1. Introduction

Mn-Co-Ni-O (MCNO) thin films belong to AB₂O₄ cubic spinel structure with excellent semiconductor properties. They are often used as thermal sensors, surge protective devices and the property of negative temperature coefficient of resistance are often used as uncooled thermal infrared detectors [1–3]. As an important optoelectronic material, the optical mechanism of MCNO thin films is deficient and the researches mainly focus on the preparation or electrical properties [4–7]. G. Ji prepared Mn_1.56Co_0.96Ni_0.48O₄ thin films by using laser molecular beam epitaxy technique and the structural and electrical properties of the films have been investigated [8]. Y. Q. Gao prepared about 2 μm Mn_1.56Co_0.96Ni_0.48O₄ thin films by the chemical solution deposition method on a Al₂O₃ substrate and the mid-infrared optical properties of the films have been investigated by analyzing transmission spectra [9]. The spectroscopic ellipsmetric properties of MCNO thin films have been extensively studied in our former paper [10] and the research about transmission and absorption in this paper can motivate some new results which cannot be deduced by spectroscopic ellipsmetric analyses. These studies provide theoretical basis for improving the optoelectronic properties of MCNO films and facilitate to narrow the disparities between the MCNO infrared detectors and the refrigerated infrared detectors. Furthermore, the application of this film in the optical field will be promoted.

2. Experimental

MCNO thin films were deposited on amorphous Al₂O₃ substrates with thickness of ∼0.75 μm by the magnetron sputtering technique introduced in reference [11], and the components were separately Mn_1.2Co_0.7Ni_1.1O₄, Mn_1.2Co_1.2Ni_0.6O₄, Mn_1.5Co₁Ni_0.5O₄, Mn₂Co_0.7Ni_0.3O₄. Additionally, 2 μm Mn_1.5Co₁Ni_0.5O₄ and 6.5 μm Mn₂Co_0.7Ni_0.3O₄ thin films were also prepared by the same deposited method. Transmission and reflection were measured by FTIR spectrometer (Bruker 80V) and then the absorptivity was calculated for those films. The spectroscopic ellipsometry was measured by SC620 (Sanco Co., Inc.) in a range of 0.3~1.1 μm and the incident angles were 50° and 60°. The XPS (AXIS, Kratos) and Raman spectra (Renishaw) were measured for parts of the films.

3. Results and discussion

Our former research instructs that the macroscopic physical properties of MCNO thin films could be explained by the free carrier model [11]. Accordingly, for the incident light with a certain wavelength, the MCNO thin film definitely has a penetration depth with the same expression (Eq. (1)) to metallic substances [12].

Where d is the penetration depth, λ is the incident wavelength, n represents the refractivity, and k is the extinction coefficient. We take the intersection between the transmissivity curve and the zero axis as the cutoff position and the corresponding wavelength is λ(T₀) (Fig. 1(a)). For 2, 0.75, and 0.5 μm Mn_1.5Co₁Ni_0.5O₄ thin films, their d values can be calculated and the results are separately 0.425 ± 0.006, 0.158 ± 0.002, and 0.109 ± 0.003 μm which are almost the same proportion to the thickness ratio (Fig. 1(b)). Therefore, we deduce that the free carrier model can explain the optical properties of MCNO thin films above 0.5 μm satisfactorily based on Eq. (1).

 

Fig. 1 (a) Transmissivities of 2, 0.75, and 0.5 μm thicknesses of Mn_1.5Co₁Ni_0.5O₄ thin films in 0.54~1.1 μm waveband. The vertical marks denote the cutoff positions which are the intersections between the curves and the zero axis. The inset shows the cutoff wavelength changes with the film thickness, which indicates that thicker film corresponds to longer cutoff wavelength; (b) The film thickness and corresponding λ(T₀) values. It can be seen that they are even the same ratios.

