CHAPTER-VI

ELECTRONIC BAND STRUCTURE, STRUCTURAL AND

OPTICAL PROPERTIES OF AgMX2 (M= AI, Ga, In; X= S, Se, Te)

6.1. INTRODUCTION

The chalcopyrite semiconductor compounds have received more attention

during the last decade. The first principle calculations are used to determine the

different properties of materials. The chalcopyrite compounds receive interest from

both experimental and theoretical points of view due to their potential applications in

visible and infrared light emitting diode, infrared detectors, optical parametric

oscillators, upconverters and far infrared generation [I]. Among the chalcopyrites

AgGaS2 and CuGaS2 have band gaps in the visible part of the optical spectrum hence,

it is easy to study with visible lasers such as Ar and HeCd lasers. The narrow gap of

AgGaSe2 makes it suitable as infrared detector including applications in photovoltaic

solar cells and also in light emitting diodes [2, 31. AgGaS2 and AgGaSe2 crystals have

received more interest for the middle and deep infrared applications due to their large

non-linear optical (NLO) coefficients and high transmission in the IR region [4 -91.

The ternary I-Ill-VI2 chalcopyrite compounds have similar physical properties

as the binary II.VI2 analogs with the cubic Zinc-blende structure. The crystal structure

of the chalcopyrites is discussed in the section 5.1. Under high-pressure, the phase

transition and electronic properties of the chalcopyrite semiconductors have

considerable attention. Due to decrease in interatomic distance, there are significant

changes in bonding, structurr and properties.

Werner et a1 [lo] performed high pressure X-ray diffraction energy dispersion

technique and predicted the pressure induced phase transition from bct to NaCl in

CuGaSz and AgGaS2. Using self consistent potential -variation mixed basis (PVMB)

band structure method, Jaffe et a1 [ I I] discussed the band gap anomaly and structural

anomalies of chalcopyrite compounds relative to their binary compounds. The

electronic band structure, charge densities, density of states and chemical bonding

were analyzed [I I]. Jaffe et a1 [12] calculated the anomalous reduction in the band

gap for ABC2 chalcopyrite semiconductor compounds relative to their 11-V1

isoelectronic analogs. The first principle pseudo-potential method within LDA was

used to calculate the electronic structure and pressure derivatives of AgGaSe2 [I 31.

Laksari el al [I41 studied the structural, electronic and optical properties of

CuGaS2 and AgGaS2 compounds by means of full potential augmented plane wave

method. In the study of optical properties [14], the complex dielectric functions,

refractive index, static dielectric constant and degree of anisotropy of the compounds

were reported and compared with the available experimental and theoretical data.

Using FP-LAPW method within LDA, Chahed et a1 studied the electronic structure

and optical properties like complex dielectric functions and refractive index of

AgGaSl and AgGaSez compounds [15]. Based on the self-consistent calculation, the

electronic structure and physical properties of AMXl (A= Cu, Ag; M= Oa, In; X= S,

Se, Te) were studied and the obtained ground state properties of the compounds were

compared with the earlier experimental data [16, 171.

Tell er a/ [IS] experimentally studied the band structure and electro

reflectance spectrum for AgMTe2 (M=AI, Ga, Te). The direct band gap for the

compounds was calculated at 77 K. Tang et a/ [I91 investigated the electronic and

optical properties of AgGaS2 and AgGaSel by theoretical and experimental methods.

The refractive index of AgGaS2 compound was measured by Boyd et a/ [20]. The

results of band structure, density of states and imaginary part of frequency dependent

linear and nonlinear optical response were reported for AgGaX2 (X=S, Se, Te)

compounds [2 I] .

The energy dispersive X-ray diffraction and energy dispersive X-ray

absorption spectroscopy was used to investigate the phase transition in AgGaS2 and

AgGaSe2 [22]. In AgGaS2 it was found that it undergoes transition from bct to

orthorhombic and in the case of AgGaSe2 the transition occurs from bct to tetragonal

through an orthorhombic phase [22]. The optical absorption, single crystal x-ray

diffraction and electronic structure calculation of AgGaSe2 was investigated by

Gonzalez et a1 [I 31.

In AgGaTe2, the structural phase transition from chalcopyrite to fcc at 4k0.5

was found Quadri er a/ [26] by means of in situ diffraction measurements of

synchrotron produced x radiation. The high pressure phases of AgGaTel was analyzed

using X-ray diffraction up to 18 GPa by diamond anvil cell using synchrotron

radiation source by lwamoto er a1 [23]. High-pressure X-ray diffraction measurement

was performed on AgGaTe2 chalcopyrite semiconductor up to 30 GPa [24,25]. Based

on the coordination number the phase transition was found to be a tentative d-Cmcm

structure under high pressure,

6.2. PRESENT STUDIES ON AgMX2 (M = Al, Ga, In; X = S, Se, Te)

The electronic structure, high pressure phase transition of the chalcopyrite

AgMX2 (M=AI, Ga, In; X=S, Se, Te) compounds are studied using self-consistent

TB-LMTO method [27-291. The ternary semiconductor compounds investigated in

the present work crystallizes in the chalcopyrite structure (bct) with space group

14-2d (space group no: 122). The atomic positions for the cations and anion of the

compounds are: Cu = 0, 0, 0, M = 0, 0, 0.5 and for X = u, 0.25, 0.125. The

experimental u value [I I] is used in the calculation. In order to find the phase stability

of the compounds the total energies are calculated for the bct and high pressure phase

and fitted Birch Mumaghan equation of states [30-3 I ] . The band structure for the

compounds is plotted to find the metallic nature ofthe compounds under pressure.

