# Optoelectronic Properties of Ultrathin Indium Tin Oxide Films: A First-Principle Study

^{*}

**—**Nano-Theory)

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{2}O

_{3}cell from the Material Project Database, where two In atoms are substituted by Sn atoms. To maintain the electroneutrality of the ITO structure, an extra O atom was incorporated into the system. We utilized the mp-22598 In

_{2}O

_{3}from Materials Project [27]. The space group was IA, and the chemical composition of the cell was In

_{32}O

_{48}. In our calculation, we chose a (001) surface and the surface was terminated with In atoms. The vacuum layer was set to be larger than 10 Å. The cut-off energy of 400 eV and Perdew–Burke–Ernzerhof (PBE) functional with the generalized gradient approximation (GGA) were adopted to describe the electronic properties of the ITO films [28,29]. The projector augmented wave (PAW) was employed to describe core–electron interactions [30,31]. The force threshold and energy threshold were set to 0.05 eV/Å and 10

^{−4}eV, respectively. The lattice parameters for the proposed structure were optimized with a 1 × 1 × 1 k-point due to the relatively large ITO structures, following the Monkhorst–Pack scheme [32]. The above configurations led to an optimized lattice constant of 10.3 Å, which well matched the experimental value of 10.08 Å [14]. As all the optimized lattice parameters were comparable to 1 nm, the optimized ITO cells were deployed to build 1 × 1 × 1, 1 × 1 × 2, and 1 × 1 × 3 supercells, corresponding to 1, 2, and 3 nm ITO structures (see Figure 1), respectively. Ab initio molecular dynamic (AIMD) simulations were used to obtain structures at different temperatures and to equilibrate the considered systems. The aforementioned settings in DFT calculations were also applied to AIMD calculations in the ab initio part, and here we used a Nosé–Hoover thermostat for the MD calculations. The time step was set to 1.25 fs. Initially, the proposed ITO structures (i.e., 1, 2, and 3 nm thicknesses) underwent relaxation at 800 K for 5000 fs, which is adequately long to attain the fully converged structures and equilibrate at high temperatures. Later on, the obtained structures were subsequently annealed with a reasonable velocity of 0.4 K/fs to 100, 200, 300, 400, 500, and 600 K, respectively. It is necessary to mention that the calculated ITO thickness is restricted to be 3 nm due to the limitation of the theoretical method. In DFT calculations, the computational time increases exponentially with the increase of atom numbers in a system, resulting in the upper limit of 3 nm in our work.

^{−7}Hartree (2.7 × 10

^{−6}eV) [37].

## 3. Results and Discussions

#### 3.1. Electronic Structure Properties of Ultrathin Films of ITO

_{2}O

_{3}structure is favorable and produces a stable species. The electron densities (obtained from the PDOS) of 1 nm ITO at different temperatures are around the Fermi level, which results in a very small bandgap for 1 nm ITO. In the case of 2 and 3 nm ITO structures, similar band positions of Sn, In, and O elements are observed. The only difference in the PDOS plots of these structures is interpreted in the form of the density variation, which is in the region of 0–5 eV (Figure 3). The 1 nm ITO has a low density in this region, while a small increase was found for the 2 and 3 nm ITO cases. This is responsible for the increased intensity of antibonding orbitals in the conduction band region. In the energy regions of −5 to −4 eV, the PDOS of Sn are relatively higher than those in the range of −2 to 0 eV. There are two possible reasons to explain such an effect. On the one hand, there are only two Sn atoms in the system, and their PDOS may be “submerged” into the PDOS of pristine In

_{2}O

_{3}. Hence, the shape of Sn PDOS may be different from that of In or O. On the other hand, although the peaks in −5 to −4 eV are higher, there are still peaks in the range of −2 to 0 eV, meaning that Sn atoms interact with the surrounding environment and the electron density overlaps with those atoms. The band structures of the proposed ITO films were also calculated, which are given in Figure 4. The results of TDOS and band structure are similar; so, here, only one certain band at 100 K is discussed. The simulated bandgap of 1 nm ITO is ~0.8 eV above the Fermi level, which results in its semiconducting nature. The band structure of the 2 nm ITO at 100 K is similar to that of the 1 nm ITO but with a large number of bands. This large number of bands may be due to a large number of atoms inside the 2 nm layer. These atoms would have a stronger interatomic effect, forming new and complex bands within the overall energy range, especially near the Fermi level. So, these extra band occupations near the Fermi level diminish the bandgap and yield a negligible gap of 0.1 eV. Similarly, the 3 nm ITO has more atoms; so, a severe situation is observed, where a large number of atoms contribute to the overall band distribution and result in a much narrower bandgap, as shown in Figure 4. Comparative analysis of the data of Figure 2; Figure 4 leads us to conclude that ultrathin films of ITO exhibit narrow bandgaps that eventually disappear with film thickness. The complex band formation near the Fermi levels of 2 and 3 nm ITO structures can enhance the electron transfer property. Thus, it was found that the thicker ITO layer has a lower resistivity and higher electrical conductivity.