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Because the thicker film corresponds to a longer cutoff wavelength, it can be deduced that MCNO thin film should oversize certain thickness in order to reduce the loss of transmissivity. It also can be seen that the incremental thickness mainly contributes to longer-wavelength absorption (Fig. 1(a)).

For 0.75 μm MCNO thin films with different component ratios, their d values in the wavelength λ(T₀) should be the same for those whose optical properties can be explained by free carrier model. The refractive index n and extinction coefficient k can be fitted by the point by point method (Fig. 2). Then their d values can be calculated according Eq. (1). It can be drawn from Table 1 that the d values are approximately equal with one another in the range of errors except for Mn₂Co_0.7Ni_0.3O₄ thin film because of its small cutoff wavelength. It means the effect of the small polaron oscillation on the optical properties cannot be ignored for Mn₂Co_0.7Ni_0.3O₄ thin film.

 

Fig. 2 (a) Transmissivity in 0.55~1.1 μm waveband for 0.75 μm MCNO thin films. The 1, 2, 3, 4 numbers mark the cutoff wavelength λ(T₀) whose values are listed in Table 1. The refractive index n (b) and extinction coefficient k (c) can be fitted by the point by point method.

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Table 1. The values of cutoff wavelength λ(T₀), refractive index n, extinction coefficient k and the deduced penetration depth d.

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For MCNO films, the inner Mn³⁺ ion and its surrounding electron are affected by john-Teller distortion to form a small polaron [13]. In terms of energy band, the local state broadening for Mn³⁺, Mn⁴⁺ ions will produce low Hubbard and high Hubbard bands separately to form a Hubbard band gap [1, 13]. Due to the electron-phonon interaction, the electron jumps from Mn³⁺ to Mn⁴⁺. This brings about the small polaron hopping to produce a quasi-free electron during the jumping process. So, the number of Mn³⁺/Mn⁴⁺ ion pairs is proportional to the number of quasi-free electrons. The XPS analyses in Fig. 3 manifest that the number of Mn³⁺/Mn⁴⁺ ion pairs is 0.44 for Mn₂Co_0.7Ni_0.3O₄ thin film while the number for Mn_1.2Co_0.7Ni_1.1O₄ thin film is 0.49 [14]. The smaller number of Mn³⁺/Mn⁴⁺ ion pairs will produce less quasi-free electrons for Mn₂Co_0.7Ni_0.3O₄ thin film.

 

Fig. 3 XPS-peak-differenations of Mn 2p_3/2 level signals for (a) Mn_1.2Co_0.7Ni_1.1O₄ and (b) Mn₂Co_0.7Ni_0.3O₄ thin films.

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Additionally, the number of small polarons is determined by the Mn³⁺ ion number. The Mn³⁺ content of Mn₂Co_0.7Ni_0.3O₄ thin film (1.14) far outnumbers the one of Mn_1.2Co_0.7Ni_1.1O₄ thin film (0.59). Consequently, the small polaron oscillation plays a more important part to be not ignored for Mn₂Co_0.7Ni_0.3O₄ film with bigger Mn³⁺ ion number, which can also explain the decreased cutoff wavelength with growing Mn ion content in Table 2.

Table 2. Percentages of Mn³⁺, Mn⁴⁺ ions for Mn₂Co_0.7Ni_0.3O₄, Mn_1.2Co_0.7Ni_1.1O₄ thin films and numbers of Mn³⁺ ion (n₁), Mn³⁺/Mn⁴⁺ pairs (n₂).