The self-consistent FP-LMTO "LMTART" [32-331 is used to study the optical

properties of the AgMX2 compounds. The threshold frequency or critical point, static

dielectric constants, refractive index and degree of anisotropy of the compounds are

calculated.

6.3. AgAIXz (X= S, Se, Te)

The self consistent TB-LMTO method is used to calculate the energy band

structures for ambient as well as high pressure phases of the alkaline earth

chalcopyrites. The exchange correlation scheme of von Barth and Hedin 1341 is

employed in the present calculations. In the present study 5s, 4d, orbitals of Ag, 3s,

3p, orbitals of Al, 3s. 3p orbitals of S, 4s, 4p of Se and 5s. 5p orbitals of Te are treated

as valence states. The calculations are performed with 384 k points within the entire

part of the Brillouin Zone for bct phase. In order to have accurate results empty

spheres are included to the open bct structure without changing the symmetry similar

to CuMX2 compounds.

6.3.1. STRUCTURAL STABILITY OF AgAIX2 COMPOUNDS

In order to find the equilibrium volume for the bct phase the total energies are

computed as function of reduced volume. The calculated total energy values are fined

with the Birch Murnaghan's equation of state. The calculated volume and bulk

modulus for the bct phase are given in Table.6.1 along with the available

experimental and theoretical value for comparison. The ratio between the calculated

and experimental volumes at zero pressure is also given. The fact that

Vo(cal) / Vo(Expt) is larger than unity for AgAlSz and AgAITe2, which is partly due to

uncertainties in the sphere radii chosen. The calculated equilibrium volume increases

linearly from AgAIS2 to AgAITez, i.e. from lower to higher atomic number

compounds. The bulk modulus at zero pressure is calculated from the P-V relation.

The experimental values of bulk modulus were determined from X- ray measurements

and sound velocity measurements. The calculated values from the first principle band

structure calculations are upper limit values were the volumes changed.

In order to check for any possible structural transition, the total energies are

computed in the fcc structure by reducing the cell volume. The calculations are

carried out with 1728 k- points in the entire part of the Brillouin Zone. In the fcc

structure, the calculations are performed with Ag at 0, 0, 0, A1 at 0.5,0.5,0.5 and X at

0.25, 0.25, 0.25. The calculated total energy values are fitted with the Birch

Murnaghan equation of state. The present calculation shows that the AgAIXz

compounds undergo transition from bct to fcc under pressure. Figs. 6.1 to 6.3

represent the total energy of AgAIXz ,compounds in the bct and fcc phase. The

calculated cell volume and bulk modulus for the fcc phase are given in Table.6.2,

which are in need of experimental data for comparison.

Fig.6.1. Total energy cuwe of AgAlSz

- .0.1 . .0.2.

x E + .0.3. E N 5 9.4.

-0.1.

-0.6- , . 300 340 400 460 SO0 110 600 610 700

Volume (a.u)'

Fig.6.2. Total energy curve of AgAISe*

-0.1 . -0.0. z

g + a0 -0.3-

35 F?

F -Oe4- -0.1 -

Fig.6.3. Total energy cuwe of AgAITez

AgAISe,

1 - 1 - 1 - 1 - . - . . , - - - - roo rso 400 .so soo sso $00 e io 760 7io 160

Table.6.1.Calculated equilibrium volume (in at. units) and bulk

modulus of the compounds

Table.6.2.Calculated cell volumes and bulk modulus for the high

Compounds

AgAIS2

AgAlSe2

AgAiTe2

pressure fcc phase.

Vo(cal) Present

573.262

640.578

- _ _ _ 803.728

From the Equation of states, the pressure at which transition occurs for the

compounds is calculated. The pressure at which the compounds undergo transition

from bct to fcc phase is 5.27 GPa for AgAIS2, 1 I .06 GPa for AgAlSe2 and 7.18 GPa

for AgAITet compound. The calculated pressure value for the compound at which

transition occurs is in need of experimental values for comparison.

Compounds

AgAlSz

AgAlSel

AgAITe2

Vo(Exp)

561.395

643.367

Cell volume (a.u)'

435.4969

494.3909

600.1 744

Ref

Exp[36]

Exp[36]

Bulk modulus (GPa)

120.87

89.84

72.27

791.119

Vo(cal) / Vo(Exp)

1.021

0.996

,

Bulk modulus

(Gpa)

68.73 75.15

66.24 62.77

40.42

Ref

Present Rep[l6]

Present Rep[l6]

Rep[l6] I

6.3.2. BAND STRUCTURE OF AgAIX2

The electronic band structure is plotted for the bct and high pressure phase in

manner similar to CuAIX2 compounds in the section 5.3.3. In the case of AgAIS2, the

band structure for bct phase shows direct band gap as shown in the Fig.5.5. The band

structure for the ambient bct phase shows the valence band maximum (VBM) and the

conduction band minimum (CBM) of the compound at point. The upper part of the

valence band is dominated by the p - orbitals of the anion and the d- orbital of the

noble metal. The lower part of the valence band is dominated by the cation-Al atom.

