V Density Functional Theory(DFT) study
It is essential to understand the electronic structure, dielectric and optical properties of DAT2 for optoelectronic applications and hence theoretically, we performed Density Functional Theory(DFT). Wien2k software (version 18.2). was used for the present work. It utilizes a hybrid, full potential, linearized augmented plane wave (LAPW) and augmented plane wave + local orbitals (APW + lo) schemes for solving the Kohn-Sham (KS) equations of the total energy of crystalline solids9. The crystal structure details were obtained from CCDC Database (CCDC-27087). The muffin-tin spheres of radii 1.05, 1.10, 0.61 were assigned by Wien2k program for C, N and H atoms respectively. The nearest neighbor bond length factor of 2, local density approximation (LDA) with −5.0 Ry cut-off energy, 100 k -points,RK max of 3.0 were used in the calculations. The self-consistent field (SCF) calculations were performed using the iterative procedure with energy convergence criterion of 0.1 mRy/unit cell. After SCF calculations converged, the electronic band structure, density of states, dielectric and optical properties were computed for DAT2.
Fig. 4 shows the calculated electronic band structure of DAT2. It is clear from the Fermi level shown by dotted lines (at 0.0 eV) that the maximum of valence band lies at the symmetry points in the k-space, Gamma, Z and Y. Whereas, the bottom of the conduction band lies at X and C. The corresponding energy gap is 1.5 eV. Thus, (DAT2) has an indirect band gap of about 1.5 eV. This is comparable with the experimental band gap value obtained from DRS analysis (~1.69 eV). It is to be noted here that, in general, the underestimation of band gap energy by DFT calculations is a known fact. The calculated total density of states (DOS) of DAT2 is shown in Fig. 5 which is consistent with the electronic band structure.
Kramer-Kroning relation : The real part (\(\varepsilon_{r}\)) and the imaginary part (\(\varepsilon_{i}\)) of the dielectric constant (\(\varepsilon\)) are related as
\(\varepsilon\ =\ \varepsilon_{r}+\ j\varepsilon_{i}\)—————- (2)
Where, \(\varepsilon_{r}=n^{2}-k^{2}\)and\(\varepsilon_{i}=2\text{nk}\). Here n and k are refractive index and extinction coefficient respectively. Dielectric contributions arises either because of intra or inter-band transitions. The indirect inter-band transitions arise from scattering of phonons and their contribution is negligible to the dielectric function when compared to direct inter-band transitions.
Fig. 6 depicts the real and imaginary parts of dielectric permittivityεr and εi of monoclinic DAT2 for crystallographic X and Y-axes. The first excitation peak at 1.6 eV is due to the excitation of an electron from the occupied valence band to the unoccupied conduction band. From the graph, it is clear that both real and imaginary part of dielectric constant increase with the increase of photon energy upto bandgap value of 1.69 eV. The imaginary part of the dielectric permittivity increases linearly with a higher value than the real part. The dielectric loss is maximum at 1.5eV. The static dielectric constant is 23 for XX direction and 18 for YY direction. The DAT2 shows dielectric behaviour until 1.7 eV and thereafter it behaves as metallic nature. The low value of dielectric constant proves DAT2 as a suitable candidate for ultrafast photonics applications. Further, from the imaginary part of dielectric constant, reflectivity R (ω ), optical conductivityσ (ω ), refractive index n (ω ), extinction co-efficientk (ω ), absorption co-efficientI (ω ) and energy loss functionL (ω ) 9 were calculated.
Reflectivity R(ω): When electromagnetic radiation is incident on a material medium, it oscillates the electron clouds, and if there is no scattering, the radiation gets reflected totally. Above plasma frequency, reflection declines and transmission start to dominate. Fig. 7a represents the reflectivity spectraRxx (ω ) andRyy (ω ) as a function of energy E . The static values of reflectivity are 65 % for XX and 55% for YY direction at 1.7 eV. Three peaks were seen at 4.5, 6.7 and 9.5 eV. These peaks occur due to inter molecular excitations. For higher energy (14 eV) both XX and YY direction show 50% reflectivity for DAT2.
Optical conductivity σ(ω): The electronic states of materials can be studied using optical conductivity. A perfect dielectric is a material that has no optical conductivity. According to the multi-component model, the real part of the optical conductivity (σ) of the crystal can be calculated using the following relations
\(\sigma(\omega)\ =\frac{\omega}{4\pi\ }\ \text{Im}\left(\varepsilon\right)\)———– (3)
The optical conductivity is calculated to be 1.5 eV, and it increases rapidly due to the high density of electrons. Several peaks are observed which corresponds to bulk plasmon excitation. The main peak was located at 1.7 eV, where the optical conductivity value is about the order of 1015(Siemens/m) The variation in the real and imaginary part of optical conductivity is depicted in Fig. 7b. The conductivity decreases as the photon energy E increases. The real part of conductivity shows maximum peaks at 2.5, 5eV and 7 eV.10
Refractive index n( \(\mathbf{\omega}\)): The refractive index valuesare required for estimation of
phase matching condition for efficient Terahertz generation. Fig. 8a shows the refractive index as a function of photon energy (E ). The static refractive index (zero photon energy) has two values as principal axes namely 2.1 for (XX) and 2.3 for (YY) direction. Then(ω) tends to increase linearly and attains maximum in the visible region (1.5 eV) and decreases in UV region. Refractive index attains a minimum around 5 eV. The extinction coefficientk(ω) shows peaks at 1.6 eV. The refractive index values in each crystallographic direction indicate that DAT2 is an optically anisotropic and suitable for phase-matched THz applications.
Electron Energy Loss, L(w): Fig 8b describes the energy loss of a fast electron traversing in DAT2. The peaks in the EEL(ω) spectra represent the characteristics associated with the plasma resonance, and the corresponding frequency is the so-called plasma frequency, above which the material is a dielectric (ε1(ω)>0) and below which the material behaves like a metallic compound (ε1(ω)<0). The energy loss is minimum at 4 eV. The electron energy loss spectrum shows five distinct peaks at 2.2, 3.2, 5.8, 8 and 9.8 eV. The maximum energy loss leads to a decrease in reflectivity.