100602 View Online Export Citation CrossMark Submitted: 25 May 2022 · Accepted: 23 June 2022 · Published Online: 18 July 2022 Zoheb Khan,1,2,a) Thomas Nuytten,1 Paola Favia,1 Claudia Fleischmann,1,2 Ingrid De Wolf,1,3 and Wilfried Vandervorst1,2 AFFILIATIONS 1imec, Kapeldreef 75, 3001, Leuven, Belgium 2Quantum Solid-State Physics Group, KU Leuven, 3001, Leuven, Belgium 3Department of Materials Engineering, KU Leuven, 3001, Leuven, Belgium a)Author to whom correspondence should be addressed: zoheb.khan@imec.be ABSTRACT Raman spectroscopy is an effective tool for stress and compositional metrology in the semiconductor industry. However, its application toward decoupling a complex stress state in semiconductor materials requires the use of liquid immersion lenses that are process line incompatible. In this work, a practical design concept for off-axis Raman spectroscopy is presented. By tilting the incident light away from the normal incident axis, forbidden Raman modes can be accessed allowing determination of the in-plane stress tensor in semiconductor materials. Furthermore, we benchmark off-axis Raman spectroscopy against oil-immersion Raman spectroscopy for stress characterization in 20 nm-wide strained Ge fin field-effect transistor channels. We demonstrate that off-axis Raman allows anisotropic stress metrology without reliance on liquid immersion lenses, highlighting its viability in the process line. The stress state is validated through nanobeam diffraction measurements. Published under an exclusive license by AIP Publishing. https://doi.org/10.1063/5.0100602 I. INTRODUCTION Strain engineering continues to drive the performance in modern three-dimensional transistor architectures. By enabling improvements in carrier mobility, it allows pushing the scaling limits and boosts electrical performance.1 Naturally, accurately probing strain/stress in nanoscale volumes is an important objective for metrology and crucial for research and development. At the same time, a nondestructive and fast technique that can conform with the requirements of the process line is critical for efficient and economical manufacturing. Currently, quantitative strain measure- ments in sub-20 nm technology nodes rely on scanning transmis- sion electron microscope (STEM)-based techniques. Typically, strain is measured by either nanobeam diffraction (NBD),2 geomet- rical phase analysis,3 or precession electron diffraction approaches.4 However, STEM techniques are destructive, time-consuming, and require specific sample preparation that notoriously induces strain relaxation.4 Alternatively, high-resolution x-ray diffraction is a non- destructive technique for the direct assessment of the lattice param- eters. However, the current fab-based tools require large spot sizes (>100 μm) and longer measurement times due to limited intensity of x-ray sources.5 Furthermore, for strain evaluation in thin films and nanostructures, reciprocal space maps have to be acquired, which significantly increases the measurement time.6 Raman spec- troscopy (RS) is a nondestructive light scattering technique that probes lattice vibrations (phonons). When a material is stressed, the vibration frequency of the phonon changes and affects the wavenumber of the associated Raman mode. If the phonon defor- mation potentials are known, a quantitative relationship between the mechanical stress and Raman peak frequency can be estab- lished.7 This has led to the widespread application of RS for mechanical stress measurements in the semiconductor industry. Regular (on-axis) RS is not able to differentiate the stress in the various axial directions and only provides the stress value for one direction or a convolution of several directions. For RS to be rele- vant to the semiconductor industry, this drawback needs to be overcome, as many of the devices used (e.g., narrow fins) have at least biaxial stress distributions. By implementing a novel way of performing RS, i.e., off-axis excitation as originally proposed by Loechelt et al.,8 we broaden the application of RS for determining stress in multiple crystal directions in nanoscale devices. Journal of Applied Physics ARTICLE scitation.org/journal/jap J. Appl. Phys. 132, 035104 (2022); doi: 10.1063/5.0100602 132, 035104-1 Published under an exclusive license by AIP Publishing D ow nloaded from http://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/5.0100602/16510500/035104_1_online.pdf This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Zoheb Khan, Thomas Nuytten, Paola Favia, Claudia Fleischmann, Ingrid De Wolf, Wilfried Vandervorst; Off-axis Raman spectroscopy for nanoscale stress metrology. Journal of Applied Physics 21 July 2022; 132 (3): 035104. and may be