4.1.

Comparison to Reference Metrology

To evaluate the validity of composition and strain results obtained by Raman scattering peak analyses and subsequent calculations with Eqs. (1) and (2), the data can be compared to reference metrology. First, the crystal quality of the non-patterned multilayer stack is evaluated for all wafers by RSMs acquired in the vicinity of the asymmetric (113) Bragg reflection [Figs. 3(a)–3(c)]. The maps confirm that all samples are fully strained as evidenced by the fact that the diffraction peaks from the substrate and the ${\mathrm{Si}}_{(1-x)}{\mathrm{Ge}}_x$ layers line up in the horizontal direction. Furthermore, the absence of any dislocation scatter around the diffraction peaks from the layers indicates a defect-free pseudomorphic growth.¹⁰

Fig. 3

Measured RSMs in the vicinity of the asymmetric (113) reflection from fully strained, unpatterned nanosheet stacks with (a) ${\mathrm{SiGe}}_{25}$; (b) ${\mathrm{SiGe}}_{35}$; and (c) ${\mathrm{SiGe}}_{50}$ layers; and correlation plots for results from Raman spectroscopy and XRD for (d) composition and (e) strain.

The sheet-specific Ge content of each wafer is determined by fitting the acquired $\omega -2\theta$ XRD scans around the (004) Bragg reflection. The average Ge content of all three SiGe sheets is then compared to Raman, which also measures an average of the probed sheets, from the same five locations. The correlation plot of XRD and Raman results for composition shows that both techniques are in excellent agreement with $R^2=0.996$ and a slope close to 1 [Fig. 3(d)]. Furthermore, the actual Ge content is close to target. Figure 3(e) shows the correlation plot of the in-plane strain as determined by Raman and XRD. Equally good agreements are observed as for composition. Note that the XRD strain values are calculated, location-specific averages of all three ${\mathrm{Si}}_{(1-x)}{\mathrm{Ge}}_x$ sheets using the XRD determined Ge content and assuming fully strained layers. Raman results yield a compressive strain of about -0.9% for wafers with $x=0.25$ and $-1.8\%$ for wafers with $x=0.5$. The presented Raman results have been obtained with an excitation wavelength of 405 nm; equally good results are achieved with 457 nm, for example. It is noticeable that the agreement between both techniques for the wafer with the nominally ${\mathrm{SiGe}}_{50}$ layers is not as good as for the other two wafers with ${\mathrm{SiGe}}_{25}$ and ${\mathrm{SiGe}}_{35}$ sheets. This is attributed to the fact that $x=0.5$ is just beyond the validity range of Eq. (2). Specifically, for germanium-rich alloys, the linear approximation used here starts failing to describe the Ge content-dependent Raman shift behavior of the Si-Ge phonon accurately.¹⁸ Hence, with equations optimized for germanium-rich alloys an accuracy improvement between Raman and XRD can be expected.

