In this paper, we have performed qualitative and quantitative analysis of LuMnO3 thin films surfaces, deposited by spin coating over Pt(111)/TiO2/SiO2/Si substrates, to evaluate their spatial patterns as a function of the film’s sintering temperature. Atomic force microscopy was employed to obtain topographic maps that were extensively analyzed via image processing techniques and mathematical tools. 3D (three-dimensional) topographical images revealed that films sintered at 650°C and 750°C presented the formation of smoother surfaces, while the film sintered at 850°C displayed a rougher surface with a root mean square roughness of ∼2.5 nm. On the other direction, the height distribution of the surface for all films has similar asymmetries and shape, although the film sintered using the highest temperature showed the lower density of rough peaks and a sharper peak shape. The advanced fractal parameters revealed that the film sintered at 850°C is dominated by low spatial frequencies, showing less spatial complexity, higher microtexture homogeneity, and uniform height distribution. These results suggest that the combination of stereometric and fractal parameters can be especially useful for identification of unique topographic spatial patterns in LuMnO3 thin films, helping in their implementation in technological applications, such as photovoltaic solar cells and information magnetic date storage and spintronic devices.
Multiferroic oxide systems of the RMnO3 type (
Some of the H-RMnO3 type rare earth (R) manganites with a perovskite structure are part of the multiferroic oxide system, and they have represented an important research area for solid-state and materials chemists and applied physicists for last decades, where “H” characterizes a hexagonal structure with space group P63cm [
H-LuMnO3-type multiferroic oxides have been extensively investigated because they exhibit both magnetoelectric [
Several experimental and theoretical studies about the structural and magnetic properties of LuMnO3 in the ferroelectric phase have been reported in the literature [
In recent years, morphological studies have been explored because AFM technique is strongly sensible and accurate. It is important to mention that multiferroic materials contribute to the development of new scientific methods [
Using a simple chemical method, we have synthesized LuMnO3 in films’ precursor solutions that were spin coated in Pt(111)/TiO2/SiO2/Si substrates. Our goal was evaluating the nanoscale patterns of the films using a combination of stereometric and advanced fractal parameters that, at the present moment, has not been reported yet. We have used several mathematical and analytical methods for obtaining the results. Specifically, we have explored the tools provided by MountainsMap commercial software to make an extensive image processing work. Moreover, we have used different algorithms for fractal parameters that are not provided by commercial software.
To produce a LuMnO3 precursor solution, lutetium (III) nitrate hydrate 99.99% pure (supplied by Aldrich), was previously dissolved, at 50°C, in glacial acetic acid (CH2CO2H) and nitric acid (HNO3), with a 2 : 1 molar ratio mixture, during 24 h. Afterwards, manganese (II) acetate tetrahydrate ((CH3COO)2 Mn•
The films morphology was analyzed by using an atomic force microscope (Veeco Multimode NanoScope IVa) working on the tapping mode, with a scan rate of 1.0 Hz, scanning areas of 2.5 × 2.5
Furthermore, we have determined advanced fractal parameters to study surface microtexture. Fractal dimension (FD) was computed using the counting box method described by Mandelbrot and Wheeler [
The average power spectrum density (PSD) of fractal regions of the spectra was calculated using linearized graphs obtained according to the mathematical theory explained by Jacobs et al. [
Fractal succolarity (FS) was calculated using the model described by Melo and Conci [
Surface entropy (
The obtained value was centralized and normalized according to equation (
To compute experiments precision, we have used variance analysis (ANOVA) and Tukey test with a
The nanoscale morphology of LuMnO3 thin films sintered at 650, 750, and 850°C is shown in Figure
3D AFM topographical maps and histogram of relative heights of LuMnO3 thin films of (a, b) LuMnO650, (c, d) LuMnO650, and (e, f) LuMnO650.
