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Effects of in-plane tensile strains on structural, electronic, and optical properties of CdSe Zeyad A. Alahmed* Department of Physics and Astronomy, King Saud University, Riyadh 11451, Saudi Arabia

a r t i c l e i n f o

a b s t r a c t

Article history: Received 21 February 2013 Accepted 29 March 2013 Available online 10 April 2013

First-principles density functional theory was used to investigate effects of in-plane strains on the structural, electronic, and optical properties of wurtzite cadmium selenide (CdSe). The results of this work show some interesting properties of this material under ﬁnite strains that do not exist in the bulk unstrained regime. The structural deformation produced by increasing the in-plane strain, including the internal parameter u, was examined. The result shows that the structure undergoes a phase transition at a strain of 9.3% due to an extraordinary increase of the internal parameter u. By analyzing the electronic band structure using the modiﬁed BeckeeJohnson approximation (mBJ), a directeindirect band gap transition at an in-plane strain of 9.3% was found. Additionally, optical dielectric constants, reﬂectivity, and refractive index were calculated at different values of the strain. These results indicate that, by controlling the CdSe biaxial in-plane lattice constant (for example, by epitaxial growth on an appropriate substrate), the electronic and optical properties can be tuned for speciﬁc device applications. Ó 2013 Elsevier Masson SAS. All rights reserved.

Keywords: Cadmium selenide DFT Strain Wurtzite CdSe Electronic band structure Optical properties

1. Introduction CdSe has received considerable attention because of its possible technological applications. Because CdSe has a direct band gap w1.84 eV [1,2], it is utilized for a number of applications such as photo-detectors, photovoltaic devices, light-ampliﬁers, lasers, and sensors for gas detection [3e6]. The tunable synthesis of CdSe nanostructures suggests the possibility of enhancing their material properties, making them good candidates for new applications in nanotechnology in the areas of light emitting diodes, photovoltaic, photonic, and optoelectronic devices and sensors [7e12]. Nanostructures containing CdSe such superlattices and heterostructures have been grown by different deposition methods such as metallorganic chemical vapor deposition (MOCVD) [13], molecular beam epitaxy (MBE) [14], pulsed laser deposition (PLD) [15], and atomic layer deposition (ALD) [16]. Extensive theoretical and experimental studies have shown an enhancement of several properties of CdSe when it is used in core/ shell QD nanocrystal. Peng and co-workers [17] have synthesized wurtzite CdSe/CdS core/shell nanocrystal with 3.4% bulk lattice mismatch. These nanocrystals show 50% increase of the photoluminescence quantum yield and an increase in the photostability.

* Tel.: þ966 14676615. E-mail address: [email protected] 1293-2558/$ e see front matter Ó 2013 Elsevier Masson SAS. All rights reserved. http://dx.doi.org/10.1016/j.solidstatesciences.2013.03.021

Zhan et al. [18] have synthesized CdSeS/ZnS core/shell QDs by employing microwave irradiation technique. They showed that CdSeS/ZnS core/shell QDs signiﬁcantly enhanced luminescence and photostability than that of CdSeS core QDs. The large mismatch 12% between ZnS and CdSe lattice parameters causes an elastic deformation that changes their optical and structural properties [19,20]. In addition, the fabrication of a ternary alloy containing CdSe has gained the interests of many researchers as a successful technique to tailor the band gap. Firszt et al. [21] reported the possibility of tuning the band gap, the complex dielectric function, and refractive index of Cd1xBexSe and Cd1xMgxSe ternary alloy. Noor and Shaukat [22] calculated the electronic and optical properties of MgxCd1xX (X ¼ S, Se, Te) in zinc-blende structures. They showed that the band gaps of these alloys are direct and increase with increasing x composition. Because this material can be fabricated and used under a large lattice mismatch, its electronic and optical properties are expected to change due to the deformation of the structure resulting from the strain. The effects of a lattice mismatch or biaxial in-plane strain on the properties of structures have motivated researchers to understand its roles on different structures of semiconductors. As demonstrated by Barruaud et al. [23], strain can be employed to enhance the electron mobility of silicon-on-insulator by a factor of 2. Tahini et al. [24] investigated the effects of strain on the band gap of Ge, and they found that strains can play important roles in introducing transformations of band gap energy from indirect to

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Table 1 Properties of CdSe in wurtzite structure compared to previous experimental and theoretical results, including lattice parameters (a, c/a and u) and the band gap energy Eg. Parameter a ( A) c/a u Eg (eV) B (GPa) a b c d

Ref. Ref. Ref. Ref.