Another comparison to reference was done after fin patterning, i.e., after the nanosheet stack is etched to form a line and space grating-like structure. The RSMs in the vicinity of the asymmetric (113) Bragg reflection can be acquired with incident beams parallel and perpendicular to the line and space patterning and allow independent access to properties pertinent to the respective directions. The longitudinal RSMs [not shown for brevity; comparable to Figs. 3(a) and 3(b)] suggest that the in-plane strain along the fins is maintained since the diffraction peaks from the multilayer fin remain accurately aligned with the Si substrate peak in the horizontal $Q_x$ direction. A small shift of the multilayer peaks in the vertical $Q_z$ direction towards the Si substrate peak indicates strain relaxation of the out-of-plane component.¹⁹ After patterning, there is still no evidence of any dislocation scatter around the diffraction peaks associated with the multilayers. The RSMs measured with an incident beam perpendicular to the fin direction for the three different sample conditions are shown in Fig. 4. In this configuration, the patterning acts as a diffraction grating resulting in multiple diffraction orders (grating rods) along the $Q_x$ direction. The distance between the equally spaced grating rods is inversely proportional to the periodicity of the fin grating and a pitch of 100 nm can be confirmed with an average $\mathrm{\Delta }{Q}_x=0.00384$.^8,20 Also here, there are no indications of non-uniformities: the grating rods and all peaks are well defined and there is no scatter or significant background noise as confirmed also by the corresponding integrated line scans [Figs. 4(d)–4(f)]. Elastic in-plane strain relaxation of the ${\mathrm{Si}}_{(1-x)}{\mathrm{Ge}}_x$ layers shifts the maximum of the intensity envelope related to the grating rods away from the substrate peak. The reciprocal space position of the grating rods along the $Q_x$ direction does not change because the pitch remains unaffected. The intensity envelope maximum can be determined from the integrated line scans. Together with the known Ge concentration $x$ from either XRD at the blanket stage or Raman spectroscopy the transverse component of the in-plane lattice strain can be calculated in a straightforward manner.¹⁰ The RSM strain results from all three multilayer samples are compared with the strain from the ${\mathrm{Si}}_{(1-x)}{\mathrm{Ge}}_x$ layers obtained by Raman spectroscopy with polarization perpendicular to the fin direction and shown in Fig. 6. The transverse strain measurements exhibit an excellent correlation with both $R^2$ and slope very close to 1. The absolute RSM values are slightly lower compared to Raman, which is related to the complex Raman scattering response and a minor influence from phonons coupling to the orthogonal direction.

Fig. 4

Measured RSMs in the vicinity of the asymmetric (113) reflection after fin etch (40-nm width at 100-nm pitch) with (a) ${\mathrm{SiGe}}_{25}$; (b) ${\mathrm{SiGe}}_{35}$; and (c) ${\mathrm{SiGe}}_{50}$ layers acquired in the direction perpendicular to the patterning. Corresponding normalized intensity profiles along h for (d) ${\mathrm{SiGe}}_{25}$ integrated from $l=2.94$ to 2.96; (e) ${\mathrm{SiGe}}_{35}$ integrated from $l=2.930$ to 2.955; and (f) ${\mathrm{SiGe}}_{50}$ integrated from $l=2.895$ to 2.915.

In addition to the non-destructive RSM strain analysis, a destructive STEM characterization was carried out from fins with a CD of 50 nm. Figure 5 shows cross-fin HAADF images of all three samples together with the corresponding in-plane PED lattice deformation maps. The color coding refers to the lattice parameter change relative to the unstrained Si substrate. It is evident that the patterning leads to a partial relaxation within the ${\mathrm{Si}}_{(1-x)}{\mathrm{Ge}}_x$ sheets, which is most pronounced at the edges and due to the creation of the unconstraint surfaces. The in-plane deformation is proportional to the Ge content and most pronounced for the wafer with ${\mathrm{SiGe}}_{50}$ sheets.

Fig. 5

HAADF STEM and corresponding PED lattice deformation maps for ${\mathrm{SiGe}}_{25}$, ${\mathrm{SiGe}}_{35}$, and ${\mathrm{SiGe}}_{50}$. The scale bar denotes the lattice deformation with respect to the unstrained Si substrate. The FEM simulation for the ${\mathrm{SiGe}}_{35}$ sample is also shown for clarity.

Furthermore, relaxation of the compressively strained ${\mathrm{Si}}_{(1-x)}{\mathrm{Ge}}_x$ sheets induces a tensile strain within the Si sheets. The finite element method (FEM) simulation depicted for the sample with the ${\mathrm{SiGe}}_{35}$ sheets is in good agreement with the PED maps and illustrates the above-discussed behaviors clearly.^5,6 For this study, no PED lattice deformation maps along the fins were obtained (along the $y$ direction). Previous studies on wafers manufactured in a similar fashion reported that, for practically infinitely long fins, no relaxation occurs and the ${\mathrm{Si}}_{(1-x)}{\mathrm{Ge}}_x$ sheets remain fully strained.^7,19 However, simulations for multilayer fins with a length of 500 nm show some relaxation even along the fins.⁶ Additionally, due to the Poisson effect tensile strain also appears in the Si sheets along the fins ($y$ direction), although at lower amounts.⁵ The $y$ direction becomes the channel and hence transport direction, and therefore the induced strain is beneficial for nFET devices since electron mobility is increased in tensile Si.

