CHAPTER-V

ELECTRONIC, STRUCTURAL AND OPTICAL PROPERTIES OF

CuMXt (M= Al, Ga, In; X= S, Se, Te)

5.1. INTRODUCTION

I-III-VI2 chalcopyrite semiconductors have attracted the attention of the

physicists due to their wide technological applications. These compounds are

isoelectronic with the Zinc-blend I1 - V1 semiconductor compounds. The chalcopyrite

structure differs from the ZnS structure in the ordered distribution of the cations. The

distribution of cations makes the tetragonal unit cell with the c-axis about twice the a-

axis of the ZB type unit cell. The ternary compounds, which are considered for the

present work, are direct band gap semiconductors with tetragonal chalcopyrite crystal

structure. The chalcopyrite semiconductor materials are utilized in many fields, which

include visible light emitting diode, infrared light emitting diode, infrared detectors,

optical parametric oscillators, up converters and far infrared generation [I]. For

instance, CuInSe2 compound was reported as the highest absorbing material [2] and a

promising material for photovoltaic solar energy application [3].

High-pressure studies of these chalcopyrite semiconductors have attracted

considerable attention due to their phase transition and electronic properties. The

original volume of the materials is reduced to their fraction of volume under high

pressure. The inter-atomic distance decreases due to reduction in volume. Due to

decrease in inter-atomic distance, there are significant changes in bonding, structures

and properties.

Under pressure, the tetrahedral coordination of the compounds undergoes

transition to a denser cubic structure [4] with octahedral coordination. This transition

is similar in nature to the corresponding IV-111-V and 11-IV families. Experimental

studies [5-71 were carried out on the electronic, electrical and optical properties of

CuAIS2 and CuAISe2 at ambient pressure. Single- crystalline samples of CuAIS2 and

CuAlSe2 were grown by chemical vapour transport method by Roa et a1 [7] and the

pressure value was determined using linear ruby scale. However, a very limited

number of studies [8, 91 on structural phase transitions of CuAIS2 and CuAISe2 were

performed under pressure. Grima Gallardo [lo] estimated the isothermal bulk

modulus of ABC2 semiconductors though semi-empirical models.

Roa et a1 [ l l ] performed X-ray diffraction studies for CuAlS2 and CuAISe2

under high pressure and determined the phase transition from chalcopyrite to cubic

phase for CuAISe2. Due to experimental difficulties it was not possible to determine

reliable parameters for the high-pressure phase of CuAIS2. Using EDXRD studies,

Ravhi et a1 [12] investigated similar phase transition under high pressure for CuAlS2

and CuA1Se2. Alonso et a1 [I31 studied the optical properties of CuAISe2 at room

temperature using spectroscopic ellipsometry technique and the energies were

assigned to certain electronic interband transition by comparing with the existing band

structure calculation.

Werner et a1 [4] perfonned high pressure X-ray dimaction energy dispersion

technique and found the pressure induced phase transition from the chalcopyrite phase

to NaCl phase at about 16 GPa in CuGaS2. Tinoco er a1 [14] used synchrotron X-ray

diffraction method and indexed a phase transition from bct to cubic phase in CuInS2

and CuInSe2 with a volume reduction of roughly 10%. Gonzalez et a1 [I 51 perfonned

optical absorption measurements as a function of hydrostatic pressure and determined

the irreversible phase transition to NaCl type structure. Using X- ray diffraction study,

Mori et a1 [I61 showed that under high pressure CuGaTe2 undergoes transition from

bct to d-Cmcm (disordered base centered orthorhombic) through d-Sc ( disordered

simple cubic) and in the case of CuInTez, the bct phase undergoes transition to

d-Cmcm. The bulk modulus for the ambient and high pressure phases of the

compounds was also determined.

Using ab inirio pseudopotential calculation, Lazewski er a1 [I71 studied the

electronic, dynamical and elastic properties of similar chalcopyrite compounds. Using

spectroscopic ellipsometry, Alonso et a1 [ I 31 calculated the complex dielectric tensor

components of similar type of chalcopyrites like CuInSe2, CuInS2, CuGaSe2, and

CuGaS2 and compared the band structure results with the earlier work. Jaffe et a1 [2,

181 used self-consistent potential -variation mixed basis (PVMB) approach to

calculate the band structure, electronic charge densities, density of states and chemical

bonding at normal pressure for the ternary chalcopyrite semiconductors. Jaffe et a1 [ 3 ]

used first principle and self-consistent mixed - basis potential- variation (MBPV)

band structure method to observe the valence-band X-ray photoemission spectra for

CuInSe, with froten Cu 3d orbitals. Based on the self-consistent calculation the

ground state properties and band structure calculation for bct phase of the chalcopyrite

compounds were reported [19-211. The electronic and optical properties for the bct

phase of the ternary AMXz (A= Cu; M= In, Ga; X=Se) chalcopyrite semiconductors

was reported [20] and compared with the available experimental results. Early

electronic structure calculations [2, 19, 20, 21,221 reveal that these compounds are

direct band gap semiconductors.

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

In the present study, the electronic structure, phase stability the chalcopyrite

CuMXz (M=AI, Ga, In; X=S. Se, Te) compounds are calculated using self-consistent

TB-LMTO method [23-251. Under ambient condition, the chalcopyrite compounds

crystallize in the body centered tetragonal structure (bct) of space group 14-2d (space

group no: 122). For bct structure, the atomic positions are: Cu = 0, 0, 0, M = 0, 0, 0.5

and for X = u, 0.25, 0.125 where u is equal to the experimental internal parameter for

all the compounds. The structural phase stability of the chalcopyrite compounds is

calculated by calculating the total energy as a function of volume. The band structure

calculation is used to predict the metallization of the compounds.

The optical properties of the above mentioned compounds are studied using

FP-LMTO "LMTART" method [26-271. The full potential method is sufficiently

accurate with no shape approximation to the charge density or potential. Inside the

muffin-tin spheres the basis functions, charge density and potential are expanded in

symmetry adapted spherical harmonic functions together with a radial function. In the

interstitial region the potential is expanded in plane waves. The full potential method

uses multibasis function to sustain a well converged wave function which provides

reliable description of the higher lying unoccupied states for the study of optical

properties. The threshold frequency or the onset of critical point, static dielectric

constants, refractive index and degree of anisotropy of the compounds are calculated.

5.3. CuAlX* (X = S, Se, Te)

Under ambient conditions, the electronic structure of the bct phase of CuAIXz

compounds is calculated using the self- consistent TB-LMTO method within ASA.