The band structure for the high pressure fcc phase shows metallic character with the

band structure profile crossing the fermi level due to broadening of the bands for the

compound. The band structure for the high pressure fcc phase is similar to CuAlXz

compound which is discussed in the section 5.3.3.

i .I0

z 0 Y P N

Fig.6.4. Band structure for BCT phase of AgAISz

m y (ev)

Fig.6.5. Density of states for BCT phase of AgAIS2

The band gap for the AgAlS2 compound is calculated from the density of state

by tetrahedron method. Fig. 5.6 represents the density of states for AgAIS2 compound.

There is a large downshift in the energy gap relative to the binary analogs. The

estimated band gap value is 1.797 eV, which is less than the experimental value of

3.13 eV. The band gaps are usually underestimated due to LDA. The calculated

density of states for fcc phase of AgAIX2 compounds shows no band gap similar to

copper chalcopyrite compounds, which is discussed in the previous chapter. The

density of states of fcc confirms the metallic nature of the compound. The present

work predicts the structural phase transition of the compounds under high pressure

along with semiconductor to metal transition.

Fig.6.6. Band structure for BCT phase of AgAISe2

In the case of AgAISe2, the band structure is plotted similar to AgAlSz

compound. The band structure shows direct band gap value with VBM and CBM at

point. Under high pressure the compounds shows metallic nature with band profiles

crossing the Fermi level similar to copper chalcopyrite compounds discussed in the

previous chapter.

The density of states for AgAlSel compound is presented in the Fig. 6.7,

which shows a well-developed band gap. The estimated band gap value for the

compound is 0.850 eV, which underestimates the experimental value of 2.55 eV. The

gap is underestimated due to LDA calculation. The high pressure fcc phase shows no

band gap which establish the transition of the compound from semiconductor to metal

under pressure.

Fig.6.7. Density of states for BCT phase of AgAISez

Fig.6.8. Band structure for BCT phase of AgAITe*

Fig.6.9. Density of states for BCT phase of AgAITe2

The band structure for AgAITe:! is given in the Fig. 6.8, which shows a well

developed direct band gap for the bct phase. The density of states for AgAlTel is

shown in the Fig. 6.9 with well developed band gap. The estimated band gap value is

0.782 eV. The estimated band gap value is given in the Table. 6.3 along with the

experimental value for comparison. The band structure and density of states for the

high pressure fcc phase of AgAITe2 shows no band gap, which confirms the metallic

nature of the compound.

Table.6.3. Band gap values for the chalcopyrite compounds with the

available exp values

1.797 Present

AgAlSe2 0.850 Present

6.3.3. OPTICAL PROPERTIES OF AgAIX2

AgAITe2

The chalcopyrite semiconductors receive more attention for the application in

nonlinear optical devices, detectors and solar cells. The optical properties are studied

using FP-LMTO "LMTART" method [32-331. The method of calculation is discussed

in section 3.2.3.

Fig. 6.10 to 6.12 represents the imaginary and real pan dielectric function of

the AgAIX2 compounds. The volume at ambient conditions is used to study the

optical properties of the compounds. The threshold frequency for the compound is

calculated by the average function of the dielectric function along the x, y and z

2.55 0.782 2.27

direction. The onset of critical point or threshold energy value for the compound is

comparable with the band gap of the compound, which is less than the experimental

value due to LDA. The threshold energy value for the AgAIX2 is due to transition

related at r symmetry point.

Exp[36] Present Exp[37]

In AgAIS2 compound the first peak, second peak, third peak and the main

peak appears at 3.547 eV, 3.964 eV, 4.837 eV and 7.914 eV respectively. The first

peak and main peak is mainly due to transition related to I' point. The second peak is

due to transition at r and X point, the third peak is due to Z point direct optical

transition. The calculated values are in need of experimental values for comparison.

In AgAISel, the first peak is at 3.299 eV which is due to transition at rand X

symmetry point. The direct optical transition at Z and I' point gives the second peak

for the compound at 4.1 70 eV. The main peak for the compound appears at 6.956 eV,

which are due to transition related to I- point.

Finally for AgAITe2 compound. the first peak, second peak or main peak, third

peak occur at 2.757 eV, 4.130 eV and 5.045 eV respectively. The first peak for

AgAITe2 appears due to X point optical transition, the second peak is due to transition

related to r point and the third peak is due to transition at Z and point. The

magnitude of the peak is high for AgAiTez, which shows the importance of anions in

the study of optical properties of the compounds. The results obtained are similar to

other chalcopyrites discussed in the previous chapter. The calculated peak values are

in need of experimental data for comparison.

6.3.3.1. STATIC DIELECTRIC CONSTANT AND REFRACTIVE

INDEX

The most important measurable quantity is the zero frequency limit E I ( O ) ,

which is the electronic part of the static dielectric constant. It strongly depends on the

band gap. This quantity may be related to the refractive index measured at a frequency

above the lanice vibrational frequencies. The static dielectric constant € 1 (0) is

calculated by averaging E,,, (a) and E,, (a) values. The calculated staic dielectric

constant €1 (0) increases from AgAIS2 to AgAISe2 and from AgAlSe to AgAITe2. The

static dielectric constant shows higher value for the compound which has lower band

gap value.

Table.6.4. Static dielectric function, degree of anisotropy and

refractive index and zero crossing point for the AgAIX2

compounds

crossing point (eV)

The refractive index for the three compounds is calculated using

n (a) =[[e1+[€12+ ~ 2 ~ ] ~ ~ ~ ] / 2 ] ~ ~ ~ Using the parallel and perpendicular static dielectric

constant, the degree of anisotropy A& for the chalcopyrite compounds are also

calculated in a manner similar to CuAIX2, which is discussed in the section 5.3.4.1.

