Structural, electronic and optical properties of silver delafossite oxides: A first-principles study with hybrid functional

Physica B 422 (2013) 20–27

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Structural, electronic and optical properties of silver delafossite oxides: A first-principles study with hybrid functional Mukesh Kumar a,n, Clas Persson a,b a b

Department of Materials Science and Engineering, Royal Institute of Technology, Stockholm, SE-100 44, Sweden Department of Physics, University of Oslo, P. Box 1048 Blindern, NO-0316 Oslo, Norway

art ic l e i nf o

a b s t r a c t

Article history: Received 4 February 2013 Received in revised form 3 April 2013 Accepted 9 April 2013 Available online 23 April 2013

Ternary delafossite compounds are potential materials for optoelectronic devices. Employing a first-principles method, we calculate the structural, electronic, and optical properties of the silver based compounds AgMO2 (M¼ Al, Ga or In), which crystallize in delafossite structure. Our calculations show that these AgMO2 oxides have indirect band gaps and the gap energies are in the region of 1.6–3.0 eV whereas, the lowest direct band gap energies are estimated in the range of 2.6–4.3 eV. Furthermore, we find that AgMO2 compounds exhibit a strong anisotropy for the dielectric function and absorption spectra. The absorption onset for these compounds occurs well above the band gap energies. Overall, we show that the hybrid functional improves the lattice parameters and band gap energies and the calculated values are in good agreement with the experimental values. & 2013 Elsevier B.V. All rights reserved.

Keywords: Transparent conductor Electronic structure Silver delafossites Density functional theory Hybrid functional Optical properties

1. Introduction Transparent conducting oxides (TCOs) are of great interest for optoelectronic devices. They are widely used in transparent contacts in flat panel displays, touch screens, photovoltaic device and photocatalytic applications [1–5]. TCOs typically have optical band gaps greater than 3.0 eV to ensure transparency to visible light. The most common examples of TCOs are SnO2, In2O3, ZnO, and ternary oxides like AIBIIIO2 (where AI ¼Cu, Ag, Pt or Pd; BIII belongs either group IIIA or IIIB elements). Good n-type dopability is achievable in most of these compounds (SnO2, In2O3, ZnO), but p-type dopability is still difficult. However, the discovery of p-type conductivity in CuAlO2 [6] during 1997 has opened the doors to explore these ternary oxide compounds for optoelectronic applications. Later on similar properties were discovered for other compounds such as CuScO2 [7], CuGaO2 [8], CuYO2 [9], and CuCrO2 [10]. Therefore it has been great interest in ternary AIBIIIO2 compounds during the previous decade [11–23]. However, one family of these compounds i.e., copper delafossites was studied extensively [11–19], whereas the Ag delafossites have not yet been explored much [20–22]. A theoretical method especially first-principles density functional theory (DFT) calculation is of special priority in the study of electronic and structural properties of materials due to its superiority in control. The DFT studies within the local density approximation (LDA), generalized gradient approximation (GGA) are commonly

used to describe the structural, electronic, and optical properties of materials. However, these calculations (LDA/GGA) suffer from spurious self-interaction and thus in general underestimate the band gap energies. Moreover, the GGA overestimates the lattice parameters, while the LDA underestimates. Therefore these approximations limit the predictive abilities and thus it is necessary to go beyond these approximations. The previous calculations [20–22] of Ag delafossites were performed within the LDA or GGA. Therefore in this study we use a Heyd–Scuseria–Ernzerhof (HSE06) [23] functional to overcome the aforementioned problems. The HSE06 is better in these aspects and successfully describes the lattice parameters, band gap energies and total energy of the system [24,25]. In this article we discuss the crystal structure, equilibrium lattice parameters, density of states (DOS), electronic band structure, and optical properties of the Ag based delafossites by employing the first-principles DFT/HSE06 calculations. We show that HSE06 noticeably improves on the band gap energies compared to previously LDA or GGA studies. Furthermore, we find that all these AgMO2 oxides have indirect band gaps and the gap energies are in the region of 1.6–3.0 eV. In addition, AgMO2 exhibits a strong anisotropy for the dielectric function and the absorption onset for these compounds occurs well above the fundamental band gap energies.

2. Computational details n

Corresponding author. Tel.: +46 8 790 8930; fax: +46 8 20 7681. E-mail addresses: [email protected], [email protected] (M. Kumar).

