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Abstract
In this study, columbite phase tin oxide film was deposited onto quartz glass using the thermal evaporation method. An ellipsometry experiment was performed at the temperature of 25 °C-600 °C. B-spline with K-K consistence was used to describe the optical constants of SnO2 film to obtain the temperature dependent film thickness and optical constants. Results of X-ray diffraction pattern (XRD) confirmed an irreversible phase transition from columbite to the rutile structure at the temperature range of 100 to 300 °C, which had remarkably reduced the film thickness and resulted in the blue shift of the absorption edge. Besides, the total and partial densities of states (TDOS and PDOS) for both rutile and columbite phase SnO2 were also calculated based on the first-principles in accordance with the density functional theory, so as to clarify the structure properties of these two phases.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Tin oxide, a kind of n-type semiconductor, has been recognized to possess numerous excellent physical properties, such as high transmittance under visible light (average of >90%), high carrier concentration (1019 ∼ 1021 cm-3), wide band gap (3.6 ∼ 4.0 eV), great conductivity, high chemical stability and thermal stability.[1–4] Therefore, it can meet the diverse requirements of optoelectronic devices, including the solar cells, light detectors, liquid crystal display (LCD), and transparent conducting electrodes.[5–10] Typically, the SnO2-based films have aroused extensive attention from many researchers due to their wide applications. [11–20]
However, the structural information and optical constants of the SnO2 thin films under different temperatures remain unclear which should be further investigated. Optical constants, which are directly associated with the dielectric constants, are important parameters due to their significant influence on all relevant optical applications. Generally, SnO2 exists in the tetragonal, orthogonal or cubic phases, and the optical constants may be completely different at various structural phases, even for the same atom component materials. According to earlier reports, the orthogonal columbite phase can only survive at high pressure, [21] while some researchers discover later that pressure is not the only approach, and the columbite phase SnO2 can sometimes be formed through an annealing process. [22] Given these disputes, the influence of temperature on the structure and optical constants of SnO2 film will be worthy of being explored.
Ellipsometry has been utilized as a unique research approach with high accuracy to determine the optical properties of materials in a noninvasive and non-contact manner. [23–26] In this study, ellipsometry experiment at variable temperature was carried out on the thin SnO2 film. Besides, B-spline model and Kramers-Kronig (KK) consistence were applied to obtain the optical constants of SnO2 film at different temperatures. Moreover, the evolution of optical constants with temperature was also summarized. Typically, the markedly reduced film thickness was confirmed to be related to the phase transition from columbite to the rutile structure, which was well consistent with the calculation results based on the density functional theory.
2. Experimental
The SnO2 thin film was prepared onto the quartz glass substrate at room temperature using the thermal evaporation method and the base pressure of the evaporation chamber was ∼10−4 Pa. Meanwhile, the ellipsometry parameters were collected using a rotating polarizer ellipsometer (J.A. Woollam Co., Inc. M-2000U) with the wavelength ranging of 300-1000 nm at an incident angle of 75°. Additionally, the measurement temperature was set to start from room temperature (25 °C) to 600 °C and then cooled to room temperature, which is also served as an annealing treatment. The temperature rose in steps of 25 °C during the heating process and decreased in steps of 50 °C during the cooling process. In addition, the X-ray diffraction patterns and surface topography of the film samples were collected before and after the annealing process through a grazing-incident XRD (Rigaku SmartLab) and an atomic force microscope (AFM) in the tapping mode (SII NanoTechnology Inc., NanoCute), respectively.
3. Results
On the hand, the ellipsometry parameters, such as amplitude $\Psi $ and phase $\Delta $, are defined by ${{{R_p}} \mathord{\left/ {\vphantom {{{R_p}} {{R_s}}}} \right.} {{R_s}}} = \tan \Psi \cdot \exp ({i\Delta } )$ , where Rp and Rs represent the complex reflection coefficients of the polarized light parallel and perpendicular to the incidence plane, respectively. To obtained the optical constants and film thickness based on the collected ellipsometry parameters, the optical constants of the SnO2 film were parameterized by B-splines and enforced to follow the KK relationship. [26] Such relationship could not only ensure a physical solution, but also reduce the number of fitting parameters, making it easier to produce a unique solution.
