Effects of lattice deformations on Raman spectra in β-FeSi 2 epitaxial films

Effects of lattice deformations on Raman spectra were investigated in β-FeSi2 epitaxial films grown on Si substrates. The lattice of the epitaxial film was deformed depending on thermal-annealing temperature (Ta). In Raman spectra, Raman lines of Ag-mode (iron displacements) showed a frequency shift with increasing Ta. The shift of Raman lines showed that the residual strain in the epitaxial films was changed by the lattice deformation. In the temperature dependence of Raman spectra, the temperature shifts of the Raman lines were found to be different between β-FeSi2(100)//Si(001) and β-FeSi2(110)(101)//Si(111) epitaxial films.


Introduction
β-FeSi2 thin films on Si substrates have attracted much interest as silicon-based optoelectronics materials as it shows photoluminescence (PL) and photoresponse at 1.54 μm [1].Band structure of β-FeSi2 single crystals is indirect transition [2], but that of β-FeSi2 epitaxial films is modified by the strain induced at the heteroepitaxial interface of β-FeSi2/Si, because β-FeSi2 is formed after a moderate distortion of the CaF2 structure by the Jahn-Teller effect [3].The strain effects on the band gap structure have been investigated by first principle calculations [4][5][6].Recently, we have investigated lattice deformations and direct transition energies (Eg) in β-FeSi2 epitaxial films on Si substrates, and revealed that the Eg shifted to lower energy with an enhanced lattice deformation by a thermal annealing [7][8][9].The experimental results indicate that the band structure is modified by the strain due to the lattice deformation.
In this study, Raman spectra of the β-FeSi2 epitaxial and polycrystalline films were measured to investigate the detailed strain effects by the lattice deformation.Raman spectroscopy is an efficient method for the characterization of the strain in semiconductors.Assuming that the lattice deformation of the β-FeSi2 epitaxial films originates from the lattice mismatch at the β-FeSi2/Si interface, the residual strain in β-FeSi2 should be different between β-FeSi2(100)//Si(001) and β-FeSi2(110)(101)//Si(111) epitaxial films.Therefore, it is expected that a clear difference is observed in the Raman spectra of the epitaxial films.

Experimental
β-FeSi2 epitaxial films were grown on n-type FZ Si(001) or Si(111) substrate by molecular beam epitaxy (MBE) using template technique.β-FeSi2(100)//Si(001) and β-FeSi2(110)(101)//Si(111) epitaxial films with thickness of 80200 nm were grown at the growth temperature of 550 °C and 670 °C, respectively.After the growth, the films were cut into pieces and annealed at thermal-annealing temperature (Ta) of 600, 700, 800 and 900 °C for 16 h in a vacuum of ~10 -3 Pa.The crystal structure was analyzed by high-resolution X-ray diffraction (HRXRD : X'pert Pro, PANalytical) at room temperature (RT).The lattice constant of a-axis was obtained by the β-FeSi2(800) peak position, the average lattice constant of b-and c-axis was evaluated by the β-FeSi2 (406)(460) peak position.The β-FeSi2 polycrystalline film was grown on Si substrates by RF magnetron sputtering method.The amorphous layer of Si and Fe with the composition ratio of Si/Fe = 2 was deposited at RT.The amorphous film was cut into pieces and annealed at 850 °C in a vacuum for 16 h to form β-FeSi2.The formation of β-FeSi2 polycrystalline thin films was confirmed by XRD.Hall measurements at RT showed that the β-FeSi2 epitaxial and polycrystalline thin films were n-type with carrier densities of 1610 16 cm -3 .
Raman measurements were carried out at a quasi-back-scattering geometry.Raman lines were excited by a 532 nm cw-laser and detected with a 55 cm focal-length spectrometer (TRIAX 550: Jobin Yvon) and a liquid nitrogen cooled CCD (Charged-Coupled Devices) front illuminated detector (Spectrum ONE: Jobin Yvon).The diameter of laser spot was about 200 μm, and the absolute Raman shift was collected by the TO-phonon line of Si substrates (520.2 cm -1 ).In the temperature dependence of Raman lines, a liquid nitrogen cooled cryostat was used to change the sample temperatures ranging from 80 to 450 K.   (b,c)-axis was expanded by Δ(b,c)/(b,c)bulk = +0.05%.The results showed that the lattice deformation of β-FeSi2 epitaxial films depends on the epitaxial relationship between β-FeSi2 and Si substrate.As Ta increased in the β-FeSi2 on Si(111), a-axis was more expanded from Δa/abulk = +0.85 to 0.88, and (b, c) was more compressed from Δ(b,c)/(b,c)bulk = 0.47 to 0.58.In the β-FeSi2 on Si(001) films, a-axis was compressed from Δa/abulk = 0.15 to 0.28, and (b, c) was expanded from Δ(b,c)/(b,c)bulk = +0.05 to +0.19.In this way, the lattice of the epitaxial films deforms by the annealing as the lattice constants deviate from that of the single crystal [7,8].

