First principles investigation of the optoelectronic properties of Molybdenum dinitride for optical sensing applications

: The electronic and optical properties of the newly synthesized Molybdenum dinitride (MoN 2 ) in the hypothetical 2H structure analogous to MoS 2 is investigated using the Density Func-tional Theory (DFT) full potential linearized augmented plane wave (FP-LAPW) method and the Modified Becke-Johnson (mBJ) approximation. The aim is to investigate the optoelectronic properties of this compound for potential optical sensing applications and compare with the capabilities of MoS 2 in this field. As compared to MoS 2 , which is a semiconductor, MoN 2 is found to be a semi metal from the band structure plots. The dielectric function, optical conductivity and the optical constants, namely, the refractive index, the reﬂectivity, the extinction and absorption coefficients are evaluated and compared with those of MoS 2 and discussed with reference to the sensing per-formance.


Introduction
The high potential of transition metal dichalcogenides (TMD) for electronic, sensing, photonic and thermoelectric device applications has been exploited this past decade and especially MoS2 a prototype TMD material has shown a lot of promise [1][2][3]. It has been studied and characterized extensively for structural, electronic, optical and transport properties both in bulk and in the 2D limit [4][5][6]. Interest in TM nitrides has been rekindled because they exhibit a number of unique and advanced catalytic properties for photo and electrochemical catalysis [7,8]. There were no layered structures in any of these studies. Layered structures provide more flexibility in doping, ease of going down to lower dimensions and materials design.
The search for layered nitrogen rich TM nitrides, particularly those of MoS2-type, led to the recent synthesis and discovery of 3R−MoN2, which has the rhombohedral MoS2 structure [9]. It was synthesized through a high P−T route of solid-state ionexchange and has shown great potential for applications in catalysis and hydrogenation. In addition, the very recent first principles study of MoN2 monolayer by Zhang et al [10] showed the 1H configuration to be the most stable among the structures considered in their study. Their study revealed the importance of 2D MoN2 as a high capacity electrode material for metal ion batteries. Further, the first principles study of Ramanathan and Khalifeh [11] has shown the 2H MoN2 to be a promising thermoelectric material.
All the above interesting results for MoN2 provide a strong motivation to study this compound. Considering that, to date no optical characterization of MoN2 has been performed; the present study is devoted to the determination of the electronic and optical properties from first principles and to look at the various possibilities for optical sensing  applications of MoN2. Since, an optical sensor measures a physical property of light and depending upon the sensor usage converts it to a readable output, it is highly essential to characterize the optical properties of the new layered material MoN2. The hypothetical 2H structure analogous to MoS2 of MoN2 is investigated using the DFT full potential linearized augmented plane wave (FP-LAPW) method and the mBJ approximation. In addition, the 2H MoS2 optoelectronic properties are determined by the same method for the sake of completeness and comparison.

Calculation details
The geometry of MoN2 is optimized using the ABINIT software program [12,13] with the generalized gradient approximation (GGA) of Perdew, Burke and Ernzerhof (PBE) PAW (projector augmented wave) pseudopotentials [14]. All the structural calculations are performed with convergence criteria of less than 1 × 10 −6 Ha for the Self Consistent Field (SCF) iterations and a threshold of less than 1 mRy/a.u. for the optimization of the geometries [15,16]. The fully relaxed MoS2 lattice constant values are taken from our previous work [6].
The optimized structures and lattice constant values are then used with the WIEN2k [17] code to perform full-potential linearized-augmented plane wave (FP-LAPW) calculation employing GGA_PBE to obtain the ground state energy and electronic properties at a 20×20×4 k-point grid. The optical properties are evaluated using denser grids of 40×40×5 with the more accurate mBJ exchange correlation of Trans Blaha (TB-mBJ).

