Raman scattering characterization of well-aligned RuO2 nanocrystals grown on sapphire substrates

Raman scattering (RS) spectroscopy is a popular measurement technique that uses inelastic scattering of monochromatic light to study vibrational characteristics of a material system. A typical application of RS is for material structure determination. This paper describes the application of RS for the characterization of the preferable growth direction of well-aligned nanocrystals (NCs) deposited on sapphire substrates. The results indicate that RS could become a powerful technique for the quick determination of the NCs orientation. The redshifts and asymmetric linewidth broadening of the Raman features of RuO2 NCs are analysed by a modified spatial correlation (MSC) model, which includes the factor of stress-induced shift. The usefulness of experimental RS together with the MSC model analysis as a nondestructive structural and residual stress characterization technique for NCs has been demonstrated.


Introduction
A wide range of nanosized oxide materials are currently the focus of intensive research owing to their potential use in nanodevice fabrication [1,2]. Among the numerous oxides, the electrically conducting RuO 2 belongs to the family of transition-metal dioxide compounds with a rutile structure [3]. The attractive properties of RuO 2 have been extensively studied for several applications, such as thick film resistors [4,5], electrode material for electrochemical devices [6,7], an electrode in ferroelectric random-access memory [8], and an electrochemical capacitor for energy storage [9,10]. Owing to their high chemical stability and high aspect ratio, RuO 2 nanocrystals (NCs) have been demonstrated to be a candidate material for vacuum microelectronic devices [11,12].
Moreover, the vibrational properties of nanosized systems are interesting from a fundamental point of view because of the changes related to the spatially confined grain size effects. The structure of their grain boundaries has been rather controversial, and their properties give a non-consistent picture that appears to depend upon which experimental technique is being used [13]. Therefore, it is very important to understand and clarify the nature of the physical properties of nanocrystalline materials.
In this article, we report the Raman scattering (RS) characterization of RuO 2 NCs deposited on sapphire (SA) substrates with different orientations via reactive radio frequency magnetron sputtering (RFMS). Combined with x-ray diffraction (XRD), field-emission scanning electron microscopy (FESEM) and modified spatial correlation (MSC) model calculations, RS is used to extract orientations and residual stress information of well-aligned RuO 2 NCs deposited on SA substrates. The usefulness of RS as a nondestructive structural and residual stress characterization technique for NCs will be demonstrated.

Experimental
The RuO 2 NCs were deposited on SA substrates with different orientations (SA(012), SA(110) SA(001), and SA(100)) via RFMS. The sputtering target was a 1-inch Ru (99.95%) metal. The reactive sputtering was carried out in a mixture of argon (11 sccm) and oxygen (1 sccm) gases. O 2 was introduced over the substrate into the sputtering chamber with Ar atmosphere. A working pressure of 7.5 mbar, radio frequency generator power of 65 W, substrate temperature of 200 • C and a 180 min deposition time were used in the experiment. The morphology of the RuO 2 NCs was studied with a JEOL-JSM6500F FESEM. XRD patterns taken on a Rigaku RTP300RC x-ray diffractometer equipped with a Cu K α radiation source and a Ni filter were used to examine the crystallographic characteristics of the NCs over a large area of the surface. RS spectroscopy was used to extract nanostructural information of the RuO 2 NCs. Raman spectra were recorded at room temperature utilizing the back-scattering mode on a Renishaw in Via micro-Raman system with 1800 grooves mm −1 grating and an optical microscope with a 50× objective. The same microscope was used to collect the signal in a backscattering geometry. The Ar-ion laser beam of the 514.5 nm excitation line with a power about 1.5 mW was focused on a spot size ∼5 µm in diameter. Prior to the measurement, the system was calibrated by means of the 520 cm −1 Raman peak of a polycrystalline Si.

