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Optical and Electronic Structural Properties of Cu3N Thin Films: A First-Principles Study (LDA + U)

A comprehensive study on the electronic structure and optical properties of a Cu3N film is performed by the first-principles study using density functional theory. The Hubbard (U) term is added in the local density approximation approach for improvement of the theoretical band gap energy. The band structure of the Cu3N unit cell shows a strong hybridization of Cu 3d and N 2p orbitals in the near-valence band region (M) because of their antibonding states which are also observed by molecular orbitals (HOMO–LUMO). The conduction band is dominated by a very small amount of Cu 3p and N 2p orbitals. The density of states exhibits a negligible deformation in Cu–N bonding. The Cu3N thin film deposited by the DC magnetron-sputtering technique shows a polycrystalline structure with a nonstoichiometric Cu3N phase. The experimentally obtained optical band gap and refractive index of the Cu3N film are 1.44 eV and 2.14, respectively, which are comparable with those from the theoretical approximation.


INTRODUCTION
The quest for new semiconducting materials is always a driving force in the field of materials science. In modern technology, it plays an important role in integrated circuits and optoelectronic research. 1 In recent years, copper nitride (Cu 3 N) has gained a lot of interest because of its application as an optical storage device in recorded media, 2−4 in laser writing, 5 and as a battery material because of its unique chemical activity. 6 Pure Cu 3 N has a cubic anti-ReO 3 -type structure, where the Cu atom is placed in the center with N 2 atoms at its corners. Though the Cu 3 N crystal is an insulator, it transforms into a semiconductor because of its vacancy doping. 7 Previously, the optical properties of Cu 3 N are reported by several authors including the effect of N 2 gas pressure on the optical band gap of the deposited Cu 3 N films. 8,9 The theoretical optical band gap of Cu 3 N is close to ∼0.9 eV, but the experimental value depends on various deposition conditions or parameters such as substrate temperature or doping. 10,11 Sahoo et al. reported that the indirect and direct band gap varies between 1.17−1.68 and 1.72−2.38 eV because of increasing pressure. 12 Xiao et al. also reported the photoluminescence property of Cu 3 N, where the band gap lies between 1.23 and 1.91 eV. 9 However, an extensive and useful study on the experimental and computational modeling methods on the band structure and optical properties of the metastable Cu 3 N film is very much needed. Earlier, a lot of reports are available on the density functional theory (DFT) calculations of Cu 3 N films including the indirect band gap, which is about 0.5 and 0.23 eV, as determined using the generalized gradient approximation (GGA) and the localdensity approximation (LDA), respectively. 13 Zakutayev et al. reported the indirect fundamental band gap of Cu 3 N as 1.0 eV with the combination of the GGA and the Coulomb interaction term U d (Cu) = 5 eV and GW quasiparticle energy calculations. 14 The position of the charge state of the defect can be in question of uncertainty by this estimation. It is known that the GGA and LDA underestimate the band gaps because of the heavy d-element of Cu and self-interactions. For improving the band gap, the LDA + U approach can be employed, which can improve the band gaps 15 than those in previous theoretical reports. 16 In this study, we have used the DFT computational approach for studying the crystal structure of cubic Cu 3 N. The band structure is explained with an indirect band gap calculation applying the LDA + U approach. Among the corrective approaches used to solve the DFT electronic band gap problem is the DFT + U correction method to mitigate this self-interaction error, which adds a Hartree−Fock-like term to localize the electron states such as 3d or 2p orbitals.
When compared with alternative approaches, DFT + U correction has been demonstrated to be reliable than the other methods, however with a vital advantage of significantly lower computational cost. By effectively correcting the electronic structure of the studied system while using the U correction, further accurate predictions of intermolecular interactions and formation energies could be reached. 17 The optical properties are studied with the help of a photon energy simulation technique. In this work, the Cu 3 N thin film is grown experimentally by the DC magnetron-sputtering process. The X-ray diffraction (XRD) analysis along with optical band gap measurements are performed at room temperature. The experimentally obtained optical constants are also calculated from ellipsometry results. Our contribution to the research of the Cu 3 N material attempts to take a different approach to compare and contribute to the study of theoretical and experimental results about the structural and optical properties.

