As shown in Fig. 1, each proposed structure has been relaxed using the LBFGS geometry optimization algorithm [51] while ensuring that each atom has a residual force less than the value of 0.05 eV/Å. The average bond lengths of the optimized structures are shown in Table-I.
The imaginary dielectric constant and refractive index are plotted with relation to energy in Figs. 3 and 5 whereas; the absorption coefficient plotted against wavelength and energy is shown in Fig. 4 for each pristine and adsorbed WSe2 nanostructure. Analyzing optical transmission data yielded the optical absorption coefficient spectra. Figure 4 shows a plot of the absorption coefficient for adsorbed WSe2 nanostructures, indicating that the optical absorption spans across the entire visible spectrum.
We calculated the binding energies (B.E.) of alkali-halogen atoms adsorbed WSe2 nanostructures to test their stability which are characterized by EB ={Eadsorbed – (EPristine monolayer+ Ealkali/halogen)} / N, where Eadsorbed, EPristine monolayer and Ealkali/halogen represents the total energies of adsorbed nanostructure, pristine WSe2 monolayer and halogens/alkali atoms, respectively, and N represents how many atoms are in an adsorbed nanostructure. For stable adsorbed structure, the binding energies should be as low as possible. The calculated binding energies per atom for Lithium(Li),Sodium(Na), Potassium(K), Rubidium(Rb), Cesium(Cs), Fluorine(F), Chlorine(Cl), Bromine(Br), Iodine(I), and Astatine(At)atoms adsorbed WSe2 are 123 eV, 197 eV, 120 eV, 122 eV, 130 eV, 438 eV, 343 eV, 360 eV, 266 eV, and 1451.62 eV, respectively. All structures attained negative binding energies during the experiment, demonstrating structural stability. Based on the amount of negative energy, it follows that the resulting adsorbed structures have high Vander-walls-forces of molecular attraction.
Electronic Properties
Figure 2 depicts the electronic band structure of a pristine WSe2 monolayer. The Brillouin-zone route is represented as A–C–B–Г–Y–X–Z–L as a representation of the unit cell's symmetrical points. The electronic direct bandgap obtained is 1.769 eV as well as the indirect bandgap is 1.589 eV, which is in consistence with the results reported in [52]. Dielectric values presented in Fig. 3 demonstrate that the bandgap in alkali-halogen adsorption monolayer has metallic features with negligible bandgaps.
Optical properties
There are two parts of the dielectric constant: a real and an imaginary portion (see Fig. 3). The dielectric constant illustrates a dielectric material's efficiency in terms of energy storage. When light passes through a structure, its dielectric constant describes how it interacts with it. A dielectric constant's imaginary part (ε2) is utilized to calculate charge excitation-based energy absorption in nanostructures, while the real part (ε1) is used to resolve anomalous dispersion and polarization effects.
It is crucial to estimate the optical absorption of 2D structure from the imaginary components of the observed dielectric function displayed along with ‘xx’, ‘yy’, and ‘zz’ directions of structures as illustrated in Fig. 3 [53]. Consequently, only xx-dimensional plots of imaginary components are examined, from which results for the other two directions can also be obtained. For pristine monolayer WSe2, a peak is obtained between 2 eV and 3 eV with the strongest one at ~ 2.56 eV, as shown in Fig. 3(a). The dielectric peaks can be analyzed similarly for other adsorbed nanostructures as shown in Fig. 3. The majority of adsorbed structures have dielectric peaks between 0 and 1 eV. Combined with the decrease in binding energies of excitons in the system, the dielectric function peaks indicate that absorption may take place in the system. Alkali metals and halogen adsorbed WSe2 nanostructures were studied as functions of energy and wavelength. The electronic bandgap structure, dielectric function, refractive index, and absorption coefficient were calculated and plotted in Figs. 2, 3, 4 and 5, respectively. We obtained the optical absorption coefficient spectrum by analyzing optical transmission measurements. According to Fig. 4, the absorption coefficient for both halogen-adsorbed WSe2 nanostructures and alkali metal-adsorbed WSe2 nanostructures expands over the entire visible spectrum. Optical absorption is determined by inter-band electronic transitions. The electronic inter-band transition between occupied and unoccupied states in semiconductor occurs as a result of photon-electron interaction.
The photon energy and the dielectric constant define the absorption coefficient. Photons are absorbed by semiconductors with a high absorption coefficient, causing electrons to enter the conduction band.
Pristine WSe2 monolayers absorb strongly over the entire UV region as well as the blue region of the visible spectrum, and weakly in another area of the visible spectrum as well as the entire IR region. Figure 4(a) shows that the absorption coefficient of WSe2 monolayer has negligible change in the range 0–1.8 eV of energy, and then starts to increase with increasing photon energy within window of 1.8–5 eV and achieve peak within the range 3–3.2 eV of energy.
The K, F, Cl, Br, and I adsorbed structures displayed a shift in the absorption peak towards to the higher energy of the spectrum as seen in the plot for absorption coefficient in Fig. 4, whereas the remaining structures showed peaks at lower energies. Blue shifts occur in structures adsorbing Li, Na, and Cs atoms, with absorption peaks shifting towards lower energies, whereas red shifts occur in remaining adsorbed structures with absorption peaks shifting towards higher energies in the absorption spectrum.
The adsorbed WSe2 structures with chlorine, bromine, and iodine have a much wider spectrum range indicating stable absorption in the visible part of the spectrum as represented in Fig. 4(h), 4(i), and 4(j), respectively. The optical absorption peaks in all adsorbed nanostructures are lower than that in pristine WSe2, although it is significant to mention that the absorption is dispersed over the whole visible region, which is needed for optoelectronics applications. For adsorbed WSe2 structures with sodium and cesium, the absorption remains almost the same as in pristine WSe2 as shown in Fig. 4(c) and 4(f).
Additionally, the ‘xx’ and ‘yy’ tensors in K, Cs, Cl, Br, I, and As adsorbed WSe2 structures nearly overlap, with ‘zz’ remaining distinct. This validates the isotropic/anisotropic property of these adsorbed structures [54]. The dielectric constants (ε1, ε2) have been used to determine the refractive index as in given Eq. (6) for all pristine and adsorbed structures considered. As presented in Fig. 5, the refractive index (η) is computed with respect to the photon energy for all structures along with the ‘xx’, ‘yy’, and ‘zz’ direction. For pristine WSe2 monolayer, the refractive index increases with energy between 0 and 2.1 eV. The adsorbed WSe2 structures have a peak value of refractive index peaks in the range of 0–0.5 eV. There is a correlation between the peak value of refractive index and the dielectric constant (as shown in Figs. 3 and 5) indicating that the refractive index follows patterns in the dielectric constant as well as the absorption coefficient. Large absorption would be stimulated in regions with high refractive indices, implying that light would be confined for a significantly longer amount of time, which in turn would enhance photon absorption in that spectral range.
A lower absorption would lead to a lower refractive index, as would be predicted by the dielectric function (ε2). The deterioration in the value of refractive index with photon energy indicates that the adsorbed WSe2 structures are dispersed normally.