0921-4526/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2013.04.035

The calculations were performed within the DFT as implemented in the Vienna ab initio simulation package (VASP) [26]. Wave

M. Kumar, C. Persson / Physica B 422 (2013) 20–27

functions are represented by a plane-wave basis with the projector augmented wave (PAW) method [27]. The electronic exchangecorrelation was treated by the hybrid (HSE06) functional. This hybrid functional combines the Perdew–Burke–Ernzerhof (PBE) [28] exchange-correlation and the Hartree–Fock exchange interaction. We used the standard range-separation parameter ω¼0.2 to decompose the Coulomb kernel. The valance electrons include the 4d and 5s orbitals for Ag and open-shell s and p orbitals for cation M (Al, Ga, or In) and anion O. A plane-wave energy cutoff of 500 eV was used for calculations. The Monkhorst–Pack scheme k-points grid sampling was set to 6  6  6 for the integration of first Brillouin zone. The lattice constants were relaxed by minimizing the total energy to an accuracy of 0.1 meV, and the ion positions were relaxed with an accuracy of 0.01 eV/Å for the forces on each atom.

3. Results and discussion 3.1. Crystal structure The crystal structure of AgMO2 shows the alternative arrangement of Ag and MO2 layer perpendicular to the c-axis (Fig. 1). Each trivalent cation i.e., Al, Ga and In is octahedrally surrounded by the six oxygen atoms, while each Ag atom is coordinated linearly with two oxygen atoms along the c-axis in a dumbbell like shape. The delafossite compounds exhibit in two different polytypes named 3R and 2H, depending on the stacking of MO6 octadedra layers. If the fundamental units stack hexagonally in a sequence of … AaBbCcAa… along the c-axis, it is called 3R polytype (space group R3m; No. 166) and if units stack in a sequence of …AaBbAa… it is called 2H polytype (space group P63/mmc, No. 194). In the case of 3R polytype, there are three layers per unit cell and the fourth layer is similar to the first one. Using the hexagonal axes for a unit cell one can find an average value of 18 Å for c-parameter. On the other hand, for 2H polytype there are two layers per unit cell with an average value of 12 Å for c-parameter. Fig. 1 shows a clear description along with the stacking sequences for both structures. The atomic positions in both structures are fixed by a symmetry

21

except the z parameter, which is used to describe the displacement of oxygen atom i.e., the oxygen atoms are on 6c positions with the fractional coordinate (0, 0, z) and (0, 0, −z), while Ag and M atoms are on the Wyckoff positions 3a and 3b respectively for 3R polytype. On the other hand, for 2H polytype, the Ag atoms are on the Wyckoff position 2c, cations M are on position 2a and anion O is on 4f position with the fractional coordinates (0.333, 0.667, z) and (0.333, 0.667, -z). Both these polytypes can be described by a set of three parameters: the lattice parameters a and c and an internal parameter z, which define the fractional coordinate of an oxygen atom along the c-axis. The calculated structural parameters with the help of PBE and HSE06 potentials are shown in Table 1. One can notice that the lattice parameters are in good agreement (especially with HSE06) with the available experimental values [29]. The Ag–O bond lengths are almost similar in all three structures, varying from 2.08 to 2.10 Å only, while the M–O bond length is dependent on the metal species. The longer c in rhombohedral unit cell corresponds to the different stacking sequence. The calculated atomic positions (z-value) of the oxygen atoms are shown in Table 1. We also calculate the total energy differences ΔEt ¼Et(3R)−Et(2H), which are quite small for all the these compounds (see Table 1). The highest calculated energy is  5 meV/atom in the case of AgAlO2, which however may less than the error from the numeric treating in DFT calculations. Hence, we believe that AgMO2 compounds can be synthesized in a coexisted 3R and 2H phases, depending upon the growth conditions. 3.2. Electronic properties In this section, we discussed the DOS and full band structures of silver delafossite compounds in 2H and 3R polytypes. 3.2.1. Density of states It is observed that different approximations changed the absolute position of the DOS peaks, but the qualitative features are same. Therefore, our analysis is based on the HSE06 results in rest of the manuscript. Fig. 2 shows the total density of states (TDOS) for AgMO2. From Fig. 2 and our discussion above, one can see that the 2H and 3R differ only in the stacking sequence, but the

Fig. 1. Crystal structure of the delafossite compound for (a) 3R polytype (space group R3m; No. 166) with AaBbCcAa… stacking along the c-axis and (b) 2H polytype (space group P63/mmc, No. 194) with an alternate AaBbAa… stacking sequence. The polyhedra and sphere represents MO6 distorted octahedra and cation Ag, respectively.