found at https://doi.org/10.1063/5.0100602 https://doi.org/10.1063/5.0100602 https://doi.org/10.1063/5.0100602 https://www.scitation.org/action/showCitFormats?type=show&doi=10.1063/5.0100602 http://crossmark.crossref.org/dialog/?doi=10.1063/5.0100602&domain=pdf&date_stamp=2022-07-18 http://orcid.org/0000-0002-9369-2194 http://orcid.org/0000-0002-5921-6928 http://orcid.org/0000-0003-3822-5953 mailto:zoheb.khan@imec.be https://doi.org/10.1063/5.0100602 https://aip.scitation.org/journal/jap https://doi.org/10.1063/5.0100602 A. The need for off-axis excitation The Raman scattering intensity (I) of a phonon vibration is given by9 I ¼ C X j jET outRjEinj2: (1) Here, C is a constant and Rj is the Raman polarizability tensor for the jth phonon, Eout and Ein are the outgoing and incoming polarization vectors, respectively (superscript T indicating the transposed vector). The tensors define the selection rules for detec- tion. For the unstressed diamond-type semiconductors like silicon and germanium, the k = 0 Raman-active phonon is triply degener- ate with two transverse optical (TO) modes (TO1 and TO2) and one longitudinal optical (LO) mode. Their polarizability tensors and respective phonon polarizations are given by10 R1(TO1) ¼ 0 0 0 0 0 d 0 d 0 0 B@ 1 CA, R2(TO2) ¼ 0 0 d 0 0 0 d 0 0 0 B@ 1 CA, R3(LO) ¼ 0 d 0 d 0 0 0 0 0 0 B@ 1 CA, (2) v1 ¼ 1 0 0 0 @ 1 A , v2 ¼ 0 1 0 0 @ 1 A, v3 ¼ 0 0 1 0 @ 1 A: (3) In the presence of anisotropic residual stress, the three phonon frequencies depend differently on all stress tensor elements.7,11 When assuming that all shear stress components are zero, the concurrent detection of LO and TO modes allows to determine the three main stress components. Experimentally, each mode can be probed by controlling the sample orientation and the polarization state of excitation and Raman scattered light. In the conventional backscattering RS, the light is incident normal to the sample surface and scattering is also collected normally. In this configuration, Ein is always parallel to the sample surface. When applied to the most relevant case for semiconductors, i.e., scattering from the (001) surface, only the LO phonon can be detected. As the frequency of this LO phonon depends on all stress tensor ele- ments, it is impossible to determine the anisotropic stress distribu- tion. To overcome this, the Raman configuration needs to be changed such that the incident electric field is not strictly parallel to the sample surface and TO as well as LO modes are excited. Several strategies have been explored in this regard, the current standard being the use of high (>1) numerical aperture (NA) objec- tives.12 Here the large focusing angle of the lens results in an increased density of photons with wave vector (~ki) tilted away from the normal direction of the plane. This tilted contribution adds an Ein⊥ component as illustrated schematically in Fig. 1(a). The tech- nique has been successfully applied for the excitation of forbidden Raman modes toward decoupling the in-plane stress tensor in nanostructures.13–16 However, such high-NA objective lenses require liquid immersion (oil/water) environments,17 contaminat- ing the sample and are a clear roadblock to its in-line adoption. To this end, a “dry” alternative is required. While oblique backscatter- ing approaches have been explored,18,19 the most efficient scattering configuration for detection of the forbidden TO mode is when inci- dent light is tilted away from the normal axis and the scattered light is collected normally [Fig. 1(b)]. For p-polarized incident light, the Ein⊥ amplitude responsible for the TO mode excitation scales with the incidence angle (Θi). Furthermore, the absorption of the incident radiation maximizes at the materials’ Brewster angle, thereby increasing the scattered signal.20 This so-called FIG. 1. A schematic comparison of (a) oil-immersion Raman spectroscopy (OIR) and (b) off-axis Raman spectroscopy (FCOR). Journal of Applied Physics ARTICLE scitation.org/journal/jap J. Appl. Phys. 132, 035104 (2022); doi: 10.1063/5.0100602 132, 035104-2 Published under an exclusive license by AIP Publishing D ow nloaded from http://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/5.0100602/16510500/035104_1_online.pdf https://aip.scitation.org/journal/jap “off-axis Raman scattering” geometry has been applied in the field of RS before.21,22 In the context of stress metrology, it was first implemented by Loechelt et al. and was used to determine the stress tensor in strained Si wafers.23 Whereas successful as a first demonstrator, their approach and instrumentation did not allow to reach the spatial resolution presently required. Indeed, the conven- tional approach of splitting the incidence