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We prepared 6.5 μm Mn₂Co_0.7Ni_0.3O₄ thin films and annealed them under 400 °C, 500 °C, 600 °C, 800 °C separately [10]. Figure 4(a) indicates that the annealing treatment enlarges the cutoff wavelengths (correspondingly 1.86, 1.865, 1.87, and 1.88 μm). It is mainly due to the enlarged Mn³⁺/Mn⁴⁺ pair number resulting from the transmission of Co²⁺ ions to the octahedron with increasing annealing temperature for the MCNO thin films with cubic spinel structure [13]. As a result, the enlarged Mn³⁺/Mn⁴⁺ pair number will increase the number of hopping small polarons to produce more quasi-free electrons, and then the number of oscillating small polarons will decrease. It has been demonstrated in other references that the absorption edge at around 2 μm results from the resonance absorption by the small polaron hopping [11]. This theory works on these cutoff wavelengths. As the wavelength increasing, the function of the incident wave on the small polaron hopping will become weaker and weaker, and then the absorption will be mainly caused by the intraband transition of the small polaron. The onsets of absorption for the samples are around 4.7 μm (Fig. 4(b) inset). So it can be deduced that the energy of intraband transition must surpass 0.26 eV. For the wavelength over 3.6 μm, the transmissivity are almost unchanged under different annealing temperatures in Fig. 4(b), which means that annealing treatment only affects optical properties at less than 3.6 μm.

 

Fig. 4 (a) Transmissivity spectra of samples annealed at unannealed, 400 °C, 500 °C, 600 °C, 800 °C separately for 6.5 μm Mn₂Co_0.7Ni_0.3O₄ thin film within 1.8~2.2 μm waveband;(b) Transmissivity spectra of samples annealed at 400 °C, 800 °C within 1.7~5.4 μm waveband. The waves are caused by optical interference of film thickness. The scatters almost coincide with the line above 3.6 μm wave. The inset is absorptivity spectrum of 400 °C annealed sample. The onset of absorption begains at 4.7 μm.

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At room temperature (300 K), the thermal energy of electron is 0.026 eV (k_BT) which is much more less than the intraband transition energy. So, the ambient temperature can be considered as perturbation to be ignored. When the frequency of optical branch in lattice vibration spectrum is the same to the incident electromagnetic frequency, the strong coupling absorption for incident wave occurs. For 4.7 μm, the electromagnetic frequency is 3.98 × 10¹⁴ rad/s and it should correspond to lattice vibration [15]. The eigenvalue of phonon energy can be expressed as En = (n + 1/2)ћω_q, (n = 0,1,2…. and ω_q representing phonon frequency). Since the bound electron in small polaron only interacts with the lattice wave, there must exists an energy transfer with ћω_q as one unit and the value is 0.26 eV which leads to the intraband transition for the electron in small polaron. Figure 5(a) is the XRD patterns of unannealed and 800 °C annealed samples. The lattice parameters can be calculated to be 8.3492 Å and 8.2700 Å respectively according to the (400) diffraction peaks. Deductively, the lattice vibration frequency (or the lattice vibration energy) only changes about 0.95%, which indicates that annealing even has no obvious effect on the frequency of lattice vibration. For 6.5 μm Mn₂Co_0.7Ni_0.3O₄ thin films annealed at different temperatures, their absorptivities in 3.6~4.7 μm are even out of relation with annealing temperature. So, the absorption in 3.6~4.7 μm waveband is brought about by the lattice resonance absorption. Comparably, there exists a more obvious differentiation for the absorptivity below 3.6 μm which indicates a role played by annealing treatment on the electronic resonance frequency.

 

Fig. 5 6.5 μm Mn₂Co_0.7Ni_0.3O₄ thin film: (a) XRD patterns of unannealed and 800 °C annealed samples; (b) Raman spectra comparison with 0.75 μm Mn₂Co_0.7Ni_0.3O₄ thin film.