This work

Experimental

Other cal.

4.2757 1.6295 0.3759 2.1 57.09

4.2985a, 4.300b 1.632a, 1.630b 0.375a 1.84a, 1.83b 53b

4.2717c 1.6336c 0.3756c 0.41d 57.58d

[1]. [35]. [4]. [38].

direct. Strained wurtzite ZnO, which has the same structure as CdSe, has been studied in detail in Ref. [25]. They showed that inplane strains can play essential roles in affecting numerous properties such as structural response, polarization, band gap, and electron mobility. They reported a phase transformation at strain of 6.8% from direct to indirect band gap. A recent theoretical work by Guoqiang et al. [26] has further investigated the relaxation behavior of lattice and internal parameters of ZnO thin ﬁlm under in-plane strains in the range of 3 to 3%. They showed that strains have a strong impact on the internal parameters and thus the electronic structure. Additionally, it was found that applying strain on the structure can reduce the Poisson ratio, decrease the piezoelectric effect, reshape the band dispersion at the G point, and reduce homogeneity of charge distribution between the two types of ZnO bonds [26]. Mandal [27] has reported full atomistic classical molecular dynamics simulations of strain induced phase transition in the wurtzite structure of CdSe nanowires. He showed that the wurtzite structure transforms into a ﬁve-fold coordinated h-MgO structure under uniaxial strain along the c-axis. The inﬂuence of lattice strain on the properties of wurtize CdSe is still poorly understood. For example, it is unclear how the strain alters the chemical bonds of wurtzite structure of CdSe although the electronic properties strongly depend on these bonds. Additionally, the effects of in-plane strain on the electronic band structure are unknown though it is crucial for optical applications. Besides, to improve the optoelectronic applications of CdSe, more information about the variation of its optical properties under

Fig. 1. Change in total energies with c/a ratio for different in-plane strains.

Fig. 2. The strain energy differences DE as a function of a/a0.

in-plane strain is required. Thus, analyzing the effects of in-plane strain on structural, electronic and optical properties of wurtzite CdSe is critical to enhance its use in several applications. In this work, the author has theoretically investigated the impact of biaxial in-plane tensile strains on wurtzite CdSe properties, including structural response, the electronic band structure, electronic charge density, optical functions, reﬂectivity, and refractive index. All electron full potential linearized augmented plane wave (FP-LAPW) was used in this work. The results of this work show some interesting properties of CdSe under ﬁnite strains that do not exist in the bulk unstrained regime and can lead to promising applications. The next section describes the calculated methods. The results of in-plane strain effects on structural and relative properties are illustrated in Section 3, and Section 4 summarizes the results of this work. 2. Theoretical methods The present results were obtained using density functional theory (DFT) [28] based on the all-electron FP-LAPW method and

Fig. 3. The bond length u and c/a ratio versus in-plane strains.

Z.A. Alahmed / Solid State Sciences 21 (2013) 11e18

5

13

5

2c

1c

1c

EF

0

-5

-10

A

Energy(eV)

Energy(eV)

2c EF

0

-5

-10

L M

A

H K

A

L

M

A

H

K

Fig. 4. Calculated electronic band structures for the value of strain as (a) h ¼ 0 and (b) h ¼ 9.3%.