^{2}) by the formula given below:

_{slab}represents the total energy of a slab structure of ITO (e.g., 1, 2, and 3 nm ITO structures), N indicates the ratio of atom numbers between the slab ITO structure and the bulk ITO structure, and E

_{bulk}represents the total energy of the bulk ITO structure. A shows the surface area of the proposed slab structure, and the coefficient 2 is considered as the slab of the ITO structure with top and bottom exposed surfaces. From Figure 5, we can see that the surface energy increases along with the increase in thickness of ITO at different temperatures. This statement is contradictory to common sense, namely, that thicker films have lower surface energies than those of thinner ones [38]. The reason behind this may be the involvement of just two Sn atoms as dopants in 1 nm ITO, which are less susceptible to the system energy. However, more Sn atoms are incorporated in the thicker ITO films, which produce large displacement during the molecular dynamics calculation, which may affect the optimization (DFT) process as well. The ITO system with fewer Sn atoms is more stable. So, this may imply that the ultrathin ITO system is more stable than the thicker structures, incapable of providing sufficient vacancies or electron holes to conduct the electron transfer. In addition, the surface energy gradually increases along with the increase in temperature. This may be readily attributed to the more drastic perturbation of the system caused by higher temperatures.

#### 3.2. Optical Properties of Ultrathin Films of ITO

_{1}) and real parts (ε

_{2}) of the dielectric constant via

_{0}is the dielectric constant in vacuum, ω is the angular frequency, C is the conduction band, V is the valence band, BZ is the first Brillouin zone, K is the electron wave vector, a is the unit direction of the vector potential A, M

_{V.C}is the transition matrix element, and the vectors E

_{C}(K) and E

_{V}(K) are the intrinsic energy levels on the conduction band and the valence band, respectively. The total dielectric constant has the equality ε = ε

_{1}+ iε

_{2}. The values of ε

_{1}and ε

_{2}can be obtained through DFT calculations, and thus the total dielectric constant is subsequently attained. All the optical properties in this work were therefore calculated based on these two values.

_{1}and ε

_{2}are the real and imaginary parts of the calculated complex dielectric constants of the ITO film at different conditions, respectively. It is clear that the values of the complex refractive index vary between 0.5 and 2.5 for all three structures of different thicknesses while being less sensitive to temperature. The 1 nm ITO structure exhibits a sharp peak in the energy range of ~1.3 eV, which is absent in the 2 and 3 nm structures. Moreover, a broad peak was found to be located at ~4.2, ~2.7, and ~2.1 eV for 1, 2, and 3 nm ITO structures, respectively, while their respective refractive index was calculated to be ~1.6, ~1.8, and ~1.9, respectively. Considering that these peaks mainly lie in the visible region of light, it is very likely that the 1 nm ITO film will generate a relatively smaller refractive index than that of the other two systems. The temperature-independent refractive index and absorption spectra can be also interpreted by the Kubo formula, which is usually adopted to calculate the optical conductivity [40]:

_{nm}is the Berry connection, and f

_{nm}is the difference in Fermi–Dirac distribution between bands n and m. The major terms that change with temperature are the distribution function, f

_{nm}, and the small broadening factor iη, but these two parameters are changing on the scale of thermal energy k

_{B}T, which is approximately 25.7 meV at room temperature. It is obvious that the temperature dependence trend becomes less apparent when the photon energy ω is much larger than k

_{B}T (i.e., in the visible range).

^{-αt}term in this case is approximately equal to 1, and the calculated transmittance of the ITO film can be determined from its reflectivity using Equation (2). As a result, the smaller reflectivity of 1 nm ITO in the visible light region allows larger transmittance compared with that of thicker ones. Further, the transmittance of 1 nm ITO with a wavelength of >780 nm was found to be smaller than that of 2 and 3 nm ITO, which exhibit almost constant transmittance in the range from 200 to 1000 nm. These results and discussions led us to conclude that thicker ITO thin film has better light transmission in the near-infrared region.