and collection optics with long working distance optical lenses does degrade the spatial resolution. At the same time, it is susceptible to aberrations and presents a technical challenge, making its routine use and imple- mentation problematic. In this work, we overcome these limitations by exploring a simplified, modular approach to off-axis Raman based on an optical fiber-coupled excitation setup, termed FCOR. II. MATERIALS AND METHODS A. Analysis techniques 1. Off-axis Raman spectroscopy (FCOR) A modular setup was realized that can be integrated with any commercial Raman spectrometer; in this case, we used a Labram HR EVO from Horiba scientific. The schematic is shown in Fig. 2(a). It comprises a linearly polarized 633 nm He-Ne laser source coupled to a polarization-maintaining optical fiber (OF). The other end of the OF is coupled to a collimator and focusing lens assembly (NA =0.09) that can focus the beam to a ∼6 μm diameter spot. This collimator is housed on an adjustable flip plat- form which controls the incidence angle. A manually operated 3D translation stage is fitted with a custom-made platform, which functions as the sample stage. The whole assembly is screwed to a custom-made aluminum breadboard. This breadboard is then placed on the 3D motorized stage of the commercial Raman spec- trometer. The scattered radiation is collected by a 50× long working distance objective (NA =0.5) and fed via an appropriate analyzer configuration to the Raman spectrograph equipped with an 1800 line/mm grating. Combining two 3D positioning stages in this way offers the necessary freedom to focus the incident beam at the focal point of the collection objective for a desired location on the sample. All measurements were performed at 60° incidence angle giving an elliptical laser spot with approximate diameters of 6 μm (minor axis) and 12 μm (major axis). The laser power density is maintained below 20 kW/cm2 to avoid heating-induced peak shifts.16 The He–Ne laser, in addition to the main lasing line at 633 nm, also produces a collection of non-lasing lines due to addi- tional transitions in the He–Ne system that appear as sharp peaks in the spectrum. These so-called “plasma peaks” are not affected by stress and offer a useful means of calibrating the spectrum against any environmental drifts of the instrument.24 We note that there are several routes to realizing a dedicated off-axis Raman setup, for instance, with higher NA long working distance objectives and a standalone spectrograph that would potentially offer higher spatial resolution. In order to ensure a modular setup, specific optical and mechanical components were chosen in our case that do not inter- fere spatially with the commercial spectrometer components. As such, we make a meaningful compromise in spatial resolution, enabling the use of a standard state-of-the-art confocal Raman spectrograph in the detection path. 2. Oil-immersion Raman spectroscopy (OIR) The OIR measurements are performed with a 633 nm linearly polarized laser source (He–Ne) and an oil-immersion objective with NA = 1.4. The laser spot diameter is about 540 nm theoreti- cally and the spectrograph details are the same as above. 3. Nanobeam diffraction (NBD) NBD is a TEM-based technique that determines nanoscale variations in the lattice parameters of crystalline materials. Typically, an electron beam is scanned along a region of interest, collecting a series of diffraction patterns. These are compared to a reference diffraction pattern representing the substrate/unstrained region. The local 2D strain is then calculated as the relative lattice mismatch Δd/d.25 The measurements here were carried out using an FEI Titan 60-300, equipped with a 20 μm condenser aperture, operating at 300 kV in a μprobe STEM-mode. Under these condi- tions, an approximate probe beam diameter of 3.5 nm is expected. B. Sample 1. Raman metrology at the nanoscale The application of FCOR, as will be shown further, generates insight into the two-dimensional strain distribution and is thus of high relevance for investigating small devices like finFETs. However, in view of their nanoscale dimensions (<20 nm), one is faced with the need for very high spatial resolution, which is not improved by off-axis Raman spectroscopy compared to OIR. Even if nm-resolution could be reached, one will be faced with the important issue of sensitivity. Indeed, the intensity of Raman FIG. 2. (a) Schematic-FCOR combined with the commercial spectrometer. (b) Schematic of fin structure exemplifying the layer stack embedded in an SiO2 matrix. (c) High-angle annular dark-field STEM image of the 20 nm-wide strained Ge (sGe) fin structure. Journal of Applied Physics ARTICLE scitation.org/journal/jap