The continued importance of strain engineering in semiconductor technology demands fast and reliable stress metrology that is non-destructive and process line-compatible. Raman spectroscopy meets these requirements but the diffraction limit prevents its application in current and future technology nodes. We show that nano-focused Raman scattering overcomes these limitations and can be combined with oil-immersion to obtain quantitative anisotropic stress measurements. We demonstrate accurate stress characterization in strained Ge fin field-effect transistor channels without sample preparation or advanced microscopy. The detailed analysis of the enhanced Raman response from a periodic array of 20 nm-wide Ge fins provides direct access to the stress levels inside the nanoscale channel, and the results are validated using nano-beam diffraction measurements.
Strain engineering of channel materials such as Si, Ge, and SiGe is an attractive approach for reaching improved performance for high device density architectures in next-generation technology nodes,1 creating the need for the quantitative analysis of stress/strain in the targeted device.2 Strain measurements in advanced semiconductor nanostructures usually rely on transmission electron microscopy (TEM)-based techniques including nano-beam diffraction (NBD), convergent beam electron diffraction (CBED), and dark-field holography3–5 which all require destructive sample preparation. High-resolution X-ray diffraction is a non-destructive technique for the direct assessment of the lattice parameters and has been successfully applied to characterize similar structures.6 However, the limited intensity of X-ray sources typically leads to long measurement times when the spot size is reduced to enable measurements in metrology pads of limited dimensions. Micro-Raman spectroscopy is widely used for non-destructive stress measurements in semiconductor materials,7–9 but as an optical technique, it is diffraction-limited to spatial resolutions of about 1 μm, still much larger than the features in current semiconductor processing. At the same time, in order to differentiate between stress in different crystallographic directions, selective excitation of longitudinal optical (LO) and transverse optical (TO) phonon modes is required. This can be achieved through, for instance, off-axis Raman spectroscopy10 or the use of an oil-immersion objective with a high numerical aperture (NA) such that out-of-plane polarization is added to the incident laser light—so-called oil-immersion Raman spectroscopy. While Raman-based techniques such as surface-enhanced Raman scattering (SERS)11,12 and tip-enhanced Raman scattering (TERS)13–15 are able to improve the spatial resolution of spectroscopic stress measurements considerably, these techniques require dedicated sample preparation or a complex characterization equipment that is difficult to integrate into large volume semiconductor process lines. However, it was recently shown that under correct polarization orientation and using an appropriate excitation wavelength, the Raman response of semiconductor fins embedded in a SiO2 matrix can be enhanced dramatically.16,17
In this paper, we show that precisely this enhancement in nano-focused Raman scattering can be combined with oil-immersion, readily providing accurate insight into the stress state of fins for fin field-effect transistor (finFET) channels in a non-destructive manner. We demonstrate that under correct interpretation, the stress can be quantified by the analysis of the enhanced Raman LO and TO modes, leading to fast and non-invasive characterization of stress in nanoscale semiconductor channels. The results as obtained by Raman are verified by quantitative NBD measurements, and the potential of the approach is projected toward advanced semiconductor devices.
The structure consists of a 30 nm-thick strained Ge (sGe) layer grown on top of a thick strain-relaxed Si0.3Ge0.7 buffer on a (001) Si substrate (see Fig. 1).18,19 The material is patterned into 20 nm-wide, 3 μm-long fins with a pitch of 180 nm, designed to lead to uniaxial stress in the longitudinal direction. Raman spectra are recorded in backscattering geometry using a Horiba Jobin-Yvon LabRAM HR confocal spectrometer equipped with an 800 mm spectrograph and coupled to a 633 nm HeNe laser, focused on the sample through a 100X 1.4NA oil-immersion objective and calibrated to bulk Ge at 301 cm−1. The incident polarization is fixed parallel to the finFET channel direction, i.e., the crystal direction , satisfying the enhancement conditions16 and increasing the Raman response of the Ge fins. The scattering polarization is selected through the use of an analyzer either parallel to (LO-active condition) or perpendicular to (TO-active condition). We note that the laser spot diameter in our Raman setup is about 0.7 μm, implying that at least three adjacent fins of 20 nm width and 180 nm pitch are probed simultaneously.