Results and discussion
RuO 2 has the tetragonal rutile structure [14] belonging to the space group D 14 4h with two RuO 2 molecules per unit cell as shown in figure 1. The cations are located at sites with D 2h symmetry and the anions occupy sites with C 2v symmetry. The Ru-ions are surrounded by six oxygen ions at the corners of a slightly distorted octahedron, while the three Ru-ions coordinating each oxygen ions lie in a plane at the corners of a nearly equilateral triangle. According to the factor group analysis, there are fifteen optical phonon modes with the irreducible representation as given in [15]. Only three modes are Raman active in the range of measurements (400-800 cm −1 ) with symmetries E g , A 1g , and B 2g , where the first is a doublet and the last two are singlets [15]. Corresponding to each Raman-active mode, there is a scattering tensor α having a distinctive symmetry. The forms of these tensors in materials of D 14 4h space group are [16]: To examine experimentally a given component α ij , the geometry is arranged such that the incident light is polarized in the 'i' direction while only the scattered light of 'j' polarization is observed. A classification of the observed Raman-active modes for (101), (100) and (001) planes of RuO 2 may be accomplished as follows. We adopt the following notation for the various axes used in this experiment: x = (100), y = (010), z = (001) and x = 1 Since it is impossible to identify the direction in the experiment for NCs, we assume that the Raman signal is the average signal from all possible geometries. The expressions for the relative Raman intensities correlating to various |α ij | 2 for the (101), (100) and (001) planes in the backscattering configuration are listed in table 1. The results show that E g , A 1g and B 2g modes are allowed for the polarization configurations for scattering from the (101) plane. The B 2g and E g modes are forbidden for all configurations from (100) and (001) planes, respectively.
The spatial correlation (SC) model of Richter et al [17] extended by Fauchet and Campbell [18] was exploited for analysing the Raman-active modes of RuO 2 NCs. The main assumption is that the phonons in nanosized systems can be confined in space by crystallite boundaries or surface disorders. Consequently, this confinement causes an uncertainty in the wave vector of the phonons and results in a red shift and asymmetric broadening of the Raman features. The intensity of the first-order Raman spectrum, I(ω), is given by [18]: where ω(q) is the phonon dispersion curve, is the natural linewidth and C(0, q) is the Fourier coefficient of the phonon confinement function. The relaxation of the q = 0 selection rule due to phonon confinement in a NC has been taken into account. Using the Gaussian confinement function and considering the column shaped crystal, the Fourier coefficient |C(0, q)| 2 can be written as follows [18]: where L 1 and L 2 are, respectively, the diameter and length of the RuO 2 NCs. For the dispersion relation, ω(q), we took the analytical model relationship based on a one-dimensional linear-chain model [19]: where A = 1.396 × 10 5 cm −2 and B = 7.39 × 10 9 cm −4 (for RuO 2 single crystal) are related to the atomic masses of the constituent atoms and the force constant between the nearest neighbour planes. To avoid any speculation of the measured Raman modes positions we used freshly grown RuO 2 single crystal by the chemical transport method [20] to determine the main signals of the Raman-active modes. The positions and the full width at half maximum (FWHM) of the E g , A 1g and B 2g modes are listed in table 2. The RS spectrum of the single crystal reveals some discrepancies in identifying the E g , A 1g and B 2g positions with the known values from the literature [21,22].    Raman modes peak positions as compared with that of the single crystal. Our calculated results of the redshift for RuO 2 (101) on a SA(012) sample using the SC model indicated a 4 cm −1 redshift and an asymmetric broadening of 21 cm −1 for the E g mode relating to the phonon confinement effect in NCs. To have a good agreement between SC model calculations and experimental data, we have to add an additional redshift of 2 cm −1 to the SC model. We have assigned this shift to the residual stress effect induced by tensile strain which is consistent with the results previously reported by Rosenblum et al [22] about observation of blueshifts on the three strongest lines induced by hydrostatic pressure in a RuO 2 single crystal. This assignment leads to a modification of the theoretical modelling. The inclusion of the additional stress-induced redshift leads to a recalculation of the A and B constants for the analytical dispersion relation as given by equation (4). Our analysis gives A = 1.41 × 10 5 cm −2 and B = 7.53 × 10 9 cm −4  Figure 3(c) shows the Raman spectrum of the RuO 2 (101) NCs on SA(110) and the fitting results (open circles) in the range of 400-800 cm −1 , in which three Raman modes, identified as E g , A 1g and B 2g were observed. These results show good agreement with the assignments given in table 1. The analysis in the MSC model revealed 4 cm −1 in redshift and an asymmetric broadening of about 22 cm −1 for the E g mode as a result of the phonon confinement effect and an additional 2 cm −1 shift due to residual stress effects. The observation of E g , A 1g and B 2g modes in the RS with the intensity of the E g peak much larger than the signal level of the A 1g and B 2g modes may be evidence of orientation of NCs in the (101) plane. From the experimental data analysed by the MSC model, the doubly tilted NCs ( figure 3(a)) showed comparable intensities of A 1g and B 2g modes, whereas a single direction tilted NCs ( figure 2(a)) showed higher intensity of the B 2g peak in comparison with A 1g . Thus, the RS of NCs correlate well with the XRD patterns and could be a powerful technique for the quick determination of the NCs orientation.  (table 1). We observe the signal of the forbidden E g mode for this configuration with an intensity slightly less than that of the A 1g and B 2g modes. The occurrence of the normally forbidden E g mode might indicate observation of the scattering from other planes of the NCs as evidenced from the pyramidal tips of the NRs (see figure 5(a)) and/or from the strain induced Raman tensor which may break down the selection rules. The soft E g signal may be evidence of the rod-like vertical aligned RuO 2 NCs with (001) orientation.

DEUTSCHE PHYSIKALISCHE GESELLSCHAFT
As shown in table 2, the values of the red shift extracted by MSC analysis, which describe the trend of peaks' redshifts and asymmetric lineshape broadening when the sizes become nanometric, are similar for all samples and are about 4 cm −1 (edge size of NCs are about 45 nm). The redshift related to residual stress exhibits different values for different NCs samples. The samples grown with the minimal mismatch (grown on SA(012), SA(110) and SA(100)) exhibit a minimal additional red shift of about 2 cm −1 and for higher mismatch (SA(001)) the value is about 4 cm −1 .

Summary
The micro-RS spectra of RuO 2 (101), RuO 2 (100) and RuO 2 (001) NCs grown on SA(012) and SA(110), SA(001) and SA(100) substrates by RFMS have been analysed. The results reveal three major Raman-active modes, identified as E g , B 2g and A 1g , respectively, in the range of 400-800 cm −1 . The RS intensity of some modes is shown to be dependent on planes of NCs and follows the selection rules reasonably well. Thus, the RS of NCs correlate well with the XRD patterns and could be a powerful technique for the quick determination of the NCs orientation. We also show that the MSC model can account for the measured redshift of the Raman active modes due to nanometric size and residual stress effects. The first component in the MSC analysis corresponds to a nanometric size effect and leads to an asymmetric broadening of the redshifted Raman mode, while the second component relates to residual stress induced redshift which depends on the lattice mismatch between the RuO 2 NCs and the substrates. The usefulness of experimental RS together with the MSC model analysis as a nondestructive structural and residual stress characterization technique for NCs has been demonstrated.