J. Appl. Phys. 132, 035104 (2022); doi: 10.1063/5.0100602 132, 035104-3 Published under an exclusive license by AIP Publishing D ow nloaded from http://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/5.0100602/16510500/035104_1_online.pdf https://aip.scitation.org/journal/jap scattering scales with the volume of material under investigation.26 Hence, the diminishing dimensions of the semiconductor devices represent a growing challenge in terms of detectability applicable to the technique under consideration. One possible solution is to make use of the fact that the Raman intensity also scales with the local electric field at the scattering site. The latter can be increased by exploiting plasmon-based enhancement methods like surface-enhanced Raman spectroscopy (SERS)27,28 or tip-enhanced Raman spectroscopy (TERS).29–32 However, the need for sample modification (SERS) and complex instrumentation (TERS) hinders the implementation of such solutions in the process line. A promis- ing alternative to “apparently” achieve the spatial resolution and increase the sensitivity is the ensemble measurement. In this concept, multiple (identical) devices are probed simultaneously thereby providing a large volume of analyzed material and thus sensitivity. Under particular conditions such as Si (or Ge) fins embedded in SiO2, the RS signal originates almost exclusively from the fin volume thus providing the required spatial resolution. Although the fin region in such a configuration only covers 1%– 10% of the total area, the signal intensity is dramatically increased by the geometry-based enhancement of the electromagnetic (EM) field. This arises from the so-called nano focusing effect, which leads to the excitation of an EM field guided mode confined inside the periodic structure.33 The necessary condition to achieve this is the presence of nm-spaced interfaces of materials, with a strong contrast in dielectric behavior. Based on this effect, Nuytten et al. showed that with incident laser light polarized along the length of semiconductor fins, their Raman response enhances dramatically.34 The concept has widespread applicability in in-line metrology as such device arrangements are universally present in current 3D semiconductor architectures. Moreover, the effect was demon- strated to be present in a variety of materials including semicon- ductors like Si, Ge, and InGaAs, but can be exploited for dimensional metrology of metal lines as well.34–36 Based on these observations, we have concentrated our FCOR studies on ensemble- based studies using samples like the one shown in Fig. 2(b). 2. Sample design The sample consists of strained Ge (sGe) fins enclosed in an SiO2 matrix. The integration scheme is based on the blanket growth of a 30 nm-thick Ge layer on top of a blanket Si0.3Ge0.7 strain relaxed buffer (SRB) on a (001) Si substrate.37 The blanket Ge is compressively strained due to the lattice misfit. This stack is then patterned into 20 nm-wide, 10 μm-long fins aligned along the [�110] crystal direction with a pitch of 180 nm, designed for uniaxial stress along the fin length.38,39 The space between the fins is refilled with SiO2 resulting in a periodic grating-like arrangement. This is shown in the schematic [Fig. 2(b)] as well as in the high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image [Fig. 2(c)]. Such fin ensembles extend over a 600 × 600 μm2 region in the die. Since the semiconductor pro- cessing is reproducible and thus individual devices are virtually identical, their collective response should be an accurate representa- tion of the individual fin state. Measuring an ensemble of 20 nm fins boosts the signal intensity by over an order of magnitude vs a blanket layer and thus provides the required sensitivity.33 III. THEORETICAL BACKGROUND The presence of strain affects both the frequency of the Raman modes and the polarizability tensor associated to them. The fins in our sample are aligned along the [�110] direction, which is the preferred orientation for performance enhancement in strained semiconductor devices. It is convenient here to work with a co-ordinate system x0y0z 0 defined by [110], [�110], and [001] crys- tallographic directions. Solving for a triaxial stress state with stress in only the principal directions as non-zero, i.e., σx0x0 = 0, σy0y0 = 0, σz0z0 = 0: (4) The stress induced Raman peak frequency shifts are given by the equations ΔωTO1 ¼ 1 2ω0 1 2 (S11 þ S12)( pþ q)þ qS12 þ r 2 S44 � � σx0x0 � þ 1 2 (S11 þ S12)( pþ q)þ qS12 � r 2 S44 � � σy0y0 þ (( pþ q)S12 þ qS11)σz0z0 �, (5a) ΔωTO2 ¼ 1 2ω0 " 1 2 (S11 þ S12)( pþ q)þ qS12 � r 2 S44 � � σx0x0 þ 1 2 (S11 þ S12)( pþ q)þ qS12 þ r 2 S44 � � σy0y0 þ (( pþ q)S12 þ qS11)σz0z0 # , (5b) ΔωLO ¼ 1 2ω0 [(pS12þq(S11þS12))(σx0x0 þσy0y0 )þ (pS11þ2qS12)σz0z0 ], (5c) with σx 0 x0, σy0y,0 and σz0z0 representing the stress across the width, along the length and normal to the fin, respectively. ω0 is the stress-free value for the Raman shift, and the stiffness tensor elements Sij and phonon deformation potentials p, q, and r are material-specific parameters. For Ge,40,41 S11 = 9.64 × 10−12 Pa−1; S12 = 2.60 × 10−12 Pa−1; S44 = 14.89 × 10−12 Pa−1; p/ω2 0 ¼ 1:45; q/ω2 0 ¼ 1:95; r/ω2 0 ¼ 1:1. The detailed derivation of Eqs. (5a)–(5c) is in Appendix A. All measurements in this work were performed in the orienta- tion which supports nano-focusing such that a component of Ein is polarized along the fin length—y0 ¼ [�110]. Once the off-axis Raman system is added to the Labram spectrometer, Ein polariza- tion is fixed. Since the incident radiation is p-polarized and under oblique incidence, it can be resolved into two components within the sample (Ein|| and Ein⊥) as shown in Fig. 1(b). While measuring, the finFET sample is oriented in such a way that Einjj ¼ [�110] and Ein⊥= [001]. The selection rules determined for this condition are summarized in Table I. Ein is fixed while a polarization analyzer is used to select specific Eout polarizations and isolate the different Journal of Applied Physics ARTICLE scitation.org/journal/jap J. Appl. Phys. 132, 035104 (2022); doi: 10.1063/5.0100602 132, 035104-4 Published under an exclusive license by AIP Publishing D ow nloaded from http://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/5.0100602/16510500/035104_1_online.pdf https://aip.scitation.org/journal/jap phonon modes. The detailed derivation of the selection rules is included in Appendix B. From Table I, by selecting Eout parallel to x0, the TO1 scatter- ing is allowed. This selection is henceforth referred to as the TO-active configuration. On the other hand, selecting Eout parallel y0, the LO and TO2 peaks are detectable. Since the refractive index of Ge is high (5.47 for 633 nm radiation42) Θt will be low, so Ein⊥< < Ein||. The relative intensity of the LO peak will expectedly dominate the spectrum masking the TO2 contribution. It is there- fore referred to as the LO-active configuration. IV. RESULTS AND DISCUSSION Figure 3(a) shows the RS measurement of a 20 nm-wide fin ensemble with FCOR, whereby the overlapping Raman spectra measured under the LO- and TO-active condition are normalized to the Ge peak. The main features are the Rayleigh scattered plasma peak around 286 cm−1 coming from the He–Ne laser, a broad feature around 293 cm−1 representing the Ge–Ge vibration in the Si0.3Ge0.7 SRB and a sharp feature around 305 cm−1 repre- senting the strained Ge (sGe) scattering. The sGe peak in the TO-active spectrum is slightly downshifted with a shoulder toward the lower wavenumber side. Due to the imperfect polarization TABLE I. Polarization selection rules for the TO1, TO2, and LO modes. Polarization Visibility Ein Parallel to Eout Parallel to TO1 TO2 LO �110 y0 �110 y0 … … X 001 z0 … X … �110 y0 110 x0 … … … 001 z0 X … … FIG. 3. (a) Normalized Raman spectra with FCOR for 20 nm fins in LO- and TO-active condition overlapped. Fitted spectra, (b) Si0.3Ge0.7 substrate, (c) fins LO-active, and (d) fins TO-active. Journal of Applied Physics ARTICLE scitation.org/journal/jap J. Appl. Phys. 132, 035104 (2022); doi: 10.1063/5.0100602 132, 035104-5 Published under an exclusive license by AIP Publishing D ow nloaded from http://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/5.0100602/16510500/035104_1_online.pdf https://aip.scitation.org/journal/jap selectivity of the analyzer and nano-focusing enhancement of Ein||, 34 it is assumed that the TO-active spectrum is still dominated by the contribution of the LO peak. This implies that the overall TO-active spectrum is still a combination of the Si0.3Ge0.7, LO, and TO1 sGe peaks. Such an overlap requires a systematic approach to the spectral data analysis: (a) First an exposed Si0.3Ge0.7 region from the same wafer is mea- sured and fitted with a constant line for background and an asymmetric pseudo-Voigt function43 for the Raman response as shown in Fig. 3(b). (b) Then, the fins are measured in the LO-active condition and the spectrum is fitted with a constant background, while the Si0.3Ge0.7 peak width and shape are locked to the substrate measurement. (c) The sGe peak is best fitted to an asymmetric Voigt shape (con- firmed with R2 analysis). The overall fit matches the measured data very well as seen in Fig. 3(c). (d) Following this, the TO-active spectrum is fitted [Fig. 3(d)], whereby the parameters of the Si0.3Ge0.7 and sGe LO peak (position, width, and shape) are fixed based on the LO spec- trum. We