Exchange and correlation is included within the local density approximation by von

Bath and Hedin [28]. The spin orbit coupling is neglected but the relativistic Mass-

velocity variation is taken into account. In TB-LMTO method, the space is divided

into muffin-tin spheres and interstitial regions. In the above method the interstitial is

effectively neglected. Outside the sphere the LMTOs are augmented by the solutions

of the Helmholtz equation at some fixed energy. The ASA works well for closed-

packed structures so two types of empty spheres are included at * (0.0,0.0,0.25); (0.5,

0.0, 0.0); (0.0, 0.5, 0.0); * (0.25, -0.25, 0.125); i (0.25, -0.25, 0.375) in the interstitial

region of the primitive cell to have a better description of the charge density. The

average Wigner Seitz radius is scaled so that the total volume of the spheres is equal to

the equilibrium volume of the primitive cell. The self-consistency in the eigenvalue

was achieved to an accuracy of 10'~ Ryd.

53.1. STRUCTURAL STABILITY OF CuAIX2

The electronic structure for CuAlX2 is calculated with 3d, 4s, orbitals of Cu,

3s, 3p, orbitals of Al, 3% 3p, orbitals of S, 4s, 4p, orbitals of Se and 5s, 5p, orbitals of

Te are treated as valence states [29]. The calculations are performed on a grid of 384

k points in the entire Brillouin Zone of bct. The calculations are carried by using the

experimental u value of the compounds. At ambient conditions, the calculated cla

ratio for CuAlS2, CuAlSez and CuAlTez is estimated and found to be 2.0, 1.98 and

1.99 respectively. It is well known that (2 - cla) measures the tetragonal distortion.

Present study reveals that the rate of change in cla with respect to pressure is very

low. Hence, experimental cla ratios for these compounds are adopted in the present

calculation.

The equilibrium volume, bulk modulus and pressure volume relation for the

CuAIX2 compounds are estimated by fitting the calculated total energy values to the

Birch Murnaghan's equation of state. The calculated values for the bct structure of all

the three compounds are compared with the available experimental values [I 1, 301,

which are given in Table 5.1. Calculated equilibrium volume for bct structure of

CuAlS2 and CuAlSe2 are in good agreement with experimental values. The ratio of

Vo (cal)/Vo (Exp) is larger than unity, which is due to the uncertainties in the

sphere radii.

The bulk modulus is calculated from the first-principle band structure

calculation. The values given here are the upper limits, since only the volumes

were changed. The calculated bulk modulus is compared with the available

experimental as well as with the earlier reported values [19]. The calculated bulk

modulus decreases from CuAlS2 to CuAlSe2 to CuA1Te2.

Table.S.1.Calculated equilibrium volume (in at. units) and bulk

modulus compared with the experimental values

In order to understand the possibility of phase transition in CuAIS2 the total

energies are calculated for the high pressure fcc phase with higher co-ordination

number. Figs. 5.1 represent the graph plotted between the fitted total energy and

volume for CuAIS2. At ambient condition, the compounds are stable in the bct

structure and undergo transition from bct to fcc structure under the application of high

pressure. In order to understand the structural phase stability of CuAIS2, the electronic

structure calculation is carried out for fcc phase with space group (Fm-3m). The

atomic position assumed in the present calculation for the fcc phase is Cu at 0, 0, 0, A1

at 0.5, 0.5,0.S and X at 0.25, 0.25,0.25. The total energy values are calculated with

1728 k points in the entire brillouin zone of the fcc phase. The fitted total energy

values predict the phase transition from bct to fcc at -18 GPa. The calculated values

for the high pressure phase of CuAIS2 are not compared due to the non availability of

experimental values.

Roa et a1 [ l l ] performed X-ray diffraction measurements on CuAlSe2 and

predicted the phase transition from bct to fcc. The transition pressure for the

compound was determined using the linear ruby scale. The compound was predicted

to undergo transition at a pressure of 12.4 GPa. The calculation for the high pressure

fcc phase is carried in a manner similar to CuAIS2 compound. The fitted total energy

values show the phase transition for CuAlSe2 from bct to fcc under pressure. Fig. 5.2

represent the fitted total energy versus volume graph for CuAlSez. The fitted total

energy shows the phase transition at about 14 GPa which agrees with the

0.00.

.0.06.

4.10.

2. -0.15-

8 g -0.20.

"7 iif -0.26- I-

.o.ao.

-036 - T I . , . , . , . r . . i

210 300 360 400 410 100 660 600

Volume (a.ula

Fig.5.1. Total energy curve of CuAISz

experimental value of 12.4 GPa [ I I ] . The cell volume is less than the available

experimental value but the calculated bulk modulus is higher which may be due to

LDA.

Volume (a.u13

Fig.5.2. Total energy curve of CuAISel

Similar to CuAIS2 and CuAISez, the total energy calculation for the high

pressure fcc phase is carried to check the possibility of phase transition in CuAlTe2

compound. The calculated total energy values are fitted with the Birch Mumaghan

equation of states. The fitted total energy values predict the phase transition from

ambient bct phase to high pressure fcc phase similar to other two compounds. The

calculated values are unable to compare due to the non availability of experimental

results. The calculated volume and bulk modulus for the high pressure fcc phase of

CuAIS2, CuAlSe2 and CuAlTel are presented in the Table.5.2, with experimental

values for comparison.

Volume (a.u)'

Fig.5.3. Total energy curve of CuAlTez

SO0

.0.01-

.0.10.

4.16.

'0 * .0.20. E 2, -0.26-

t q -0.30. - -0.36.

-0.40.

.0.46.

Table.5.2. Calculated Cell volume and bulk modulus for fcc phase

FCC

* , . , . , . , . , . 400 100 600 700 600

CuAlS2 I 397.371 1 109.27 I present I I

Ref

It is found that the calculated cell volume for normal and high pressure phases

increases from CuAIS2 to CuAITe2. However, the calculated bulk modulus of CuAlXz

Bulk Modulus (GPa)

Compounds

CuAISe2

CuAlTe2

Cell Volume (a,".)3

461.906 543.402

565.528

96.04 SO* 3

73.61

Present E x ~ [ l l l .

Present

shows a linear decrease from CuAIS2 to CuAITe2, i.e. from the lower to the higher

atomic number of X atom. From the values of bulk modulus, it suggests that CuAlTe?

is more easily compressible than the other two compounds.

The pressure at which the enthalpies are same for both the structures is

referred as transition pressure. From the Equation of states, the volume collapse for

these compounds is estimated. Fig. 5.4 and 5.5 represents the EOS graph for CuAlS2

and CuAlSe2 with the available experimental values. The EOS of CuAlTe2 is not

presented due to the non availability of experimental values. The high-pressure phase

of CuAIS2 is found to occur at - I8GPa with 17.5% volume collapse (-AVNo) per

formula unit, which agrees with the earlier work [ l I ] . In the case of CuAlSe2 phase

transition occurs at 14.4 GPa with a volume collapse of 13%, which agrees with

experimental observations of 12.4 GPa [ l I].