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M. Kumar, C. Persson / Physica B 422 (2013) 20–27

Table 1 Calculated lattice parameters (a, c, and z), bond lengths (dAg–O and dM–O), and total energy difference (ΔEt) for 2H (for 3R in parenthesis) polytypes of AgMO2 compounds. AgMO2

Phase

Lattice constant (Å)

ΔEt (eV)

Bond length (Å)

a

c

z

dAg–O

dM–O

[Et(3R)−Et(2H)]

AgAlO2

PBE HSE06 Exp.

2.902 (2.890) 2.880 (2.870) 2.890 7 2a

12.245 (18.442) 12.153 (18.317) 18.277 2a

0.077 (0.115) 0.077 (0.115) –

2.11 (2.12) 2.09 (2.10)

1.93 (1.92) 1.91 (1.91)

0.000 (0.005)

AgGaO2

PBE HSE06 Exp.

3.013(3.013) 2.990 (2.990) 2.989 7 2a

12.453 (18.683) 12.357 (18.536) 18.534 7 2a

0.081 (0.113) 0.081 (0.113) -

2.10 (2.09) 2.09 (2.09)

2.01 (2.01) 2.00 (1.99)

0.000 (0.002)

AgInO2

PBE HSE06 Exp.

3.310 (3.310) 3.291 (3.292) 3.2777 3a

12.715 (19.068) 12.641 (18.961) 18.881 7 3a

0.086 (0.109) 0.085 (0.109)

2.09 (2.09) 2.08 (2.08)

2.20 (2.20) 2.19 (2.19)

0.001 (0.001)

a

Ref. 2.

3R

2H 15

Total DOS (1/eV cell)

AgAlO2

AgAlO2

18

12

15 12

9

9

6

6 3

3 VBM

0 -10

-8

-6

-4

-2

0

VBM

0 2

4

6

8

-10

-8

-6

-4

-2

0

2

4

6

8

15

Total DOS (1/eV cell)

AgGaO2

AgGaO2

18

12

15 12

9

9

6

6 3

3 VBM

VBM

0

0 -10

-8

-6

-4

-2

0

2

4

6

8

-10

-8

-6

-4

-2

0

2

4

6

8

15

Total DOS (1/eV cell)

AgInO2

AgInO2

18

12

15

9

12 9

6

6 3

3 VBM

VBM

0

0 -10

-8

-6

-4

-2

0

2

4

6

Energy (eV)

8

-10

-8

-6

-4

-2

0

2

4

6

8

Energy (eV)

Fig. 2. Total density of states for AgMO2 in (a) 2H and (b) 3R polytypes.

overall local bonding environments and the positions of the peaks are rather similar. So, it is expected that both these structures may have similar electronic features. In the simplest ionic model, the valence band is mainly composed of Ag d and O p states. The upper part of the valence band results from the weak antibonding interactions between Ag d states and O p states. The antibonding feature of the valence band maximum (VBM) is expected for silver delafossites, because a similar behavior has been reported

previously for copper based delafossites [13]. The DOS peak representing the M–O bond is 5–7 eV lower than the VBM, which results from the weak bonding interactions mainly between O p and s states of cation M along with a small contribution from Ag d states. The conduction band minimum (CBM) is composed of Ag s and O p states. In the case of AgGaO2 and AgInO2, though the overall features of the curves are same, but the energy range and the shape of the peaks are different for Ga and In. This is due the

M. Kumar, C. Persson / Physica B 422 (2013) 20–27

23

2H

2.0

3R Ag-d Al-s O-p

Ag-d Al-s O-p

PDOS (1/eV atom)

1.5

1.0

0.5

0.0 -10

-8

-6

-4

-2 0 2 Energy (eV)

4

6

8

10

-10

-8

-6

-4

-2 0 2 Energy (eV)

4

6

8

10

Fig. 3. Partial DOS of AgAlO2 for two representative cases are shown: (a) 2H and (b) 3R polytypes.

fact that the Al has no d band contribution as compared to the filled d bands of Ga and In. The partial density of states (PDOS) plots throws more light on the behavior of these compounds. Fig. 3a and b show the PDOS of AgAlO2 as a representative case for 2H and 3R structure respectively. One can see that, the CBM of AgAlO2 consists of Ag d states (3–5 eV), O p states (4–5 eV) and a long tail of Al s and O p states from 8 to 10 eV.