In order to reliably characterize stress in our structures based on Raman peak shifts, it is important to select an adequate excitation laser power density to avoid undesired peak shifts due to local sample heating.20,21 A measurement of the peak position as a function of laser power density revealed that an excitation power density of about 20 kW/cm2 did not lead to a heating-induced peak shift. Additionally, rather than using absolute peak positions, the relative position of the signal of interest with respect to a plasma line coming from the HeNe laser was used for the stress calculations, effectively eliminating any tool- or environment-induced peak shifts from the measurements.22 NBD measurements were carried out using an FEI Titan 60-300, equipped with a 20 μm condenser aperture, operating at 300 kV in μprobe STEM-mode. Under these conditions, an approximate probe beam diameter (lateral resolution) of 3.5 nm is obtained.
The fins in the current sample are oriented along the  direction, as is commonly the case in nanoelectronic devices, implying that great care should be taken when studying the relation between stress σ and Raman frequency shift. The secular equation, describing the Raman frequency in the presence of strain,23 is valid in the Cartesian coordinate system , , and , and hence the stress tensor elements which are here measured in the sample system , , and  need to be calculated in the Cartesian system. This procedure is described in detail by De Wolf7 and yields the following equation for the stress-induced Raman frequency shift of the LO and TO1 phonons, in the case of purely in-plane stress (σ33 = 0, zero stress in the growth direction and no shear stress components):
where σ11 and σ22 are the stresses across and along the fins, 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, with for Ge,24,25; ; ; , , and . In general, the difficulty for Raman stress measurements of small and confined volumes lies in the intermixing of the relevant signals with a broad background from the surrounding materials. Taking into account that the sGe channel material takes up only a very small fraction (an estimated 1%) of the total confocal volume probed in the experiment, the Ge–Ge scattering coming from the region of interest would hardly be detectable against the background of the underlying SiGe and Si substrate. To surpass this limitation, we employ the recent finding of an enhancement effect for deep-subwavelength semiconductor channels.16,17,26,27 In order to achieve a considerable increase in intensity, over orders of magnitude, it is important that the channels are narrow and are surrounded by a medium with a lower refractive index, like SiO2 in the current sample. In this configuration and under the correct experimental conditions, the total system can act as a photonic crystal where the transmission into the sGe is enhanced compared with a similar blanket layer stack. Furthermore, the use of an oil-immersion objective results in a non-zero z-component for enabling separate detection of the LO and TO peak shifts28–30 required for the calculation of the two perpendicular in-plane stress components using Eq. (1). The combination of both approaches then leads to a strong Raman response from the sGe channel material, where the LO and TO components can be fitted independently as illustrated in Fig. 2 for a TO-mode spectrum, with an average LO and TO full width at half maximum of 4.2 and 4.0 cm−1, respectively. The inset of Fig. 2 shows a comparison of a TO- and LO-mode spectrum taken at the same location and with the same experimental parameters. In TO-mode, the analyzer is used to select a perpendicular orientation of with respect to , a configuration in which in principle the LO scattering is forbidden. Due to imperfect optics and the fact that the oil-immersion objective only realizes a very small out-of-plane polarization component, a TO-mode spectrum will always contain convoluted LO and TO peaks, and the intensity in TO-mode is generally very weak requiring very long integration times of, in this particular example, 500 s per spectrum. The fitting procedure31 relies on the use of a constant background on top of which a SplitVoigt profile for the SiGe-related scattering; and two Voigt profiles for TO and LO components are added. Finally, a Gaussian profile is used for the sharp plasma calibration line coming from the laser, and it can be verified in Fig. 2 that the total fit follows the experimental data very well.
In the current experiment, the laser spot is scanned along the 3 μm-long fins and a spectrum is recorded every 0.1 μm from which the LO and TO peak shifts are extracted. Using Eq. (1), we calculate the stress along and across the fin resulting in the profile shown in Fig. 3. The short edges, i.e., the beginning and end of the fin in the Raman linescan, can readily be identified from the drop in intensity of the Ge–Ge scattering coming from the sGe channel. The resulting region where the fin is probed is indeed 3 μm long, and within that range a clear distinction between the stresses in both in-plane directions is observed. In the perpendicular direction (σ11), a small but non-zero compressive stress component is detected, revealing that the stress in the fins is not purely uniaxial as intended. In the longitudinal direction (σ22), the compressive stress is much larger but quite uniform especially in the middle of the fin. In Fig. 3, we calculated upper margins for the uncertainties on the stress values given a challenging fitting procedure for profiles where the LO and TO Raman peaks are very close to each other (see Fig. 2). Nonetheless the overall trend of the stress profile is smooth and consistent which testifies to the robustness of the analysis and to the fact that the practical error is smaller than the upper limits indicated.