The calculated degree of anisotropy is small and negative for AgAIS2 and AgAlSe2 but

in the case of AgAITe2 it is small and positive. The compounds taken for the present

calculation exhibit birefrigent property. The birefringence depends on the magnitude of

anisotropy of the crystal. The zero crossing point for the compounds is calculated from

the real part dielectric function of the compounds and it is found that the value

decreases linearly from AgAlSl to AgAITe2. The calculated static dielectric constant,

refractive index, degree of anisotropy and zero crossing point are given in the

Table.6.4. The calculated values are in need of earlier data for comparison.

-1 - .2 - .... ..I....... ..I.... -3 ,

0 2 4 6 0 1 0 1 2 1 4

Energy (eV)

Fig.6.10. Imaginary and Real part of AgAISz compounds

Fig.6.11. Imaginary and Real part of AgAiSez compounds

-1 - -2.

-5. .... ,....,..-.... ... (....'

4 . 2 8 1 0 1 2 1 4 Energy (eV)

-1 - .,..,,.. -.... .,...... - ...' 4.

. . . . . . . 7 . 1 . 1 . 1 . 1 . 1 . 1 . 1 0 2 4 6 8 40 12 14

Energy (eV)

Fig.6.12. Imaginary and Real part of AgAITet compounds

6.4. AgGaX2 (X= S, Se, Te)

The electronic structure, structural phase stability and optical properties of

AgGaX* compounds are studied using the self consistent TB-LMTO. The calculations

are performed with 5s, 4d orbitals of Ag, 4s 4p orbitals of Ga, 3s 3p orbitals of S, 4s

4p orbitals of Se and 5s, Sp, orbitals of Te as valence states. The calculations are

carried out using 384 k- points in the entire part of brillouin zone for the ambient bct

phase of the compounds.

6.4.1. STRUCTURAL STABILITY OF AgGaX2 (X= S, Se, Te)

In AgGaXz compounds, the equilibrium volume in the bct phase is calculated

by total energy calculation for different volumes i.e. from 1.2 VNo to 0.7 VNo where

Vo = Expt Volume. The Birch Murnaghan equation of state is fitted to the total

energies. The theoretically calculated equilibrium volume is given in the Table.6.5,

The ratio between the calculated and experimental volume is taken, which is greater

than unity due to uncertainties in the sphere radii. The bulk modulus obtained from

the P-V relation is given in the Table.6.5, which is also in close agreement with the

earlier available data.

Table.6.5. Calculated equilibrium volume (in at. units) and bulk

modulus of the compounds

Bulk Compounds

modulus

VO (cal)

Present

Vo

(Expt)

Ref

, VU (cal) l

VU (Expt)

Using X- ray absorption spectroscopy at the Ga K-edge and X-ray diffraction

at room temperature, Tinoco el a1 [22] observed that three crystallographic transitions

(5, 12, and 16.5 GPa) for AgGaS;, compound. However only the phase between 12

and 16.5 GPa has been indexed as an orthorhombic structure. In order to understand

the phase transition, the total energies of AgGaS2 with the primitive orthorhombic

structure is calculated as a function of reduced volume. Present calculations reveal

that primitive orthorhombic phase is energetically not favourable when compared to

ambient bct phase. Hence, the total energies are computed with other possible

structure namely base centered orthorhombic structure with 256 k-points in the entire

part of the Brillouin zone. Fitted total energies of base centered orthorhombic

structure shows that there is a possibility of phase transition from bct to orthorhombic

at about 7.34 GPa which is less than the experimental value of 12 GPa [22]. The

calculated equilibrium volume for the orthorhombic phase is 500.4745 (a-u)', which is

in agreement with the experimental value of 526.582 (a.u).'. The calculated bulk

modulus for the compound is 88.75 GPa.

In addition, total energies are also computed for AgGaS2 with fcc structure. k

- point convergency is achieved for 1728 -k points in the entire part of the Brillouin

zone. Fig. 6.13 shows the total energies of AgGaS2 as a function of molecular volume

for normal and high pressure phases. Fitted total energies show that fcc structure is

more stable at high pressures. The transition pressure to fcc phase is about 16.07 GPa

which agrees with the experimental pressure value (1 7 GPa) of unknown phase [22].

The calculated equilibrium cell volume of fcc phase is 467.6101 (a.u)' and the bulk

modulus is 84.34 GPa.

V o l u m e (a.u)'

Fig.6.13. Total energy curves for ambient and high pressure Phases

Phase transitions in ternary chalcopyrite AgGaSe2 were investigated up to 160

kbar using Raman scattering, which indicates a reduced stability of the tetragonal

structure under pressure [39]. Using X- ray absorption technique, Tinoco el a1 [22]

identified four structural phase transitions for AgGaSez at 5, 10.18 and 18-25 GPa.

Experimentally, the phases at 10 and 18 GPa were determined as orthorhombic and

tetragonal structure. In order to understand the structural phase transition under high

pressure, total energies for the primitive orthorhombic structure is calculated, which is

energetically not favorable when compared to ambient bct phase. So, the total

energies for the base centered orthorhombic phase of AgGaSe2 are calculated as a

function of reduced volume. The fined total energy values shows that AgGaSe2

compound undergoes structural transition from bct to orthorhombic at about 27.75

GPa which is higher than the experimental value of 10 (jpa. The calculated

equilibrium volume for the orthorhombic phase is 566.538 (a.u13, which is higher than

the experimental value of 492.968 (a.u)'. The calculated bulk modulus for the

compound is 60.70 Gpa. The overestimation of transition pressure and volume may be

due to approximate choice of symmetry group namely base centered orthorhombic.