Structural and electronic
The 2H-MoN2/MoS2 unit cells have hexagonal symmetry and consist of two stacks of 3 atomic layers; each stack consists of a Mo atomic plane sandwiched between two N/S atomic planes respectively. The atoms are bonded covalently in plane and the stacks are held together by weak Van der Waals force.
The non-magnetic state is the ground state for both the layered compounds and the structural relaxation of the system with a complete relaxation of all the atoms simultaneously gives us the equilibrium geometry. The lattice parameter a and c values of MoN2 are 3.094 and 11.975Å respectively. The lattice parameter values of MoN2 are much smaller than that of MoS2 due to the shorter bond lengths of Mo-N as compared to Mo-S. The lattice parameters for MoS2 a=3.193 and c=12.359Å taken from previous work [6] using the LDA (local density approximation) are in good agreement with the experimental values [19]

Optical Properties
The TB-mBJ proves to be an excellent choice with a 40×40×5 grid for calculating the optical properties with a high degree of accuracy for MoN2 and MoS2. This section is devoted to the presentation and discussion of the results for the dielectric function and optical conductivity. In addition, the optical constants namely the refractive index, the reflectivity, the extinction and absorption coefficients are obtained and interpreted.
The complex dielectric function (ε = ε1 + iε2) is a function of the amount of light absorbed by the material. The imaginary part of dielectric function, ε2(ω) , which represents absorption behavior, can be calculated from the electronic band structure of solids. The real part of dielectric function, ε1(ω), which represents the electronic polarization under incident light can be calculated according to Kramers-Kroing relation [20,21]. Figure 2 shows the real and imaginary plots for the dielectric function for MoN2 and MoS2 in the photon energy range of 0-14eV. We see from the plots the anisotropy of the dielectric function. The general trend is the in-plane values are almost double that of the out of plane direction and the peaks are shifted more towards the right with higher energies. The complex index of refraction of the medium N is defined as = √ = + Where n is the refractive index and k the extinction coefficient. These are depicted in Figure 3. Once again we see the anisotropy in the two directions for these optical constants. The amplitudes in the xx direction is larger and closer to the visible range for both n (ω) and k (ω) for both compounds. We notice that MoN2 has large static (ω=0) refractive index values of ~11 and 4 in the xx and zz directions respectively. In contrast the corresponding values for MoS2 are 4 and 3. The larger values of n(ω) imply higher electron density. In contrast to MoS2, MoN2 has peak extinction coefficient values at ω =0 of 4.4 and 0.9 in the xx and zz directions respectively. Both MoN2 and MoS2 show low k(ω) values in the infra red and MoS2 continues to have almost zero values upto 1.5 and 2.5eV for xx and zz directions respectively. The first maxims of MoS2 are at 3eVof the spectra and the magnitude in the xx direction almost six times larger than in the zz direction. The second k peak for zz direction is in the UV region and slightly larger than the first xx peak.
The conductivity and absorption coefficient graphs for MoN2 and MoS2 are shown in Figure 4. The graphs show for the xx in-plane direction maximum conductivity is in the UV region for MoN2 whereas for MoS2 it is in the visible part of the photon energy. The conductivity in the zz direction has peak positions in the UV region around 8 and 5eV for MoN2 and MoS2 respectively. The absorption on the other hand shows the first peak in the visible and second broader peak with a much higher magnitude in the UV region for MoN2; and a very broad peak of almost constant magnitude for MoS2 covering the visible and the UV region in the in plane xx direction. Beyond 10eV both MoN2 and MoS2 show a rise in the absorption coefficient. With respect to the zz direction there are a set of small peaks beyond the visible and a sharp maximum value peak at around 9eV of the UV region for MoN2; whereas for MoS2 the peaks are around 6, 10 and 12eV in the UV region. These characteristics confirm the suitability of MoN2 and MoS2 for visible and UV sensing applications. The reflectance is depicted in Figure 5 and we observe large static reflectance value greater than 0.7 for MoN2 that is double of MoS2 in the xx direction. In the zz direction the values are 0.35 and 0.25 for MoN2 and MoS2 respectively. The graphs show that MoN2 is a good infra-red reflector, whereas MoS2 reflects best just beyond the visible range.

Conclusions
In conclusion as opposed to MoS2, MoN2 is a semi metal. Both layered materials show anisotropy for all the optical properties with different magnitudes and peak positions, although the shapes of the graphs for the same property are similar in the two directions.
The large values of refractive index and good conductivity, absorption and reflectance results obtained reinstate the suitability of these materials for sensing applications in the visible and UV region.