 Open Access
 Total Downloads : 2
 Authors : P.K. Saini, D. Singh, D.S. Ahlawat
 Paper ID : IJERTCONV1IS01014
 Volume & Issue : AMRP – 2013 (Volume 1 – Issue 01)
 Published (First Online): 30072018
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Electronic band structure and elastic properties of CdSe by DFT
P.K. Saini1,3, D. Singp* , D.S. Ahlawat3
1Department of Applied Sciences, J.C.D.M. College of Engineering, Sirsa, India
2Department of Applied Sciences, Panipat College of Engineering &Technology, Panipat ,India
3Department of Physics, Chaudhary Devilal University, Sirsa, India
*corresponding author: dharmbir@yahoo.com
Abstract
The electronic band structure and elastic properties of cubic (B3) cadmium selenide CdSe have been reported using the full potential linearized augmented plane wave (FPLAPW) method. In this approach, generalized gradient approximation (GGA) and EngelVosko generalized gradient approximation (EVGGA) were used for the exchange correlation potential. The calculated band structure and elastic properties have been compared with the previously reported results. The calculated results are found to be in good agreement with earlier reported results.
Keywords: Band structure, elastic properties, FPLAPW, DFT, GGA

Introduction
In recent years, there has been a renewed interest in various properties of IIVI binary semiconductor compounds and alloys [14]. Among these materials, CdX (where X= S, Se & Te) semiconducting compounds are found to be very important materials due to their technological applications particularly in optoelectronics devices. There have been several experimental and theoretical studies on these materials [58]. For example, K. O. Magnusson et.al. studied electronic band structure of CdSe experimentally by angle resolved photoemission [7]. Similarly, SuHuai et al. studied the structural and electronic properties of binary CdX (X= S, Se, Te) semiconductors using LDA [8]. Further, Ab initio calculations based on normconserving pseudopotentials and density functional theory using LDA, have been performed to investigate elastic, electronic and lattice dynamical properties of cadmium chalcogenides [9]. In these studies, LDA based theoretical calculated results of band gap are found to be lower than the experimental observed value of band gap which is quit common with such LDA based calculation[10].
This above mentioned problem of underestimating the LDA based calculated band gap may be solved using EV GGA [11, 22] which motivated us to take up the problem with EVGGA approach to improve the band gap. Since, we have carried out similar computational work for various materials with different methods [1215], particularly, recently for some IIVI semiconducting compounds [1618 ], and so, in the present work, as a part of this series of semiconducting compounds, we have investigated electronic band structure and elastic properties of binary semiconductor compound CdSe using full potential linearized augmented plane wave (FPLAPW) method within a framework of
density functional theory (DFT) with GGA and EVGGA. The paper is organized as follows: Section 2 describes the method of calculation. Further, results and discussion are presented in section 3. Finally, results are concluded in section 4.

Method of Calculation
As mentioned above, the calculations are performed using the FPLAPW method within DFT, as implemented in the WIEN2K code [19]. The exchangecorrelation potential has been calculated using GGA within the parameterization of PerdewBurkeErnzerhof (PBE)[2021]. Moreover, the EngelVosko GGA formalism is applied so as to optimize the corresponding potential for band structure calculations to improve the band gap [11]. In these calculations, the unit cell was divided into two regions. The spherical harmonic expansion was used inside the non overlapping spheres of muffintin radius (Rmt) and the plane wave basis set was chosen in the interstitial region (IR) of the unit cell. The Rmt for Cd and Se were chosen in such a way that the spheres did not overlap.
To get the total energy convergence, the basis functions in the IR were expanded up to Rmt_Kmax = 7.0 inside the atomic spheres for the wave function. The maximum value of l were taken as lmax = 10, while the charge density is Fourier expanded up to Gmax = 12 a.u1. The atomic positions for Cd (0, 0, 0) and Se (1/4, 1/4, 1/4) were taken in cubic CdSe B3 phase. For electronic and elastic properties calculation we have used 72 kpoints in the irreducible Brillouin zone for structural optimization. The selfconsistent calculations are considered to be converged only when the calculated total energy of the crystal converged to less than 104 Ry. In order to obtain the elastic constants of CdSe compound with cubic structure we have used a numerical firstprinciples calculation by computing the components of the stress tensor for small strains, using the method developed by Charpin and integrated it in the WIEN2K code [19].

