A density functional theory (DFT) employing generalized gradient approximation (GGA) have been used to study the electronic and optical properties of AlSb. The transition along Γ point predict this material to be a direct band-gap semiconductor. The presence of band gap 1.0-2.0 eV shows great interest due to their band gap matching with the optimized incident photon energy (UV-range). Also the presence of hybrid bands at the maxima of the valence region, that is the combination of the sharp and the flat bands enhances the electron transports. Thus AlSb can be a better prospectus for solar cell devices.
Keywords: Semiconductor, band gap, GGA, GGA-SO, FPLAPW .
The Aluminium based binary compounds, AlX (X=N, Sb, In etc.) having zincblende structure  are of scientific interest due to their wide band gaps and can be exploit in semiconductors technology. The other importance of these materials are high Curie-temperature, low densities, extremely high thermal conductivities, large resistivity, electronic and optical applications . So far these compounds have been studied by many methods with different approximations to produce the accurate description of electronic properties [3-6]. Soma  was successful in computing the total energy and bulk modulus of III-V and II-VI tetrahedral covalent compounds using Ashcroff’s empty core potential within local HeineAbarenkov models . D.P. Rai et al. have also studied the BeX (X=S, Se &Te) type semiconductor using mBJ potential which gives improved band gaps compared to GGA . Others have also reported the improved semiconductor band gaps by using the mBJ potential [10, 11, 12] which are larger than the one obtained from the standard functional such as the generalized gradient approximation (GGA) .
Experimental lattice constants were used for volume optimization to obtain optimized lattice parameters. In this work, we have employed the FP-LAPW method  within the framework of the density functional theory (DFT)  as implemented in the WIEN2k code  that has been shown to yield reliable results for the electronic of AlSb.
The zinc-blende structure of AlSb with the Wyckoff positions Al (0,0,0) and Sb(1/4,1/4,1/4) is presented in Fig. 1(a). A plot of total energies as a function of AlSb is shown in Fig. 1(b).
The curve is obtained by fitting the calculated values of energies to the Murnagan’s equation of state . The variations of the lattice constants are in compliance with the size of atoms in their compounds. The calculated lattice constants and bulk modulus are presented in Table 1.
Table 1: The calculated lattice constants,band gaps and bulk modulus
|Lattice constant (a)Å||Bulk modulus(GPa)||Energy gap (eV)|
|6.20||6.134 ||56.20||59.30[2,4]||1.50(GGA)||2.6 |
The electronic structures (DOS and band structure) calculated within GGA within FPLAPW method are presented in Fig.2. The DOS below 0 eV is the valence band due to the completely filled states on the other hand, the conduction band above 0 eV is due to the unoccupied states. In the valence band the majority contribution is from the Sb-p states whereas conduction band is due to the Al-p states. The lowest sharp band in the conduction region is due to the electron effective mass. Whereas along the same symmetry the maximum of valence band is a hybrid of flat and sharp band. The flat band represents the low electron mass. The combination of flat and sharp band enhances the electron transport, as the flat band is responsible for the higher value of electron electrical conductivity at the same time the sharp band gives the Seebeck coefficient. Thus the hybrid band is more effective for solar cell materials. The maximum energy of valence band and the bottom of the conduction band occur at Γ, the energy gap is a direct band gap. The measure of the semiconductor band gap is around 1.50 eV within GGA [see Fig. 2]. The calculated band gap obtained from GGA is less than the experimental value 2.6 eV , this due the deficiency of GGA in treating the core electronic states. The inclusion of Spin Orbit effect has reduced the band gap with degenerate Sb p-states in the core and semi-core region [see Fig.2(right) blueline]. The calculated band gaps are compared with the previous results and presented in Table 1.
Materials micro-morphology can be visualized from the TEM analysis. TEM image of the Cu24In16Ga4Se56 is showing non uniform agglomerated nanocrystals (see Figure 3 (a)) with the distinguishable grain boundaries. While, the relatively smaller crystal size and high order agglomeration is appeared (See Figure 3 (b) ) for the Cu24In16Ga7Se53 composition. This might be due to higher order phase mixing of the alloying elements within the configuration. The TEM image analysis gives the overall particle size around 40 to 60 nm.
Moreover the alloying elemental presence and their distributions are demonstrated from the EDS and mapping. Figure 4 represents the EDS patterns and their elemental mapping for the Cu24In16Ga4Se56 composition. Existence of the every alloying elemental peak in their compositional ratio (± 2 %) reveals the appropriate material configuration.
We have also calculated the optical conductivity and energy loss function (EEL) using equations 1 & 2 respectively.
where ε1(ω) and ε2(ω) are the real and imaginary parts of the dielectric function respectively.
The optical conductivity and electron energy loss (EEL) function calculated within GGA are shown in Fig. 3. The real part of the dielectric function represent the transmitted amount of light whereas the imaginary part of the dielectric function represents the amount of light interacted or absorbed by the material medium (atoms) to initiate the electron transition from valence band to conduction band. The Spectral peak (2.8-4.2 eV) in the optical response is due to the electrical dipole transitions from valence band to conduction band. The importance of maximum electron transitions at that energy range indicate that the material is optically active at ultra-violet (UV) range. The sudden rise of the optical conductivity curve somewhere at 1.45 eV [see Fig. 3 (left)] can be compare with the energy band gap [see Fig.3(Left-black-line)]. The EEL is maximum at the higher photon energy (12-13) eV. The maxima in EELS related to collective oscillation of valence electrons (Plasmon excitations). The efficiency of the solar cell materials with the variation of band gap of semiconductor is presented by fitting the parabolic equation . The efficiency of the solar cell materials with the variation of band gap of semiconductors is presented in Fig 3(right).
From the results of DOS and band structures we can conclude that Zinc blende AlSb is a direct band gap (1.45/1.50 eV) semiconductor within both GGA+SO and GGA respectively. The direct band gap has a technological importance due to band matching with the incident photon energy. Also the presence of lowest sharp band in the conduction region and the maximum hybrid band in the valence region enhances facilitates the electron transport. Thus this material can be a better prospectus for solar cell devices. The other important features are the maximum optical conductivity at lower photon energy and the maximum electron energy loss function at higher energy, makes better candidate for optoelectronic devices as well.