Local and anisotropic strain in AlN film on sapphire observed by Raman scattering spectroscopy

Samples described in this paper are schematically illustrated in Figs. 1(a)–1(c). Three kinds of samples were prepared by sputtering of AlN films on c- and a-plane sapphire substrates. AlN films were deposited by RF sputtering with a sintered AlN target. During the deposition of sputtering, the substrate temperature, RF power, and Ar/N₂ gas flow ratio were kept constant at 600 °C, 700 W, and 1/4, respectively. Subsequently, the FFA was conducted at 1700 °C for 3 h in N₂ atmosphere.¹⁶⁾ Finally, homoepitaxial growth of AlN on the FFA-sp-AlN film was performed by metalorganic vapor phase epitaxy (MOVPE). Trimethylaluminum and ammonia were used as the Al and N precursors, respectively. The MOVPE growth temperature and reactor pressure were maintained at 1300 °C and 30 Torr, respectively. In addition to c-plane AlN on c-plane sapphire, c-plane FFA-sp-AlN film was fabricated on a-plane sapphire substrate with same sputtering and FFA condition as c-plane sapphire, but without MOVPE growth. To investigate structure effects for local and anisotropic strain distributions, patterned AlN films on c-plane sapphire substrates were fabricated by photolithography and reactive ion etching.

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Strain states were evaluated by means of Raman scattering spectroscopy and XRD-RSMs. Polarized micro Raman spectra of c-plane FFA-sp-AlN films were measured with the backscattering geometry of Z(XX)$\bar{{Z}}$ and Z(YY)$\bar{{Z}},$ which were parallel to AlN[11–20] and [1–100], respectively. All the Raman measurements were performed using a confocal Raman microscope at room temperature (RT). The 532 nm line of the DPSS laser was used for excitation and was focused below 1 μm by an objective lens with a magnification of 100 times and a high numerical aperture of 0.9. Laser power was set to around 40 mW. This value is even lower than that in the previous study (∼150 mW), in which dislocations in GaN are detected by Raman frequency shifts.²¹⁾ In addition, we should note that there were no Raman frequency shifts by illumination. Thus, this laser power was low enough to avoid heating of the sample, which causes Raman frequency shifts.^8,14) Raman spectra was dispersed with a 50 cm focal length spectrometer equipped with a grating of 2400 grooves mm⁻¹ and detected with a charge coupled device.

In the equibiaxially strained case of an AlN c-plane growth, a Raman shift Δω is derived as

$$\begin{eqnarray}&&{\rm{\Delta }}\omega =\left(-\displaystyle \frac{{{C}}_{33}}{{{C}}_{13}}\alpha +\beta \right){{\epsilon }}_{ZZ},\end{eqnarray} \tag{ 1 }$$

where α and β are PDPs, C₁₃ and C₃₃ are elastic stiffness constants for AlN, and ε_ZZ is strains along c-direction, respectively. ε_ZZ can be discribed as

$$\begin{eqnarray}&&{{\epsilon }}_{{Z}{Z}}=\displaystyle \frac{{c}_{{\rm{film}}}-{c}_{{\rm{bulk}}}}{{c}_{{\rm{bulk}}}},\end{eqnarray} \tag{ 2 }$$

where c_film and c_bulk are film- and bulk-lattice constants along c-direction. By substituting Eq. (1) to (2), c_film can be derived. The parameter set^{3,15,22–25)} used in this study are listed in Table I. PDPs used in this study for ${{{E}}_{2}}^{{\rm{low}}}$ and ${{{E}}_{2}}^{{\rm{high}}}$ was experimentally determined from AlN bulk crystals. In addition, the elastic stiffness constants used in this study²⁴⁾ is well agree with results from free exciton transition energies with uniaxial pressure in AlN bulk crystal.²⁶⁾ To get accurate Δω value from our measurement setup, all Raman spectra of AlN on sapphire substrate were calibrated by Raman peak shift of sapphire E_g of 576.7 cm⁻¹,²⁷⁾ and the bulk AlN crystal grown by the physical vapor transport method was used as a reference, i.e., strain free AlN phonon frequencies for ${{{E}}_{2}}^{{\rm{low}}},$ ${{{E}}_{2}}^{{\rm{high}}}$ and A₁(LO) peaks in our setup.