implemented in WIEN2k code [29]. In FP-LAPW calculation, the minimum radius of the mufﬁn-tin (MT) spheres (RMT) values for Cd and Se atoms were assumed to be 1.9 and 1.66 a.u., respectively. These values were chosen carefully to avoid the overlap of RMT in the selected range of biaxial tensile strain. In these values, there is no charge leakage from the core of the atomic spheres. The exchange and correlations effects were treated ﬁrst by local density approximation (LDA) [30] to optimize the atomic positions. At the equilibrium volume of the crystal at each set of in-plane strain, LDA, the PerdeweBurkeeErnzerhof generalized gradient approximation (GGA) [31], the EngeleVosko (EV-GGA) [32], and the modiﬁed BeckeeJohnson method (mBJ) [33] were used for electronic properties. The cutoff of the wave functions for the plane wave expansion was decided by the maximum modulus for the reciprocal lattice vector Kmax as 7/RMT. The angular momentum quantum number lmax ¼ 10 and Fourier expanded up to Gmax ¼ 12 (a.u.)1 were used for the change density. The self consistency for CdSe was obtained by 396 k-points in the irreducible wedge of the ﬁrst Brillouin zone (IBZ) where the total energy is stable within 105 Ry. The structure of CdSe used in this calculation is wurtzite structure (B4),pand ﬃﬃﬃ the lattice vectors p ofﬃﬃﬃ its unit cell are deﬁned as a1 ¼ að1=2; 3=2; 0Þ; a2 ¼ að1=2; 3=2; 0Þ; and a3 ¼ c(0,0,1). The unit cell contains two Cd atoms and two Se atoms. The Cd atoms are located at rðCd1 Þ ¼ 0 and rðCd2 Þ ¼ ð1=3Þa1 þ ð1=3Þa2 þ ð1=2Þa3 . Se atoms are located at rðSe1 Þ ¼ u a3 and rðSe2 Þ ¼ ð1=3Þa1 þ ð1=3Þa2 þ ð1=2 þ uÞa3 . Parameter u characterizes the distance between the collinear CdeSe in which the Cd and Se atoms are laid directly above each other along the c-axis. The in-plane strain is applied perpendicular to the c axis and deﬁned as h ¼ hx ¼ hy ¼ (a ao)/ao, where a and ao are the lattice constants of unit cell with and without applied strain. The author considers biaxial tensile strain in the range from 0 to 16%. In each set of in-plane strains, the total energy calculation versus the c/a parameter was carried out with free relaxation of its internal parameters using converging forces less than 1 mRy/a.u. on the atoms. To come over the well known underestimation of band gap energy by LDA and GGA methods [34], the energy band gap was calculated using mBJ which improves the calculation and produces energy band gap that is in good agreement with experiments.

3. Results and discussion 3.1. Effects of strain on structural properties The optimized lattice parameters of unstrained wurtzite CdSe are calculated, and the results, a ¼ 4.2757 A, c/a ¼ 1.6295 and u ¼ 0.3759, are in good agreement with previous works as listed in Table 1. For strained CdSe, the total energy with respect to c/a for different in-plane strains is shown in Fig. 1. At a ¼ ao, the structure has a parabolic relationship for E versus c/a. As the strain increases, the minimum of the total energy shifts toward higher energy. It can be seen in Fig. 1 that two minima appear for strains larger than h ¼ 8%. The ﬁrst minimum is at c/a ¼ 1.4, at which the structure is

Fig. 5. Direct energy gap GVBM GCBM and in-direct energy gap HVBM GCBM transitions with respect to a/a0.

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Z.A. Alahmed / Solid State Sciences 21 (2013) 11e18

more stable than that in the second minimum, which occurs at c/ a ¼ 1.22. For a strain of htr ¼ 9.3% (a ¼ 1.093ao), the two minima occur at c/a ¼ 1.35 and 1.20, and they almost have the same total energy. At larger strains of h > 9.3%, the structure becomes more stable at the second minimum. In addition, the parabolic relationships in the second minima have larger gradients than those in the ﬁrst minima for each in-plane strain. Fig. 2 shows the differences in total energies DE between the unstrained equilibrium structure Eo and the relaxed structures under in-plane strain Eh. Two different regions with parabolic relationships are revealed. The ﬁrst region (A) is from zero to 9.3% in-

plane strain, and the other region is (B) for in-plane strains larger than 9.3%. The gradient of DE in region (A) is lower than that in region (B), which indicates that the structure in region (A) has low sensitivity to the c/a deformation and is more stable than region (B). The structural characteristics of the two regions can be understood by looking at the lattice parameter c/a and the corresponding total energy. Fig. 3 shows the c/a ratio resulting from various inplane strains. A remarkable change of c/a caused by in-plane strain is found at a ¼ 1.093ao. In addition to the change of the parameter c/a, relaxation of the internal parameters including u,

70

a=ao a=1.093 x ao

60 DOS(States/eV)

50 40 30 20 10 0 -10

0.3

a=ao

0 Energy (eV)

5

10

0.3

(Cd-s) (Cd-p) (Cd-d)

0.2 0.15 0.1 0.05

(Se-s) (Se-p)

0

5

0.2 0.15 0.1 0.05

0

0 -10

-5

0

5

10

-10

-5

Energy (eV)

0.3

10

Energy (eV)

0.3

a=1.093 x ao (Cd-s) (Cd-p) (Cd-d)

a=1.093 x ao (Se-s) (Se-p)

0.25 DOS(States/eV)

0.25 DOS(States/eV)

a=ao

0.25 DOS(States/eV)

DOS(States/eV)

0.25

-5

0.2 0.15 0.1 0.05

0.2 0.15 0.1 0.05

0

0 -10

-5

0 Energy (eV)

5

10

-10

-5

0 Energy (eV)

5

10

Fig. 6. (a) Calculated total density of states (TDOS) for both h ¼ 0 and 9.3%. Calculated partial density of states (PDOS) for (b) Cd-s,p,d at a ¼ ao, (c) Se-s,p at a ¼ ao, (d) Cd-s,p,d at a ¼ 1.093 ao and (e) Se-s,p at a ¼ 1.093 ao.

