Optical Properties
5.2. EFFECT OF JDOS AND OME ON OPTICAL PROPERTIES 141
Figure 5.20: (a) real part of dielectric function (b) refractive index.(Top panel) : ZnMnIn2T e4 and (Bottom panel)ZnOIn2T e4.
compare our calculatedǫ2 for the cases ZnMnIn2T e4 andZnOIn2T e4 with the result of Ganguli et.al. for the case ofZnIn2T e4 to study the effect of substitution in the de-fect chalcopyrite. Comparing figure 5.19(right-bottom panel), figure 5.9(a) (top panel) and figure 5.10(a) (top panel), we find there is an incremnt in ǫ2 in both Mn and oxy-gen substituted cases compared to ZnIn2T e4. Similar picture we may expect in case of absorption co-efficients also. The static dielectric constant in case of ZnMnIn2T e4
and ZnOIn2T e4 (figure 5.20 (a) top and bottom panel) are comparatively larger than ZnIn2T e4 as seen from figure 5.19(right-top panel). So we expect similar enhancement in refractive indices of both the systems.
Chapter 6
Conclusion
In general our study of structural, electronic and optical properties of many pure, de-fect and substituted chalcopyrite semiconductors by DFT based first principle TB-LMTO method give satisfactory result. Our result agrees well with the available experimental and other calculated results for the systems studied by others. Our calculated band gaps are found to be lower than the expected. This is purely due to the underestimation by LDA, which is a well known fact. Considering this limitation of LDA, our results are quite accurate. We have, in general, provided quantitative calculations of the effects of p-d hybridization and structural distortion on band gaps and other electronic properties and optical properties. We have also been able to provide detailed study of linear optical properties of few defects and substituted systems. We have shown the effects of various factors like DOS, OME etc in optical properties. Therefore we have provided deeper understanding of physics of these effects. Specifically we have following important out-comes.
1. Structural parameters, such as lattice parameters, anion displacements, tetragonal distortion and bond-lengths show good agreement with the available experimental
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results for systems studied by others.
2. Bulk modulus are calculated for all these systems exceptZnXIn2T e4 (X = O, Mn).
Results show inversed proportionality relation between lattice parameters “a” and bulk modulus for all the systems as expected, except in the case ofCu2InSe4.
3. Band structure and total density of states(TDOS) of all the systems show they are direct band gap semiconductors.
4. AAl2Se4 (A = Ag, Cu), CuIn2Se4, CuIn2S4 and Cu2InSe4 are found to be p-type semiconductors. But CdXGa2S4 (X = Ag, Al) and ZnXIn2T e4 (O, Mn) are n-type semiconductors.
5. Band gap increases in defect chalcopyrites in comparison to their corresponding pure and substituted chalcopyrites.
6. Study of partial density of states(PDOS) reveals that the contribution to upper valance band comes from the cation d and anion p hybrid orbitals in case of group I − III − V I2,I2− III − V I4,I − III2− V I4 and their substituted chalcopyrites semiconductors. This leads to strong p-d hybridizations in these cases. But in case of groupII −IV −V2,II −III2−V I4and their substituted chalcopyrites, the main contribution to upper valance band comes from the anion p states. Cation d states behave like core states in these types of compound and contribute to inner valance band. Therefore they do not participate in p-d hybridization. Major contributions come from the anion p states to the conduction band.
7. We have found significant effect of p-d hybridization on band gap reduction in ZnSnX2 (X = P, As, Sb). but the same is not found in other systems in the same
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group (II − IV − V2).
8. The quantitative estimate of the effects of p-d hybridization on band gap shows that the% of band gap reduction is more in case of the pure chalcopyrites compared to their corresponding defect chalcopyrites.
9. Though Li & Na do not have d orbitals contribution to upper valence band, they act like catalyst in reducing the band gap in cases ofCuLiIn2Se4 &CuNaIn2S4
respectively compared to their corresponding defect chalcopyrites.
10. Significant increment in band gaps are found in the case ofAgAlM2(S, Se, T e) and AAl2Se4(Ag, Cu, Cd, Zn) chalcopyrites due to structural distortion. But the effect is reversed in case ofZnSnX2 (X = P, As, Sb), CuInSe2,CuIn2S4,CuIn2Se4, CuNaIn2S4 andCuLiIn2Se4 compounds. That is, this effect leads to decrement in band gap for the above systems.
11. Quantitative estimate of the effect of cation-electronegativity on band gap in cases of ZnSnX2 (X = P, As, Sb) chalcopyrites show that there is an increment of band gap with respect to their binary analogs GaInP2, InGaAs2 and GaInSb2
respectively due to this effect.
12. Our study of linear optical properties for defect and substituted semiconductors show that optical properties strongly depend on optical matrix elements (OME) in the infrared and visible region of optical spectrum.
13. Optical properties in the UV region is mainly controlled by the joint density of states (JDOS).
14. Major structures and peaks in imaginary part of the dielectric function (ǫ2) in in-frared and visible region come from the contribution of OME in most of the cases.
In few cases like CuIn2S4, AgAl2Se4 and CuNaIn2S4 JDOS always plays im-portant role in this region of spectrum.
15. Significant effects of structural distortion and p-d hybridization are also found on ǫ2, OME and JDOS ofCuIn2S4,AgAl2Se4andCuNaIn2S4 chalcopyrites.
16. Substitution by Na in CuIn2S4 and Mn & Oxygen inZnIn2T e4 changes optical properties of the host significantly.
17. We have explicitly calculated the optical properties & OME for photon, polarized along c and⊥ to c-axis as well as the average value for all the above systems. The average value is calculated for CuIn2S4. Our study shows that chalcopyrites are anisotropic in nature and the properties get enhanced when photon is polarized⊥ to c-axis.
18. Calculation of static dielectric constantsǫ1(0) agrees well with the available exper-imental result in case ofCdIn2T e4 andCdGa2T e4.
19. Our calculation ofǫ1 andǫ2 in the cases of CdIn2T e4 andCdGa2T e4 agrees well with the result of Ozaki et. al.