Table I.  PDPs, elastic stiffness constant and c lattice constant used in this study.

	${{{E}}_{2}}^{{\rm{low}}}$	${{{E}}_{2}}^{{\rm{high}}}$	A1(LO)
α (cm−1)	1083,15,22)	−11453,15,22)	−73923)
β (cm−1)	−2373,15,22)	−10233,15,22)	−73723)
C13 (GPa)		9524)
C33 (GPa)		40224)
cbulk (Å)		4.980825)

In addition to Raman scattering measurements, XRD-RSM measurements were performed to get the macroscopic strain using Cu Kα radiation (λ = 1.5406 Å). In the case of the c-plane FFA-sp-AlN film on c-plane sapphire, measurements of XRD-RSMs were employed with the X-ray incident direction of AlN m-direction. Diffraction peaks with Miller indices of AlN (10–15) and sapphire (11–2 12) were adapted. The peak position of AlN (10–15) is effected not only by lattice constants but also by the misorientation of the film. In the case of samples described in this study, the misorientation angle of the film and the off-cut angle of the substrate were identical. Thereby, followed by 2θ offset correction based on sapphire (11–2 12), to compensate the effect from the misorientation of the film, the position of AlN (10–15) was normalized by the coordinate transformation based on the position of sapphire (11–2 12), which indicates the substrate off-cut angle. As for sapphire (α-Al₂O₃) lattice constants, standard parameters, i.e., a = 4.758 Å and c = 12.991 Å, were used. These values are commonly used in literatures.^28–30) In the case of the c-plane FFA-sp-AlN film on a-plane sapphire, in addition to XRD-RSM measurements of AlN (10–15) and sapphire (41–5 0), XRD-RSM measurements of AlN (11–24) and sapphire (22–4 3) with the X-ray incident direction of AlN a-direction were performed to unambiguously obtain three lattice constants from a film with an anisotropic strain. These methods have already been utilized to get anisotropic strains in the case of semipolar growths of nitride semiconductors such as InGaN³¹⁾ and AlInN.³²⁾

Figures 2(a)–2(c) show Raman spectra of Z(Y-)$\bar{{Z}}$ for ${{{E}}_{2}}^{{\rm{low}}},$ ${{{E}}_{2}}^{{\rm{high}}},$ and A₁(LO) from the c-plane FFA-sp-AlN film on c-plane sapphire. Red lines are obtained from the c-plane FFA-sp-AlN film on c-plane sapphire, and black lines are bulk AlN results observed from the exactly same Raman measurement setup. Intensities were normalized by ${{{E}}_{2}}^{{\rm{high}}}$ peak intensities for each sample. The XRD-RSM around AlN (10–1 5) and sapphire (11–2 12) of the c-plane FFA-sp-AlN film on c-plane sapphire is shown in Figs. 3(a) and 3(b), respectively. Based on sapphire (11–2 12) position: −0.4204 rlu for q_a and 0.9234 rlu for q_c, AlN (10–1 5) position q_m and q_c were transformed from −0.3727 and 1.002 rlu to −0.3726 and 1.002 rlu, respectively. Observed values are summarized in the Table II with those obtained from XRD-RSMs. ε_ZZ and c_film were calculated from Eqs. (1) and (2) by substituting obtained Raman shift Δω.

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Table II.  Obtained results from the c-plane FFA-sp-AlN film on c-plane sapphire.