Detailed experimental high pressure crystallographic data is necessary to compare the

present prediction. In addition to onhorhombic structure, the total energy values are

calculated for the primitive tetragonal for AgGaSe2 compound. The present study is

able to predict the phase transition under very high pressure of 67.5 1 GPa.

-ORTHO BCT

Fig.6.14. Total energy curves of AgGaSe2

In order to understand the appearance of unknown phase at 18-25 GPa, total

energies are calculated for the possible fcc structure and fined with the Birch

Mumaghan equation of state. Fig.6.14. show the total energy versus volume for the

ambient and high pressure phases. The compound undergoes the phase transition at

about 30.52 GPa, which closely matches with the experimental pressure value (18-25

GPa) of unknown phase [22]. The calculated volume is 541.936 (a.u)' and bulk

modulus for the compound is 65.8 GPa. The calculated volume and bulk modulus for

the high pressure fcc phase are in need of experimental results for verification.

High pressure X-ray diffraction measurement by Mori el a1 [25], observed that

the peaks of chalcopyrite coexist with the tetragonal P 4 structure under pressure.

- They also found that the peaks of tetragonal P 4 coexist with disordered base

centered orthorhombic (d-Cmcm) structure on further increase of pressure [24, 251.

Based on the coordination, it was finally reported that the high pressure is disordered -

Cmcm phase (Disordered means original atoms are replaced by pseudo atoms).

In order to understand the high pressure phase transition in AgGaTe2, the total

energies of P 4 phase are calculated and fitted with the Birch Murnaghan equation of

state. The calculations are carried out for P 4 structure with 152 k-points. Total

energy results show that P 4 not stable at ambient as well as at high pressures. To

check the existence of d-Cmcm phase, total energies are calculated for primitive

orthorhombic. In present calculation, disorder is taken into account by considering

orthorhombic structure with small change in atomic positions without breaking the

symmetry. It is found that orthorhombic with atomic positions displaced by 10%

along c axis is favorable when compared to bct at high pressure. Phase transition

pressure is about 3.62 GPa, which is comparable with the experimental value of 5.4

GPa. The calculated equilibrium volume is 649.239 (a.u)' where as the experimental

value of 723.719 (a.u)3 The calculated bulk modulus for the compound is 67.79 GPa

Experimental studies by Qadri et al [26] show that AgGaTe? undergoes

structural phase transition from bct to fcc at 4.010.5 GPa. In order to understand this

phase transition, the total energies for the fcc phase of AgGaTe2 is calculated as a

function of reduced volume and fitted with the Birch Murnaghan equation of state.

Fig. 6.15 represents the fitted total energy versus volume for different phases of

compound of AgGaTe2 compound. Present calculation shows that AgGaTe2

undergoes from bct to fcc at 6.95 GPa. The calculated cell volume is 613.59 (a.u)',

which agrees with the experimental value of 622.573 (a.u)" "The calculated bulk

modulus for the compound is 67.37 GPa..

AgGaTe,

- -0.6 w FCC

-1 .O BCT 4 , . , . , . , . , . , .

400 500 BOO 700 800 800 1

~olume(a.u)'

Fig.6.15. Total energy curve of AgGaTel

6.4.2. BAND STRUCTURE OF AgGaX2 (X= S, Se, Te)

The band structure for bct and high pressure phase of AgGaX2 compounds is

calculated. The compounds show direct band gap at ambient condition. In the band

structure for the high pressure the band protiles cross the Fermi level showing the

metallic nature of the compounds. From this it is understood that under high pressure

the compounds undergo structural transition as well as semiconductor to metallic

transition.

Table.6.6. Band gap values of AgGaX2 chalcopyrite compounds

The DOS and PDOS are calculated for the compounds. Using DOS the band

S.No

1

2

3

gaps are estimated which underestimates the available experimental value due to

LDA. The band gap value for the compounds is presented in the Table. 6.6 along with

Compounds

AgGaS2

AgGaSe2

AgGaTe2

the available experimental and theoretical data. The calculated band gap value

decreases from AgGaS2 to AgGaTel. The partial density of states are calculated and

Band gap (eV)

0.614 2.5 1 0.95 0.193 1.83 0.19

0.187 1.326 0.42

found that the valence band is due to the Ag 4d states and anion p state of the

Ref

Present Exp[361 Rep[l5] Present Exp[431 Rep[l5] Present Re8371 Rep[2 1 ]

compounds. The s orbital of the anion lies in the lower part of the valence. The one of

the cations Al, Ga and In lies in the upper part of the conduction band in their band

structure and they show negligible contribution to the valence band.

6.4.3. OPTICAL PROPERTIES OF AgGaX2

The optical properties of the AgGaX2 compounds are studied using FP-LMTO

'LMTART' method in a manner similar to AgAIX2 compounds. Figs.6.16 to 6.18.

represent the imaginary and real part dielectric function of the AgGaX2 compounds.

The critical point or threshold energy value for the compounds is calculated from the

imaginary part of the compounds. The static dielectric constants. refractive index,

degree of anisotropy and zero crossing of the compounds are calculated from the real

part of the dielectric function.

