**3. Results and discussions**

#### **3.1 Ground state**

The position of Be atom is the corner (0, 0, 0), while the Se atom takes place at (1/4, 1/4, 1/4) and (1/3, 2/3, 1/4) for zinc blend and NiAs phases. **Figure 1(a)** gives

*Contribution to the Calculation of Physical Properties of BeSe Semiconductor DOI: http://dx.doi.org/10.5772/intechopen.102888*


**Table 1.**

*Lattice parameters, bulk modulus, and its pressure derivative for BeSe in zinc blend and NiAs structures within GGA-PBE, LDA, and HSE hybrid functional.*

the plots of total energy versus unit cell volume, where the zinc blend phase is more stable. **Figure 1(b)** visualizes the effect of pressure on formation enthalpy. The two enthalpy-pressure diagrams show a transition region around 55 GPa [1]. We report in **Table 1** that the lattice parameters, bulk modulus, and its pressure derivative are calculated with GGA, LDA, and HSE hybrid. Our results agree well with experimental measurements [15] and theoretical data [4, 16–25]. The HSE hybrid underestimates the lattice parameters.

#### **3.2 Elastic constants and mechanical parameters**

**Table 2** includes elastic moduli of BeSe in both phases within GGA and LDA. Our elastic constants of zinc blend structure agree with theoretical values [18, 22, 26, 27]. The following relationships [28, 29] ensure the elastic stability of BeSe.

Zinc blend

$$0\left\langle \mathbf{C}\_{11} + 2\mathbf{C}\_{12}, \mathbf{0} \left\langle \mathbf{C}\_{44}, \mathbf{0} \left\langle \mathbf{C}\_{11} - \mathbf{C}\_{12}, \mathbf{C}\_{12} \right\rangle \mathbf{B} \left\langle \mathbf{C}\_{11} \right\rangle \right. \tag{1}$$

NiAs

$$\mathbf{0} \left| \mathbf{C}\_{11} - \left| \mathbf{C}\_{12} \right|, \mathbf{0} \left( \mathbf{C}\_{33} (\mathbf{C}\_{11} + \mathbf{C}\_{12}) - 2 \mathbf{C}\_{13}^2, \mathbf{0} \left( \mathbf{C}\_{44} \right) \right. \tag{2} \right. \tag{2}$$

**Figure 2** shows the dependence of elastic moduli on pressure for beryllium selenide in zinc blend and NiAs phases. We list in **Table 2** the bulk modulus, shear modulus, Young's modulus, Poisson's ratio, anisotropy factor, and BH/GH ratio. The Poisson's ratio and anisotropy factor indicate the covalent bonding and strong anisotropy in BeSe. The reported BH/GH value translates the brittle zinc blend phase and ductile NiAs structure. **Figure 3** visualizes the effect of orientation on Poisson's ratio (a) and shear modulus (b) in xy, xz, and yz planes. It can be seen that the two parameters are isotropic only in the B8 phase and in the xy plane. **Table 3** predicts the maximum and minimum values of Young's modulus, linear compressibility, shear


#### **Table 2.**

*Elastic constants Cij, Debye temperature ΘD, bulk modulus B, shear modulus G, Young's modulus EH, Poisson's ratio σH, anisotropy factor A<sup>U</sup> and ratio BH/GH for BeSe in zinc blend and NiAs structures.*

modulus, and Poisson's ratio. **Table 2** reports the Debye temperature of BeSe, which agrees with the theoretical value [26]. **Table 4** predicts elastic wave velocities along [100], [110], [111], and [001] directions.

## **3.3 Electronic parameters**

**Figure 4** shows the band structure of BeSe using GGA-PBE and HSE hybrid functional. We observe the indirect bandgap Γ-X (Γ-K) in the zinc blend (NiAs) structure. **Table 5** reports the bandgap between various symmetry points. The bandgap of BeSe in the zinc blend structure agrees with other calculations [3, 16, 23, 31]. **Figure 5** displays the dependence on the pressure of the direct and indirect bandgap. The bandgap calculated using the HSE hybrid agrees with the experimental one [3, 32, 33]. **Figure 6** shows the plots of total and partial densities of states. Se-p and Be-s orbitals are responses for the upper valence band. The first conduction band is wider for both structures and consists of Be-s and Se-p orbitals, with a small contribution of the Se-s site. The optical transition occurs from Se-p state to the Be-s site. There is a hybridization between Se-p and Be-s in the upper valence band, which translates their covalent bonding.

