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Bandgap engineering of Cd1-xSrxO

Structural, electronic and optical properties of Cd1-xSrxO (0 \leq x \leq 1) are calculated for the first time using density functional theory. Our results show that these properties are strongly dependent on x. The bond between Cd and O is partially covalent and the covalent nature of the bond decreases as the concentration of Sr increases from 0 to 100%. It is found that Cd1-xSrxO is an indirect bandgap compound for the entire range of x and the bandgap of the alloy increases from 0.85 to 6.00 eV with the increase in Sr concentration. Frequency dependent dielectric functions {\epsilon}1({\omega}), {\epsilon}2({\omega}), refractive index n({\omega}) and absorption coefficient {\alpha}({\omega}) are also calculated and discussed in details. The peak value of refractive indices shifts to higher energy regions with the increase in Sr. The striking feature of these alloys is that Cd0.5Sr0.5O is an anisotropic material. The larger value of the extraordinary refractive index confirms that the material is positive birefringence crystal. The present comprehensive theoretical study of the optoelectronic properties of the material predicts that it can be effectively used in optoelectronic applications in the wide range of spectrum; IR, visible and UV.


Introduction
Group II-VI semiconductors have extensively studied due to their effective use in optoelectronic industry. These compounds are commonly used in many established commercial electronic and optoelectronic devices operating in blue to ultraviolet spectral regions [1][2][3][4][5][6].
Optically transparent and electrically conductive nature of CdO makes it an important member of the group. Its industrial applications are not limited to solar cells, transparent electrodes, ohmic contacts to LEDs, smart windows, optical communications, flate panel displays, phototransistors, photovoltaics, gas sensors, low-emissive windows, thin-film resistors [7][8][9][10][11][12][13] but it is also efficiently used as a high reflective compound in the infrared region while high transparent material in the visible region [11]. Bandgap of CdO is 0.85 eV, while strontia (SrO) is an insulator with bandgap of 5.71 eV [14,15]. Strontia is used as a catalyst in chemical engineering [16] and is also used in cathode ray tubes for the blocking of X-ray emission.
Knowledge of bandgap engineering and optical properties of semiconducting compounds is a promising field of study for the design of optoelectronic and photonic devices. A systematic change in the bandgap of a binary material can be achieved by the partial substitution of anion or cation of a crystal by an element of desirable properties.
In the present theoretical work bandgap of rock salt CdO is varied systematically by alloying with Sr. In order to investigate optoelectronic nature of these alloys their structural, electronic and optical properties are calculated. All calculations are based on density functional full potential linearized augmented plane wave (FP-LAPW) method with Wu-Cohen generalized gradient approximation (GGA).

Theory and calculation
The calculations are performed by FP-LAPW approach within the framework of densityfunctional theory (DFT). The exchange-correlation energy of electrons is described by GGA.
The GGA functional form Wu-Cohen is used within the wien2k package [17].
In the full potential scheme both, the potential and charge density are expended into two different basis. Within the atomic sphere the potential is expanded in spherical harmonics while outside the sphere (interstial region) it is expanded in plane wave basis. The expanded potentials are: Where E 0 is the total energy of the supercell, V 0 is the unit volume, B 0 is bulk modulus at zero pressure and B / 0 is derivative of bulk modulus with pressure.
Optical properties of Cd 1-x Sr x O are calculated using a fine k mesh of 3500 points for the present calculation. The dielectric function of a crystal depends on the electronic band structure and its investigation by optical spectroscopy is a powerful tool in the determination of the overall optical behavior of a compound. It can be divided into two parts; real and imaginary: The imaginary part of the complex dielectric function, ε 2 (ω), in cubic symmetry compounds can be calculated by the following relation [19,20]: While ε 2 (ω) is used to calculate the real part of the complex dielectric function [13,16]: Refractive index is calculated in terms of real and imaginary parts of dielectric function by the following relation: While absorption coefficient can be calculated by [20]:

III. Result and Discussion
In order to study the structural properties of Cd The substitution of Sr does not affect the indirect bandgap nature of the compound but increases the gap which is clear from Fig. 2(d). The indirect bandgap varies from 0.85 to 6.00 eV and the direct bandgap also increase from 2.8 to 6.2 eV with the increase in Sr concentration. It is obvious from the data presented in Table 2 The above relation can be used to calculate E g using values of ( )  can be observed in the form of a hump in the spectrum at a particular energies and, second; the maxima shifts to higher energy region with the increase in Sr concentration. The third important point is that the refractive index drops below unity at certain energy ranges. For a refractive index lesser than unity (v g =c/n) means that the group velocity of the wave packet is larger than c.
In other words group velocity shifts to negative domain and the medium shifts from linear to non-linear and hence the material becomes superluminal for high energy incident photons [32,33].

Conclusion
Density functional calculations are carried out for the first time to investigate structural and optoelectronic properties Cd 1-x Sr x O (0 ≤ x ≤ 1). Structure as well as bonding nature of the material significantly varies with Sr concentration. The lattice constant of the crystal increases linearly with x, except for x=0.5 because of its tetragonal rather than cubic structure.