The onset of critical point or threshold energy value for the compounds for

AgGaS2, AgGaSe2 and AgGaTe2 compounds is less than the experimental band gap

value due to LDA. The threshold energy value for the all the three compounds of

AgGaX2 is due to transition related to r. In AgGaS2 compound, the first peak, second

peak and main peak is at 2.674 eV, 3.507 eV and 6.249 eV respectively. The first

peak for the AgGaS2 compound is mainly due to transition related to X point, the

second peak value is due to r a n d L and the main peak is due to transition related to Z

and r point respectively. The peak values match with the earlier work of Laksari el a1 1141, Chahed el a1 [15].

In AgGaSe* compound, the first peak appears at 2.134 eV which is also called

as main peak as it possesses higher peak value. The first peak for the compounds is

due to transition related to r a n d X point. The second peak for the compound appears

at 2.716 eV, which is due to transition at r point. The third peak for the compound

occurs at 3.797 eV, which is due to transition related to and Z point. The peak for

AgGaSe2 agrees with the earlier work of Chahed et 01 [ I 51.

In the case of AgGaTe2 compound, the first or main peak. second peak and

third peak appear at 1.761 eV. 2.634 eV and 3.839 eV respectively. The first peak

value may be due to transition related at I- and X symmetry point. The second peak for

the compound appears due transition at r a n d Z symmetry point. The third peak is due

to transition related to l- point. In the above three compounds also the magnitude of

peak is high for AgGaTe2 similar to other chalcopyrites discussed in the previous

chapter. The calculated peak values of AgCaTe2 are in need of experimental results for

comparison.

Fig.6.16. Imaginary and Real part of AgGaS2

Energy (eV)

Fig.6.17. Imaginary and Real part of AgCaSez

Fig.6.18. Imaginary and Real part of AgGaTel

6.4.3.1. STATIC DIELECTRIC CONSTANT AND REFRACTIVE

INDEX

The important zero frequency limit ~ ~ ( 0 ) is calculated from the real part o f the

dielectric function of the compounds. The static dielectric constants for the compounds

are calculated from the average of parallel and perpendicular components o f dielectric

function. The AgGaTe2 compound shows the high static dielectric constant values

when compared to other two compounds. The static dielectric constant increases from

AgGaS2 to AgGaSe2 and then to AgGaTe2 as their band gap value decreases. In the

same way, AgGaTe2 shows high refractive index value compared to AgGaS2 and

AgGaSez compound, which shows the importance o f anion in the optical properties o f

the compounds. The degree o f anisotropy o f the compounds is calculated from the

static dielectric constant which shows small and positive value for all three

chalcopyrites o f AgGaX2 compounds. The zero crossing point for the compounds is

calculated, which shows a decreasing trend from S to Te. The calculated static

dielectric constants, degree o f anisotropy, refractive index and zero crossing point for

the AgGaX2 compounds are given in the Table.6.7 along with the experimental data for

comparison.

Tabie.6.7.Static dielectric function, degree of anisotropy, refractive

index and zero crossing point for the chalcopyrites

6.5. AgInX2 (X=S, Se, Te)

The electronic band structure and high pressure phase transition for AglnX;!

compounds are calculated by self- consistent TB-LMTO method. 'The 5s. 4d orbitals

of Ag, 5s 5p orbitals of In, 3s 3p orbitals of S, 4s 4p orbitals of Se and 5s, Sp, orbitals

of Te are treated as valence states in the present theoretical work. The calculations are

carried out in a manner similar to other chalcopyrite compounds. The optical

properties of the compounds are studied using FP-LMTO method. The optical

constants are calculated in a manner to similar to the AgAIXz compounds.

6.5.1. STRUCTURAL STABILITY OF AgInXz COMPOUNDS

The ground state properties for the AgAIX2 compounds are studied by total

energy calculation for the chalcopyrite structure systematically by changing the

molecular volume. The calculated total energies are fitted with the Birch Murnaphan

equation of state. The calculated volume and bulk modulus are given in the Table. 6.8.

along with the experimental value for the comparison. The ratio between the

calculated and experimental volume at zero pressure is also given. The calculated

volume is in good agreement with the compared experimental value. The calculated

bulk modulus is found to decrease from AglnS: to AglnTe? similar to other

chalcopyrites.

The total energy calculations for high pressure fcc phase is carried out to

check for the possibility o f phase transition from bct to face centered cubic phase for

AglnX2 compounds. The present calculations are carried out with 1728 k points in the

entire part of the Brillouin Zone. The position of atoms is same as AgAIX2

compounds. The calculated total energies for the high pressure fcc phase are fined to

calculated the cell volume and bulk modulus for the compounds. 'The calculated cell

volume and bulk modulus for the high pressure phase is given in the Table. 6.9. The

calculated values are in need o f experimental data for verification. Figs. 6.9 to 6.11

represent the total energy graph for the ambient bct and high pressure fcc phase of the

compounds. The pressure at which transition occurs is calculated and presented in the

Table. 6.10. The calculated pressure value for the cornpounds is in need of

experimental data for verification.

Fig.6.19. Total energy graph for AgInS* compound

Fig.6.20. Total energy graph for AgInSel compound

Fig.6.21,Total energy graph for AgInTel

.?.O

.I.=.

-7.4- u 5 -7.a- B 3 “.a:

-8.0.

4.2.

4 .4 .

Table.6.8. Calculated volume and experimental volume (in at. units)

and calculated bulk modulus for AgInXz compounds

AglnTe,

FCC

BCT

, . 400 600 600 700 800 BOO -000

Table.6.9. Calculated cell volume with the bulk modulus for the high

pressure fcc phase of the compounds.