Results and Discussion
Figure 2 shows Raman spectra of the as-grown epitaxial films and the polycrystalline films at RT.The intensities of Raman spectra were shifted for clarification.The group factor analysis of orthorhombic lattice predicted 36 Raman active lines including 24 external modes and 12 internal modes [10,11].In the range between 180 and 280 cm -1 , the Raman lines produced by iron displacements exist.The vibrational features of both iron and silicon atoms displacements are dominant in 280380 cm -1 and that of only silicon displacements exist above ~400 cm -1 [12].In Fig. 2, Raman active lines about 20 were observed.The assignment of all the Raman lines is not established, the intense Raman lines at around 194 and 248 cm -1 have been assigned as Ag-mode of iron displacements [11,13].In this study, the frequency shift of the Ag-mode line at ~248 cm -1 was investigated in detail to clarify the effects of strain induced by the lattice deformations.Figure 3 and 4 show the annealing-temperature dependence of Ag-mode line in the β-FeSi2(100)//Si(001) and β-FeSi2(110)(101)//Si(111) epitaxial films, respectively.In the both epitaxial films, the frequency of Ag-mode was found to shift to lower wavenumber as Ta increased.In the β-FeSi2 polycrystalline film, such a frequency shift with Ta was not observed.To clarify the relationship between the lattice deformation and the Raman line, the frequency shifts of Ag-mode are plotted as a function of Δa/abulk in Fig. 5(a).The shifts of the direct transition energies in the epitaxial films [8] are also plotted in Fig. 5(b).As seen in the figures, the frequency of Ag-mode shifts to lower wavenumber as the absolute values of the lattice constants deviate from the lattice constants of the single crystal.The frequency shift of Ag-mode by the lattice deformation is consistent with that of direct transition energy.These results revealed that there is a clear correlation between the frequency of Ag-mode and Eg.
Figure 6 shows the temperature dependence of Ag-mode in the as-grown epitaxial films and polycrystalline one.A remarkable finding is that the temperature shift of Ag-mode is different  between them.The solid lines in Fig. 6 are fitting results using an empirical formula of () =  0 − [exp ( • ℏ 0 /  ) − 1] −1 for the Raman shifts [14].The fitting parameters A, B, and  0 are summarized in Table I.
As described before, the Raman lines at ~194 and ~248 cm -1 are dominated by the motion of Fe atoms.It has been reported that the line at ~194 cm -1 is associated with angular motions (either twist or flap), while the line at ~248 cm -1 is associated with the radial motions of Fe atoms [15].The radial motions at ~248 cm -1 are strongly affected when the bond length between Fe and Si is changed by the local strain.The change of lattice constants obtained by HRXRD (Fig. 1) such as Δa/abulk represents the average value of the lattice deformation, but it does not correspond to the changes in the local strain.In this situation, the clear correlation between the Raman line at ~248 cm -1 (Ag-mode) and the lattice deformation of Δa/abulk was successfully obtained in Fig. 5(a).The result revealed that the local strain around Fe atoms was changed by the lattice deformation.Therefore, the results of Fig. 5 support the model that the electric structure of β-FeSi2 is modified by the strain induced by the lattice deformation.
In the temperature dependence of Raman lines, the frequency shift was different in the three films.The frequency shift of Raman line by temperature is the convolution effects of lattice thermal expansion and phonon anharmonicity.In β-FeSi2, it has been reported that the effects of phonon anharmonicity is much small, then the thermal expansion is considered to be main effect in the temperature shift of Raman line [15].Therefore, the different frequency shift in the three films indicates that the thermal expansion coefficients are different due to the influence of strain induced

Conclusion
The clear correlation between the Raman line at ~248 cm -1 (Ag-mode) and the lattice deformation of Δa/abulk was observed in the β-FeSi2(100)//Si(001) and β-FeSi2(110)(101)//Si(111) epitaxial films.The result revealed that the local strain around Fe atoms was changed by the lattice deformation.The fact supports the model that the electric structure of β-FeSi2 is modified by the strain induced by the lattice deformation.