also fix the TO peak width and shape to the LO value assuming that any asymmetric broadening is the same for both. The TO peak height and position are free parameters and the variables to the optimization algorithm (Levenberg– Marquardt optimization).44 (e) Finally, the peak positions obtained are subtracted from the positions of the Raman peak of a stress-free bulk Ge to calcu- late ΔωTO1 and ΔωLO. To account for instrumental/environ- mental effects, all peak position values are calibrated against the plasma line from the He–Ne laser, itself fitted to a Gaussian shape. FIG. 4. (a) Schematic comparison of the FCOR and OIR measurement areas. (b) ΔωLO for the OIR line scan and FCOR single spectrum. FCOR single spot vs OIR line scan comparison (c) ΔωLO (d) ΔωTO1. Journal of Applied Physics ARTICLE scitation.org/journal/jap J. Appl. Phys. 132, 035104 (2022); doi: 10.1063/5.0100602 132, 035104-6 Published under an exclusive license by AIP Publishing D ow nloaded from http://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/5.0100602/16510500/035104_1_online.pdf https://aip.scitation.org/journal/jap For validation, the stress measurements with the off-axis Raman technique (FCOR) are compared to state-of-the-art oil- immersion Raman spectroscopy (OIR) measurements done in the backscattering configuration. The OIR laser is linearly polarized with Ein|| also along the fin length. The selection rules are the same as in Table I. We note that in view of the different areas probed by OIR (∼0.23 μm2) and FCOR (∼56 μm2), the entire FCOR illumi- nated area must be spatially mapped in both LO- and TO-active FIG. 5. NBD line profile of lattice mismatch vs Si0.3Ge0.7 (a) across the fin lamella (b) along the fin lamella (inset scale bar =50 nm). (c) Schematic description of the finFET (d) Stress distribution in the Ge channel calculated from the cross-sectional measurement of lattice mismatch (valid only in sGe layer). (e) In-plane stress values in the Ge channel region compared across the measurement techniques. (d) is adapted from Nuytten et al., APL Mater. 6, 058501 (2018); licensed under a Creative Commons Attribution (CC BY) license. Journal of Applied Physics ARTICLE scitation.org/journal/jap J. Appl. Phys. 132, 035104 (2022); doi: 10.1063/5.0100602 132, 035104-7 Published under an exclusive license by AIP Publishing D ow nloaded from http://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/5.0100602/16510500/035104_1_online.pdf https://aip.scitation.org/journal/jap conditions with OIR to compare the two techniques. However, considering the long measurement times associated with mapping (especially for TO-active condition), OIR line scans were performed at the FCOR measurement spots. A schematic comparison of the measurement areas is shown in Fig. 4(a). The step size of the OIR line scan is maintained at 600 nm (spot size 542 nm) to ensure full coverage and the scan is restricted to the length of the fin. Figure 4 (b) plots ΔωLO for such a line scan against the result from a single FCOR spectrum. The error limits shown represent the standard deviation in the peak position obtained after spectrum fitting.44 A clear variation in the peak positions is noted along the fin length. This variation is attributed to local differences in the stress state within the fin. TEM images taken across the fin cross sections have shown misfit dislocations at the sGe-Si0.3Ge0.7 interface. Such dislo- cations can locally relax the epitaxial strain affecting the Raman peak position. Indeed, this result underscores the importance of comparing single FCOR spectra with OIR averages and justifies the asymmetric shape of the sGe peak. Other factors affecting the Raman peak shape include doping,45,46 laser-induced heating, and geometrical confinement.47 Since the processing scheme for the fabrication of the sGe fins did not involve a doping step,39 a doping induced peak broadening is not expected in our results. Furthermore, considering the laser power and the geometrical size of the fins, heating and confinement factors can also be neglected. Such an FCOR vs OIR comparison is repeated for six different locations in the die. The spectra from an OIR line scan are averaged and fitted with the same fitting routine discussed above. Figures 4(b) and 4(c) compare ΔωLO and ΔωTO1 for single FCOR spectra vs the OIR line scan average. The two techniques agree very well across the six measurement spots. To determine the stress state of the fins, we can substitute ΔωLO and ΔωTO1 values into Eqs. (5a) and (5c) which leads to a system of two equations with three vari- ables (σx0x0, σy0y,0 and σz0z0). Here, it is typical to assume a biaxial stress state with σz0z0 = 0, to simplify the equations. However, in