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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 2 — Jan. 23, 2006
  • pp: 710–716
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Theoretical investigation of the electronic and optical properties of pseudocubic Si3P4, Ge3P4 and Sn3P4

Ming Xu, Songyou Wang, Gang Yin, Liangyao Chen, and Yu Jia  »View Author Affiliations


Optics Express, Vol. 14, Issue 2, pp. 710-716 (2006)
http://dx.doi.org/10.1364/OPEX.14.000710


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Abstract

Group-IV phosphides are relatively unknown materials as compared to the Group-IV carbide. In this work, we detailed the first principles calculations of the electronic and optical properties of the pseudocubic M3P4 (M=Si, Ge, Sn) using the density function theory (DFT). Results are in good agreement with those previous works. Furthermore, the optical constants, such as the dielectric function, energy loss function and effective number of valence electrons are calculated and presented in the study.

© 2006 Optical Society of America

1. Introduction

IV-V compounds have attracted great attentions in the last decade due to their important applications. C3N4, Si3N4 and Ge3N4 are well known for their high bulk moduli and wide band gaps to be used as the high-performance engineering materials [1–3

1. M. L. Cohen, “Predicting useful materials,” Science 261, 307(1993). [CrossRef] [PubMed]

]. Recently, Feng et al investigated the structural properties and bulk moduli of C3P4, Si3P4, Ge3P4 and Sn3P4 by using the first principles calculations successfully to predict that the most stable phase of those compounds is the pseudocubic structure [4–9

4. A. T. L. Lim, Y. P. Feng, and J. C. Zheng, “Stability of Hypothetical Carbon Phosphide Solids,” Int. J. Mod. Phys. B 16, 1101 (2002). [CrossRef]

]. Their results show that the bulk modulus decreases as the group-IV atom changed from C to Sn and it is much smaller than that of the corresponding Nitrides. For Bulk M3N4, however, there is still lack of the experimental data for the crystalline M3N4. In this work, we made continuous efforts to study the structural and optical properties of bulk M3N4 in consideration of their stable phase.

The electronic structures and optical properties of pseudocubic M3N4 are studied based on the first-principles density function theory [10

10. P. Hohenberg and W. Kohn, “Inhomogeneous electron gas,” Phys. Rev. 136, B864 (1964). [CrossRef]

, 11

11. W. Kohn and L. J. Sham, “Self-consistent equations including exchange and correlation effects,” Phys. Rev. 140, A1133 (1965). [CrossRef]

] with the generalized gradient approximation (GGA) [12

12. J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865 (1996). [CrossRef] [PubMed]

]. We first carefully calculated the electronic structures, because the optical properties depend on both the inter- and intra-band transitions. Afterwards, we present the optical properties of pseudocubic M3N4 in our work, including the dielectric function, electron energy loss function and effective number of the valence electrons. The paper is organized as follows: A brief description of the calculation method is given in Sec. II; the results for optimized structural parameters, band structures, dielectric properties and some discussions are shown in Sec. III; and a summary is finally drawn in Sec. IV.

2. Computational method

First-principles total-energy calculations were performed using the CASTEP code [13

13. M. Segall, P. Lindan, M. Probert, C. Pickard, P. Hasnip, S. Clark, and M. Payne, “First-principles simulation: ideas, illustrations and the CASTEP code,” J. Phys. Condens. Matter 14, 2717(2002). [CrossRef]

]. The generalized gradient approximation for exchange-correlation effects and the Vanderbilt ultrasoft pseudopotentials were used in the calculations. The maximum plane-wave cutoff energy was taken as 300eV and the numerical integration of the Brillouin zone was performed using a 5×5×5 Monkhorst-Pack k-point sampling procedure.

3. Results and discussion

Fig. 1. Ball-stick model of pseudocubic-M3N4

Table 1. Calculated equilibrium structure parameters and properties of the pseudocubic M3N4

table-icon
View This Table

The calculated band structures of the pseudocubic M3N4 are plotted in Fig. 2. The results show that they all have the small and indirect band gaps. The indirect band gap of Si3P4 occurs between the A and Γ points corresponding to the valence and conduction bands, respectively. The tops of the valence bands of the Ge3P4 or Sn3P4 structures, however, are located at the points that are near the Γ point along the Γ-M direction.