The calculated average relaxation along the $x$ direction considering the lattice deformation of all three ${\mathrm{Si}}_{(1-x)}{\mathrm{Ge}}_x$ sheets (average across the entire width) is 40.4%, 71.8%, and 75% for the wafers with ${\mathrm{SiGe}}_{25}$, ${\mathrm{SiGe}}_{35}$, and ${\mathrm{SiGe}}_{50}$ sheets, respectively. Except for the ${\mathrm{SiGe}}_{25}$ sample, the relaxations for samples with ${\mathrm{SiGe}}_{35}$ and ${\mathrm{SiGe}}_{50}$ sheets are larger than expected, which can be attributed to the destructive sample preparation process and the thinness of the specimen. For example, nanobeam diffraction studies have shown that strain relaxation originating from a fin edge can still affect the lattice more than 100 nm away from that unconstraint surface.¹⁹ Previously, it was assumed that the complex response from transverse Raman scattering may be a measure of the average in-plane strain along the $x$ and $y$ directions, which matched the calculated in-plane average from PED analyses.²¹ However, simulations and the excellent correlation between Raman and RSM shown in Fig. 6 suggest that the Raman scattering observed with polarization perpendicular to the grating-like pattern is strongly dominated by the transverse properties along the $x$ direction. To minimize the influence of a potential relaxation caused by the destructive sample preparation, lattice deformation read-out was limited to center of the first ${\mathrm{Si}}_{(1-x)}{\mathrm{Ge}}_x$ sheet (average of 20 pixels) as the bottom part is least affected from edge relaxation.¹⁹ The correlation between computed transverse PED in-plane strain and corresponding transverse Raman spectroscopy results is shown in Fig. 6. While the $R^2=0.95$ confirms a very good linear behavior, the slope of $<1$ reveals some discrepancies. For ${\mathrm{SiGe}}_{25}$ sheets, both techniques are in excellent agreement with a compressive strain of $\sim -0.006$. However, with increasing germanium concentration, PED results suggest less strain and hence more relaxation in the ${\mathrm{Si}}_{(1-x)}{\mathrm{Ge}}_x$ sheets compared to Raman. As discussed above, this is mainly attributed to the destructive sample preparation procedure and the thinness of the specimen leading to additional relaxation.

Fig. 6

Transverse in-plane strain as obtained by Raman, RSMs, and PED. The RSMs and PED results are from fins with a width of 40 and 50 nm, respectively, and compared to Raman results from corresponding fin dimensions. The Raman results represent the average strain of the probed ${\mathrm{Si}}_{(1-x)}{\mathrm{Ge}}_x$ layers as obtained from a measurement with polarization perpendicular to the fin direction. The transverse RSM results represent the average response from the ${\mathrm{Si}}_{(1-x)}{\mathrm{Ge}}_x$ layers within multilayer fin pattern. The PED results are obtained by averaging a region of interest ($10\times 2\text{pixels}$) from the center of the first ${\mathrm{Si}}_{(1-x)}{\mathrm{Ge}}_x$ sheet.

4.2.