In order to obtain structure-specific verification of the Raman results, both parallel and perpendicular lamellae were prepared from the fins for the analysis of the strain along all three major axes through NBD.4 Using Hooke’s law, the resulting stress was calculated32,33 along , , and  corresponding to σ11, σ22, and σ33, respectively, using the stiffness matrix for Ge.24 The result for a perpendicular cut is shown in Fig. 4. The e-beam is scanned from the top of the fin toward the base (see the arrow in the inset of Fig. 4) and in order to highlight that the strain to stress conversion is only valid inside the Ge, the datapoints corresponding to locations in the SiGe are greyed out. We emphasize that the NBD results are from a cross-sectional measurement while the Raman linescan was performed in the top-view so the Raman value represents the average stress in the sGe channel (assuming a uniform light absorption). The results obtained by NBD reveal the same trends as in the Raman linescan; the stress is most pronounced in the direction along the channel (σ22), but a small, non-zero compressive component is also present in the perpendicular direction (σ11). However, the average values for both σ11 (−0.4 GPa) and σ22 (−1.8 GPa) are higher than the ones obtained through Raman (−0.2 GPa and −1.4 GPa, respectively). At the same time, it is found that the stress in the out-of-plane direction (σ33) is non-zero as well, while in the Raman experiment σ33 was assumed to be zero to be able to calculate the other stresses in this geometry [see Eq. (1)]. However, it was verified that feeding the NBD-obtained values for σ33 into the non-simplified version of Eq. (1) resulted in only marginal changes to the results for σ11 and σ22 (less than 5% difference—not shown).7 Hence it is concluded that the out-of-plane stress is not at the origin of the difference between the Raman and NBD results, and its omission from the Raman calculations remains a good approximation.
In order to understand the discrepancy between the Raman and NBD results, we start by pointing out that there exists a difference in surface sensitivity between the two techniques. Figure 4 shows that the NBD experiment finds lower stress values near the surface of the Ge channel, and since the penetration depth of the 633 nm laser light in bulk Ge is only about 30 nm (i.e., of the order of the film thickness), the Raman experiment will be more sensitive to the surface compared to the deeper region of the sGe as the incident light decays travelling through the sGe. On the other hand, phonon confinement effects in nanoscale semiconductor structures are known to lead to a redshift of the Raman signal,34 which would again lead to an underestimate of the stress present in the sGe. While not shown here, Raman stress measurements do agree with NBD values on larger metrology pads, which further suggests a size-dependent shift of the Raman peak at these dimensions. It is unclear to what extent these phenomena may contribute to the mismatch between the Raman and NBD results and the precise mechanism behind the disagreement remains the subject of further study, but these observations suggest that a uniform stress measurement using nano-focused Raman spectroscopy on similar structures will require an additional calibration, for instance, on stress-free structures with the same dimensions. We emphasize that local heating of the region under investigation by the laser would lead to the same effect, but this possibility was ruled out by selecting an appropriately low laser power based on a power-dependent measurement of a calibration structure.
To summarize, we have demonstrated that through nano-focusing of the excitation laser light into narrow sGe finFET channels, Raman spectroscopy enables quantitative non-destructive stress measurements in deep-subwavelength semiconductor structures. We described how simultaneous LO/TO phonon selectivity using high-NA oil-immersion Raman spectroscopy further enabled accurate metrology of anisotropic biaxial stress, and the results were cross-validated against strain measurements using NBD. It was shown how ultimately this combination of experimental approaches leads to non-destructive, quantitative stress measurements in structures far beyond the diffraction limit.
The authors would like to gratefully acknowledge R. Loo, the EPI team, and Logic Program of imec for sample growth, documentation, and assistance. This work has been partially funded by the Electronic Component Systems for European Leadership Joint Undertaking under Grant Agreement No. 692527. This Joint Undertaking receives support from the European Union’s Horizon 2020 research and innovation programme and the Netherlands, Belgium, France, Hungary, Ireland, Denmark, and Israël.