Determination of Phonon Deformation Potentials in Carbon-doped Silicon
Authors: Yoshioka Kazutoshi , Yokogawa Ryo , Murakami Tatsumi , Komago Shota , Sawamoto Naomi , Ogura Atsushi 
Published: February 2020

Background and purpose

Carbon-doped silicon (Si:C) is used as a stressor to the channel of n-type MOSFET [1]. However, there are few report directly evaluated the strain states of Si:C. The strain-Raman coefficient that relate Raman shift to in-plane strain has not been derived yet. In this study, we determined the strain-Raman coefficient for Si:C using water-immersion Raman spectroscopy in conjunction with X-ray diffraction (XRD) measurement.

Experimental method

Si:C films were grown on (001) Si substrate by molecular beam epitaxy. The film thickness were 43, 50 and 37 nm, with C concentration of 0.600%, 0.826% and 1.14% respectively. The film thickness and the C concentration were confirmed by cross section TEM and SIMS measurement, respectively. Raman peak shift was measured by water immersion Raman spectroscopy. For the Raman evaluation, the numerical aperture of the water immersion lens and the refractive index of the medium were 1.2 and 1.3, respectively. The wavelength of the excitation light source and the focal length of the spectrometer were 355 nm and 2000 mm. Here, the penetration depth is approximately 5 nm. All the Raman spectroscopy were performed under the LO-active conditions. The in-plane and out-of-plane strain were measured by XRD. Part of the XRD measurement was performed at SPring-8 using synchrotron radiation as X-ray source.

Results and Discussion

Figure 1 shows the Raman peak shift obtained from Si:C with various C concentration. The spectra were calibrated with the strain-free single crystalline-Si (c-Si) at 520 cm-1. From Fig. 1, the Raman shift is decreased as the C concentration increases. This reflect the tensile strain is applied to Si:C. Table 1 shows the results of the XRD, and the in-plane and out-of-plane strain in Si:C. Here, ε
|| and ε
⊥ are the in-plane and out-of-plane strain, respectively. The in-plane and out-of-plane lattice spacing of c-Si is 1.357525 Å. From Table 1, it is clear that the tensile strain is applied to Si:C. This is consistent with the Raman spectroscopy result. There should be a relationship such as the following equation between Raman shift and in-plane strain.

ω
Si:C = ω
Si + ax +
bε
|| (1)
Here, ω
Si:C and ω
Si are the Raman shift of Si:C and Si, x is C concentration, and a and b are the alloy-disorder coefficient and strain-shift coefficient, respectively. In this study, we used the value of a coefficient to be 210 cm-1 to determine b coefficient [2]. From Eq. (1), the in-plane strain ε
|| can be obtained by the following equation using LO phonon Raman wavenumber shift from the strain-free Raman shift ω
0

Δω
LO = ω
Si:C – ω
0 = bε
||, (2)

ω
0 = ω
Si + ax = 520 + 210x. (3)
Figure 3 shows Raman wavenumber shift Δω
LO as a function of the in-plane strain ε
|| obtained from the XRD.　The dotted line is the linear fit to the experimental data. As shown in Fig. 3, although the C concentration x range is very narrow, we confirmed that the Δω
LO shows a linear dependence on the in-plane strain ε
||. Finally, we have succeeded to determine the value of strain-Raman (b) coefficient: b = -539.5 cm-1.

Acknowledgements

The XRD measurement of 0.600 and 1.06% Si:C was performed at SPring-8 (JASRI) with proposal number of 2015A1971, 2015B1925.

References

[1] Tsung-Yang Liow, et al., IEEE Trans. Electron Devices 55, 2476 (2008).
[2] H. Rücker and M. Methfessel, Phys. Rev. B 52, 11059 (1995).

Figure 1