Z.A. Alahmed / Solid State Sciences 21 (2013) 11e18

which represents the separation between each Cd and Se atom laid directly on top of each other along the c direction, plays an important role in making strained structures stable. This change in the u parameter leads to a lengthening of the bonds between Cd and Se when vertically oriented by increasing the in-plane strain, as shown in Fig. 3. An extraordinary increase in bond length is found as the in-plane strain reaches h ¼ 9.3% and then becomes constant for larger strain. O atoms show signiﬁcant displacement. They move to the center of the c/a ratio. Because the off center displacement of O atoms is reduced by increasing the strain, a reduction of the spontaneous polarization is expected in this material with large strain. 3.2. Electronic properties The author has calculated the band structure at various inplane strains. Fig. 4(a) and (b) present the band structure of unstrained CdSe and at an in-plane strain of 9.3%, respectively. The unstrained CdSe has a direct band gap energy of 2.1 eV at the G point. This is in good agreement with the experimental result [35] (see Table 1). The indirect band gap at H is 3.2 eV. At strain of 9.3%, an indirect band gap energy of 0.7 eV is observed at H. Additionally, another variation of 1.2 eV on the valence band edge can be seen at L point due to the strain. The variation of the band gap energy with respect to the in-plane strain can be seen in Fig. 5. As the in-plane strain increases from h ¼ 0e9.3%, the maximum variation of the direct band gap energy reaches 0.4 eV. However, the band gap energy between the conduction band minimum (CBM) at G and the valence band maximum (VBM) at H shows a linear decrease as the strain increases from 0 to 9.3%. Also, it is noticed that strain induced a sharp change of 1.0 eV at the value of 9.3%. The energy level G2c of unstrained conduction band is reduced by the strain and becomes the lowest conduction band G2c < G1c at strain 9.3%. More insight about the electronic structures can be obtained from analyzing the total density of states (TDOS) and its partial components (PDOS) of Cd and Se atoms. Fig. 6 illustrates the calculated TDOS and PDOS for both h ¼ 0 and h ¼ 9.3%. In Fig. 6(a), the total density of both structures have some variation including the region around the Fermi energy. Following the ﬁgure, the two structures have two main valence regions. The ﬁrst energy band for h ¼ 0 extends from 8 to 7 eV, and the highest peak in this region is centered at 7.5 eV. This band originates mainly from the d orbital of Cd with mixture of s and p states of Se as shown in Fig. 6(b) and (c). This band shifts by 0.5 eV toward lower energy when applying strain of h ¼ 9.3%. The second valence band region for h ¼ 0 extends from 4 eV to the Fermi energy level, and it is mainly composed of Cd d/s and Se p with mixture of Cd p and Se s. While in the case of h ¼ 9.3%, the band starts from 4.4 eV as shown in Fig. 6(d) and (e). Above Fermi energy, the conduction band region starts from 2.2 eV for h ¼ 0 and is shifted by 1 eV toward the Fermi energy with the in-plane strain due to the shift of s state of Cd atom. The variation of the charge transfer of the system with the inplane strain can be seen from the charge density of the system. A comparison between contour plots of the charge density on the lattice plane (110) for both unstrained CdSe and for in-plane strain of h ¼ 9.3% are illustrated in Fig. 7(a) and (b), respectively. It can be noticed that new electron disruptions introduced by rearrangement of atomic positions caused by deformation along the c/a direction. The electron density without strain shows a strong distribution of electron density around Cd compared to that around Se. Also, it can be seen that the distribution of electron density for Se is not symmetric, and the electron densities between Se1eCd2 and between Cd2eSe2 are high. By contrast, Fig. 7(b) shows that the electron densities between Cd1eSe1 and between Cd2eSe2 become