In the case of CuAITe2, estimated lattice parameters at ambient pressure are

slightly more than the available experimental data. Since experimental EOS is not

available, the EOS for CuA1Te2 is calculated by considering the calculated Vo instead

of experimental volume as reference. For CuAlTe2, the high-pressure structure

appears at 8.29 GPa with a volume collapse of about 20%. These values are in need of

experimental data for comparison.

Pressure (GPa)

Fig.5.4. Pressure versus volume for CuAIS2

ss

1 .oo - CUAIS,

. .... . Exp

0.88 - '. TB-LMTO

B 0.55:

0.60 - 0 .

Fig.5.5. Pressure versus volume for CuAlSet

TB-LMTO

. . , . , . , . , . , . , . , . , . , .

1.00- CuAlSe,

: ~ ~ ~ ~ p eA

a o.as TB-LMTO

o 6 10 15 20 2s 30 3s 40 48 so

5 - 0.00-

P 9) 0.76- .L * 1 0.70-

d 0.66 - 0.60

E ~ P 5 * A

@ a A

TB-LMTO

. 3 10 15 20 26 30 55 10 1 . * . 1 - 1 . 1 . 1 - 1

Pressure (GPa)

5.3.2. BAND STRUCTURE OF CuAIX2

The band structures for CuAlS2, CuAISe2 and CuAlTe2 are computed for the

bct phase at equilibrium volume. It is well known that energy band structures of II-

IV-V2 compounds are similar to that of 111-V compounds. However energy band

structures of ternary analogs of 11-IV compounds are different from that of I-111-IV2

compounds. This is mainly due to the difference of uppermost valence band in I-III-

V12 compounds from those of 11-VI compounds.

Fig.S.6. Band structure profiles for bct phase of CuAIS2

The calculated band structures of CuAIS2 compound for the bct and fcc

structures are presented in Fig. 5.6 and 5.7. The band structure for the ambient bct

phase of CuAIS2 shows direct band gap. The valence band maximum (VBM) and the

conduction band minimum (CBM) of the compound occurs at the r symmetry point.

The uppermost valence bands ate derived from a combination of the p - orbitals of

the anion with the d- orbital of the noble metal, while the conduction band is derived

from the s- states of the cation.

Fig.5.7. Band Structure for the fcc phase of CuAlS2

The band structure for the high pressure fcc phase shows that the band profile

crosses the Fermi level which shows the metallic nature of the compounds under

pressure. So, it is confirmed that the compounds undergo transition frorn

semiconductor to metal under the application of pressure.

The Density of States (DOS) for both the bct and fcc structures of CuA1S2 is

calculated by tetrahedron method. The DOS for bct of CuAIS2 is presented in the

Fig. 5.8. The valence band of the compound results from a hybridization of the noble-

metal d levels with p levels on the other atoms. The DOS shows a well-developed gap

at EF for bct structure.

=(m

Fig.5.8. Density of States for the bct phase of CuAISz

EmRwl

Fig.5.9. Density of States for the fcc phase of CuAIS2

The estimated band gap for CuAIS2 compound is 2.25 eV, which is less than

the experimental value of 3.49 eV [2]. There is a large downshift in the energy gap

relative to the binary analogs. The band gap is underestimated due to LDA. The band

gap value for the above compound is compared with the available experimental and

theoretical data in the Table.5.3. Fig. 5.9 represents the DOS for high pressure fcc

phase of CuAIS2 compound. The DOS for the fcc phase shows no band gap, which

confirms the metallic nature of the compound under pressure.

Fig.S.lO. Band Structure for the bct phase of CuAlSe*

In the case of CuAISe2, the band structure and DOS for the bct and fcc phase

are plotted and presented in the Figs.5.10 to 5.13. The band structure for bct phase of

CuAISez shows direct band gap similar to CuAIS2 compound. The band structure for

the high pressure fcc phase shows the band profile crossing the Fermi level which

shows the metallic nature of the compound. The DOS for the compound is calculated

in a manner similar to CuAIS2 compound. The DOS for the bct phase shows a band

gap of 1.63 eV. The experimental band gap value for the CuAISe2 compound is 2.67

eV. The calculated band gap value is underestimated due to LDA. The DOS for the

high pressure fcc phase of CuAlSe2 shows no band gap. The DOS for the fcc phase

establish the transition of the compound from semiconductor to metallic nature under

pressure.

Fig.S.ll. Band Structure for the fcc phase of CuAISe2

Fig.5.12. Density of States for the bct phase of CuAlSe*

Fig.5.13. Density of States for the fcc phase of CuAISez

The band structure and DOS for CuAITel are presented in the Figs. 5.14 to

5.17. The band structure for the ambient bct phase of CuAlTel shows direct band gap

similar to other above two compounds. The band structure for high pressure fcc phase

shows the metallic nature of the compound with valence band profiles crossing the

Fermi level. The DOS for the bct phase shows 1.5 eV band gap, which is

underestimated than the available experimental value of 2.06 eV [2]. The band gap is

underestimated due to LDA. The DOS for the fcc phase of CuAlTe2 shows the

metallic nature of the compound similar to CuAlS2 and CuAlSez compounds.

Fig.5.14. Band Structure for the bct phase of CuAITez

ENmBr caw

Fig.5.16. Density of States for the bct phase of CuAITez

Fig.5.17. Density of States for the fcc phase of CuAITe2

Table.5.3. Band gap for the CuAIX2 semiconductors

Domashevskaya et al [34] had reported that the excluding of Cu 3d electrons

as valence states, led to overestimation of the band gaps for similar other

semiconductors. Shay et a1 [35] had predicted that without d- states for CuInSe2, band

Structure shows an indirect energy band gap. The indirect energy band gap is a

Compounds

CuAIS2

CuAlSea

CuAITe2

Band gap (eV)

2.25 2.05 3.49 1.63 1.65 2.67 1 .S 2.06

Ref

Present Rep[ 181 Exp[3 1 ] Present Re~[ lg l Exp[32] Present Exp[33]

surprising result. This motivated us to perform the calculation for the CuA1X2

compounds without considering 3d orbitals as valence states. However, these states

are treated as core electrons, which overestimate the band gap values, which agree

with the earlier prediction [36]. The calculated band structure values are larger than

that of the experimental values and follow the same trend of decreasing magnitude

from CuAIS2 to CuAITe2. The present study reveals that the d-states of noble metals

have to be treated as valence states to get the correct nature of the energy band gaps.