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The above results can also explain the thinner MCNO films with different components. Figure 6 shows that the first absorptivity edge λ₁ is about 4.5 μm which is brought about by the lattice resonance absorption for 0.75 μm MCNO films and smaller than the absorptivity edge of 6.5 μm Mn₂Co_0.7Ni_0.3O₄ thin film (4.8 μm). From Raman spectra in Fig. 5, it can be gotten that Raman active vibrational modes locate around 551 cm⁻¹ and 547 cm⁻¹ respectively and they are both brought about by Mn-O ion clusters [1]. The comparison shows that the thicker film has a smaller Raman shift. It can be deduced that the MCNO thin films deposited on amorphous Al₂O₃ have compressive stress near the interface, and the stress will decrease with growing thickness. The compressive stress will also result in a higher lattice resonance frequency (i.e. lower λ₁ value) for 0.75 μm MCNO films. Because the intraband transition of the electron in small polaron due to the energy transfer of lattice vibration puts the small polaron in excited state, it is reasonable to suppose that the second absorptivity edge λ₂ resulting from the resonance absorption of electrons corresponds to the hopping of the small polaron in excited state consequently. According to the former analyses, the upper part of the film mainly assimilates shorter wavelengths, and so the compressive stress of the film has little effect on the shortwave absorption. As a result, it is reasonable to take 0.26 eV as the transferred lattice energy just like thick MCNO films. Then the resonance frequency ω_e of the small polaron in ground state can be calculated by adding up the electronic thermal energy 0.026 eV, the transferred lattice energy 0.26 eV and the excited energy corresponding λ₂ points together and ћω_e is the ionization energy of small polaron (Table 3). The resonance wavelengths λ_e of the small polaron hopping from ground state to quasi-free state for Mn_1.2Co_0.7Ni_1.1O₄, Mn_1.2Co_1.2Ni_0.6O₄, Mn₂Co_0.7Ni_0.3O₄ thin films can be calculated to be successively 1.56 ± 0.05, 1.54 ± 0.04, and 1.59 ± 0.04 μm, which even coincide with the third absorptivity edge λ₃ values 1.59, 1.57, and 1.62 μm within the range of errors.

 

Fig. 6 Absorptivity spectra of Mn_1.2Co_0.7Ni_1.1O₄, Mn_1.2Co_1.2Ni_0.6O₄ and Mn₂Co_0.7Ni_0.3O₄ thin films. The λ₁, λ₂, λ₃ values denote three absorptivity edges separately. The enlarged views of λ₁(Mn_1.2Co_1.2Ni_0.6O₄), λ₃ values are displayed in the insets for more clear show. The λ₂ values correspond the inflection points of curves and the ranges of errors are marked with coarse pink lines.

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Table 3. λ₁, λ₂, λ₃ values, ionization energy ћω_e of small polaron, resonance frequency ω_e and coupling wavelengths λ_e of the small polaron in ground state. The values in parentheses are the energies separately corresponding λ₁, 4.7 μm waves and thermal energy at room temperature.

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4. Conclusions

In summary, we have analyzed the cutoff wavelengths of 2, 0.75, and 0.5 μm thickness of Mn_1.5Co₁Ni_0.5O₄ thin films and demonstrated the free carrier model can well explain the optical properties of MCNO thin films above 0.5 μm without considering the small polaron oscillation. The study of MCNO thin films with different components shows that the small polaron oscillation cannot be ignored with increasing Mn ion content. Consequently, the cutoff wavelengths of most MCNO films are above 0.5 μm except for that of Mn₂Co_0.7Ni_0.3O₄ thin film which has more small polarons. The comparison of Raman spectra of Mn₂Co_0.7Ni_0.3O₄ thin films with the thickness of 0.75 μm and 6.5 μm indicates that the MCNO thin films deposited on amorphous Al₂O₃ have compressive stress. For 6.5 μm thickness of Mn₂Co_0.7Ni_0.3O₄ thin films underwent annealing treatment, it is lattice resonance absorption coupling with incident electromagnetic wave in 3.6~4.7 μm waveband and annealing has no obvious effect on the lattice resonance frequency. However, the electronic resonance frequency suffers remarkable influence of annealing treatment. The spectra analysis of MCNO films with different components instructs that the first absorption edge of absorptivity is brought about by lattice resonance, the second one results from the absorption hopping of the small polaron in the excited state and the third one is due to absorption hopping of the small polaron in the ground state.