15

weaker because of the displacement of Se atoms toward the center of the c/a direction. Additionally, the electron density between Se1eCd2 and between Se2eCd1 without strain is stronger than that at h ¼ 9.3%. 3.3. Optical properties Since in-plane strain can affect the electronic band structure of CdSe, it is useful to evaluate the interband optical functions [36] to distinguish between unstrained and strained structures. The wurtzite CdSe has two principal complex tensor components; 3 xx(u) and 3 zz(u). The imaginary part components 3 2xx(u) and 3 2zz(u) of the optical function dispersion are shown in Fig. 8(a) for different set of h to be able to see the variation with respect to in-plane strains. Following the top panel of this ﬁgure, one can see that the spectra of the xx component has two main regions starting from 4 to 6.5 eV and from 6.5 to 9 eV. The highest peak of the ﬁrst region occurs at 6 eV for h ¼ 0, and by increasing h to 9.3% the peak moves to 5 eV and its height increases by w30%. The highest peak in the second region occurs at 7 eV for h ¼ 0. For strain h 9.3%, the peak moves toward 7.5 eV, and its height reduces by w32%. The bottom panel of Fig. 8(a) shows the variation of 3 2zz(u). For h ¼ 0, there are three peaks centered at 5, 7, and 8 eV. These peaks shift toward lower energy with increasing the strain up to 9.3%. For strain h 9.3%, the height of the ﬁrst peak signiﬁcantly increases by w75%. Comparing between xx and zz elements for both h ¼ 0 and 9.3%, Fig. 8(b) reveals that optical constants are anisotropic for strain 9.3%. Also, the component 3 2zz(u) is dominant for h ¼ 0 from 4.5 to 5.5 eV while the component 3 2zz(u) and 3 2xx(u) are dominant from 4 to 6.5 eV and from 6.5 to 9 eV for h ¼ 9.3%, respectively. The

Fig. 7. Contour plot of the charge density in (110) plane for CdSe at (a) h ¼ 0 and (b) h ¼ 9.3%.

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Z.A. Alahmed / Solid State Sciences 21 (2013) 11e18

10 8

=0 =8% =9% =9.3% =10% =12%

2xx

mBJ

6 4

=0 =8% =9% =9.3% =10% =12%

2zz

mBJ

0

5

12

10 Energy (eV)

=0 mBJ

8

15

( )

0 14 12 10 8 6 4 2 0

2

2

( )

2

20

1 xx 1 zz

=9.3% mBJ

8

1 xx 1 zz

R( )

1

( )

0

4 0 -4 0

5

10 Energy (eV)

15

20

2xx 2zz

=0 mBJ

2xx 2zz

=9.3% mBJ

0

4

-4 12

14 12 10 8 6 4 2 0 14 12 10 8 6 4 2 0

5

0.5 0.4 0.3 0.2 0.1 0 0.5 0.4 0.3 0.2 0.1 0

10 Energy (eV)

20

Rxx Rzz

=0 mBJ

Rxx Rzz

=9.3% mBJ

0

15

5

10 Energy (eV)

15

20

Fig. 8. (a) Changes in the imaginary part 3 2(u) of the optical function’s with respect to the in-plane strain. (b) Calculated the imaginary part of the optical function 3 2xx(u) and 3 2zz(u) for h ¼ 0 and 9.3%. (c) Calculated the real part of the optical function 3 1xx(u) and 3 1zz(u)for h ¼ 0 and 9.3%. (d) Calculated the reﬂectivity R(u)for h ¼ 0 and 9.3% using mBJ.

real parts 3 1xx(u) and 3 1zz(u)are obtained using the Kramers-Kronig (KK) relations [37] and shown in Fig. 8(c). It is found that for h ¼ 0 the optical constants 3 1xx(0) ¼ 3 1zz(0)are equal to 4.9. For h ¼ 9.3%, the elements 3 1xx(0) and ε1zz(0) are 5.4 and 5.9, respectively. The ﬁrst peaks for xx and zz-components occur at 2.74 eV without strain. However, under strain, the height of the peaks increase by about 30% and 33% for xx and zz elements, respectively. The highest peak for zz-component without strain occurs at 4.74 eV and shifts toward lower energy 4.28 eV in the case of in-plane strain with signiﬁcant increase in height. The reﬂectivity spectra along x and z axis are illustrated in Fig. 8(d). At zero energy, both Rxx(0) and Rzz(0) are equal to 0.142 for unstrained CdSe, and they increase to Rxx(0) ¼ 0.158 and Rzz(0) ¼ 0.173 for h ¼ 9.3%. From energy 4.5e 6 eV, the zz element of the reﬂectivity is larger than Rxx without strain. After applying strain, a substantial increase of the Rzz and the range extends from 3 to 7 eV. Another difference is that the height of the highest peak for h ¼ 0, which occurs at 8 eV, decreases by 15% and shifts to 9 eV. The refractive index dispersions for both h ¼ 0 and h ¼ 9.3% are shown in Fig. 9(a). The maximum values of the refractive indices for unstrained structure occur at 4.69 eV (nxx ¼ 2.86) and 4.8 eV (nzz ¼ 3.16). For strained CdSe, the highest peaks occur at 4.58 eV (nxx ¼ 2.938) and 4.34 eV (nzz ¼ 3.785). It can be noticed that the anisotropy increases signiﬁcantly in the case of strain 9.3%. The calculated values of nxx(0) and nzz(0)for unstrained CdSe are both 2.21. For h ¼ 9.3%, the refractive indices nxx(0) and nzz(0) are 2.32