The morphology evaluated is similar to that found on other works previously published, where the effect of the sintering temperature was studied, and it was confirmed that only after 850°C there was the complete formation of pure polycrystalline phase of LuMnO3 [
Height surface parameters of LuMnO3 thin films, according to ISO 25178-2:2012.
Parameter | Unit | LuMnO650 | LuMnO750 | LuMnO850 |
---|---|---|---|---|
Sq | (nm) | 0.30 ± 0.03 | 0.61 ± 0.35 | 2.48 ± 0.53 |
Ssk | (—) | 0.33 ± 0.15 | 0.39 ± 0.43 | 0.22 ± 0.08 |
Sku | (—) | 3.60 ± 0.31 | 4.24 ± 1.37 | 3.17 ± 0.45 |
Sp | (nm) | 1.38 ± 0.21 | 2.78 ± 1.86 | 8.23 ± 0.82 |
Sv | (nm) | 1.18 ± 0.16 | 2.62 ± 0.95 | 9.09 ± 1.94 |
Sz | (nm) | 2.56 ± 0.18 | 5.40 ± 2.80 | 17.27 ± 2.32 |
Sa | (nm) | 0.24 ± 0.02 | 0.45 ± 0.22 | 1.81 ± 0.43 |
The relative frequencies of the topographic heights shown in Figures
The relationship between topographic patterns and the microtexture of the films was evaluated using stereometric parameters [
Stereometric parameters of the LuMnO3 thin films, in accordance with ISO 25178-2:2012.
Parameter | Unit | LuMnO650 | LuMnO750 | LuMnO850 |
---|---|---|---|---|
Smc | (nm) | 0.39 ± 0.04 | 0.70 ± 0.32 | 3.04 ± 0.80 |
Sxp | (nm) | 0.54 ± 0.05 | 1.10 ± 0.59 | 4.23 ± 0.57 |
Sk | (nm) | 0.72 ± 0.07 | 1.23 ± 0.40 | 6.00 ± 1.69 |
Spk | (nm) | 0.39 ± 0.05 | 0.98 ± 0.86 | 2.58 ± 0.20 |
Svk | (nm) | 0.27 ± 0.04 | 0.60 ± 0.40 | 2.00 ± 0.30 |
Smr1 | (%) | 12.43 ± 0.85 | 11.87 ± 2.13 | 12.88 ± 0.68 |
Smr2 | (%) | 90.57 ± 0.88 | 88.70 ± 3.53 | 90.55 ± 2.62 |
Vmp | ( | 1.9 | 5.1 | 1.2 |
Vmc | ( | 2.6 | 4.7 | 2.0 |
Vvc | ( | 3.8 | 6.8 | 2.9 |
Vvv | ( | 3.1 | 6.8 | 2.3 |
Spd | (1/ | 122.04 ± 12.04 | 53.56 ± 29.05 | 10.73 ± 2.78 |
Spc | (1/ | 2.82 ± 0.08 | 3.73 ± 0.76 | 7.56 ± 0.16 |
Sdq | (—) | 0.01 ± 0.00 | 0.02 ± 0.00 | 0.05 ± 0.01 |
Sdr | (%) | 0.01 ± 0.00 | 0.02 ± 0.00 | 0.14 ± 2.78 |
The feature parameters reveal that LuMnO850 shows a lower density of rough peaks and a more pointed peak shape, as it presents lower peak density (Spd) (∼10
As an important qualitative observation tool available in MountainsMap and widely used for the evaluation of surface microtextures of thin films or other systems [
Qualitative renderings of contour lines and furrows systems of the surface microtexture of (a, b) LuMnO650, (c, d) LuMnO750, and (e, f) LuMnO850.
Surface microtexture parameters of LuMnO3 thin films, according to ISO 25178-2:2012.