METHODS
2.1. Computational Details. Computational simulations have been done using a DFT 18 -based plane-wave pseudopotential approach. All the computations are carried out using the Cambridge Serial Total Energy Package (CASTEP) 19 performed with Material Studio 8.0. 19,20 The 3D cubic structure of Cu 3 N belongs to the space group Pm3̅ m (no. 221), which is illustrated in Figure 1a. The lattice parameter of Cu 3 N is a = b = c = 3.837 Å, α = β = γ = 90°. The cubic structure of the unit cell contains six Cu atoms, whose fractional coordinates are (0, 0.5, 0.5); (0.5, 0, 0.5); and (0.5, 0.5, 0). The fractional coordinate of N is (0.5, 0.5, 0.5), which is in the center position of the Cu molecules. Figure 1b shows the first Brillouin zone of the Cu 3 N crystal, which has highsymmetry points G, M, R, and X connected by lines of pink color. The calculated Cu−N and Cu−Cu bond lengths are 1.99 and 2.82 Å, respectively. LDA with the Ceperley−Alder− Perdew−Zunger functional has been used for evaluating the exchange−correlation function. 20−22 The wave function is expanded as much as 440 eV of plane-wave cutoff energy. To make certain the standards of convergence for the electronic characteristic calculation and geometry optimization, 8 × 8 × 8 k-points were applied for Cu 3 N. To describe the electron−ion interaction, Vanderbilt-type ultrasoft pseudopotential has been used. The Broyden−Fletcher−Goldfarb−Shanno relaxation plan is useful for optimizing the structure. The structure cell and atomic relaxations are conducted as long as the recurring forces are beneath 0.02 eV. Geometrical search engine optimization was executed making use of the full vitality at 5 × 10 −6 V/atom (at an optimum force of 0.01 eV/Å and a maximum tension of 0.02 GPa) as well as the highest atomic displacement of 5 × 10 −4 Å.
2.2. Thin-Film Deposition and Characterization. Copper nitride films are prepared by the DC magnetronsputtering process. The 2″ sputter target was made of oxygenfree copper with a purity of 99.9%. The films are deposited on quartz glass substrates for optical characterization and XRD measurements. All substrates are washed well and ultrasonically cleaned in acetone. The vacuum chamber is evacuated to a base pressure of less than 10 −5 Pa by a turbo molecular pump. The working gas with the enclosed sputter chamber was 99.999% pure N 2 . The N 2 gas flow rate is varied between 3.5 and 4.0 sccm. The chamber pressure during the magnetron operation was maintained at 1 Pa. Typical discharge power during the sputter deposition was 100−130 W (discharge voltage 325 V, plasma current 0.4 A). The deposition took place at room temperature and with electrically floating substrates. The films were deposited for 30 min on a quartz glass substrate. After deposition, the films were taken out of the chamber and employed for further characterization.
2.3. Film Characterization. The crystalline structure of the deposited Cu 3 N thin film is examined by XRD with Cu Kα 1 radiation. The measurements were carried out using a Bruker D8 ADVANCE X-ray diffractometer with a step size of 0.05°. Optical transmission studies were carried out to estimate the band gap of the Cu 3 N film using a UV−vis double-beam spectrophotometer (PerkinElmer) at a step length of 2 nm in the wavelength range between 300 and 1100 nm. The Cu 3 N sample is placed in front of the sample beam and the identical glass substrate was placed in front of the reference beam. The ellipsometric measurements have been performed through a spectroscopic ellipsometer S2000 (Rudolph Research) for calculating the optical constants with data analysis software WVASE (Woollam).  ACS Omega http://pubs.acs.org/journal/acsodf Article R. The k-points are sampling points in the first Brillouin zone of the material, the specific region of reciprocal-space, which are usually called the Γ points. The maximum value of the conduction band and the minimum value of the valence band are situated on the R and M bands. The calculated indirect band gap is found to be 1.4 eV on applying the LDA + U approach, which is much close to our experimental value (as discussed later in the optical band gap analysis). It is known that the GGA and the LDA underestimate band gaps because of the heavy d-element of Cu and self-interactions. For improving the band gap, the LDA + U approach has been employed and we obtained an improved band gap [15] than previous theoretical reports. 16 Figure 2b shows the total and partial densities of states (DOSs) of Cu 3 N. Among the three regions, −17 to −15 eV is related to N 2s, −8 eV is related to N 2p, and the wide valence band at −5 eV is related to Cu 3d. Therefore, strong hybridization has occurred between Cu 3d and N 2p orbitals, which dominates the valence band due to antibonding states near the valence band M. The conduction band is dominated by a very small amount of Cu 3p and N 2p. It is observed from Figure 2b (total DOS) that the intensity of N is very small because the Cu 3d orbital dominates the valence band. There is no difference between the intensities of Cu and N for total DOS, as shown in Figure 2b. A noticeable improvement has been observed in the band gap and electronic structure compared with the other theoretical reports. 23,24 The molecular orbital of the Cu 3 N films is illustrated in Figure  2c,d. The frontier molecular orbital theory says the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) have significant appearance in chemical reactions. The high kinetic stability and occasional chemical reactivity are shown because of the large HOMO−LUMO energy gap. 25 Figure 3 shows the distribution of electronic charges of the optimized Cu 3 N structure. The calculated value of chargedensity-mixing amplitude is about 0.5 and the spin-densitymixing amplitude is about 2. A negligible deformation is observed between the Cu−N bond, which is seen from Figure  3a (2D view) and Figure 3b (3D view). The average bond length between N and Cu is calculated to be 1.914 Å and the average bond length of the Cu−Cu bond is calculated to be 2.706 Å.