3.2.2. Full band structure Fig. 4 shows the full band structures of AgAlO2, AgGaO2, and AgInO2 for (a) 2H and (b) 3R polytpes along the high-symmetry lines of first Brillouin zone. One can observe that for 2H (3R) polytype the VBM occurs either at the M (F) point (for AgGaO2) or near to the M (F) point (for AgAlO2 and AgInO2), while the CBM is at Γ for all these compounds. Hence, these AgMO2 compounds are indirect band gap semiconductors. The calculated fundamental indirect band gaps for 2H (3R) polytype are 2.96 eV (2.87 eV), 2.11 eV (2.06 eV), and 1.62 eV (1.58 eV) for AgAlO2, AgGaO2 and AgInO2 respectively. On the other hand, the smallest direct band gaps of these compounds occurs at Γ and estimated as 4.31 eV (4.29 eV), 3.57 eV (3.57 eV), and 2.58 eV (2.58 eV) for AgAlO2, AgGaO2, and AgInO2 respectively. There is an improvement in band gap energies compared to available LDA calculation [20]. Their reported band gap energies are 1.7 eV (AgAlO2), 1.2 eV (AgGaO2), and 0.6 eV (AgInO2) for 3R polytype compounds. On the other hand, optically measured experimental band gaps for these silver delafossites are 3.6 eV (AgAlO2) [20], 4.12 eV (AgGaO2) [30], and 4.2 eV (AgInO2) [31]. It is interesting to note that the optically measured band gap energies for these compounds increase when the ionic radius of cation M increases. However, our calculated band gap energies decrease. This is totally an opposite trend compared to the conventional semiconductors containing group IIIA elements such as CuMX2 (M ¼Al, Ga, or In and X ¼S or Se). Here, the fundamental direct band gap decreases when the ionic radius of the cation of group IIIA elements increases [32]. A similar phenomenon has been reported for copper based delafossites [33] and it has been said that the fundamental direct band gap at Γ point decreases for delafossites and thus follows the trend observed for group IIIA containing semiconductors. As we noticed above, the calculated band gap values are smaller than the optically measured band gaps. Ingram et. al., [13] have reported that the optically measured band gap

transition for delafossite compounds occurs at the point M (L) for the 2H (3R) ploytype and which are assigned to transitions from the valence hybridized copper/silver d and oxygen p states to copper/silver p states in the conduction band. This is due the fact that the transitions across the fundamental direct band gap are dipole forbidden because the conduction and valance band states have the same parity. Therefore the optical measured band gap transition of these delafossite compounds occurs at the next lowest energy where the dipolar optical transition matrix element is high i.e., at M point for 2H polytype and L point for 3R polytype [20,33]. Therefore, it would be interesting to calculate the band gap energies at theses aforementioned points. Our calculated direct band gaps at M (L) point are 4.19 eV (4.21 eV), 4.06 eV (4.11 eV), and 4.47 eV (4.50 eV) for AgAlO2, AgGaO2, and AgInO2 respectively and thus follow the trends observed during optically measured experimentally band gaps i.e., band gaps increase with increasing ionic radius of the cation M in general. The slight decrease for AgGaO2 is due to the much lower energy of Ga 4s orbital than that of having Al 3s orbital. A similar kind of observations is reported for copper delafossites where the calculated direct band gap energies at the L point (for 3R ploytype) are 2.68 eV (CuAlO2), 2.54 eV (CuGaO2), and 3.08 eV (CuInO2) [33]. As we know for many materials the agreement of HSE06 band gaps are good with the experimental values, similarly here also, the HSE06 based band gap energies shown much better agreement in general with optically measured band gap values. Moreover, one should also not forget that the optical band gap does not originate form bulk, but from the surface and defects [34] and it may leads to small variation in band gaps. Furthermore, the theoretical gap energy should be considered as an estimate, and we should not be surprised if HSE06 generate variation of 0.2 eV in band gap values [35]. Table 2 shows the band gap energies of AgMO2 with the available theoretical and experimental data. One can see from Table 2 that the direct band gap energies for these compounds are typically greater then 3.0 eV, which in general needed to ensure the transparency to visible light.