The calculated density of states of these compounds in fcc structure

confirms the metallic nature. The present investigation predicts that application of

high pressure on these compounds leads to structural phase transition along with

semiconductor to metal transition.

5.3.3. OPTICAL PROPERTIES OF CuAIX2

The chalcopyrite semiconductors receive more attention for their application

in nonlinear optical devices, detectors and solar cells 137-381. The optical properties

of CuAIX2 compounds are studied using the self-consistent FP-LMTO 'LMTART'

[25-261 method with Barth and Hedin [27] exchange correlation as discussed in the

section 3.2.4. The optical properties of condensed matter solids are described using

the complex dielectric function E (o) = E I ( a ) + i ~ ~ (0). The complex dielectric

function is known to describe the optical response of the medium at all photon energy

E=hw.

The optical properties of the compounds are studied for ambient volume.

Fig. 5.18 to 5.20 represents the imaginary and real part dielectric function of CuAlXz

compounds. The threshold frequency and the peak value for the compounds is

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

direction. The magnitude of the peak in 82 ( a ) increases from CuAISz to CuAISe2 and

from CuAlSe2 to CuAlTe2. The magnitude of peak shows the importance of anions in

the optical properties of the compounds. It would be worthwhile to attempt to identify

the transitions that are responsible for the structure in ~2 (a) .

Energy (eV)

Fig.5.18. Imaginary and Real part of CuAIS2 compound

The onset of critical point or the threshold energy value for the CuAIXz (X= S,

Se, Te) compounds is less than the experimental value due to LDA. The threshold

value is due to direct optical transition at r symmetry point. The first peak appears at

4.363 eV which is mainly due to transition at Z and X point in CuAlS2 compound. The

second peak is at 6.048 eV which is due to direct transition at T. The main peak is the

one which possesses higher peak value, which appears at 6.71 lev . The main peak for

CuAlS2 is due to direct transition at T.

4

I . I ' I . I . I . I ' m l 0 2 4 6 6 10 12 14 16

Energy (eV)

Fig.5.19. Imaginary and Real part of CuAISez compound

In CuAlSe2 the first peak occurs at 3.961 eV, which appears due to direct

optical transition at and X. The main peak for CuAlSe2 occurs at 7.333 eV, which are

due to optical transition at r point. Finally for CuAITel, the magnitude of &2(w) is high

for CuAITe2 among the other two compounds, which shows the importance of anions.

The first peak value for the compound is 2.541 eV. The peak for the compound appears

mainly due to transition at X point. The second and main peak for the compound

appears at 3.339 eV and 5.691 eV which is due to transition related to r point. Among

the above three chalcopyrites, CuAITe2 shows the main peak with higher magnitude of

&I(@). The calculated values are in need of experimental values for comparison,

162 + 14- CuAITe,

-2 - ...... ,.....--... 4- ', . . . . , . . . . . . . .'. -6 , . , . , . , . , .

0 2 4 6 8 10 12 1 16

Energy (eV)

Fig.5.20. Imaginary and Real part of CuAITe2 compound

5.3.3.1. STATIC DIELECTRIC CONSTANT AND REFRACTIVE

INDEX

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

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

band gap. The general shape of the real part of the dielectric function is like the

harmonic oscillator of the resonant frequency, which varies for each compound. The

static dielectric constants for the above chalcopyrites are calculated using EI,, (o) and

elz (0) values. The el (0) is found to increase from CuAIS2 to CuAlSez and from

CuAISel to CuA1Te2. The trend of increase in the static dielectric constant agrees with

the earlier calculation [39]. The static dielectric constant increases when band gap

decreases based on Penn model [39].

The refractive index for the three compounds is calculated, which shows linear

increase from lower atomic number of CuAIS2 to higher atomic nunlber of CuAlTe2.

The degree of anisotropy for the compounds is calculated by AE = (81 - EL) /E (0). For

CuAlS2 compounds the degree of anisotropy is small and negative but in the case of

CuAlSez and CuAlTez the value is found to small and positive. The chalcopyrite

materials taken for the present calculation are uniaxial material and therefore

birefrigent. The birefringence occurs only if the structure of the material is anisotropy.

Depending on the magnitude of the birefringence, the phase matching in linear and

non-linear optical interaction of the compounds occurs.

Table.5.4. Static dielectric function, refractive index, degree of

anisotropy and zero crossing point of CuAIXz Compounds

In contrast to refractive index of the compounds the calculated zero crossing

point is found to decrease from CuAIS2 to CuAISez and from CuAISe2 to CuAlTez for

the chalcopyrite compounds. The calculated values of static dielectric constants,

degree of anisotropy, refractive index and zero crossing point for the compounds are

given in the Table. 5.4. The calculated values in the table are in need of experimental

data for comparison.

5.4. CuGaX2 (X= S, Se, Te)

Like CuAlX2, CuGaX2 also crystallizes in the bct structure. In the present

study the electronic and structural phase stability for CuGaXz (X=S, Se, Te) are

studied by TB-LMTO method. The calculations are done in a manner similar to

CuAlX2, which is discussed in section 5.3. The available experimental u value for the

compounds is taken for the calculation. The structural stability and electronic

structure calculations are carried with 384 k- points in the entire part of the Brillouin

zone for the bct phase.

5.4.1. STRUCTURAL STABILITY OF CuGaX2

The equilibrium volume is calculated by total energy calculation for the

compounds. The calculations are performed with 3d 4s orbitals of Cu, 4s 4p orbitals

of Ga, 3s 3p orbitals of S and 4s 4p orbitals of Se and Ss, Sp, orbitals of Te as valence

states. The total energy values are calculated as a function of reduced volume and

fitted with the Birch Mumaghan equation of state. The equilibrium volume and bulk

modulus are calculated and presented in the Table.S.5. The ratio between the

calculated volume and experimental volume is calculated and presented in the table.

The calculated bulk modulus presented in the table is the upper limit value, since only

the volumes are changed. The calculated bulk modulus decreases from CuGaS2 to

CuGaSe2 to CuGaTe2. The agreements of the calculated equilibrium volume and bulk

modulus are found to be good with the experimental values.