and 2.42, respectively. One can calculate the birefringence from the difference between the extraordinary and the ordinary refractive indices Dn(u) ¼ ne(u) no(u), where ne(u) and no(u) are the refractive indices along the c-axis and perpendicular to the caxis, respectively. The unstrained CdSe has no birefringence Dn(0) ¼ 0 at zero frequency while for h ¼ 9.3% the birefringence is equal to 0.1 at u ¼ 0. These changes are essential to be considered for fabricating CdSe as an optical material under large in-plane strain. The calculated absorption is shown in Fig. 9(b). The ﬁgure shows that one noticeable variation between the absorption spectra of h ¼ 0 and 9.3% occurs in the range of 4 eVe7 eV, where the height of the zz element increases by 40% compared to that of h ¼ 0. Also, it can be seen that the strain shifts the highest peak of h ¼ 0 from 8.4 to 9.12 eV. The energy loss function is presented in Fig. 9(c). The main distinction between the energy loss functions for both h ¼ 0 and 9.3% is that the multi peaks from 13 eV to 16.5 eV of h ¼ 0 become ﬂat. Fig. 9(d) shows the optical conductivity s(u)for both cases h ¼ 0 and 9.3%. There are three strong peaks without strain at 6.2 eV (5.34), 7.03 (7.03), and 8.2 eV (8.2 eV) for sxx (szz). The value of the highest peak at 7.03 eV is equal to 8502.07 U1 cm1. For strain h ¼ 9.3%, the anisotropy becomes large in the range of 3e12.5 eV. Also, the highest peak in the case of h ¼ 0 signiﬁcantly decreases to 5800 U1 cm1, and the ﬁrst peak at 4.72 eV becomes the highest with a value of 9034.83 U1 cm1.

Z.A. Alahmed / Solid State Sciences 21 (2013) 11e18

=0 mBJ

3

nxx nzz

200

100

=9.3% mBJ

3

nxx nzz

4

n( )

0

( ) (10 / cm)

1

2 1

50 0 200

xx zz

=9.3% mBJ

150 100 50

0

0

0

5

2

10 Energy (eV)

15

20

0

8

0.5

2

1.5

(1/ .cm) x10

-3

4

=9.3% mBJ

10

15

20

Lxx Lzz

1 0.5

xx zz

=0 mBJ

6

1

0 2

5

Energy (eV)

Lxx Lzz

=0 mBJ

1.5

L( )

xx zz

=0 mBJ

150

2

17

0 8

xx zz

=9.3% mBJ

6 4 2 0

0 0

5

10 Energy (eV)

15

20

0

5

10

15

20

Energy (eV)

Fig. 9. Calculated (a) the refractive index n(u), (b) the absorption a(u), (c) the energy loss function L(u), and (d) the optical conductivity s(u)for both h ¼ 0 and 9.3% using mBJ.

4. Conclusions The author has investigated the behavior of structural, electronic, and optical properties of wurtzite CdSe semiconductor under tensile in-plane strains using density functional theory. The result shows that the material undergoes a structural phase transition for in-plane strain of 9.3% due to the signiﬁcant displacement in the parameter u. As a result, the system changes from polar to non-polar material. Interestingly, the result demonstrates that at the same strain value the band band gap energy transforms from direct to indirect. Additionally, with large strain CdSe becomes an anisotropic crystal. The result shows that strain induced large variation of the refractive index, reﬂectivity, and optical conductivity. This work can serve as a tool to tune optical properties of CdSe, which can be useful in speciﬁc device applications. Acknowledgments This work was supported by grants from Research Center of College of Science at King Saudi University. References [1] [2] [3] [4] [5]

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