Results and Discussion

Band structure
To get the equilibrium lattice parameter we fitted Murnaghan equation of state which gives the value of equilibrium lattice parameter 6.21 A0. Using this equilibrium lattice parameter, we have calculated and plotted the band structure of cubic B3 phase of CdSe. This selfconsistent scalar relativistic band structure of CdSe is obtained within both the GGA and EV GGA schemes. The electron dispersion curves along the high
symmetry directions in the Brillouin zone for B3 phase at ambient pressure are plotted in Fig. 1(a) &(b) within the GGA and EVGGA schemes respectively. As mentioned in earlier section, it is well known fact that the LDA and the GGA usually underestimate the energy band gap [810, 22 23]. This is mainly due to the fact that LDA & GGA have simple forms which are not sufficiently flexible for accurately reproducing both exchangecorrelation energy and its charge derivative. By considering these shortcoming, Engel and Vosko constructed a new functional form of the GGA which was able to reproduce the exchange potential better at the expense of less agreement as regards the exchange energy[11]. This approach, which is called the EV GGA, yields a better band splitting and some other properties which mainly depend on the accuracy of the exchange correlation potential. The band structure calculated using the GGA and the EVGGA for CdSe was similar except for the value of their band gap which was higher within the EV GGA.
Fig. 1(a) Band structure using GGA; (b) band structure using EVGGA
Material
Calculations
Direct band gap
( eV) at point
CdSe
This work
1.12
Theory (Ref.
[24])0.76
Exp.(Ref.[25])
1.90
Table 1. The calculated directband gaps of CdSe (within EVGGA) compared with the earlier reported theoretical and experimental work.
The calculated band structure was found well in agreement with the already available experimental results on band structure [7]. In order to indicate the overall profile of the different bands of CdSe, we have identified the bands with their corresponding electronic states and the Fermi energy (EF) is identified by the dotted line. The lowest lying band shown in the graph arises mainly from Cds valence states. The upper valence bands lie above this band are due to p states with the top occurring at the point. The conduction band arises mainly from the Cdd state with the minimum energy occurring at X points.
Further, the calculated band structures of CdSe indicate a direct band gap equal to 1.12 eV at pont. The calculated result of band gap (within EV GGA formalism) is found better than earlier reported theoretical result and found to be in good agreement with earlier reported experimental result as shown in the table 1. However, the calculated result of the band
(a)
(b)
gap (within EV GGA formalism) is still lower as comparatively to that of earlier reported experimental result, but this may be due to the fact that the calculation has been carried out at 0 K while the experiment has been performed at room temperature.

Elastic properties

As mentioned in section 2, in order to obtain the elastic constants of CdSe compound with cubic structure (B3) phase, we have used a numerical firstprinciples calculation by computing the components of the stress tensor for small strains [9]. A cubic crystal has only three independent elastic constants, C11, C12 and C44. Hence, a set of three equations is needed to determine all the constants. Therefore, only three types of strain must be applied to the crystal structure. The first equation involves the bulk modulus B of the crystal. For a cubic crystal, the bulk modulus can be defined as
B= (C112C12)/3 — (1)
The second equation is associated with the relationship between C11 and C12 and can be obtained by applying a volume conserving tetragonal strain to calculate the shear elastic constant, CS = (C11C12)/2 . The strain tensor is given as
0
0 –
0
0
–(2)
0
0
2 /(1 2 )
Here, is the deformation parameter.The total energy of the system under the tetragonal shear strain is given by
E( ) E0 2CsV0 2 O( 4 ) — (3)
Where E0 is the energy of unstrained state,
Cs is the cubic shear constant,
V0 is the zero strain volume.
And the last equation is associated with C44. A parabolic fit to the strain energy vs. strain 2 yields the result of shear
elastic constant. To determine the pure shear elastic constant,
agreement with the already available experimental results on band structure. The electronic band structure reveals the existence of band gap 1.12 eV at point. Our calculated band gap using EVGGA approach is found close to the experimental value as compared to other theoretical calculations. The little difference with earlier reported experimental result is explained with the fact that the
C44
we use volume conserving tetragonal strain tensor which
calculation has been carried out at 0 K while the experiment
has been performed at room temperature. For the elastic
is given by the following relation
properties, our calculated results are found in similar to the other available reported results. The predicted values of
0 / 2
0 –(4)
elastic constants (C11, C12, and C44) and bulk modulus B in
/ 2 0 0
0
0
2 /(4 2 )
which yields the total energy as following
phase B3 obey generalized elastic stability criteria.
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Table.2 The Calculated elastic constants Cij (GPa), bulk modulus B (GPa) and Kleinmann parameter for CdSe in the B3 structure
Method
C11
C12
C44
B
CdSe
This
work
51.7
41.3
55.1
44.7
0.85
Theory
(Ref27)
65
49
Theory
(Ref. 9)
88.1
53.6
27.4
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