Table.5.5. Calculated equilibrium (in at. units) and bulk modulus for

bct of CuGaXl compounds

Compounds

CuGaS2

Vo(cal) Present

CuGaSe2

Werner et al [4] based on his X-ray diffraction experiments showed the

transition of CuGaS2 from bct to fcc phase. The transition pressure for the compound

was measured at 16.9 -22.5 GPa with a volume collapse of 16%. Besides the pressure

value, the bulk modulus for the compound was given as 94k15 GPa. In the present

study, the structural phase transition from bct phase to face centered cubic phase of

CuGaS2 compound is investigated by the total energy calculation. The total energy

values for the fcc phase is calculated with 1728 k- points in the entire part of the

Brillouin zone. The calculated total energy values are fitted with the Birch Mumaghan

equation of state. Fig. 5.21 represents the fitted total energy versus volume graph for

498.123

CuGaTe2

586.898

Ref Vo(Exp)

505.39 485.001

728.569

582.902 561.693

Ref

Exp[30] Exp[36]

721.914 723.470

Exp[36] Rep[20]

Vo(cal) / Vo(Exp)

0.986 1.027

Exp[36] Exp[l6]

Bulk modulus

(GPa)

1.007 1.045

87.88 96*10

1.009 1.007

Present Exp[4]

70.75 71 57.84

Present EXP[ 1 1 Rep[20]

51.04 44

Present Exp[40]

bct and fcc phase. The total energy values show the structural phase transition from

bct to fcc under pressure in CuGaSl compound.

The calculated total energy values shows the transition from bct to fcc at a

pressure of 27.93 GPa with a volume collapse of 15%, which agrees with the

experimental pressure value of 16.9 -22.5 GPa [4]. The calculated cell volume and

bulk modulus for the fcc phase of CuGaS2 are 404.3 15 (a.u)' and 100.82 GPa. The

calculated bulk modulus agrees well with the experimental value of 94*15 GPa [4].

Volume (a.u)'

Fig.5.21. Total energy versus volume curve of CuGaS2

In order to look for any possible structural transition in CuGaSez, the total

energies are computed for the fcc phase by reducing the cell volume. The calculated

total energy values for the high pressure fcc phase are fitted with the Birch

Murnaghan equation of state. The equilibrium cell volume and bulk modulus for the

compound are calculated as 466.318 (a.u13 and 97.93 GPa. Due to the non availability

of the experiments, the present results are left without comparing. The calculated

values are in need of experimental data for comparison. Fig. 5.22 represents the fitted

total energy as a function of volume per molecule for CuGaSel compound. The

transition pressure is calculated from the pressure-volume relation. The pressure value

at which transition occurs is 17.39 GPa with a volume collapse of 15% for CuGaSe2,

which is in need of experimental data for comparison.

Volume (a.uf

Fig.5.22. Total energy versus volume curve of CuGaSe2

Using high pressure X- ray diffraction studies, Mori et a1 [16] observed two

phase transitions for CuGaTe2. According to experimental results, CuGaTez was

indexed to undergo phase transition from bct to d-Sc (disordered simple cubic) at 9.4

GPa and then to d-Cmcm (disordered base centered orthorhombic) phase at 18 GPa.

Disordered means original atoms are replaced by pseudo atoms. In order to check the

appearance and stability of high pressure d-Sc total energies are calculated for simple

cubic as well as d-Sc (cations are displaced from the original position without

breaking the simple cubic symmetry). Present calculation shows the existence of

disordered simple cubic, which is energetically not favorable when compared to bct

phase.

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. From the calculated total energies, it is found that

orthorhombic with displaced atoms along c-axis by 10% is most favorable phase

when compared to bct at high pressures. The transition pressure is calculated as 10.71

Gpa, whereas the experimental value is 15.3 GPa. The calculated volume for the

orthorhombic is 570.381 (a.uP and bulk modulus is 79.92 GPa.

Similar to other compounds, the total energies are also calculated to check the

phase transition to the fcc phase. Fig.5.22 represents the total curve for the ambient

and high pressure phases of CuGaTez compound. The fitted total energy values show

the transition at about 20.5 GPa. The calculated volume is 541.529 and bulk

modulus is 55-83 GPa, which are in need of experimental results for verification.

FCC I

q 4.80

+ ::::I , . -Bc; 1 -0,76

400 500 600 700 500 BOO

Volume (a.u)'

Fig.5.23. Total energy versus volume cuwe of CuGaTet

5.4.2. BAND STRUCTURE OF CuGaXz

The LMTO band structures of CuGaSz, CuGaSel and CuOaTe* along the high

symmetry directions are plotted for the bct phase at equilibrium volume. The band

profiles show the valence band maximum (VBM) and conduction band minimum

(CBM) at r indicating direct band gap for the compounds similar to CuAlXz

compounds. The band structure for the high pressure phases is plotted which shows

that the profiles cross the Fermi level for the compounds. The band struckre for the

high pressure phase shows the metallic character of the CuGaX2 compounds, which is

similar to CuAIX2 compounds.

The density of states for both the bct and high pressure structures is calculated

by tetrahedron method. The calculated density of states shows a band gap E, for bct

structure. There is a large downshift in the energy gaps relative to the binary analogs.

The calculated band gap values for the three compounds are presented in Table.5.6

with available experimental and theoretical values. The calculated band gap values

underestimate the experimental value due to LDA.

The PDOS for the compounds are calculated to find the contributions of s, p, d

states of Cu, Ga and anion X atoms. At higher energy in the upper part of the valence

band, the Cu -d state hybridizes with the anions p state and contributes for the direct

band gap of the compounds. The contributions of Ga- d states and S-p states are at the

lower part of the valence band.

The calculated density of states for the high pressure phases shows no band

gap, which confirms the metallic nature of the compounds. The present study predicts

that the compounds undergo transition from semiconductor to metal transition under

the application of high pressure.

Table.5.6. Estimated band gap value for the bct phase of CuGaXz

compounds

Ref

Present Rep[ 1 81 Expi4 1 1 Present Rep[ 181 Exp[3 1 I Present Exp[431 A

Compounds

CuGaS2

CuGaSe2

CuGaTe2

Band gap (eV)

0.625 1.25 2.43 0.382 0.48 1.68

0.286 1.24

5.43. OPTICAL PROPERTIES OF CuGaX2

The self-consistent FP-LMTO 'LMTART' [26-271 method with Barth and

Hedin [28] exchange correlation is used to study the optical properties of CuGaX2

compounds at ambient conditions. The full potential method is sufficiently accurate

with no shape approximation to the charge density or potential. The calculations are

carried out in similar manner as discussed in section 5.4.3. The LMTO basis set

expanded in spherical harmonics up to 1,, =6.

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

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

direction. The onset value is less than the experimental value due to LDA. Fig. 5.24 to

5.26 represents the imaginary and real part dielectric function of CuGaX2 compounds.

The threshold frequency value is due to direct optical transition at r point similar to

CuAIX2 compounds. The first peak for CuGaS2 occurs at 2.277 eV, which is due to r

transition. The second peak appears at 4.05 eV for CuGaS2, which appears mainly due

to transition related to Z. The main peak occurs at 6.179 eV, which appears due to

transition related to Z symmetry point. The peak values for CuGaS2 agree with the

earlier calculation [21].