*Contribution to the Calculation of Physical Properties of BeSe Semiconductor DOI: http://dx.doi.org/10.5772/intechopen.102888*

**Figure 2.** *Elastic moduli versus pressure in zinc blend (a) and NiAs (b) phases.*

#### **3.4 Phonon frequencies**

**Figure 7** shows the phonon dispersion curve of BeSe in zinc blend structure. Optical (acoustic) phonons exhibit two couplets of longitudinal optical (LO)

**Figure 3.** *The orientation effect on Poisson's ratio (a) and shear modulus (b) in zinc blend and NiAs phases.*


#### **Table 3.**

*The maximum and minimum values of Young's modulus E, linear compressibility β, shear modulus G, and Poisson's ratio σ for BeSe in zinc blend and NiAs structures.*

*Contribution to the Calculation of Physical Properties of BeSe Semiconductor DOI: http://dx.doi.org/10.5772/intechopen.102888*


#### **Table 4.**

*Sound velocities for BeSe along with main directions in zinc blend and NiAs structures.*


#### **Table 5.**

*Band gaps for BeSe at equilibrium between various symmetry points in zinc blend and NiAs structures.*

**Figure 5.** *The band gaps versus pressure in zinc blend and NiAs phases.*

*Contribution to the Calculation of Physical Properties of BeSe Semiconductor DOI: http://dx.doi.org/10.5772/intechopen.102888*

**Figure 6.** *Total and partial densities of states.*

{longitudinal acoustic (LA)} and transverse optical (TO) {transverse acoustic (TA)} modes and confirm the dynamical stability of BeSe. The frequency 16.06 cm<sup>1</sup> (198 cm<sup>1</sup> ) separates optical (acoustic) longitudinal and transversal branches. The maximum of longitudinal optical phonons is at X point. **Figure 8** shows the effect of pressure on phonon frequencies ωLO and ωTO of BeSe. The equilibrium values of ωLO and ωTO at Γ point are 537 cm<sup>1</sup> and 471 cm<sup>1</sup> .

**Figure 7.** *The phonon dispersion curves.*

### **3.5 Optical parameters**

#### *3.5.1 Loss function*

We plot in **Figure 9** the loss function spectra versus wavelength for BeSe in zinc blend and NiAs structures. The high-loss region has a wavelength ranging from 42 nm to 90 nm. The low-loss function has a wavelength range less than 40 nm and greater than 90 nm. The maximum loss function reaches the value of 4.84% (4.49%) at 60.32 nm (57.25 nm) in the zinc blend (NiAs) structure. There is no loss in the ultraviolet and visible light domain.

*Contribution to the Calculation of Physical Properties of BeSe Semiconductor DOI: http://dx.doi.org/10.5772/intechopen.102888*

**Figure 8.** *The phonon frequency versus pressure at Γ point.*

**Figure 9.** *The loss function versus wavelength.*

### *3.5.2 Optical absorption*

We applied a smearing value of 0.1 to obtain more distinguishable absorbance peaks. We attribute the absorption peaks as depicted in **Figure 10** to the photo transition energies from the maximum valence band to the minimum conduction band under ultraviolet light irradiation. BeSe absorbs a maximum of ultraviolet light 331,971 cm<sup>1</sup> (335,643 cm<sup>1</sup> ) at wavelength 163.6 nm (163 nm) in zinc blend (NiAs) structure, shows narrow indirect bandgap, then it is a good candidate for photocatalysis in the ultraviolet light domain (120–400 nm).

#### *3.5.3 Optical reflectivity*

The reflectivity estimates the amount of incident light on the surface of photocatalytic material. The reflectivity of BeSe, as shown in **Figure 11**, starts at 0.007

**Figure 10.** *The absorption versus wavelength.*

**Figure 11.** *The reflectivity versus wavelength.*

and corresponds to a wavelength around 33 nm. It reaches a maximum value 0.63% (0.56%) at 149 nm (136.5 nm) in zinc blend (NiAs) structure. The reflectivity in the ultraviolet light domain (120 nm–400 nm) is 0.63% (0.56%) in zinc blend (NiAs) structure. While in the visible light (400 nm–800 nm), it is 0.43% (0.23%) for zinc blend (NiAs) phase.