3.3. Optical properties In this section, the optical properties are presented in terms of the complex dielectric function ε(ω)¼ε1(ω)+iε2(ω) and the absorption coefficient α(ω).

M. Kumar, C. Persson / Physica B 422 (2013) 20–27

Energy (eV)

24

AgGaO2

AgAlO2

10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 M

L

A

H

K

M

L

AgInO2

A

H

K

M

L

AgGaO2

AgAlO2

A

H

K

AgInO2

10 9 8 7 6

Energy (eV)

5 4 3 2 1 0 -1 -2 -3 -4 F

L

Z

F

L

Z

F

L

Z

Fig. 4. The calculated electronic band structure of AgMO2 compounds for (a) 2H and (b) 3R polytypes along the high-symmetry lines of the first Brillouin zone with the help of HSE06 potential. The zero of the energy is taken as the top of valence band.

Table 2 Calculated band gap energies (in the unit of eV) for 2H (for 3R in parenthesis) polytype in comparison with other theoretical and experimental data. Methods

PBE HSE06 LDAa Exp. a b c

AgAlO2

AgGaO2

AgInO2

Eind g

EΓ−Γ g

EM−M ðEL−L g g Þ

Eind g

EΓ−Γ g

EM−M ðEL−L g g Þ

Eind g

EΓ−Γ g

EM−M ðEL−L g g Þ

1.51(1.47) 2.96(2.87)

2.60(2.58) 4.31(4.29) 1.7

3.05(3.07) (4.19)4.21

(0.65)0.63 2.11(2.06)

1.82(1.83) 3.57(3.57) 1.2

2.93(2.94) 4.06(4.11)

0.24(0.23) 1.62(1.58)

1.03(1.01) 2.58(2.58) 0.6

3.29(3.31) 4.47(4.50)

3.6a

4.1b

4.2c

Ref. 20. Ref. 30. Ref. 31.

3.3.1. Dielectric functions One of the main optical characteristics of a solid is its complex dielectric function. It is an important property for describing the electronic screening near the dopants, defects, and dislocations.

The imaginary part ε2 of the dielectric function is calculated from the joint DOS integrated over the Brillouin zone with the weight of momentum matrix elements while the real part ε1 is related to the imaginary part by Kramers–Kronig transformation [36]. Fig. 5

Dielectric function

10 9 8 7 6 5 4 3 2 1 0

Dielectric function

10 9 8 7 6 5 4 3 2 1 0

Dielectric function

M. Kumar, C. Persson / Physica B 422 (2013) 20–27

10 9 8 7 6 5 4 3 2 1 0

2H

0

1

2

3

25

3R

10 9 8 7 6 5 4 3 2 1 0 4

5

6

7

8

0

1

2

3

4

5

6

7

8

0

1

2

3

4

5

6

7

8

0

1

2

3

4

5

6

7

8

10 9 8 7 6 5 4 3 2 1 0 0

1

2

3

4

5

6

7

8

10 9 8 7 6 5 4 3 2 1 0 0

1

2

3

4 5 Energy (eV)

6

7

8

Energy (eV)

Fig. 5. The dielectric function ε(ω) ¼ε1(ω)+iε2(ω) for (a) 2H and (b) 3R polytypes of AgMO2 compounds. Here, the thin black lines represent the real part ε1(ω) and the red lines represent the imaginary part ε2(ω). Both the transverse (xy; solid lines) and longitudinal (z; dotted lines) components are shown. One can observer a strong anisotropy in both parts of the dielectric function. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

shows the dielectric function ε(ω) of AgMO2 compounds generated with the help of HSE06 potential. Overall, these compounds show similar dielectric function over a broad range of energy. It is obvious form Fig. 5 that the dielectric functions show a significant anisotropy of its components perpendicular and parallel to the caxis. The average high frequency dielectric constants ε∞ calculated for 2H (3R) are 3.3 (3.8), 3.4 (3.9), 3.09 (3.7) for AgAlO2, AgGaO2, and AgInO2 respectively. The dielectric constant ε∞ is related to the bands near the VBM and CBM, which involves energies close to the band gap energies.