To be more practical, film thickness was also set as a variable parameter during the fitting process. The temperature-dependent film thickness was shown in Fig. 1. According to our calculation, the initial thickness was about 472 nm. The film thickness was sharply decreased as the temperature in the green region rose from 75 °C to 300 °C during the heating process. After the temperature of 300 °C, the film thickness was decreased at a slower rate which was close to 394 nm at the temperature of 600 °C. By contrast, the film thickness showed a slight linear decrease until 390 nm when it recovered to room temperature during the cooling process, which could be attribute to the cold contraction principle.
To explain the remarkably decreased film thickness during the heating process, XRD was performed on the SnO2 thin film before and after the annealing treatment, respectively, as presented in Fig. 2. The SnO2 film was composed of nanocrystals, so its diffraction peaks were apparently broadened due to the finite size of the crystallites, which was known as the Debye-Scherrer broadening. Besides, the film is not thick enough would also result in the broadened diffraction peaks. Before the annealing treatment, the diffraction peaks could be identified using the columbite phase SnO2 (C-SnO2), while those after the annealing treatment could be identified using the rutile phase SnO2 (R-SnO2). The standard powder diffraction lines of C-SnO2 and R-SnO2 were also showed in Fig. 2. Accordingly, it could be concluded that the SnO2 film had exhibited an irreversible phase transition from columbite to rutile phase during the heating process. [22] On the other hand, considering the broadened diffraction peaks, the possibility cannot be ruled out that there existed a certain amount of amorphous phase of SnO2.
Such structure transition did not lead to any prominent change in the film surface topography. The AFM images in Fig. 3 showed that the SnO2 film always crystallized in nanograin about 100 nm in diameter, either before or after annealing treatment. Meanwhile, the roughness was increased from 0.97 ± 0.10 nm to 1.40 ± 0.12 nm following the annealing treatment. Besides, the surface color of the SnO2 film was markedly changed after the annealing treatment. According to the inset in Fig. 3, the SnO2 film color was canary yellow before annealing, which became more transparent after treatment at 600 °C. To clarify such variation, the optical constants should be considered.
The temperature-dependent optical constants, such as refractive index and extinction coefficient, are displayed in Fig. 4. As could be observed from Fig. 4 (b), the SnO2 films at all temperatures were transparent at a longer wavelength region. At room temperature, C-SnO2 exhibited no absorption until at the wavelength of <500 nm, suggesting that the C-SnO2 film could only absorb light at the wavelength band from green to UV rather than from green to IR light, thereby leading to a canary yellow color of the film. However, the mixture phase SnO2 film after annealing could only absorb UV light rather than the whole visible light wavelength band, as a result, the film looked totally transparent without any color.
Besides, there was an obvious blue shift of the absorption edge from 100 °C to 300 °C, which has increased the band gap, suggesting that the mixture phase had a larger band gap than that of the rutile phase. In addition, the optical constants tended to be stable from 300 °C to 600 °C. During the cooling process, the absorption edge showed a slightly blue shift, along with a slightly increased band gap, indicating that the phase transition from C-SnO2 to R-SnO2 during the heating process was irreversible, which would not return to the initial stage after cooling to room temperature.
To obtain the specific band gap values of the two phases, the absorption coefficient was calculated from the extinction coefficient according to the following equation:
Figure 5 displays the relationship between ${({\alpha h\nu } )^2}$ and photon energy at different temperatures, in which the values regarding the intersections of the tangent lines and the horizontal axis represent the band gap of SnO2 at different temperatures. As could be seen from Fig. 5, the band gap of the rutile phase SnO2 before annealing was 2.5 eV, while that of the mixture phase SnO2 after annealing was increased by 1.2 eV to 3.7 eV. Meanwhile, the band gap of our rutile phase SnO2 film was 1.1 eV, which was smaller than that of the bulk material (3.6 - 4.0 eV); such results might be probably ascribed to the interface effects in the film material rather than the bulk material.To examine the structural, electronic band and density of states properties, theory calculation was done for both ohases of SnO2 (namely the rutile and columbite phase) based on the density functional theory (DFT) in the generalized gradient approximation (GGA) [27,28] for the exchange-correlation term according to the Perdew-Burke-Ernzerhof (PBE). [29] Typically, the Projector augmented wave (PAW) [30,31] was selected as the pseudopotential and the Vienna ab initio simulation package (VASP) was used. [32,33]
The equilibrium structures were obtained through optimizing the unit cell structures of the two phases of SnO2, the. The optimized crystal structures of the rutile and columbite phase SnO2 are shown in Fig. 6. As for the stable crystalline phase, the rutile phase SnO2 belongs to the tetragonal system and $P42/mnm({D_{4h}^{14}} )$ space group, whereas the the columbite phase SnO2 belongs to the orthorhombic system and Pbcn space group.