Table.6.10.Transition pressure value for the compounds

Compounds

AglnS2

6.5.2. BAND STRUCTURE OF AgInXl

The electronic band structure is plotted for the bct and high pressure Tcc phase

of the AglnX2 (X= S, Se, Te). The compounds for the ambient bct phase shows the

direct band gap with valence band maximum (VBM) and conduction band minimum

(CBM) at r point. The upper part of the valence band for the compounds is mainly

due to the contributions of p- states of anions and d- states of Ag atom. The band

structure for the high pressure fcc phase shows the band structure profile crossing the

fermi level, which confirms the transition from semiconductor to metallic nature

under pressure.

Cell volume (a.u)'

488.7438

Bulk modulus (GPa)

102.89

Using the density of states, the band gap for the above three compounds is

calculated. The band gaps are usually underestimates then the experimental due to

LDA. The band gap value for AglnX2 is calculated and presented in Table. 6.1 1 with

the available experimental data for comparison. The calculated density of states for

fcc phase of AglnX2 compounds shows no band gap which confirms the metallic

nature. The band structure results of AglnX2 compounds agree with the band structure

results of other chalcopyrite compounds.

Table.6.11. Band gap values for the bct phase of AgInX2 Compounds

Compounds Bang gap (eV)

AglnS2 0.210 Present

AglnSe2 0.186 Present

AglnTe2 0.127 Present Ex 36

6.5.3. OPTICAL PROPERTIES OF AgInX2 COMPOUNDS

In the present theoretical work the optical properties are studied using FP-

LMTO "LMTART" method [33-341 within LDA. The dielectric complex functions

for the AglnX2 chalcopyrite compounds are calculated at ambient conditions. The

frequency dependent complex dielectric function ~ ( o ) = ~ l ( o ) + ic2(o) describes the

optical response at all energies. Fig. 6.22 to 6.24 represents the average of parallel and

perpendicular components in the imaginary and real part dielectric function of

AglnX2 compounds.

In AglnX2 compounds. the onset of critical point or threshold energy value

starts is less than the experimental value due to LDA. The onset of critical point is due

to transition related to r point for all the AglnX2 compounds.

In AglnS2 compound, the first peak, second peak, third or main peak for the

compound is at 2.636 eV. 3.257 eV and 4.712 eV respectively. The first peak for the

compound appears mainly due to transition related to X. The second peak for the

compound is mainly due to transition at I- and Z point. The third peak for the

compound is due to transition at Z and symmetry point. Finally the main peak for the

compound is mainly due to transition at I- point.

In AglnSe2, the first, second or main and third appears at 2.051eV. 2.882 eV,

4.380 eV and 7.252 eV respectively. The first peak for the compound is due to

transition at X, the second peak is due to Z and T, the third peak and the main peak for

the compound appears due to transition related to T symmetry point.

Finally in the case of AglnTe2, the first peak for the compound appears at 1.898

eV. The first peak for the compound is due to transition related at T and X. The second

peak for the compound is also called as main peak as it possesses higher peak value.

The second peak for the compound occurs at 4.181 eV which is due to transition

related to T symmetry point. The third peak for AglnTel occurs at 5.212 eV which is

due to Z and r point transition. The calculated peak values for AglnX2 compounds are in need of experimental results for comparison.

'. .2. ...... ......................... 4 . , . , , , .

0 2 4 6 8 1 0 1 2 1 4 Energy (eV)

FIg.6.22. Imaginary and Real part of AgInS2 compounds

Fig.6.23. Imaginary and Real part of AgInSe2 compounds

-2 - ....... t..., ............ ........... - 4 . I

o i 4 8 8 1 0 1 2 1 4 Energy (eV)

Fig.6.24. Imaginary and Real part of AgInTe* compounds

6.5.3.1. STATIC DIELECTRIC CONSTANT AND REFRACTIVE

INDEX

The zero frequency limit EI(O) is the electronic part of the static dielectric

constant. The static dielectric constant for the compound is calculated by averaging the

Elll (0) and E , ~ (0). The calculated static dielectric constant increases from AglnS2 to

AgInSe2 and then from AglnSe2 to AglnTe2 due to decrease in their band gap value.

The calculated values are in need of experimental results for verification. The

refractive index for the compound is calculated from the real part and imaginary part

dielectric function of the compounds. The refractive index for the compounds increases

from AgInS2 to AglnTe2 similar to static dielectric constant. The linear increase of the

static dielectric constant and refractive index gives the idea on the imponance of the

anions in the optical properties. The calculated refractive index for the compound is

presented in the Table. 6.12 along with the static dielectric constants. The degree of

anisotropy is oalculated from the parallel and perpendicular components of static

dielectric constants. The AglnS2 and AglnSel compounds show small and negative

degree of anisotropy. In the case of AglnTe2, the compound shows small and positive

value. The point at which the real part dielectric function crosses the zero level is also

estimated. The estimated zero crossing point decreases from AglnSl to AglnTe2 as

expected i.e. from lower to higher atomic number.

Table.6.12, Static dielectric function, degree of anisotropy and

refractive index and zero crossing point for AgInX2

compounds

point (eV)

6.6. CONCLUSIONS

The electronic band structure and structural stability of AgMX2 compounds

are studied using the tight binding version of LMTO method. Besides the electronic

structure and the optical properties of the compounds at ambient are studied using the

full potential method. The calculations are carried out with the experimental internal

parameter value for the ambient bct phase of the AgMX2 compounds.