In CuGaSel, the first or main, second and main peak occur at 1.51 1 eV, 3.132

eV and 4.795 eV. The first peak for the compound is due to transition related to and T,

the second peak is due to transition related to X symmetry point and the third peak is

mainly due to direct optical transition at Z and T. The frequency values of CuGaSe2

agree with the earlier calculation [20].

In CuGaTe2, the first peak, second peak, and the main peak occur at 1.843 eV,

3.174 eV, and 4.753 eV respectively. The first peak occurs mainly due to transition at

r and X. The second peak, third peak and the main peak for CuGaTe2 occur mainly

due to transition related r symmetry point. The CuGaTe2 shows peak with higher

magnitude of ~ 2 ( 0 ) similar to CuAIX2 compounds The frequency values for CuGaTe2

compound are in need of experimental data for comparison.

5.4.3.1. STATIC DIELECTRIC CONSTANT AND REFRACTIVE

INDEX

The zero frequency limit E I (0) is most important measurable quantity. It

strongly depends on the band gap. The static dielectric constant, which is related to

the refractive index, is also calculated. The static dielectric constants for the above

chalcopyrites are calculated by averaging the E , , (a), E, , (w) and E I , (w) values. The EI

(0) is found to increase from CuGaS2 to CuGaTe2 for CuGaX2 compounds i.e. from

lower to higher atomic number compounds. The static dielectric constants show

higher value for the compound which possesses lower band gap value. The

calculation is carried out to show the importance of anions in the estimation of static

dielectric constants.

The calculated refractive index for the three compounds are calculated and

found to increase linearly from lower atomic number of S to higher atomic number of

Te. The degree of anisotropy AE for the above chalcopyrite compounds is calculated

using static dielectric constants. The calculated degree of anisotropy is found to small

and positive for CuGaXl compounds. The birefringence occurs depending on the

anisotropy of the compounds. The phase matching in linear and non-linear optical

interaction occurs based on the magnitude of the birefringence

Table.5.7 Static dielectric function, degree of anisotropy, refractive

index for the chalcopyrites

The calculated zero crossing point decreases linearly from CuGaS2 to

CuGaTe2 of the compounds, which is in contrast with the refractive index of the

compounds. The calculated static dielectric constants, degree of anisotropy and

refractive index of the compounds are given in the Table.S.7. The calculated

refractive index for CuGaS2 compound is in close agreement with the compared

experimental value.

Fig.5.24. Imaginary and Real part of CuGaSz compounds

12

-2 - ........ ...... .................. 4-

3 - i i i i l o i 2 14

Energy (eV)

Fig.5.25. Imaginary and Real part of CuGaSe* compounds

Fig.5.26. Imaginary and Real part of CuGaTe2 compounds

5.5. CuInX2 (X= S, Se, Te)

Under normal conditions, CuInX2 crystallizes in the body centered tetragonal

structure. The electronic structure, high-pressure phase transition and optical

properties of CuInX2 compounds are studied similar to CuAIX2 and CuGaX2

compounds. The atomic position for the ambient phase is similar to CuAIX2, which is

given in section 5.3. The experimental internal parameter u value for the compounds

is used in the calculation to total energy calculation.

5.5.1, STRUCTURAL STABILITY OF CuInX2

The electronic structure and structural phase stability are studied at ambient

and high pressure phase of the compounds. The calculations are performed with 384

k- points in the entire part of the Brillouin zone for the bct phase. The calculations are

performed with 3d 4s orbitals of Cu, 5s 5p orbitals of In, 3s 3p orbitals of S and 4s 4p

orbitals of Se and 5s, 5p, orbitals of Te as valence states. The equilibrium volume for

the compounds is calculated by total energy calculation as a function of reduced

volume.

Equation of state is fitted to the total energies and the equilibrium volume and

bulk modulus is calculated for the compounds. The calculated equilibrium volume

and bulk modulus for the compounds are given in the Table.5.8. The ratio between the

calculated equilibrium volume and compared experimental equilibrium volume are

also given in the Table.5.8. Due to uncertainties in the sphere radii, the calculated

ratio is larger than unity for CuInS2 and CuInTe2 compound. The calculated bulk

modulus is slightly less than the experimental value. The experimental values were

determined from the X-ray measurements and sound velocity measurements. The bulk

modulus is calculated by the first principle method and it is the upper limit value since

only the volumes are changed for the compounds. The calculated bulk modulus for

the compounds is found to be in good agreement in the earlier reported values [ I 91.

Table.5.8. Calculated equilibrium volume and bulk modulus for bct

of CuInX2 compounds

The high pressure phase transition in CulnSz compound was predicted

Compounds

CuInS2

CuInSel

CuInTe2

experimentally by Tinoco el a1 [14] by his the X-ray diffraction using synchrotron

Vo(cal) Present

radiation technique. Experimentally at a pressure of 12.8 GPa the compound was

Vo(Exp)

581.976

622.945

801.547

indexed to undergo transition from bct to NaC1 type structure. The electronic structure

Ref

calculations are carried out to understand the high pressure phase transition in CuInS2

Ref VO (cal) / VO (Exp)

579.971 569.870 656.991 649.5 15

800.255

compound. The calculation for the high pressure phase is carried out with 1728 k-

Bulk modulus

points in the entire part of the Brillouin zone. Fig.5.27 represents the total energy

Exp[l4] Exp[30] Exp[l4] Exp[40]

Exp[4O]

curves for the ambient and high pressure phase of CuInSz compound. The cell volume

and bulk modulus for the high pressure is calculated as 457.328 (a.u13 and 107.94

1.004 1.021 0.948 0.959

1.002

GPa. The calculated bulk modulus agrees well with the experimental value of 123 i 1 5

GPa [14]. From the equation of state the transition pressure and volume collapse for

64.87 75*5 58.01 48.2 53.22 72i2 43.47 45.4 45

the compounds are calculated. The pressure of structural transition from bct to fcc

Present Exp[l4] Present Exp[41] Rep[2O] Exp[l4] Present Exp[41] Rep[l9]

occur at 16.1 1 GPa with a volume collapse of about 15% for CuInS2 compound. The

wansition pressure agrees well with the experimental value of 12.8 GPa. [14].

Volume (a.u)"

Fig.5.27. Total energy versus volume graph of CuInSz

Similar to CulnS2 compound, it was experimentally proved that CuInSez

undergoes transition from bct to NaCl type by Tinoco el a1 [14]. The electronic

structure calculation for the high pressure phase is carried out to calculate the cell

volume, bulk modulus and bulk modulus for CuInSe2 compound. The calculated cell

volume for CuInSel compounds is 5~6.88l(a.u)~. The calculated bulk modulus for

CuInSe2 is 89.58 GPa. The calculated bulk modulus is compared with the

experimental value [14]. The fitted total energy values are plotted as a function of

volume. Fig: 5.28 show the total energy graph for CuInSe2 compounds. From the

equation of state the transition pressure for CuInSe2 is calculated as 21.66 GPa, which

is compared with the experimental value [I41 The volume collapse for the compound

is around 12.5% for CuInSe2, which agrees with the experimental volume collapse of

10%.

4.2.

4.3.

4.6- c: 4.7.

-0.6,. , . . , . . . . , . . . , loo rso 460 MO sio 660 aio aso 760 760 rio

Fig.5.28. Total energy versus volume curve of cu185e2

Using X- ray diffraction analysis, the high pressure studies for CulnTe2 was

performed by Mori et a1 [16] up to a pressure of 13 GPa. They found that CuInTe2

undergoes a phase transition from bct to d- Cmcm at a pressure of 3.6 GPa and the

bulk modulus was determined to be 77 GPa.

Total energies for the d-Cmcrn phase are calculated in a manner similar to

CuGaTe2. The total energy calculations are carried out by displacing the atoms along

c- axis by about 10% as function of reduction volume. The fitted total energy values

show that there is a possible phase transition from bct to orthorhombic structure under

pressure.

The calculated equilibrium volume of d-Cmcm phase is 647.253 (a.u)'. The

calculated bulk modulus is about 71.63 GPa, which agrees well with the experimental

value of 77 GPa [16]. The pressure at which bct undergoes transition to dCmcm is

2.86 GPa, which is in close agreement with the experimental value of 3.0 GPa [16].

In order to check for further phase transition, total energies for fcc phase is

also calculated. Fig.S.29 represents the total energy curve versus volume for CulnTe2

compound. The compound shows the phase transition at 10.44 GPa. The calculated

volume for the fcc phase is 625.475 ( a . ~ ) ~ and bulk modulus is 66.84 GPa, which is in

need of experimental results for comparison.

Volume (a.u)'

Fig.5.29. Total energy versus volume curve of CuInTel

5.5.2. BAND STRUCTURE OF CuInXt

The band structure for the bct and high pressure phases are ploned for CuInX2

compounds. For the ambient bct phase the valence band maximum and conduction

band minimum meets at r point, which shows that the compounds are direct band gap

semiconductors. The lower part of valence band is due to the d -states of In atom. The

upper part of the valence band at higher energy is mostly derived from the cation Cu

d- states hybridized with the anions p -states of the compounds.

Under pressure, broadening of bands occurs and so the profile crosses the

fermi level. From the band structure calculation for high pressure phases it is

confirmed that CuInX2 compounds also exhibit metallic character when it transforms

from bct to high pressure phases.

Table.5.9. Estimated band gap for CuInXz compounds

The band gap value for bct phase of CuInX? compounds is calculated using

density of states by tetrahedron method. In TableS.9, the calculated band gap values

Compounds

CuInS2

CuInSe2

CuInTe2

Band gap (eV)

0.074 1.53

0.062 1.04

0.103 1.06

Ref

Present Exp[4 11 Present Exp[35] Present Exp[44]

for CuInX2 are compared with the available experimental and theoretical values. In

the case of fcc phase, the density of states shows no band gap which shows that the

compounds undergo transition from semiconductor to metal under pressure.

5.5.3. OPTICAL PROPERTIES OF CuInX2 COMPOUNDS

In the present calculation the optical properties of the above chalcopyrites are

studied using the self- consistent FP-LMTO "LMTART". In the full potential

calculation, the non-spherical terms in the potential are taken into account and so they

provide accurate results for the compounds.

Fig: 5.30 to 5.33 represent the imaginary and real part curve of the dielectric

function. The calculated threshold energy value or the onset of critical point occurs

are comparable with the calculated band gap values, which are less than the

experimental value due to LDA. The threshold energy value is due to transition

related to r symmetry point. The first peak, second peak, and the main peak positions

for CuInSz are 1.636 eV, 3.712 eV, and 5.292 eV respectively. The first peak and

second peak for the CulnSz occur mainly due optical transition at T. The third peak is

due to transition at Z point and the main peak for CuInS2 is mainly due to r point

transition. In CuInSe2, the first peak is at 1.594 eV which is mainly due to r and X

point transition. The second peak and the main peak for the compound are at 3.257

eV, and 4.67 eV, which are due to transition related to rpoint.

In CuInTe2 compound the first peak or main peak, second peak and third peak

for the compounds appear at 1.884 eV, 3.424 eV and 4.422 eV respectively. The first

peak or the main peak is due to direct optical transition at r and X point. The second

peak for the compound is due to transition related to r point. The third peak for the

compound is due to transition at and Z symmetry point. Similar to the other

chalcopyrites CuInTe2 shows peaks with magnitude of ~ ( 0 ) . The calculated

frequency values are in need of experimental values for comparison.

5.5.3.1. STATIC DIELECTRIC CONSTANT AND REFRACTIVE

INDEX

The zero frequency limit EI (0) is the electronic part of the static dielectric

constant. It strongly depends on the band gap. The band gaps are underestimated due

to LDA. The static dielectric constants for the above chalcopyrites are calculated by

averaging the EI,, (w), EI, (o) and EIZ (a) of real part dielectric function. The

calculated static dielectric constant values increases from CulnS2 to CulnSe2 and from

CuInSe* to CuInTe2, which is shows the importance of anion in the calculation of

static dielectric constants.

The refractive index for the compounds is calculated using the real part

dielectric function. The values are found to increase linearly from lower atomic

number of S to higher atomic number of Te. The calculated static dielectric constant

€1 (0) and refractive index n (0) for the above chalcopyrite semiconductors are

tabulated in the Table. 5.10. In the table along with the EI (0) and n (0) the calculated

values for ~1~ (0), elll (0) are also given. The degree of anisotropy A E for the

chalcopyrite compounds are also calculated which is found increase from S to Te.

The degree of anisotropy AE for the above delafossite compounds is calculated

and found to be small and positive for CulnSz and CuInSel compounds. In the case of

CuInTe2 it is found that the degree of anisotropy is small and negative. The zero

crossing point for CuInS2, CulnSe2 and CuInTe2 are calculated and found decreasing

linearly from S2 to Tez. The calculated degree of anisotropy values and zero crossing

point for the compounds are given in the Table.5.10 along with the static dielectric

constant and refractive index. The calculated values are in need of experimental

values for comparison.

Fig.5.30. Imaginary and Real part of CuInSa compounds

-2 - 4.