#### 3.3. Electrical Transport Properties of Ultrathin Films of ITO

_{σ}is given by

^{(K)}indicates the k-revolved transmission, which can be attained through the NEFG calculations.

^{4}(Ωcm), which shows good agreement with the experimental data of 2.11 × 10

^{4}(Ωcm) [42]. The main reason behind this discrepancy is the strain effect of ITO films. According to the simulations, the 1 nm ITO film is largely strained, with an average length of 0.96 Å at a temperature range of 100–600 K. On the other hand, 2 and 3 nm ITO films exhibit the average strain length of 0.99 and 1.01 Å, respectively. It can be therefore speculated that the thinner ITO film is highly strained, thus resulting in a shorter atomic bond length. Such shorter bonds may increase the free path of the electron transport, which consequently induces poor electrical conductivity. On the contrary, the strain impact on the thicker ITO films (similar to bulk ITO) is remarkably attenuated, consequently rendering the 2 and 3 nm ITO films less electrically resistive. In addition to the strain effect, the narrow bandgaps present the thicker inside of ITO films. These are likely to facilitate the carrier mobility and mitigate the electrical transport characteristic. The electrical conductivity can be defined as σ = n

_{0}qμ

_{n}+ p

_{0}qμ

_{p}, where μ

_{n}and μ

_{p}correspond to the mobility of electron and hole, respectively, and n0 and p0 relate to the bandgap.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Simulated structures of indium tin oxide (ITO) with different thicknesses. The atomic structures are extracted from the molecular dynamics calculations at a random step.

**Figure 2.**Total density of states (TDOS) of 1 nm (

**a**), 2 nm (

**b**), and 3 nm (

**c**) ITO models near the Fermi level (−5 to 5 eV) at temperatures ranging from 100 to 600 K.

**Figure 3.**Projected density of states (PDOS) of the ITO films with thicknesses of 1 nm (

**a**), 2 nm (

**b**), and 3 nm (

**c**) at temperatures varying from 100 to 600 K over Sn, O, and In atoms. PDOS over In, O, and Sn atoms are denoted by red, green, and blue colors.

**Figure 4.**Band structures of 1 nm (

**a**), 2 nm (

**b**), and 3 nm (

**c**) ITO near the Fermi level (−5 to 5 eV) at 100 K.

**Figure 6.**Absorption coefficient (in cm

^{−1}) spectra of 1 (

**a**), 2 (

**b**), and 3 (

**c**) nm ITO models at temperatures ranging from 100 to 600 K. Upper panel shows the spectra in the energy range between 0 and 30 eV. The lower panel highlights the region near the visible light zone bounded by two gray dashes (energy varies from 1.63 to 3.11 eV).

**Figure 7.**(

**a**) Reflectivity spectra and (

**b**) refractive index of 1, 2, and 3 nm ITO models at temperatures ranging from 100 to 600 K.

**Figure 8.**(

**a**) Energy loss spectrum and (

**b**) extinction coefficient of 1, 2, and 3 nm ITO models at temperatures such as from 100 to 600 K.

**Figure 9.**Transmittance spectra of 1 (

**a**), 2 (

**b**), and 3 nm (

**c**) ITO models at temperatures ranging from 100 to 600 K.

**Figure 10.**The plot of resistivity vs temperature ranging from 100 to 600 K of ITO structures at different thicknesses.

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**MDPI and ACS Style**

Liu, X.; Wang, L.; Tong, Y.
Optoelectronic Properties of Ultrathin Indium Tin Oxide Films: A First-Principle Study. *Crystals* **2021**, *11*, 30.
https://doi.org/10.3390/cryst11010030

**AMA Style**

Liu X, Wang L, Tong Y.
Optoelectronic Properties of Ultrathin Indium Tin Oxide Films: A First-Principle Study. *Crystals*. 2021; 11(1):30.
https://doi.org/10.3390/cryst11010030

**Chicago/Turabian Style**

Liu, Xiaoyan, Lei Wang, and Yi Tong.
2021. "Optoelectronic Properties of Ultrathin Indium Tin Oxide Films: A First-Principle Study" *Crystals* 11, no. 1: 30.
https://doi.org/10.3390/cryst11010030