	${{{E}}_{2}}^{{\rm{low}}}$	${{{E}}_{2}}^{{\rm{high}}}$	A1 (LO)	XRD-RSM
Raman shift (cm−1)	246.6	663.1	892.2	—
Δω (cm−1)	−0.8	+6.6	+4.0	—
εZZ (%)	0.12	0.17	0.17	0.19
cfilm (Å)	4.987	4.989	4.989	4.990

From Table II, the lattice constant c obtained from ${{{E}}_{2}}^{{\rm{high}}}$ peak well agrees with that from the XRD-RSMs. This indicates that the parameter set that shown in Table II is quite accurate especially for ${{{E}}_{2}}^{{\rm{high}}}$ PDPs. In the same time, these results imply that the c-plane FFA-sp-AlN film on c-plane sapphire shown here has high crystalline quality, which phonon characteristics are comparable with those of bulk AlN crystals and the AlN film on a SiC substrate.^3,15,22) It is worthy to note that the FWHM values of XRD rocking curves (XRC-FWHM values) of the sample are 15 and 240 arcsec for AlN (0002) and (10–12) diffractions, respectively. The values of ε_ZZ calculate from ${{{E}}_{2}}^{{\rm{high}}}$ and A₁(LO) are quite agreed with each other even without consideration of a coupling with plasmon mode for A₁(LO). Secondary ion mass spectroscopy measurements revealed that oxygen and silicon concentration for the MOVPE-grown AlN film on the c-plane FFA-sp-AlN template were 6 × 10¹⁶ and 5 × 10¹⁵ cm^-3, respectively. These impurity concentrations are too low to couple with plasmon mode, and that is why there is no effect of coupling with plasmon mode for A_l(LO) peak shift. This is same as the reported result of the AlN film on a SiC substrate.³⁾ These results given above show a validity of parameter sets in this study, i.e., PDPs, elastic stiffness constants, and c lattice constant of bulk AlN shown in Table I. Hereafter, we will focus on analysis of an ${{{E}}_{2}}^{{\rm{high}}}$ Raman peak shift, which has larger PDPs.

Raman and XRD-RSM measurements were performed for the c-plane FFA-sp-AlN film on an a-plane sapphire substrate. From XRD phi-scan measurement results, the epitaxial relationship of this sample was ascertained as schematically illustrated in Fig. 4(a). This epitaxial relationship is different from the sample grown by MOVPE³³⁾ and HVPE at higher temperature (1450 °C–1550 °C),^34,35) and same as the samples grown by HVPE at lower temperature (700 °C).³⁴⁾ Comparing with above mentioned literature, it can be speculated that the epitaxial relationship of this sample ascribes the sputtering temperature (600 °C). For the 180 nm thick c-plane FFA-sp-AlN film on a-plane sapphire, XRC-FWHM values of AlN (0002) and (10–12) are 18 and 425 arcsec, respectively. The crystalline quality of the sample on a-plane sapphire is slightly inferior to that on c-plane sapphire. Nevertheless, these values indicate better crystalline (smaller XRC-FWHM values) than previous reports,³³⁾ which was grown by MOVPE. Additionally, above shown XRC-FWHM values of this sample are even smaller than that of c-plane GaN films on a-plane sapphires.^36–38) Therefore, the crystalline quality of the c-plane FFA-sp-AlN film on a-plane sapphire regards as high enough to discuss the strain relaxation. Note that the optimization of fabrication conditions of c-plane FFA-sp-AlN films on a-plane sapphires is beyond the scope of this paper and will be discussed elsewhere. The XRD-RSM around AlN (10–1 5) and (41–5 0), and AlN (11–2 4) and sapphire (22–4 3) of the c-plane FFA-sp-AlN film on a-plane sapphire is shown in Figs. 5(a)–5(d), respectively. After coordinate transformation based on sapphire positions, AlN lattice constants toward a-, and m- were calculated to be 3.095 and 3099 Å. Note that the lattice constants along c-axis derived from two different Miller indices AlN (10–1 5) and (11–2 4) were almost identical: 4.991 and 4.992 Å. This coincidence indicates validity of the coordinate transformation in XRD-RSMs. Then, ε_xx, ε_YY, and ε_zz, (strain toward a-, m-, and c-direction of AlN) were obtained to be −0.52%, −0.41%, and 0.22%, respectively. These values clearly indicate the in-plane anisotropic compressive strain. The origin of this anisotropy might be in-plane anisotropy of the underlying substrate. In the literature the thermal expansion coefficients of sapphire c- and a-direction are reported as 8.11 × 10^–6 and 7.28 × 10⁻⁶ K⁻¹, and both values are larger than that of AlN (5.27 × 10⁻⁶ K⁻¹ for a-direction).³⁹⁾ Therefore, the anisotropic strain in the c-plane AlN film on a-plane sapphire might be caused by the anisotropy of the thermal expansion coefficient of sapphire during cooling down from annealing temperature of 1700 °C to RT.