Raman Strain Monitoring

With the assurance that strain results obtained by Raman spectroscopy are in good agreement with reference metrology for blanket and patterned targets, all presented strain results from here on are from Raman metrology only. Figure 7(a) shows the compressive strain in ${\mathrm{Si}}_{(1-x)}{\mathrm{Ge}}_x$ sheets for all three samples as a function of all 21 dies measured across the wafer. The four graphs correspond to measurements of an unpatterned blanket target and three-patterned targets with different fin CDs (40, 50, and 70 nm). A representative cross-section of the patterned target with 40-nm fin CD is also depicted [inset in Fig. 7(b)]. As discussed already before, the strain increases with Ge content due to the increasing lattice mismatch. The consistent measurements across the wafer indicate that metrology noise and processing variations are very low, and no across wafer signature is observed. The average across wafer Ge content determined by Raman is 25.2%, 37.2%, and 49.2% for the nominally ${\mathrm{SiGe}}_{25}$, ${\mathrm{SiGe}}_{35}$, and ${\mathrm{SiGe}}_{50}$ samples, respectively. With patterning and the creation of unconstraint surfaces, relaxation occurs, which depends on the fin CD, i.e., with smaller CDs greater relaxation is observed. This can be explained with the increasing surface-to-volume ratio with decreasing CDs and hence the increasing dominance of the strong edge relaxation. Across the three samples, the average measured relaxation with polarization along the fins is approximately constant with 19%, 22%, and 25% for the 70-, 50-, and 40-nm features, respectively. It is noteworthy that long multilayer fins (from $\sim >300\mathrm{nm}$ away from a fin end¹⁹) remain fully strained along the fin direction, which is also confirmed by the RSM analyses. Hence, the Raman scattering response with polarization parallel to the fin direction comprises contributions from both in-plane orientations. Strongly dominated by the LO phonon mode, it is approximately a measure of the average in-plane relaxation.

Fig. 7

${\mathrm{Si}}_{(1-x)}{\mathrm{Ge}}_x$ (a) and Si (b) strain for blanket and three different fin CDs (40, 50, and 70 nm) as a function of measured dies across the wafer. The three vertical sections in (a) and (b) represent the three different samples with ${\mathrm{SiGe}}_{25}$, ${\mathrm{SiGe}}_{35}$, ${\mathrm{SiGe}}_{50}$ sheets. The inset in (b) shows a STEM cross-section of the ${\mathrm{SiGe}}_{25}$ sample with 40-nm fin CD. All results are obtained with polarization along the fin direction.

Figure 7(b) shows the same graph but for tensile Si sheets. It is noteworthy that at the unpatterned blanket stage, the Si sheets do not exhibit any strain. In this case, the Si-Si LO-TO Raman phonon of the unstrained Si sheets is identical to the phonon mode of the strain-free Si substrate. Hence the simulated data points at zero strain are not measurements and only added for convenience. Once the blanket multilayer stack is patterned and the strained ${\mathrm{Si}}_{(1-x)}{\mathrm{Ge}}_x$ relaxes, a tensile strain is induced in the Si sheets. The tensile strain in Si depends on the Ge content within the ${\mathrm{Si}}_{(1-x)}{\mathrm{Ge}}_x$ and on the sheet CD. The Si strain for the wafer with the ${\mathrm{SiGe}}_{50}$ sheets is about a factor of two larger compared to the multilayer stacks with ${\mathrm{SiGe}}_{25}$ sheets. Furthermore, the sheets with the smallest CD (40 nm) exhibit the largest strain and there is a linear relationship between strain and CD within the measured range.

As discussed earlier already, there is a directional strain dependence post fin patterning, which can be distinguished based on the polarization direction of the probing light. Polarization-dependent results of the compressive strain in ${\mathrm{Si}}_{(1-x)}{\mathrm{Ge}}_x$ after fin patterning are shown in Fig. 8. The box chart is vertically sectioned accommodating the three sample scenarios and the $x$ axis sorts the four targets by increasing CD (the unpatterned blanket can be understood as having an infinitely large CD). The blanket strain probed with parallel and perpendicular polarization states is practically identical. This is expected, as the Raman peak position for two orthogonal directions from a Si (100) wafer is identical.¹⁴ The patterned sites on the other hand exhibit a strong polarization-dependent strain difference. When probing the strain with polarization parallel to the fins, the value is larger compared to a polarization perpendicular to the fins. This general observation is in agreement with previously published results and corresponding simulations.^5,6,8 Furthermore, the compressive strain difference increases significantly with decreasing CD, and the measurement with perpendicular polarization is more sensitive to CD changes. In general, the trends for the wafers with different Ge concentrations are comparable but differ in amplitude.

Fig. 8

Polarization dependence of ${\mathrm{Si}}_{(1-x)}{\mathrm{Ge}}_x$ strain results post fin patterning. The chart is split into three vertical sections representing the three sample types with different Ge content under investigation. The $x$ axis within each section groups the results by fin CD and includes the unpatterned blanket site. The blue and red boxes denote the results for polarization parallel and perpendicular to the fins, respectively. The black arrows are merely a guide to the eye.

Similar to the size-dependent strain behavior along the fin direction, a linear relationship between transverse strain and width is observed within the measured range. The experimentally determined relaxation of 49% for multilayer ${\mathrm{SiGe}}_{35}$ fins with a 40-nm CD is already in good agreement with a reported simulated strain relaxation of 58% for similar fins with a 35-nm CD.⁶ An extrapolation beyond the measured CD range toward fins with a width of 35 nm for the sample with ${\mathrm{SiGe}}_{35}$ comes with 52.5% relaxation even closer to the literature value.

While this paper only focuses on strain characterization, which is based on the determination of the phonon mode energy, it should be noted that Raman intensities (phonon-mode amplitude) may be used to measure the CD.²²

4.3.

Strain Tracking Through FEOL Patterning

Figure 9 shows the ${\mathrm{SiGe}}_{25}$ strain evolution through FEOL patterning after six important processing steps: blanket (nanosheet stack deposition), FinEtch (fin patterning along $y$; “nanosheet stack lines”), GateEtch (dummy gate patterning), FinRecess (fin patterning along $x$; “nanosheet stack pillars”), S/D epi (Si:P epitaxy), and PolyPull (dummy gate removal). The five insets at the top schematically depict the structure at the respective processing step with an orientation parallel to the original fin direction (channel direction). PolyPull is the last opportunity to measure the sacrificial ${\mathrm{Si}}_{(1-x)}{\mathrm{Ge}}_x$ sheets as they get removed at the next processing step. Focus is put on nFET devices and polarization along the $y$ direction (original fin direction). The boxes and whiskers represent measured values for all fin and gate CDs and indicate the across wafer variation convoluted with some metrology uncertainty.

Fig. 9

${\mathrm{SiGe}}_{25}$ strain evolution through FEOL patterning measured after six processing steps. Results depicted are for nFET devices and polarization along the $y$ direction. The insets at the top schematically depict the structure at the respective processing step with a view parallel to the $y$ direction (along the fins).

As discussed before, processing starts with fully strained ${\mathrm{SiGe}}_{25}$ layers at the blanket stage due to a defect-free pseudomorphic growth. After the first patterning step (FinEtch) already the most significant impact on strain is observed with on average $>20\%$ relaxation. At GateEtch a small relaxation is observed, which is mostly attributed to several thermal processing steps within the fin module. It is noteworthy that at GateEtch the major contribution to the Raman response is from the exposed fin areas not covered by the dummy gate. The next step is FinRecess, which is a fin patterning perpendicular to the original fin direction defining the gate length. This leaves nanosheet stack pillars with dimensions of the fin CD in one direction and dummy gate CD in the other direction. On average, some further relaxation is observed, which is due to the creation of more unconstraint surfaces. Additionally, an increase in the data spread is noticed and mainly caused by the influence of the now present and varying gate CD. Similar to previously discussed trends related to the fin CD, with decreasing gate CD the sheet relaxation increases but not as dramatic as compared to what was measured at FinEtch. Nonetheless, the gate CD-dependent strain behavior does not explain all observed variation. The reduced amount of sheet volume together with the polycrystalline dummy gate, which causes a broad Raman background thereby contributing to measurement uncertainty, and likely some process-related variations add to the overall data spread. It is noteworthy that light needs to pass through the polycrystalline dummy gate twice before Raman scattering can be collected.

For this wafer, the strain remains approximately constant after S/D epitaxy with an equally large distribution. After PolyPull, when all polycrystalline dummy gate material is removed, an increased compressive ${\mathrm{SiGe}}_{25}$ strain is measured again. Further studies also supported by strain modeling are required to fully understand what is happening. Possibilities may be related to dummy gate clamping, S/D epi strain, processing, or strain modeling inaccuracies due to the polycrystalline material at the previous steps.

Figure 10(a) shows the Si tensile strain evolution through FEOL patterning after six important processing steps: FinEtch, GateEtch, FinRecess, S/D epi, PolyPull, and Release. The latter step refers to the removal of the sacrificial ${\mathrm{SiGe}}_{25}$ sheets. At each step, the strain is plotted for all three fin CDs. The boxes and whiskers represent all measured values and the across wafer variation convoluted with some metrology uncertainty. It is noteworthy that the blanket step is not included because the Si sheets do not exhibit any strain before patterning. The results at FinEtch have been discussed in detail already above [Fig. 7(b)]; briefly, CD-dependent tensile strain is generated by the ${\mathrm{SiGe}}_{25}$ relaxation. It is noticeable at GateEtch that the difference between the three fin CDs is less pronounced as compared to FinEtch and mainly related to the strain decrease of the 40 and 50 nm device structures. This may be caused by thermal processing in the fin module. At FinRecess, there is a small increase in strain due to further edge relaxation of the ${\mathrm{SiGe}}_{25}$ sheets along with a significant increase in the data spread. This data spread increase was also observed for the ${\mathrm{SiGe}}_{25}$ strain at the same process step and is related to the different gate CDs with additional contributions from possible process variations and an increased measurement uncertainty due to the smaller Si sheet area located underneath the thick polycrystalline gates. A substantial increase post S/D epitaxy is observed with no major strain changes transitioning to PolyPull. After removal of the polycrystalline dummy gate material the data spread decreases again slightly. It is noteworthy that since the measured devices are nFETs, the S/D and the channel are comprised of epitaxial Si. It has been confirmed that the selected experimental settings allow for probing the Si nanosheet channels only, independent of the S/D region. Choosing a different measurement configuration, it is possible to probe the S/D epitaxial Si:P only.

Fig. 10

(a) Tensile Si strain evolution through FEOL patterning measured after six processing steps, where each box per step represents a different fin CD. Results depicted are for nFET devices with ${\mathrm{SiGe}}_{25}$ sheets; (b) Si stress post channel release as a function of fin CD and Ge%. Only strain and stress values from measurements with polarization along the $y$ direction are compared.

After the complete removal of the sacrificial ${\mathrm{SiGe}}_{25}$ nanosheets (Release), a significant size-dependent strain relaxation is observed. However, the Si nanosheets still remain under tensile strain. Now, the smallest fin CD exhibits also the smallest tensile strain and with increasing CD the strain increases substantially. This trend is opposite to what was observed at FinEtch and likely related to edge relaxation, which is more pronounced when the surface-to-volume ratio is large. The gate CD plays a minor role only at PolyPull and Release and is not discussed.

A more detailed analysis after the Release step is shown in Fig. 10(b). The Si strain was converted to stress in GPa using a Young’s modulus $E=180\mathrm{GPa}$. Besides looking at CD-dependent stress behavior, results from the wafers with different Ge content are presented. For each measured CD, the stress increases with Ge content. This means that strain tuning of the Si channel is possible by variation of the Ge content in the sacrificial ${\mathrm{Si}}_{(1-x)}{\mathrm{Ge}}_x$ nanosheets.

Most observed trends are in agreement with previously published simulations by Reboh et al.⁶ Specifically, the emergence of tensile strain after fin patterning and the fact that tensile strain post channel release depends on the Ge content of the sacrificial ${\mathrm{Si}}_{(1-x)}{\mathrm{Ge}}_x$ nanosheets. Notably, simulations suggest an average stress of $\sim 0.3\mathrm{GPa}$ for devices using sacrificial ${\mathrm{SiGe}}_{30}$, which is close to what is measured by Raman spectroscopy on wafer.