....... : . . . . . . . . . . .. . . . . . . '.'

i i L i o 1 0 1 2 1 4 , . 1 . . . 8

Energy (eV)

-2 - ..... ................. .... ...... 4 -

I . , . , . , . , 0 2 4 6 8 10 12 14

Energy (eV)

Fig.5.31. Imaginary and Real part of CuInSe2 compounds

Fig.5.32. Imaginary and Real part of CuInTez compounds

.2 - 4-

.... ......... --.-.. .......... ........... - 6 . I - I - I - I

o i: i i i o i z 1 4

Energy (eV)

Table.S.lO. Static dielectric constants, refractive index, degree of

anisotropy and zero crossing point for the CuInX2

chalcopyrites

5.6. CONCLUSION

Compounds

CuInSz

CuInSe2

CulnTe2

The ground state properties and high-pressure behaviour of CuMX2 (M=AI,

Ga, In X=S, Se, Te) are studied using the self-consistent TB-LMTO method. Using

total energy calculation, the equilibrium volume and bulk modulus are calculated and

compared with the available experimental data.

Pressure induced phase transition for CuAISez from chalcopyrite structure to

cubic structure was observed at a pressure of 12.4 GPa by Roa el al. The present

calculation shows the phase transition from bct to fcc at 14.4 Gpa which is in close

agreement with the experimental observation. The cell volume and bulk modulus are

calculated for CuAlSe2 and compared with experimental value.

81 (0)

5.738

5.777

7.429

For both the structures, the lattice parameter increases from CuAIS2 to

CuAlTe2. This increase of lattice parameter from CuAISz to CuAlTe2 agrees well with

the available experimental results, which may be due to the increase of anion radius of

~ ~ ~ ( 0 )

5.676

5.757

7.839

EIII(O)

5.862

5.817

6.609

Zero crossing

point (eV) 5.709

6.583

4.670

A 8

0.032

0.010

-0.165

n (0)

2.395

2.404

2.726

the compounds. At the same time, the bulk modulus decnases from CuAISz to

CuAITe2 in both the structure. The calculated lattice parameter and bulk modulu's of

fcc structure of CuAlS2 and CuAITe2 are in need of experimental data for comparison.

In the band structure calculation the importance of 3d orbital is studied, the band

structures of these compounds in bct structure is calculated with 3d electrons as

valence and also without considering 3d orbitals of the copper as valence states.

When 3d orbitals are included, DOS shows large downshifts in the energy gaps

relative to the binary analogs. The bct phase of CuAIX2 shows direct band gap. The

band gap for all the three compounds shows the decreasing trend from CuAlS2 to

CuAITe2. The calculated band structure for the fcc phase of these compounds shows

the metallic nature. It is concluded that the compounds undergo not only structural

phase transition but also undergo semiconductor to metallic transition.

The calculated equilibrium volume, bulk modulus and estimated band gap for

the compounds are compared with the available experimental and reported values

which follow the same trend of CuAIX2 compounds which is due to the atomic size

effect of the compounds.

The high pressure phase @ansition of CuGaSz compound at 27.93 GPa agrees

with the experimental work of 16.9 - 22.5 Gpa by Werner et a1 [4]. The calculated

bulk modulus of 100.82 GPa for the high pressure phase agrees with the experimental

value of 94*15 GPa. The high pressure phase transition from bct to fcc phase of

CuGaSe2 is in need of experimental results for comparison. The high pressure results

of CuGaSel are similar to the behavior of the above chalcopyrites under pressure.

Using X- ray diffraction technique, Mori et 01 [16] observed the phase

transition from bct to d- Sc and then to d- Cmcm phase for CuGaTe2 under pressure.

The present calculation of CuGaTel shows the possibility of phase transition to simple

cubic, which is energetically not favorable. To check the existence of d- Cmcm phase

total energy calculations are carried out for primitive onhorhombic by disordering the

atoms along c- axis without breaking the symmetry. The compound shows the phase

transition at about 10.71 GPa, which is less than the experimental value of 15.3 GPa,

Similar to above chalcopyrites the total energies for fcc phase are calculated to check

the possibility of phase transition to fcc phase. The compound shows transition at 20.5

GPa, which is in need of experimental value for comparison.

The electronic structure calculation for the ambient phase of CuInX2

compounds is calculated. The equilibrium volume and bulk modulus are calculated

from the total energy calculation for the bct phase which are in good agreement with

the experimental values. The high pressure phase transition results of CuInS2 and

CuInSel agree with the experimental results of Tinoco er ul. The calculated bulk

modulus for CulnS2 and CuInSe2 are in agreement with the experimental data.

In the case of CuInTez it was experimentally proved by Mori et ul [I61 that it

undergoes transition to d- Cmcm phase under pressure. The electronic structure

calculations for the d- Cmcm are carried out by displacing the atoms along c- axis

similar to CuGaTea compound. The calculated bulk modulus of 71.63 GPa is in close

agreement with the experimental value of 77 Gpa. The pressure at which transition

occurs for the compound is calculated as 2.86 GPa, which is in agreement with the

experimental value of 3.0 GPa. In order to check the possibility of phase transition to

fcc, the total energies are calculated for the fcc phase. The fitted values show the

phase transition at about 10.44 GPa. The calculated value is in need of experimental

results for verification.

Band structures for bct and high pressure phases of the above chalcopyrites are

calculated. The bct phase of the compounds shows direct band gap. The band gap

value for the bct phase of the compounds is calculated using density of states and

compared with the available experimental and theoretical data. In the case of high

pressure phases the band structure shows metallic character. From the band structure

calculation it is concluded that the compounds transform from semiconductor to metal

under pressure.

In the study of optical properties of CuMX2 (M=AI, Ga,. In; X=S, Se, Te), the

dielectric functions of compounds are calculated using FP-LMTO method. The

calculation for the compounds is performed with the estimated lattice constant for the

equilibrium volume. The threshold energy or the onset of critical point for the

compounds is calculated from the imaginary pan of dielectric function of the

compounds. The peaks in the imaginary part show higher magnitude for the telluride

compounds when compared with the sulfur and selenide compounds, which show the

importance of anions. The threshold energy value is less than the experimental value

of the compounds due to LDA. The static dielectric constants for the compounds

show linear increase from S to Se and from Se to Te due to the decrease of band gap

value of the compounds. The calculated refractive index of the compounds also

increases from S to Te i,e from lower to higher atomic number. The degree of

anisotropy of the compounds is found to be small and positive for all compounds

except CuAIS2 and CulnTe2. The calculated static dielectric constants. refractive

index, degree of anisotropy and zero crossing point show the influence of anion in the

optical properties of the compounds. The calculated values are in need of

experimental values for comparison.

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