Fig. 2. Calculated band structure for pseudocubic-M3N4. (a) Si3P4, (b) Ge3P4 and (c) Sn3P4

The values of calculated band gaps of Si3P4, Ge3P4 and Sn3P4 are 0.33eV, 0.17eV and 0.83eV, respectively. Since the GGA method may underestimate the band gap and there is no experiment carried out for these compounds, the band gap calculated by GW quasiparticle theory may give more accurate value [14

14. M. S. Hybertsen and S. G. Louie, “Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies,” Phys. Rev. B 34, 5390 (1986). [CrossRef]

, 15

15. M. P. Surh, S. G. Louie, and M. L. Cohen, “Quasiparticle energies for cubic BN, BP, and BAs,” Phys. Rev. B 43, 9126 (1991). [CrossRef]

]. Anyway, the results show that all three compounds are indirect band gap semiconductors and the band gap of Sn3P4 is wider than the others.

The gross features of the density of states (DOS) from M3N4 compounds are quite similar, so we only show the result for Si3P4 as an example in Fig. 3. It can be seen that there are three regions in the energy range of the valence band. In the first region, the band with the energy ranging from -14 eV to - 9 eV is mainly from the 3s states of P and Si sites. In the second region, the band with the energy ranging from -9 eV to - 6 eV is hybridized by the 3s and 3p states. The third region of the valence band ranging from -6eV to 0 eV, combined with the conduction band above the energy level of 0 eV, is mostly originated from the 3p states of the P and Si sites.

Fig. 3. Calculated total and partial density of states for pseudocubic- Si3P4

It is well known that the linear electronic response of a system to an external electromagnetic field can be measured by the complex dielectric function ε(ω)=ε1(ω)+iε2(ω). The imaginary part of the dielectric function ε2(ω) can be obtained from the electronic structure calculations by using the matrix elements between the occupied and unoccupied wave functions.

In terms of the electric-dipole approximation, the imaginary part of the dielectric functions can be calculated by the following formula:

ε2(ω)=8π2e2ω2m2Vc,vkc,kêp|v,k2δ(Ec(k)Ev(k)ħω)
(1)

where c and v represent the conduction and valence bands, respectively; ∣n,k> is the eigenstate obtained from band structure calculations; p is the momentum operator; ê is the external field vector; and ω is the frequency of incident photons.

The real part ε1(ω) can be derived from the ε2(ω) by the Kramer-Kroning transformation. Furthermore, other optical properties like the energy loss function L(ω) can be derived from ε1(ω) and ε2(ω) as

L(ω)=ε2(ω)(ε12(ω)+ε22(ω))
(2)

We calculated both of the longitudinal and transverse dielectric functions to see that these two functions are almost identical within the difference of about 1%. It indicates that the IVV compounds with the pseudocubic phase are not strongly anisotropic though they are structurally asymmetric. Therefore, only the longitudinal optical properties of M3N4 are taken into consideration in the study.

The comparison of the calculated optical properties for the three pseudocubic compounds is given in Fig. 4. The imaginary dielectric function ε2(ω) represents the optical absorption of the material. Each spectrum has a prominent absorption peak. They are located at about 4.0, 3.9 and 3.5 eV photon energy, respectively. The imaginary part ε2(ω) of Si3P4 around 4.0 eV is mainly attributed to the transitions at the Γ point from 0.41 eV to 4.05 eV and 4.28 eV to 0.09 eV. The ε2(ω) peak of Ge3P4 is located at about 3.9 eV, corresponding to the transitions from 0.17 eV to -3.9 eV and 4.1 eV to -0.1eV at the Γ point. For the Sn3P4 structure, the peak occurs at about 3.5 eV and is due to the main part of transitions from 1.6 eV to -1.9eV at the Γ point. It is noted that the peak shown in the ε2(ω) spectra is not just due to the single interband transition since the multiple direct and indirect transitions will happen around the same energy peak positions.

Fig. 4. Dielectric functions (a) and energy-loss function (b) of M3N4

The real dielectric function ε1(ω) is obtained from ε2(ω) by the Kramers-Kronig transformation. In the zero frequency limit, ε1(ω) is the static dielectric constant, excluding any contribution from the lattice vibrations. The static dielectric constants for the three compounds are 14.66, 18.03 and 15.32, respectively. These values seem larger than that of c-(Si, Ge)3N4 in the cubic spinal structure [16

16. W. Y. Ching, Shang-Di Mo, and Lizhi Ouyang, “Electronic and optical properties of the cubic spinel phase of c-Si3N4, c-Ge3N4, c-SiGe2N4, and c-GeSi2N4,” Phys. Rev. B 63, 245110(2001). [CrossRef]

].

The energy loss function is an important optical parameter to show the peak often associated with the plasma frequency and described as the plasma resonance [17

17. S. Saha, T. P. Sinha, and A. Mookerjee, “Electronic structure, chemical bonding, and optical properties of paraelectric BaTiO3,” Phys. Rev. B 62, 8828 (2000). [CrossRef]

]. Above and below the plasma frequency the material will have the dielectric and metallic properties, respectively. The calculated peak of L(ω) of Si3P4 is located at about 18 eV, while those of Ge3P4 and Sn3P4 are shifted to lower energies at about 17.5 eV and 15 eV, respectively.

Since the plasma resonance is intrinsically arisen from the collected oscillations of free electrons, the effective number neffm) of valence electrons per atom that contributes to the interband transitions can be calculated in terms of the expression as

neff(ωm)=2mε0πe20ωmωε2(ω)
(3)

where ωm denotes the upper limit of integration, and the quantities m and e are the electron mass and charge, respectively. The results are shown in Fig. 5. The effective number of valence electrons of M3N4 decreases with increasing atomic number. The saturated neff(ωm) above 10 eV is close to the average number of the valence electrons per atom in M3N4. The discrepancies of peak positions in the energy loss function [see Fig. 4(b)] partly attribute to the different saturated values of neff for the Si3P4, Ge3P4 and Sn3P4 structures.

Fig.5. The calculated effective number of valence electrons (neff) participating in the interband optical transitions of M3N4

4. Conclusion

Acknowledgments

This work was partially supported by the Natural Science Foundation of China (Grant No. 60578046) and the Shanghai Science and Technology Commission (Grand No. 05PJ14016).

References and links

1.

M. L. Cohen, “Predicting useful materials,” Science 261, 307(1993). [CrossRef] [PubMed]

2.

J. L. He, L. C. Guo, D. L. Yu, R. P. Liu, Y. J. Tian, and H. T. Wang, “Hardness of cubic spinel Si3N4,” Appl. Phys. Lett. 85, 5571(2004). [CrossRef]

3.

B. Molina and L. E. Sansores, “Electronic structure of Ge3N4 possible structures,” Int. J. Quantum Chem. 80, 249 (2000). [CrossRef]

4.

A. T. L. Lim, Y. P. Feng, and J. C. Zheng, “Stability of Hypothetical Carbon Phosphide Solids,” Int. J. Mod. Phys. B 16, 1101 (2002). [CrossRef]

5.

A. T. L. Lim, Y. P. Feng, and J. C. Zheng, “Interesting electronic and structural properties of C3P4,” Mater. Sci. Eng. B 99, 527 (2003). [CrossRef]

6.

M. Huang, Y. P. Feng, A. T. L. Lim, and J. C. Zheng, “Structural and electronic properties of Si3P4,” Phys. Rev. B 69,054112 (2004). [CrossRef]

7.

M. Huang and Y. P. Feng, “Further study on structural and electronic properties of silicon phosphide compounds with 3:4 stoichiometry,” Comput. Mater. Sci. 30, 371 (2004). [CrossRef]

8.

M. Huang and Y. P. Feng, Phys. Rev. B 70,184116 (2004); [CrossRef]

9.

M. Huang and Y. P. Feng, “Theoretical prediction of the structure and properties of Sn3N4,” J. Appl. Phys. 96, 4015 (2004). [CrossRef]

10.

P. Hohenberg and W. Kohn, “Inhomogeneous electron gas,” Phys. Rev. 136, B864 (1964). [CrossRef]

11.

W. Kohn and L. J. Sham, “Self-consistent equations including exchange and correlation effects,” Phys. Rev. 140, A1133 (1965). [CrossRef]

12.

J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865 (1996). [CrossRef] [PubMed]

13.

M. Segall, P. Lindan, M. Probert, C. Pickard, P. Hasnip, S. Clark, and M. Payne, “First-principles simulation: ideas, illustrations and the CASTEP code,” J. Phys. Condens. Matter 14, 2717(2002). [CrossRef]

14.

M. S. Hybertsen and S. G. Louie, “Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies,” Phys. Rev. B 34, 5390 (1986). [CrossRef]

15.

M. P. Surh, S. G. Louie, and M. L. Cohen, “Quasiparticle energies for cubic BN, BP, and BAs,” Phys. Rev. B 43, 9126 (1991). [CrossRef]

16.

W. Y. Ching, