**3. Results and discussion**

#### **3.1. Excitation of TO phonon modes in oil-immersion Raman spectroscopy**

Fig. 14 shows the Raman spectra of the LO phonon modes from the SSOI substrate in the oblique incident light configurations with the glancing angles of 30 and 90. Two peaks are seen in the Raman spectra because the excitation light ( = 532 nm) penetrates the strained Si layer, the BOX layer, and reaches the Si substrate. Therefore, the wavenumber on the highfrequency side (defined to be 520 cm−1 in this study) originates from the Si substrate, and the wavenumber on the low-frequency side originates from the strained Si layer with the isotropic biaxial tensile stress state. The Raman intensities obtained in the 30 and 90 configurations are almost the same, which is consistent with the calculations shown in Fig. 2. Fig. 15 shows the Raman spectrum from the SSOI substrate in the TO active configuration. The glancing angle was 30. The fitting curves for the strained Si layer and the Si substrate are also shown in Fig. 15. The explanation about the peak positions of the LO and TO phonon modes for SSOI are shown later.

From the results, the intensity ratio of the TO phonon mode from the strained Si layer obtained in the TO active configuration to the LO phonon mode from the strained Si layer obtained in the LO active configuration was calculated to be approximately 0.04. This value is almost the same as the theoretical value shown by Eq. (3). Using the oblique incident light configuration, the TO phonon modes were excited even for (001) Si. It is possible to completely eliminate the intensity of the LO phonon mode in the oblique incident light configuration in theory. Nevertheless, as shown in Fig. 15, the LO phonon mode was observed in the TO active configuration. This result is considered that there are misalignments of polarization between the incident/scattered light and the orientation of the Si substrate. It is considered that this behavior easily happens because the intensity of the LO phonon mode is much higher than that of the TO phonon mode.

**Figure 14.** Raman spectra in 30° and 90° configurations

**Figure 15.** Raman spectrum in TO active configuration with fitting curves

Fig. 16 shows the Raman spectra from SSOI in the LO and TO active conditions, respectively, obtained by oil-immersion Raman spectroscopy. The light-exposure time is 5 s and 300 s for the excitations of the LO and TO phonons, respectively. The Raman intensity shown in Fig. 16 was normalized by the Raman signal from the strained Si layer. It should be noted that the low-frequency peak from strained Si in the LO active condition is lower than that in the TO active condition, although the peaks from the Si substrate in each condition are at the same wavenumber. The difference of the peak positions can be explained by Eq. (17); the LO phonon mode is more affected by biaxial stress than are the TO phonon modes.

Fig. 17 shows the result of fitting each peak. The LO phonon mode is detected irrespective of the TO active condition. This fact arises because the incident light with the polarization in the [010] Si direction generates even in configuration (c) shown in Fig. 12 due to depolarization effects [24]. It is considered difficult to avoid the depolarization effects for the SSOI substrate. On the other hand, it is reported that the contribution of the LO phonon modes can be decreased for the SSOI nanostructures because the depolarization effects relax due to the nanostructure [24]. It is considered that the peak separation of the LO and TO phonon modes is needed for the SSOI substrate to analyze the Raman spectrum obtained in the TO active configuration, while not necessary for the SSOI nanostructure.

**Figure 16.** Raman spectra from SSOI in TO and LO active configurations

266 Advanced Aspects of Spectroscopy

is almost the same as the theoretical value shown by Eq. (3). Using the oblique incident light configuration, the TO phonon modes were excited even for (001) Si. It is possible to completely eliminate the intensity of the LO phonon mode in the oblique incident light configuration in theory. Nevertheless, as shown in Fig. 15, the LO phonon mode was observed in the TO active configuration. This result is considered that there are misalignments of polarization between the incident/scattered light and the orientation of the Si substrate. It is considered that this behavior easily happens because the intensity of the

LO phonon mode is much higher than that of the TO phonon mode.

SSOI

**Figure 14.** Raman spectra in 30° and 90° configurations

Raman intensity [arb. unit]

Raman intensity [arb. unit]

TO phonon modes.

**Figure 15.** Raman spectrum in TO active configuration with fitting curves

SSOI

Fig. 16 shows the Raman spectra from SSOI in the LO and TO active conditions, respectively, obtained by oil-immersion Raman spectroscopy. The light-exposure time is 5 s and 300 s for the excitations of the LO and TO phonons, respectively. The Raman intensity shown in Fig. 16 was normalized by the Raman signal from the strained Si layer. It should be noted that the low-frequency peak from strained Si in the LO active condition is lower than that in the TO active condition, although the peaks from the Si substrate in each condition are at the same wavenumber. The difference of the peak positions can be explained by Eq. (17); the LO phonon mode is more affected by biaxial stress than are the

500 505 510 515 520 525 530 535 Raman shift [cm-1

500 505 510 515 520 525 530 535 Raman shift [cm-1

> TO LO

90º <sup>a</sup>

]

]

Si. sub.

Si. sub.

30º

**Figure 17.** Raman spectrum in TO active configuration with fitting curves

The wavenumber shift of the LO phonon mode for the strained Si layer in the TO active configuration was −4.56 cm−1, which is consistent with the value of −4.60 cm1 for the Raman peak obtained in the LO active configuration. Furthermore, the Raman peak intensity from the Si substrate in the TO active condition is higher than that in the LO active configuration. This behavior indicates that the Raman peak that originates from the LO phonon mode is superimposed onto the Raman peak that originates from the TO phonon mode. We claim that the TO phonon mode was excited by using the high-NA oil-immersion lens.

Fig. 18 shows the Raman spectra from SSOI obtained by conventional Raman spectroscopy with the use of the NA = 0.7 objective. The dashed and solid lines denote the Raman spectra in the LO and TO active configurations, respectively. The light-exposure time of 3600 s for the TO active configuration is 400 times longer than that of 9 s (0.25% of 3600 s) for the LO active configuration. The intensity ratio of the TO to LO phonon modes are anticipated by the calculation shown in Table 2. In Fig. 18, the Raman intensity in each configuration is close to one another. Furthermore, the difference of the peak positions of the strained-Si layer in each configuration is confirmed, similarly to the results in oil-immersion Raman spectroscopy. These results indicate that the TO phonon mode was excited even in conventional Raman spectroscopy. However, the signal to noise ratio of the Raman intensity is bad. Moreover, the extremely long time measurements are necessary. In fact, it is difficult to perform mapping for obtaining biaxial-stress distributions in conventional Raman spectroscopy. We consider that it is important to use the high-NA liquid-immersion lens in order to excite TO phonon mode effectively and obtain biaxial-stress distributions in a realistic time.

**Figure 18.** Raman spectra from SSOI with use of dry objective.

#### **3.2. Measurements of anisotropic biaxial stress states in SSOI nanostructures**

In-plane XRD measurements were performed to confirm strain in the strained Si layer. The diffraction from Si (220) and (220) were measured (the results are not shown). As a result, *xx* and *yy* were 7.5 103 and 7.4 103, respectively. These results indicate that the stress state in the strained Si layer is almost isotropic biaxial throughout the wide area which is equivalent to the footprint of the incident X-ray.

PDPs were evaluated by oil-immersion Raman spectroscopy. The calculated biaxial stresses *xx* and *yy* in the strained Si layer are summarized in Fig. 19. In the calculation of the biaxial stresses, PDPs reported in 1970, 1978, and 1990, as mentioned above, were used and Eqs. (19)-(21) were used for the stress calculations. In the oil-immersion Raman measurements, five points were obtained. The solid symbols indicate the average values. From the results, it appears that the biaxial stress values fluctuate in the range of 50–150 MPa, which is attributed to the dislocation conditions in the strained Si layer [61-63]. It should be noted that the apparent anisotropic natures of biaxial stress states were observed in the case of using PDPs reported in 1970 and 1978. The differences in the biaxial stresses are 530 and 170 MPa for PDPs reported in 1970 and 1978, respectively, which are inconsistent with the results of XRD. On the other hand, the isotropic nature was clearly observed in the case of using PDPs reported in 1990. As a result, PDPs of *p*/02 = 1.85, *q*/02 = 2.31, and *r*/02 = 0.71 reported by Anastassakis *et al*. in 1990 are considered the most accurate for evaluating stress in Si among the three sets of PDPs.

268 Advanced Aspects of Spectroscopy

realistic time.

*xx* and 

*xx* and 

**Figure 18.** Raman spectra from SSOI with use of dry objective.

Raman intensity [arb. unit]

equivalent to the footprint of the incident X-ray.

**3.2. Measurements of anisotropic biaxial stress states in SSOI nanostructures** 

 TO active (3600 s) LO active (9 s)

SSOI

In-plane XRD measurements were performed to confirm strain in the strained Si layer. The diffraction from Si (220) and (220) were measured (the results are not shown). As a result,

505 510 515 520 525 530 535 Raman shift [cm-1

]

Si. sub.

state in the strained Si layer is almost isotropic biaxial throughout the wide area which is

PDPs were evaluated by oil-immersion Raman spectroscopy. The calculated biaxial stresses

stresses, PDPs reported in 1970, 1978, and 1990, as mentioned above, were used and Eqs. (19)-(21) were used for the stress calculations. In the oil-immersion Raman measurements, five points were obtained. The solid symbols indicate the average values. From the results, it appears that the biaxial stress values fluctuate in the range of 50–150 MPa, which is attributed to the dislocation conditions in the strained Si layer [61-63]. It should be noted

*yy* were 7.5 103 and 7.4 103, respectively. These results indicate that the stress

*yy* in the strained Si layer are summarized in Fig. 19. In the calculation of the biaxial

Fig. 18 shows the Raman spectra from SSOI obtained by conventional Raman spectroscopy with the use of the NA = 0.7 objective. The dashed and solid lines denote the Raman spectra in the LO and TO active configurations, respectively. The light-exposure time of 3600 s for the TO active configuration is 400 times longer than that of 9 s (0.25% of 3600 s) for the LO active configuration. The intensity ratio of the TO to LO phonon modes are anticipated by the calculation shown in Table 2. In Fig. 18, the Raman intensity in each configuration is close to one another. Furthermore, the difference of the peak positions of the strained-Si layer in each configuration is confirmed, similarly to the results in oil-immersion Raman spectroscopy. These results indicate that the TO phonon mode was excited even in conventional Raman spectroscopy. However, the signal to noise ratio of the Raman intensity is bad. Moreover, the extremely long time measurements are necessary. In fact, it is difficult to perform mapping for obtaining biaxial-stress distributions in conventional Raman spectroscopy. We consider that it is important to use the high-NA liquid-immersion lens in order to excite TO phonon mode effectively and obtain biaxial-stress distributions in a

Figs. 20(a) and (b) show the Raman spectra from the SSOI nanostructures with *W* = 1.0 and 0.05 m, respectively, in configuration (c). *L*s of the nanostructures were both 5.0 m. We subtracted the signal of the Si substrate fitting curves from the raw data in order to analyze the spectra from the SSOI nanostructures in detail. From Fig. 20(b), the signal from the SSOI nanostructure even with *W* = 50 nm can be clearly observed. This observation is attributed to the high spatial resolution in oil-immersion Raman spectroscopy.

**Figure 19.** Biaxial stresses *xx* and *yy* in SSOI obtained by oil-immersion Raman spectroscopy using three sets of PDPs.

**Figure 20.** Rama spectra from SSOI nanostructures with *W*s of (a) 1.0 and (b) 0.05 m. *L* is both 5.0 m.

The normalized Raman spectra as a function of *L* are shown in Fig. 21. *W* was fixed to 0.2 m. The peaks from bulk Si are shown for comparison. The peak positions of strained Si gradually shift toward the high-frequency side with the decrease in *L* from 5.0 to 0.5 m, as shown in Fig.21. Using Eq. (21), the anisotropic biaxial stresses *xx* and *yy* in the SSOI nanostructures were calculated, as shown in Fig. 22. Figs. 22(a) and (b) show the results for the SSOI nanostructures with the thickness of 50 and 30 nm, respectively. The results of the Raman measurements were compared with those of FEM. The example of the FEM calculations is shown in Fig. 23. Fig. 23 shows the three dimensional distribution of the *xx* component for the SSOI nanostructure with *L* = 1.0 and *W* = 0.2 m. From the results of FEM, the stress relaxation is confirmed at the edge of the SSOI nanostructure, while large tensile stress remains in the center of the SSOI nanostructure and at the interface of the strained Si layer and the BOX layer. There is a good correlation between the results of oil-immersion Raman spectroscopy and FEM, as shown in Fig. 22. *xx* decreases with the decrease in *L* for the SSOI nanostructures with the thickness of 50 and 30 nm, while *yy* remains almost constant. Moreover, the values of *yy* for the SSOI nanostructures with the thickness of 30 nm are larger than those of 50 nm. Therefore, the thin SSOI nanostructures had immunity to the stress relaxation. Using oil-immersion Raman spectroscopy, the evaluation of the anisotropic biaxial stress states was accomplished for the SSOI nanostructures. It is considered that the results obtained in this study have important implications for the SSOI nanostructure fabrication.

**Figure 21.** Normalized Raman spectra from SSOI nanostructures as a function of *L* in (a) LO and (b) TO active configurations.

## **3.3. Measurements of anisotropic biaxial stress states in strained SiGe nanostructures**

In this section, the evaluation of the anisotropic biaxial stress states in the SiGe nanostructures is shown. For the SiGe nanostructures, large compressive stress is induced because the lattice constant of SiGe is larger than that of Si. The stress states in the SiGe nanostructures are considered to be expressed by Eq. (12) similar to the stress states in the SSOI nanostructures. The crystal structure of SiGe remains diamond type, i.e., the methodology of evaluation for the anisotropic biaxial stress in Si shown above can be directly applied to strained SiGe.

270 Advanced Aspects of Spectroscopy

The normalized Raman spectra as a function of *L* are shown in Fig. 21. *W* was fixed to 0.2 m. The peaks from bulk Si are shown for comparison. The peak positions of strained Si gradually shift toward the high-frequency side with the decrease in *L* from 5.0 to 0.5 m, as

nanostructures were calculated, as shown in Fig. 22. Figs. 22(a) and (b) show the results for the SSOI nanostructures with the thickness of 50 and 30 nm, respectively. The results of the Raman measurements were compared with those of FEM. The example of the FEM calculations is shown in Fig. 23. Fig. 23 shows the three dimensional distribution of the

component for the SSOI nanostructure with *L* = 1.0 and *W* = 0.2 m. From the results of FEM, the stress relaxation is confirmed at the edge of the SSOI nanostructure, while large tensile stress remains in the center of the SSOI nanostructure and at the interface of the strained Si layer and the BOX layer. There is a good correlation between the results of oil-immersion

nm are larger than those of 50 nm. Therefore, the thin SSOI nanostructures had immunity to the stress relaxation. Using oil-immersion Raman spectroscopy, the evaluation of the anisotropic biaxial stress states was accomplished for the SSOI nanostructures. It is considered that the results obtained in this study have important implications for the SSOI

> 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

W = 0.2 **(a) (b)** <sup>m</sup> W = 0.2 <sup>m</sup> LO mode TO mode

**Figure 21.** Normalized Raman spectra from SSOI nanostructures as a function of *L* in (a) LO and (b) TO

Raman intensity [arb. unit]

In this section, the evaluation of the anisotropic biaxial stress states in the SiGe nanostructures is shown. For the SiGe nanostructures, large compressive stress is induced because the lattice constant of SiGe is larger than that of Si. The stress states in the SiGe nanostructures are considered to be expressed by Eq. (12) similar to the stress states in the

**3.3. Measurements of anisotropic biaxial stress states in strained SiGe** 

]

L = 5.0 m 3.0 2.0 1.5 1.0 0.8 0.5

*xx* and

*xx* decreases with the decrease in *L* for

*yy* for the SSOI nanostructures with the thickness of 30

510 515 520 525 530 Raman shift [cm-1

Bulk Si

]

L = 5.0 m 3.0 2.0 1.5 1.0 0.8 0.5

*yy* in the SSOI

*yy* remains almost

*xx*

shown in Fig.21. Using Eq. (21), the anisotropic biaxial stresses

the SSOI nanostructures with the thickness of 50 and 30 nm, while

Raman spectroscopy and FEM, as shown in Fig. 22.

510 515 520 525 530 Raman shift [cm-1

Bulk Si

constant. Moreover, the values of

nanostructure fabrication.

2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

Raman intensity [arb. unit]

active configurations.

**nanostructures** 

**Figure 22.** Biaxial stresses *xx* and *yy* as a function of *L* for (a) 50-nm-thick and (b) 30-nm-thick SSOI nanostructures.

**Figure 23.** Three dimensional stress distribution obtained by FEM.

Fig. 24 shows the examples of Raman spectra from the SiGe nanostructures. As shown in Fig. 24, the intensity from Si-Si phonon mode in SiGe appeared to be weak, while the intensity of the Si substrate is very strong. This behavior makes the analysis difficult. Nevertheless, the LO and TO phonon modes can be separately obtained. The peak positions of the TO and LO phonon modes for the SiGe nanostructures with *L* = 5.0 and *W* = 1.0 m are clearly different. Moreover, it should be noted that the difference decreases with the decrease in *W*. For *W* = 0.1 m, there is little difference between the peak positions of the TO and LO phonon modes. This behavior indicates that the stress states in the SiGe nanostructures change from a biaxial state to a uniaxial state.

**Figure 24.** Raman spectra of TO and LO phonon modes from SiGe nanostructures.

Fig. 25 shows the Raman shifts of the TO and LO phonon modes for the SiGe nanostructures with *W* = 1.0, 0.5, and 0.1 m as a function of *L*. First, the large compressive stress exists because the Raman shift of stress-free SiGe with the 30% Ge concentration is approximately 500 cm-1 [64,65]. From the results, the clear dependence of the Raman shifts on *L* and *W* were observed. It appears that the evaluation of the anisotropic biaxial stress states in strained SiGe is accomplished by oil-immersion Raman spectroscopy similar to evaluating strained Si. However, it is considered that the evaluation of strained SiGe is more difficult than that of Si. There are several unknown parameters for measuring stress in strained SiGe, e.g., PDPs of SiGe, precise Ge concentration, and peak position of stress-free SiGe. Various parameters have so far been suggested [64-70]. These problems are now under investigation.

#### **3.4. Measurements of nondiagonal stress components**

First, (the contribution of *z* polarization) was determined from the Raman intensity ratio of the TO to LO phonon modes (the results are not shown). From the results, was calculated to be 0.09 in the water-immersion Raman measurements. Fig. 26 shows the comparison between the measured and calculated data of the Raman shifts dependences on the sample rotation angle. The experimental results were obtained by high-NA waterimmersion Raman spectroscopy. The measurement position was the region at the edge of the SiN film (the edge under the SiN film rather than in the space region). Features indicating the induction of stress with the nondiagonal component are clearly observed in the experimental results; the profiles of the Raman shift dependence on the sample rotation angle are asymmetric relative to 45 from 0 to 90 (or relative to 135 from 90 to 180). As previously shown, this behavior indicates that the shear stress component *xz* is induced in Si at the edge of the SiN film. From Fig. 26, there is a good correlation between the measured and calculated data. On the other hand, disagreements appear around sample rotation angles of 45 and 135. One possible explanation is that the polarization of the electrical fields of the incident and scattered light is modified by the SiN film. This modification is not included in the calculation.

272 Advanced Aspects of Spectroscopy

**Figure 24.** Raman spectra of TO and LO phonon modes from SiGe nanostructures.

Intensity [arb. unit]

Intensity [arb. unit]

Intensity [arb. unit]

TO

*L*: 5.0 m *W*: 1.0 m

*L*: 5.0 m *W*: 0.5 m

*L*: 5.0 m *W*: 0.1 m

LO

TO

LO

TO

LO

**3.4. Measurements of nondiagonal stress components** 

First, 

Fig. 25 shows the Raman shifts of the TO and LO phonon modes for the SiGe nanostructures with *W* = 1.0, 0.5, and 0.1 m as a function of *L*. First, the large compressive stress exists because the Raman shift of stress-free SiGe with the 30% Ge concentration is approximately 500 cm-1 [64,65]. From the results, the clear dependence of the Raman shifts on *L* and *W* were observed. It appears that the evaluation of the anisotropic biaxial stress states in strained SiGe is accomplished by oil-immersion Raman spectroscopy similar to evaluating strained Si. However, it is considered that the evaluation of strained SiGe is more difficult than that of Si. There are several unknown parameters for measuring stress in strained SiGe, e.g., PDPs of SiGe, precise Ge concentration, and peak position of stress-free SiGe. Various parameters have so far been suggested [64-70]. These problems are now under investigation.

490 500 510 520 530 Raman shift [cm-1

490 500 510 520 530

490 500 510 520 530

**Si-Si of SiGe**

]

(the contribution of *z* polarization) was determined from the Raman intensity ratio

was

of the TO to LO phonon modes (the results are not shown). From the results,

**Figure 25.** Raman shifts of TO and LO phonon modes for SiGe nanostructures as a function of *L*.

**Figure 26.** Comparison between measured and calculated data of Raman shift dependences on sample rotation angle.

The Raman shifts appear to be small. This is explained as follows. The stress induced at the edge of the SiN film is localized in width and depth. It is considered that the measured stress is averaged in the region of approximately 390 and 450 nm which are the spot size and optical penetration depth of the laser, respectively. From the water-immersion Raman measurements, *xz* was approximately 0.1 GPa. This value was consistent with the result obtained by the edge force model after the correction for the spot size and the optical penetration depth of the laser (the results are not shown) [46,58]. The methodology described here has the potential to measure complicated stress states in Si and SiGe even those with nondiagonal stress components.

#### **4. Conclusion**

We demonstrated the measurements of the complicated stress states in Si by high-NA liquid-immersion Raman spectroscopy. The *z* polarization was obtained due to the high-NA liquid-immersion lens, which allows for exciting the forbidden modes, the TO phonon modes, even under the (001) Si backscattering geometry. First, the TO phonon mode of the strained Si layer was observed in oil-immersion Raman spectroscopy. The peak positions of the strained Si layer were clearly separated in the TO and LO active configurations, although the Si substrate peaks remain at the same position in each configuration. This behavior indicates that the biaxial isotropic tensile stress state in the strained Si layer gives rise to the splitting of the optical phonon modes in Si. From the results, the LO phonon mode was more affected by biaxial stress than the TO phonon mode, which was consistent with the result obtained by solving the secular equations. Using the TO phonon mode as well as the LO phonon mode, the anisotropic biaxial stress states in the SSOI nanostructures were measured. As a result, the clear dependences of the biaxial stresses *xx* and *yy* on *L* and thickness were observed. *xx* decreased with the decrease in *L*, especially under *L* = 1.5 m, while *yy* remains almost constant. The values of *yy* for the SSOI nanostructures with the thickness of 30 nm are larger than those of 50 nm, which indicates that the thin SSOI nanostructures had immunity to the stress relaxation. The results obtained by oil-immersion Raman spectroscopy were consistent with the FEM calculations. We also measured the anisotropic biaxial stress states in the strained SiGe nanostructures by the same technique. Consequently, the clear dependence of the Raman shifts on *L* and *W* were observed similarly to the results for the SSOI nanostructures. Furthermore, the stress with the nondiagonal component, the shear stress component, in Si was measured by water-immersion Raman spectroscopy. As a result, the asymmetric profile was obtained for the dependence of the Raman shifts on the sample rotation angle. This behavior indicates that the shear stress component *xz* is induced in Si at the edge of the SiN film. There is a good correlation between the measured and calculated data. High-NA liquid-immersion Raman spectroscopy enabled us to measure the complicated stress states in strained Si and SiGe with high spatial resolution even those with the nondiagonal stress component.

## **Author details**

Daisuke Kosemura, Motohiro Tomita and Atsushi Ogura *School of Science and Technology, Meiji University, Kawasaki, Japan* 

Koji Usuda

274 Advanced Aspects of Spectroscopy

those with nondiagonal stress components.

*yy* on *L* and thickness were observed.

This behavior indicates that the shear stress component

measurements,

**4. Conclusion** 

*xx* and

especially under *L* = 1.5 m, while

nondiagonal stress component.

The Raman shifts appear to be small. This is explained as follows. The stress induced at the edge of the SiN film is localized in width and depth. It is considered that the measured stress is averaged in the region of approximately 390 and 450 nm which are the spot size and optical penetration depth of the laser, respectively. From the water-immersion Raman

obtained by the edge force model after the correction for the spot size and the optical penetration depth of the laser (the results are not shown) [46,58]. The methodology described here has the potential to measure complicated stress states in Si and SiGe even

We demonstrated the measurements of the complicated stress states in Si by high-NA liquid-immersion Raman spectroscopy. The *z* polarization was obtained due to the high-NA liquid-immersion lens, which allows for exciting the forbidden modes, the TO phonon modes, even under the (001) Si backscattering geometry. First, the TO phonon mode of the strained Si layer was observed in oil-immersion Raman spectroscopy. The peak positions of the strained Si layer were clearly separated in the TO and LO active configurations, although the Si substrate peaks remain at the same position in each configuration. This behavior indicates that the biaxial isotropic tensile stress state in the strained Si layer gives rise to the splitting of the optical phonon modes in Si. From the results, the LO phonon mode was more affected by biaxial stress than the TO phonon mode, which was consistent with the result obtained by solving the secular equations. Using the TO phonon mode as well as the LO phonon mode, the anisotropic biaxial stress states in the SSOI nanostructures were measured. As a result, the clear dependences of the biaxial stresses

SSOI nanostructures with the thickness of 30 nm are larger than those of 50 nm, which indicates that the thin SSOI nanostructures had immunity to the stress relaxation. The results obtained by oil-immersion Raman spectroscopy were consistent with the FEM calculations. We also measured the anisotropic biaxial stress states in the strained SiGe nanostructures by the same technique. Consequently, the clear dependence of the Raman shifts on *L* and *W* were observed similarly to the results for the SSOI nanostructures. Furthermore, the stress with the nondiagonal component, the shear stress component, in Si was measured by water-immersion Raman spectroscopy. As a result, the asymmetric profile was obtained for the dependence of the Raman shifts on the sample rotation angle.

the SiN film. There is a good correlation between the measured and calculated data. High-NA liquid-immersion Raman spectroscopy enabled us to measure the complicated stress states in strained Si and SiGe with high spatial resolution even those with the

*yy* remains almost constant. The values of

*xx* decreased with the decrease in *L*,

*xz* is induced in Si at the edge of

*yy* for the

*xz* was approximately 0.1 GPa. This value was consistent with the result

*Green Nanoelectronics Collaborative Research Center, AIST, Tsukuba, Ibaraki, Japan* 

#### **5. Acknowledgement**

The authors thank Ryosuke Shimidzu of PHOTON Design Corporation for the fruitful discussion about the *z* polarization. The authors thank Dr. Kazuhiko Omote of Rigaku Corporation for his great help in high-resolution XRD measurements. This study was partially supported by the Semiconductor Technology Academic Research Center (STARC), the Japan Society for the Promotion of Science (JSPS) through the "Funding Program for World-Leading Innovative R&D on Science and Technology", "Scientific Research B"and the Japan Science and Technology Agency through the "Adaptable and Seamless Technology transfer Program (A-STEP) through target-driven R&D."

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