3.3.2. Absorption coefficient The absorption coefficient α(ω) is obtained directly from the dielectric function by [24,35,36] 1=2 pffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi aðoÞ ¼ 2ω=c ε1 ðωÞ2 þ ε2 ðωÞ2 −ε1 ðωÞ where c is the speed of light. The calculated absorption coefficients of AgMO2 compounds are shown in Fig. 6. Since the absorption is obtained directly from the dielectric function, similarities in the polarization response are

reflected also in the absorption coefficient. In Fig. 6, we show the transverse (xy) and longitudinal (z) contribution of the polarization-independent absorption spectra. The calculated absorption of these compounds reveals that, the direct optical onset does not occur at photon energies ℏω≈Eg as one may expect, but occurs well above the band gap energy, i.e., at the energy Eg+Δ. Τhe estimated optical band gap energies are 4.05 (4.12), 3.65 (3.69), and 3.35 (3.42) eV for 2H (3R) polytype for AgAlO2, AgGaO2, and AgInO2 respectively. Thus, all these compounds have comparable absorption coefficient for ħω¼ 4 eV i.e., α(ω)¼ 2  104 cm−1. A broad peak that starts at  4 eV and having maxima at  5.5 eV, mainly dominates the absorption spectra of these AgMO2 compounds. This peak corresponds to a linear optical response from the valence bands to the lowest conduction bands. On the other hand for large photon energies (i.e., 46 eV), the peaks involve contributions from several conduction bands and energetically low-lying valence bands and therefore α(ω) in this energy region is dependent of the full band structure of the materials. Hence it can be said that the onset of absorption for these compounds is at photon energy ħω¼  4 eV, which is a typical requirement for any material to be used for optoelectronic applications [36] . Overall, the calculated optical properties (dielectric function and

26

M. Kumar, C. Persson / Physica B 422 (2013) 20–27

Absorption coefficient (10 4/cm)

2H AgAlO2

Absorption coefficient (10 4/cm)

140

120

120

100

100

AgAlO2

80

80 60

60

z

xy

40

40

20

20

z

xy

0

0 0

1

2

3

4

5

6

7

8

140

9

10

AgGaO2

0

120

100

100

80

80

60

1

2

3

4

6

7

8

9

10

AgGaO2

60

xy

5

140

120

xy

40

40 z

20

z

20 0

0 0

Absorption coefficient (10 4/cm)

3R

140

1

2

3

4

5

6

7

8

9

0

10

1

2

3

4

5

6

7

8

9

10

140

140

AgInO2

120

AgInO2

120 100

100

80

80

xy

xy

60

60 40

40

z

z

20

20

0

0 0

1

2

3

4

5

6

7

8

9

0

10

1

2

3

Energy (eV)

4

5

6

7

8

9

10

Energy (eV)

Fig. 6. The absorption coefficient α(ω) for (a) 2H and (b) 3R polytypes of AgMO2 compounds. Here, the solid black lines represent the transverse (xy) contribution while the dotted lines show the longitudinal (z) contribution.

absorption) indicate that AgMO2 compound has a good potential to be used in optoelectronic devices however, more theory and experimental studies are required to establish these compounds.

energies. Overall, AgMO2 compound has good potential to be used in optoelectronic devices.

Acknowledgments 4. Conclusions Using a first-principles hybrid functional (HSE06) calculation, the crystal structure, electronic and optical properties of AgAlO2, AgGaO2, and AgInO2 delafossites compounds have been studied. It has been found that these compounds have rather similar electronic band structure and optical absorption coefficients. Total energy calculation revealed that these compounds can be stabilized in either hexagonal (2H) or rhomodedral (3R) structure depending upon the growth conditions. All these compounds have indirect band gap and the calculated fundamental band gaps energy are in the region of 1.6–3.0 eV. We also estimated the lowest direct band gap energy and which is estimated in the range of 2.6–4.3 eV. The calculated band gap energies at the M (L) point for 2H (3R) phase are 4.19 eV (4.21 eV), 4.06 eV (4.11 eV), and 4.47 eV (4.50 eV) for AgAlO2, AgGaO2, and AgInO2 respectively, which are in good agreement with the optically measured band gap energies. Optical characteristics demonstrated that these compounds show a significant anisotropy of its components and the absorption onset of these compounds occurs well above the fundamental band gap

This work is supported by the Swedish Energy Agency, the Swedish Research Council, and the computers centers NSC and HPC2N through SNIC/SNAC and Matter network. The authors acknowledge financial support from the Swedish Institute and the Erasmus Mundus External Cooperation Window program India4EU. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]

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