It is found that in AgAIX2. the calculated total energies shows the phase

transition from ambient bct to fcc under pressure. The calculated volume for the

ambient bct phase increases from AgAIS2 to AgAITe2. which are due to atomic size

effect of the compounds. The ratio between the calculated and experimental volume is

very close to unity. In some compounds, the ratio is greater than unity due to the

uncertainties in the chosen sphere radii. Similar to bct phase, the calculated cell

volume for the high pressure phase increases from AgAIS2 to AgAITe2. The

calculated bulk modulus for the compounds shows the decreasing trend for both the

phase of the compounds. The bulk modulus of the compound is calculaied from the P-

V relation and it is the upper limit value where the volumes are changed. The pressure

at which the compounds undergo transition is calculated to be 5.27 Gpa, 11.06 GPa

and 7.18 GPa for AgAIS2, AgAlSe2 and AgAITel. The direct band gap is calculated

from the band structure and density of states for the ambient bct phase of AgAIX2

compounds. The band structure and density of states for the high pressure phase are

calculated and found to undergo transition from semiconductor to metallic nature.

The ground state properties of AgGaX2 (X=S, Se, Te) are studied in similar

way to AgAIX2 compounds. The calculated equilibrium volume and bulk modulus for

the compounds are compared and found to be in good agreement with the earlier data.

Tinoco et a1 [22] used his EDX and XAS technique at room temperature to

observe the phase transition in AgGaS2 under pressure. At about 12 GPa, the structure

was indexed to be orthorhombic. In the present calculation, total energies for the

primitive orthorhombic structure are calculated. which is energetically not favorable.

Hence total energies for base centered orthorhombic are calculated. The fitted

energies show the possibility of phase transition at about 7.34 GPa. which is less than

the experimental value of 12 GPa. The calculated volume is in agreement with the

experimental value. In order to check the existence of' f'cc phase. total energies are

calculated and the fitted values show the phase transition at 16.07 GPa. The transition

pressure value agrees with the experimental value of 17 GPa of unknown phase 1221.

Similarly for AgGaS2, Tinoco el a1 [ 2 5 ] predicted the phase transition from

bct to orthorhombic structure and then to tetragonal structure in AgGaSe2 compound.

The high pressure calculations for the orthorhombic phase are carried out in a manner

similar to AgGaS2 and it is found that it undergoes transition from bct to base

centered orthorhombic structure at 27.75 GPa. For tetragonal structure, total energies

are calculated for primitive orthorhombic structure, which shows phase transition at

very high pressure of 67.51 GPa. Detailed experimental data are necessary for

comparison. Similar to other chalcopyrites, the existence of fcc phase is checked for

the compound. The compound shows phase transition at 30.52 GPa which matches

with the unknown phase value of 18-25 GPa [22].

High pressure X-ray diffraction measurements by Mori et a1 [25] on AgGaTe2

- predict the coexistence of chalcopyrite and P 4 peaks under high pressure. On further

- increase of pressure they found the coexistence of P 4 and dCmcm peaks . Based on the coordination, it was finally confirmed that the high pressure phase is the dCmcm

phase. In order to check the possibilify of phase transition, the total energies for

- P 4 phase are calculated which is not stable at ambient as well as at high pressure. The

presence of dSmcm is checked by calculating the total energies for primitive

onhorhombic structure with displaced atomic position. The fitted total energy values

show transition at 3.62 GPa, which agree with the experimental value of 5.4 GPa. In

order to check the transition for fcc phase, total energy values are calculated. The

fined values show the phase transition at 6.95 GPa, which agree with the experimental

value of 4.0+0.5 GPa [26].

The band structure for AgGaX2 is calculated, which shows similar results as

AgAIX2 for the ambient and high pressure phases. From the band structure it is

confirmed that AgGaX2 compounds undergo transition from semiconductor to metal

under pressure.

In the case of AglnX2, the equilibrium volume and bulk modulus are estimated

from the fined total energy values. The calculated values are in close agreement with

the available earlier data. The high pressure phase transition tiom bct to fcc is studied

to understand the possibility of phase transition. The calculated cell volumes, bulk

modulus and transition pressure value are in need of experimental data for

comparison. Similar to the above chalcopyrites, AglnX2 also show metallization

under pressure.

The optical properties of AgMX2 (M-AI, Ga,. In; X=S, Se, Te) are studied

using FP-LMTO method within von Barth exchange correlation. The onset of critical

point or threshold energy for the compounds is calculated from the imaginary part of

dielectric functions. The values are calculated by averaging the parallel and

perpendicular components of the imaginary part of dielectric functions. The first

important three peaks and the main peak are calculated for the compounds. The

magnitude of the peaks increase from AgMS2 to AgMSe2 and from AgMSe2 to

AgMTe2, which establishes the importance of anions in the study of optical properties

of the compounds.

The static dielectric constants are calculated from the real part of dielectric

function. The calculated static dielectric constant increases from sulphur to selenide

and from selenide to telluride compounds. The static dielectric constant is inversely

proportional to the band gap value and so, the static dielectric constant increases with

the decrease of band gap value. The refractive index for the compounds is calculated

from the real and imaginary part of dielectric function, which shows the same trend as

that of static dielectric constants. The degree of anisotropy is found to be small and

positive for all the chalcopyrite except the AgAIS2 and AgAISe2. The calculated static

dielectric constants, refractive index, degree of anisotropy and zero crossing point for

the compounds show the supremacy of anion in the optical properties.

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