The lattice constants of the optimized structure are listed in Table 1 which are similar to those reported in previous work. [34] Typically, the calculated lattice constants were on the high side as usually found within GGA approximation, with the errors relative to the experiment data of < 2%. [35] As for the columbite phase, the difference with respect to previous DFT study at B3LYP level was < 2%. [36] The volume of the unit cell is also listed in the Table 1. Clearly, the volume per atom at the columbite phase was larger than that at the rutile phase, indicating that the volume would be reduced when SnO2 was transformed from columbite to rutile phase. Thus, these results could well explain our phenomenon of the reduced thickness during the heating process from 100 °C to 300 °C.
Table 1. Lattice constants of the optimized structure for rutile and columbite phase SnO2.
The total and partial densities of states (TDOS, PDOS) for rutile and columbite phase SnO2 are shown in Fig. 7. In general, there was no significant difference in the distribution of TDOS and PDOS. The p orbital of O contributed to the lower energy region of the valence band, while the high energy region of the valence band consisted of the s and p orbitals of Sn as well as the predominant p orbital of O, which took part in the chemical bonding with Sn. There was an anti-bonding character at the bottom of the conduction band, which arose from the s orbital of Sn and the p orbital of O for both rutile and columbite phases. The p and d orbitals of Sn, together with the p orbital of O, constituted the higher part of the conduction band. Our DOS results at the rutile phase were well consistent with those from previous DFT work. [34,37]
Figure 8 shows the band structure along a selected path of the Brillouin zone of the two phases SnO2. Both the two phases of SnO2 were suggested as the direct band gap semiconductors. The direct band gap values at G were 0.63 eV and 0.98 eV for rutile and columbite phases, respectively. As expected, the band gap exhibited an increasing trend, yet the band gap values were much smaller than the experimental data. As a matter of fact, DFT approximations would undervalue the excited state energies, and the smaller results of band gap were obtained. Such large difference might be primarily ascribed to the strong electronic correlation effects, since both the two phases of SnO2 were inclined to be the Mott insulators.
This experimental result can also be explained in another way. The unannealed sample may contain a high concentration of defects, such as atoms in non-equilibrium positions and oxygen vacancies, which were not considered in this DFT approach. If oxygen vacancy is introduced in SnO2 supercell and then the structure is optimized, DFT band gap calculation would tell us these things: 1. the Fermi level moves from valence band maximum (in pristine SnO2) to some energy level in direction of the conduction band minimum. If oxygen vacancy concentration is high, the Fermi level can be found inside the conduction band. Thus, the observed free-like electrons can be modeled with Drude classical theory. Therefore, the band gap and the optical band gap are not equaling. 2. The band gap is shrinkage as resulted from scattering against ionized defects. Due to these two factors, a renormalization process takes place and the optical transitions occur out of the Brillouin zone center. Thus, the increase in the optical band gap in the annealed sample in comparison with that in the as deposited sample, and the thin film thickness evolution can be understood as a reduction in the defect concentration, mainly oxygen vacancies, and a lower amorphous degree due to the thermal process.
4. Conclusion
In this study, the columbite phase tin oxide film was deposited onto the quartz glass using the thermal evaporation method. Meanwhile, ellipsometry experiment was performed at the temperature of 25 °C-600 °C. Moreover, the B-spline model with K-K consistence was employed to describe the optical constants of SnO2 film and the effects of temperature on the film thickness and optical constants were also summarized. Results of X-ray diffraction pattern (XRD) had confirmed an irreversible phase transition from columbite to rutile structure at the temperature range of 100 to 300 °C, which had remarkably reduced the film thickness and resulted in the blue shift of the absorption edge. The optical properties tended to be stable after 300 °C. During the cooling process, the thickness was slightly decreased, and the absorption edge exhibited a slightly blue shift. To gain more insight into the structural nature, GGA calculation was achieved for the two phases of SnO2. The results could well explain the decrease in the thickness during the phase transition. Additionally, the large difference in band gap was compared with the experimental data, which suggested that these two phases of SnO2 were both the Mott insulators.
Funding
Science Challenge Project (TZ2016001); National Natural Science Foundation of China (NSFC) (11304300, 11674324, 51677175).
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