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.