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Polarized Raman spectra of the sample with configurations of Z(XX)$\bar{{Z}}$ and Z(YY)$\bar{{Z}}$ are shown in Figs. 4(b), 4(c). As it has been reported,⁴⁰⁾ sapphire A_1g peak appeared when the polarization is parallel to sapphire c-direction (Z(XX)$\bar{{Z}}$). Polarized Raman spectra of c-plane AlN on a-plane sapphire around AlN ${{{E}}_{2}}^{{\rm{high}}}$ peaks are shown in Fig. 4(c) with those on c-plane sapphire for the comparative study. In the case of c-plane AlN on a-plane sapphire, ${{{E}}_{2}}^{{\rm{high}}}$ frequency is slightly different between two polarization directions, while there is no difference in c-plane AlN on c-plane sapphire. This difference is very small, but it should be noted that the results are reproducible. In addition, same phenomenon has been observed in c-plane GaN on a-plane sapphire and that frequency difference was also below 1 cm⁻¹.⁷⁾ Although quantitative understanding has not been completed, we could know that the anisotropy of strain could be observed by not only from XRD-RSMs but also from polarized Raman spectra.

Figures 6(a) and 6(b) show the optical microscope image and correspondent one dimensional Raman spectra contour map of Z(Y-)$\bar{{Z}},$ of which x-and y-axis are Raman shift and sample position, respectively. AlN ${{{E}}_{2}}^{{\rm{high}}}$ peaks only exist at AlN locations. Meanwhile, sapphire E_g peaks are observed from all points. To show local and anisotropic Raman peak shift clearly, Raman spectra from the patterned AlN center and edge points, and polarized Raman spectra observed at the edge point are shown in Figs. 6(c) and 6(d), respectively. As shown in Fig. 6(c), shorter frequency peak was observed remarkably at the edge point. This indicates the local strain relaxation. Moreover, polarized spectra observed at the edge shows the frequency difference, as shown in Fig. 6(d). Lower-frequency peak was observed when the polarization is perpendicular to stripe. Therefore, Raman peak at the edge point of the patterned AlN film shows local and anisotropic strain relaxation.

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To know the AlN ${{{E}}_{2}}^{{\rm{high}}}$ peak shift distribution, two dimensional (2D) Raman ${{{E}}_{2}}^{{\rm{high}}}$ shift maps were made by 2D Raman spectra measurements of patterned AlN films with width of 7, 5, and 2 μm and Lorentzian fitting of all points, as shown in Figs. 7(a), 7(c), and 7(e), respectively. Optical microscope images of the measurement positions of Figs. 7(a), 7(c), and 7(e) are shown in Figs. 7(b), 7(d), and 7(f), respectively. From Figs. 7(a) and 7(c) (patterned AlN films with width of 7 and 5 μm), lower-frequency peak is clearly seen at the edge point of the patterned AlN films. This indicates local strain relaxation at the edge point. It should be mentioned that peak frequencies at the center of 5 and 2 μm width samples are different from that of the 7 μm width sample. From these results, occurrence of strain relaxation not only at the edge but also at center could be observed. These kind of strain distributions have been observed from cantilevers of GaN⁴¹⁾ and AlN.⁴²⁾

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