this case, we benefit from nanobeam diffraction (NBD) measurements done on a similar structure for the validation of the Raman results. Since NBD analysis is done on the projection through the thickness of the sample, it is not possible to deduce the strain parallel to the electron propagation direction. As a result, both across [inset Fig. 5 (a)] and along (longitudinal) the fin [inset Fig. 5(b)] TEM cross section lamellae are needed to evaluate strain along the three prin- cipal directions x0, y0, and z0. The vertical line profiles in Figs. 5(a) and 5(b) plot the relative lattice mismatch in the specimen against the lattice constant of the Si0.3Ge0.7 substrate. The dashed line marks the interface between sGe and Si0.3Ge0.7. The e-beam is scanned from the top of the fin to the SRB as indicated by the arrow. Analyzing the line profiles reveals that the sGe conforms with the Si0.3Ge0.7 lattice constant in the y0 direction but deviates in the x0 direction suggesting a relaxation of the misfit strain in x0. This lattice mismatch is used to calculate the material strain (with respect to bulk Ge) and finally the stress in the three principal directions, plotted in Fig. 5(d). Since photons of the wavelength used for the current Raman analysis can penetrate the full sGe layer, the Raman response is an average value for the whole sGe depth. Hence, for comparison, we calculate the average stress values from the NBD results. The stress is most pronounced in the direction along the channel σy0y0=−1.84 GPa, with a small, nonzero compressive component present both across σx0x0=−0.43 GPa, and in the vertical direction σz0z0=−0.35 GPa. Then, by substituting σzz0 =−0.35 GPa, in Eqs. (5a) and (5c) σx0x0 and σy0y0 are determined for the Raman results of Figs. 4(c) and 4(d). The results are plotted in Fig. 5(e) and their averages indicated in Table II. Expectedly from the peak position comparison, the results for the two Raman techniques agree within the uncertainties. At the same time, the mostly uniaxial trend is compatible with the NBD result. This mostly uniaxial stress state is induced from elastic relax- ation at the fin edges due to volume expansion into the free space generated by patterning. We note the difference between the two techniques with Raman showing a lower stress state as compared to NBD. This discrepancy is assumed to be a direct consequence of the difference in the probed areas. While Raman results are an average over the length of an ensemble of fins, the values encom- pass any relaxation due to defects as highlighted in Fig. 4(b). On the other hand, the nanoscale NBD lamellas give a localized result from seemingly defect free regions and expectedly a higher stress state. V. CONCLUSIONS In summary, we have implemented an off-axis design concept for Raman spectroscopy. The technique can access the forbidden transverse optical mode necessary for anisotropic stress measure- ments while remaining fully non-contact. Aided by nano-focusing of the excitation light, the methodology can readily be applied to nanoscale transistor architectures with adequate sensitivity. We evaluate the stress in 20 nm-wide strained Ge channels revealing a mostly uniaxial stress state, cross-validated with nanobeam diffrac- tion. Overcoming the reliance on liquid immersion lenses truly unlocks the nondestructive advantage of the Raman spectroscopy technique for advanced stress metrology in the process line. Moreover, the application of the off-axis configuration extends to applications beyond stress measurements. For instance, gaining access to both LO and TO modes will increase the accuracy of com- position measurements in III-V-based devices. Our results high- light the utility of Raman spectroscopy in the current semiconductor metrology landscape. ACKNOWLEDGMENTS The authors would like to acknowledge R. Loo, the EPI team, and Logic Program of imec for sample growth, documentation, and assistance. TABLE II. Average stress values in the Ge channel. FCOR and OIR are averaged over six measurement spots and uncertainties represent the standard deviation. NBD values are averaged over Ge depth for a single measurement and error values are the standard deviation obtained over the averaged region. Technique σx0x0 (GPa) across fin width σy0y0 (GPa) along fin length FCOR −0.34 ± 0.05 −1.59 ± 0.05 OIR −0.36 ± 0.04 −1.54 ± 0.05 NBD −0.43 ± 0.19 −1.84 ± 0.03 Journal of Applied Physics ARTICLE scitation.org/journal/jap J. Appl. Phys. 132, 035104 (2022); doi: 10.1063/5.0100602 132, 035104-8 Published under an exclusive license by AIP Publishing D ow nloaded from http://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/5.0100602/16510500/035104_1_online.pdf https://aip.scitation.org/journal/jap