Optical Properties.
Optical spectroscopy is the most useful and prominent characterization in modern technology to understand the energy band structure and dielectric properties of solid materials. The photon energy with different frequencies is employed on Cu 3 N to obtain the transmittance plot, refractive index, dielectric function, and electrical conductivity. All these simulation plots are determined using the formalism developed by CASTEP. 26,27 Figure 4a shows the transmittance plot of cubic Cu 3 N as a function of photon energy E. The peak value is observed at an energy of 1.2 eV and the transmission has become almost saturated after a photon energy of 2.8 eV. The optical transmittance of Cu 3 N majorly depends on the N 2 flow rate and substrate temperature. 28 The Cu content has also influenced the transmittance as it acts as a light-scattering center. 30 Cu 3 N films are transparent in the IR region and also show interband transitions in the visible region. 28 The transmittance of Cu 3 N at such an energy level is very much favorable to be used as an optical recording media. 30 Figure 4b shows the refractive index of the Cu 3 N structure with real and imaginary parts. The maximum value of the real part (concerned with scattering) and the imaginary part (concerned with absorption) is bound at photon energies of 0.5 and 1.0 eV, respectively. The peak value of the real and imaginary part attains values of 2.25 and 1.52, respectively, after which it decreases to become almost saturated at photon energies of 2.0 and 3.0 eV, respectively. The obtained refractive index value is very much comparable to those published by  In the design of optical reflectors, such semi-

ACS Omega
http://pubs.acs.org/journal/acsodf Article conductor optoelectronic devices require a refractive index typically between 2.25 and 2.5 for ambient light propagation. 32 The dielectric function explains the response of the semiconductors based on their band structure to the electromagnetic radiation by the interactions of photons and electrons. 33 The dielectric function can be determined using the frequency-dependent functions, ε(ω) = ε 1 (ω) + iε 2 (ω), which are closely connected to the band structure of a material. The imaginary part of dielectric function ε 2 (ω) is acquired in the momentum matrix elements between the occupied and unoccupied electronic states using the following equation 20 where e is the electronic charge, u is a vector which defines the polarization of the incident electric field, ω is the light frequency, and ψ k c and ψ k v are the conduction and valence band wave functions, respectively. The real dielectric function can be obtained from the Kramers−Kronig transformation equation where p signifies the principal value of the integral. The dielectric functions of Cu 3 N are illustrated in Figure 4c. The static dielectric constant can be obtained from the real part at zero photon energy. It is observed that the static dielectric constant of Cu 3 N is about 15. The imaginary part at zero photon energy is found to be about 6. The real part decreases exponentially with increasing photon energy, and it became almost saturated after a photon energy of 2.8 eV. The imaginary part reveals the band energy at which the photon energy begins and which occurs at a minimum direct band gap. 23 Figure 4d shows the photon energy-dependent electrical conductivity of the Cu 3 N structure. The real part has exponentially increased to 3.6 × 10 4 S/m and gets saturated. The imaginary part increases to 1.5 × 10 4 S/m and gets saturated from 1.9 eV. These values nearly satisfy the previous reports by Du et al. 34 The increase in photon energy leads to the formation of excitons which dissociate into free charges. The dependence of the Cu content readily influences the electrical conductance behavior reflecting the percolation mechanism. 34 In the Cu 3 N structure, Cu resides in the center and acts as an electron donor and thereby increases the electrical conductivity. 35 The semiconducting nature of Cu 3 N is observed in many reports, where conductivity is explained with an indirect transition from the R point in the valence band to the M point in the conduction band. 36,37 The n-type conductivity of Cu 3 N often increases with the effect of improved crystallinity with increasing grain size. 30 The XRD patterns (discussed later) of the deposited Cu 3 N films have revealed the polycrystalline nature, which satisfies the increasing conductivity of the films.