Parameter | Unit | LuMnO650 | LuMnO750 | LuMnO850 |
---|---|---|---|---|
Maximum depth | (nm) | 0.83 ± 0.07 | 1.34 ± 0.34 | 6.05 ± 0.11 |
Mean depth | (nm) | 0.35 ± 0.02 | 0.55 ± 0.15 | 2.15 ± 0.19 |
TI | (%) | 56.48 ± 9.39 | 56.50 ± 12.54 | 56.92 ± 5.68 |
Sal | ( | 0.19 ± 0.02 | 0.23 ± 0.04 | 0.21 ± 0.03 |
Str | (—) | 0.56 ± 0.09 | 0.56 ± 0.12 | 0.57 ± 0.06 |
First direction | (°) | 128.39 ± 23.41 | 135.00 ± 0.01 | 107.26 ± 18.79 |
Second direction | (°) | 134.99 ± 13.09 | 105.88 ± 27.50 | 83.89 ± 41.92 |
Third direction | (°) | 96.62 ± 41.71 | 76.77 ± 44.95 | 121.50 ± 22.70 |
The specific texture parameters shown in Table
Polar representation of texture directions of surface microtexture of (a) LuMnO650, (b) LuMnO750, and (c) LuMnO850.
To understand better the effect of the sintering temperature on the formation of topographic spatial patterns of the films, we computed advanced fractal parameters. Figure
Surface lacunarity and PSD of (a-b) LuMnO650, (c-d) LuMnO750, and (d-e) LuMnO850, respectively.
This pattern affected the signal quality of the dominant spatial frequencies because LuMnO850 exhibited a higher Hurst coefficient (
A major contribution of the effect of sintering temperature on the surface microtexture of the films is relative to their surface heterogeneity. The reorganization of the crystal for high sintering temperature promotes a most homogeneous microtexture, as LuMnO850 shows the lowest value of the lacunarity coefficient (
Fractal and parameters’ advanced fractal of LuMnO3 thin films.
Parameter | Unit | LuMnO650 | LuMnO750 | LuMnO850 |
---|---|---|---|---|
FD | (—) | 2.391 ± 0.011 | 2.331 ± 0.062 | 2.264 ± 0.020 |
(—) | 0.113 ± 0.016 | 0.273 ± 0.027 | 0.863 ± 0.013 | |
ǀ | (—) | 5.33 | 2.06 | 6.97 |
FS | (—) | 0.522 ± 0.002 | 0.512 ± 0.013 | 0.510 ± 0.027 |
(—) | 0.973 ± 0.004 | 0.952 ± 0.046 | 0.977 ± 0.014 |
The spatial patterns of LuMnO3 thin films were studied from topographic maps obtained by atomic force microscopy. The morphology of sintered films with lower temperatures was smoother, while the higher temperature promoted a rougher surface, which was confirmed by the topographic parameters of height. Advanced stereometric parameters revealed that the roughness distribution of films sintered at lower temperatures was uniquely different from the film sintered at 850°C, where the peak shape was more sharp and the distribution of roughness was less dense, which influenced the thickness and volume of material present in the core of the surfaces. Qualitative renderings of the material’s microtexture confirmed the observed morphological differences, although specific texture parameters computed by Fourier transforms on the height function have suggested that the microtextures of the films were assigned to be similar. Nevertheless, the spatial patterns proved to be different because the advanced fractal parameters revealed that the film sintered at 850°C presents less spatial complexity and that it is dominated by low dominant spatial frequencies. This higher sintering temperature coalesced the grains so that their microtexture became more homogeneous. Moreover, because of the uniform deposition process, the surface porosity and topographic uniformity of the films did not fluctuate when sintering temperature has increased. Therefore, our results showed that a combination of stereometric and fractal parameters can be especially useful for controlling the process of fabrication of thin films based on rare-earth-based perovskites oxides.
The data presented in this study are available from the corresponding author upon request.
The authors declare no conflicts of interest.
The authors thank the Federal University of Amazonas (UFAM) for the infrastructure of the Analytical Center. Av. General Rodrigo Octavio Jordão Ramos, 1200-Coroado I, Manaus, Amazonas, 69067-005, Brazil.