AUTHOR DECLARATIONS Conflict of Interest The authors have no conflicts to disclose. Author Contributions Zoheb Khan: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Project administration (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review and editing (equal). Thomas Nuytten: Conceptualization (supporting); Supervision (supporting); Writing – review and editing (equal). Paola Favia: Investigation (supporting); Writing – review and editing (supporting). Claudia Fleischmann: Supervision (support- ing); Writing – review and editing (equal). Ingrid De Wolf: Conceptualization (supporting); Supervision (equal); Writing – review and editing (equal). Wilfried Vandervorst: Conceptualization (supporting); Supervision (equal); Writing – review and editing (equal). DATA AVAILABILITY The data that support the findings of this study are available from the corresponding author upon reasonable request. APPENDIX A: RELATION BETWEEN RAMAN FREQUENCY AND RESIDUAL STRESS The effect of strain on frequency can be deduced by solving the secular equation:7 pϵxx þ q(ϵyy þ εzz)� λi 2rεxy 2rεxz 2rεxy pϵyy þ q(ϵxx þ εzz)� λi 2rεyz 2rεxz 2rεyz pϵzz þ q(ϵxx þ εyy)� λi ������ ������ ¼ 0, (A1) where p,q,r are the phonon deformation potentials describing the elastic properties of the specific phonon mode of the strained crystal and, εij are the components of the strain tensor. The eigenvalues λi from Eq. (A1) are related to the Raman mode frequencies λi ¼ ω2 i � ω2 0, (A2) where ω0 and ωi are the frequencies of unstrained and strained Ge, respectively. Since Δωi � ωo, Eq. (A2) can be simplified to Δωi ¼ ωi � ωo ¼ λi 2ωo (A3) (ωi= 1,2,3 labels the TO1, TO2, and LO mode, respectively). Since the fins in our sample are aligned along the �110, it is convenient here to work with a co-ordinate system x0y0z0 defined by [110], [�110], and [001] crystallographic directions. Solving for a triaxial stress state with stress in only the principal directions as non-zero, i.e., σx0x0 = 0, σy0y0 = 0, σz0z0 = 0: (A4) Then, the strain tensor elements εij are related to σx0x0, σy0y0, and σz0z0 by Hookes law, ϵxx ¼ ϵyy ¼ 1 2 (S11 þ S12)(σx0x0 þ σy0y0 )þ S12σz0z0 , ϵzz ¼ S12(σx0x0 þ σy0y0 )þ S11σz0z0 , ϵxy ¼ 1 4 S44(σx0x0 � σy0y0 ), ϵxz ¼ ϵyz ¼ 0, (A5) where Sij are the elastic compliance coefficients. Considering ϵxx ¼ ϵyy and ϵxz ¼ ϵyz ¼ 0, Eq. (A1) reduces to ( pþ q)ϵxx þ q(εzz)� λi 2rεxy 0 2rεxy ( pþ q)ϵxx þ q(εzz)� λi 0 0 0 pϵzz þ 2qϵxx � λi ������ ������ ¼ 0, (A6) with eigen vectors vi_st, v1 st ¼ 1ffiffiffi 2 p 1 1 0 0 @ 1 A , v2 st ¼ 1ffiffiffi 2 p �1 1 0 0 @ 1 A, v3 st ¼ 0 0 1 0 @ 1 A, (A7) giving eigenvalues λ1 ¼ ( pþ q)ϵxx þ qϵzz þ 2rεxy , λ2 ¼ ( pþ q)ϵxx þ qϵzz � 2rεxy , λ3 ¼ pϵzz þ 2qϵxx: (A8) Journal of Applied Physics ARTICLE scitation.org/journal/jap J. Appl. Phys. 132, 035104 (2022); doi: 10.1063/5.0100602 132, 035104-9 Published under an exclusive license by AIP Publishing D ow nloaded from http://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/5.0100602/16510500/035104_1_online.pdf https://aip.scitation.org/journal/jap Then, from Eqs. (A3), (A5), and (A8), Δω1(TO1)¼ 1 2ω0 " 1 2 (S11þS12)(pþq)þqS12þ r 2 S44 � � σx0x0 þ 1 2 (S11þS12)(pþq)þqS12� r 2 S44 � � σy0y0 þ ((pþq)S12þqS11)σz0z0 # , (A9a) Δω2(TO2)¼ 1 2ω0 " 1 2 (S11þS12)(pþq)þqS12� r 2 S44 � � σx0x0 þ 1 2 (S11þS12)(pþq)þqS12þ r 2 S44 � � σy0y0 þ ((pþq)S12þqS11)σz0z0 # , (A9b) Δω3(LO) ¼ 1 2ω0 ½( pS12 þ q(S11 þ S12))(σx0x0 þ σy0y0 ) þ ( pS11 þ 2qS12)σz0z0 �: (A9c) The detailed explanation of tensor rotations can be found elsewhere.48 APPENDIX B: SELECTION RULES FOR RAMAN SCATTERING INTENSITY To identify the selection rules for each mode, we determine the strain-modified Raman tensors in the x’y’z’ system. First, the Raman tensors for strain-perturbed phonons can be expressed as linear combinations of the tensors in Eq. (2),23 Ri st ¼ X3 k¼1 (vi st)kRk, (B1) where (vi_st)k denotes the kth component of the ith eigenvector vi_st [Eq. (A7)], R1 st ¼ 1ffiffiffi 2 p 0 0 d 0 0 d d d 0 0 B@ 1 CA, R2 st ¼ 1ffiffiffi 2 p 0 0 d 0 0 �d d �d 0 0 B@ 1 CA, R3 st ¼ 0 d 0 d 0 0 0 0 0 0 B@ 1 CA: (B2) While measuring, the finFET sample is oriented in such a way that Einjj ¼ [�110] and Ein⊥= [001]. Under this orientation, the “strained tensors” Ri_st in Eq. (B2), must be rotated by 45° about the [001] axis to determine the selection rules,18 R0 i st ¼ A(45�):Ri st :A(45 �)T : (B3) With A as the Euler rotation matrix A(45�) ¼ 1ffiffiffi 2 p 1 1 0 �1 1 0 0 0 ffiffiffi 2 p 0 @ 1 A, (B4) R0 1 st(TO1) ¼ 0 0 d 0 0 0 d 0 0 0 B@ 1 CA, R0 2 st (TO2) ¼ 0 0 0 0 0 �d 0 �d 0 0 B@ 1 CA, R0 3 st(LO) ¼ d 0 0 0 �d 0 0 0 0 0 B@ 1 CA: (B5) The selection rules from Eq. (B5) are summarized in Table I. 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