3.2. Experimental Results. 3.2.1. XRD Analysis. Figure 5 shows the XRD patterns of the deposited Cu 3 N thin film with indexed peaks. The polycrystalline single phase of Cu 3 N is observed from the diffraction peaks at θ = 23.20°(100), θ = 40.64°(111), and θ = 47.46°(200). 8,38 There is no evidence of pure Cu, as observed in the XRD patterns. The Cu 3 N(100) plane has the highest intensity owing to the distinct synthesis process adopted here and follows the principle of preferential growth because of the lowest crystal-free energy. 9 A detailed study on the XRD patterns of Cu 3 N films is reported in our previous study, where a comparison with the experimental data is shown with simulated patterns. 38 The microstructure of the Cu 3 N thin film is studied based on its lattice constant (using eq 4), which is calculated from interplanar spacings using Bragg's law (eq 3) Here, d hkl is the interplanar spacing of particular Miller indices, n = 1 (order of diffraction), λ is the wavelength of X-rays, and θ is the diffraction angle. The average lattice constant a of the Cu 3 N thin film acquired is 0.3812 nm. The value of the lattice constant is very much close to those of previous reports on the deposition of Cu 3 N film by the magnetron-sputtering technique 9 and to the simulated results obtained in this research. There is no preferred orientation in the XRD pattern as the nonstoichiometric Cu 3 N film has resulted in a lattice constant in the range between 0.375 and 0.384 nm. 10 Pierson has explained the effect of the N 2 flow rate on the stoichiometric phase of the Cu 3 N film, which is in good agreement with our result. 39 The formation of a Cu 3 N phase takes place because of Cu−N bonding as a result of the absorbing N 2 atom being placed in the Cu lattice. Both the atoms of Cu (having a high kinetic energy) and N 2 (having a comparatively lower kinetic energy) contribute to the formation of the Cu 3 N crystal structure. 8 3.2.2. Optical Band Gap Analysis. Figure 6a shows the UV−vis absorption spectrum of the Cu 3 N thin film with its corresponding Tauc plot (Figure 6b) to measure the optical band gap. The photon absorption in the Tauc plot is defined by the Tauc relation in eq 5 In this equation, α is the absorption coefficient, h is the Planck constant, ν is the photon frequency, E g is the band gap energy, ACS Omega http://pubs.acs.org/journal/acsodf Article and B is a constant. The x factor depends on the nature of the electron transition and is equal to 1/2 or 2 for the direct and indirect transitions, respectively. The optical energy band gap (E g ) is determined using the curve of (αhν) 1/2 versus photon energy hν by extrapolating the line to the abscissa of hν according to the standard plot technique of Tauc et al. 40 The indirect allowed transitions of the Cu 3 N semiconductor are reported by Dorranian et al. 41 The measured optical band gap (E g ) at room temperature is 1.44 eV, which is very close to those in previous reports 6,8 along with the calculated or theoretical band gap. The tangential line (position) drawn in the Tauc plot is very much optimistic with an error bar approximately equal to ±0.2 eV. It depends on the position on the curve where the line started. The absorption started at and around 580 nm with a sharp fall up to 700 nm. A drastic absorption is observed in between 600 and 800 nm. At 900 nm, the absorption attains a maximum value (far-infrared region). Figure 7 shows the optical constants, viz., refractive index (n) and extinction coefficient (k) as a function of wavelength (λ) of the deposited Cu 3 N films. Ellipsometric measurements are performed on a spectroscopic ellipsometer S2000 (Rudolph Research). Data analysis was made with software WVASE (Woollam).
The optical constants are derived by the ellipsometric measurements from a fit using the Cauchy dispersion relation (polynomial). In this process, the real part of the refractive index is about 1.48 in the UV region (300−400 nm), which gradually increased with a peak value of 2.15 at 730 nm and saturated up to 800 nm with the same value, and at 900 nm, it became 2.10. The extinction coefficient (k, imaginary part) is 1.85 around 350 nm, which gradually increased up to 530 nm and attained a maximum value of 2.02. Thereafter, it starts to decrease (with small saturation up to 570 nm) gradually up to 900 nm. The peak value of the real and imaginary parts attains values of 2.15 and 2.02, respectively, whereas in theoretical approximation, these values are 2.25 and 1.52, respectively. Both the values of n and k are comparable with those of simulation studies as a function of photon energy (already discussed) and also with those of the previous report. 32 The optical properties show that the visible light is absorbed maximum in between 500 and 800 nm (Figures 6 and 7), but after 800 nm, it shows a transmission property.
The theoretically simulated value of the band gap energy is about 1.4 eV, which is comparable with the experimentally obtained optical band gap energy (1.44 eV) by UV−vis absorption spectroscopy ( Figure 6). The measured band gap here with a lattice constant greater than 0.38 nm (as discussed in XRD Analysis) is very true with the indirect semiconductor Cu 3 N phase. 38,39 The dependence of optical band gap varies from the energy level defect, electron transition of Cu atoms, to electron transition at Cu 3 N grain boundaries. The semiconducting nature of the Cu 3 N film is related to the electron-density distribution, which is influenced due to the presence of weak localization electrons in the Cu 3 N lattice with covalent bonding. 9 It also depends on the mobility of Cu and N atoms contributing to Cu 3 N film growth. The kinetic energy of Cu is more than that of N 2 while reaching the substrate material; N 2 often reacts with Cu and then reaches the substrate. Consequently, the Cu content is very much responsible in determining the growth and conductivity of the Cu 3 N films.
It is known that the GGA and LDA underestimate band gaps because of the heavy d-element of Cu and self-interactions. For improving the band gap, the LDA + U approach has been employed, and we obtained an improved band gap than the previous theoretical reports. There is a qualitative difference in the LDA and LDA + U approach to give an approximation on the ground-state energy. The perturbative LDA + U calculation is the Hubbard (U) potential correction, which has a selfconsistent unperturbed value. The strong Coulomb interaction of localized electrons can be treated by an additional Hubbardlike term in the LDA approach, which is not correctly described by LDA and GGA. The Coulomb interactions are especially strong for d and f electrons, but it can be important for p-localized electrons too. However, a huge variety of exchange−correlation functionals are involved in molecular cases that need a sophisticated calculation.
The trace of N 2s electron states is found to have a −15 eV HOMO−LUMO gap, whereas it is −8 eV in the case of N 2p electrons (Figure 2). A small HOMO−LUMO energy gap is essential for low chemical stability because adding electrons to some high-lying LUMO and/or elimination of electrons from the low-lying HOMO are energetically favorable in almost any potential reaction. 42,43 The low HOMO−LUMO gap in this material predicts highly stable thin films. N 2s shows low chemical stability in the formation of Cu 3 N. The presence of 2s electrons with a high HOMO−LUMO gap creates interstitial defects, and because of these defects, the thin film exhibits the polycrystalline property. XRD results also show the polycrystalline single phase of Cu 3 N film. The metal component Cu 3p shows a very low-intensity valence band (∼1 eV). Cu 3d

CONCLUSIONS
The Cu 3 N film has been deposited by the DC magnetronsputtering technique. The lattice parameter of the simulated film (0.3837 nm) is comparable with that obtained from the deposited film (0.3812 nm) by the XRD method. The deposited films are polycrystalline with a single Cu 3 N phase. Strong hybridization of Cu 3d and N 2p orbitals in the nearvalence band region (M) takes place because of their antibonding states. The DOS evidenced a negligible deformation of Cu−N bonding. The calculated indirect band gap of the Cu 3 N film from the first-principles approach with an additional Hubbard term (LDA + U) is 1.4 eV, which is close to the obtained value of 1.44 eV from the UV−vis absorption spectrum. The real part of the refractive index attains a peak value of 2.15, which is in well agreement with the theoretically estimated value of 2.25. The imaginary part of the refractive index shows a difference in the peak value of 0.5 with respect to theory and experiment.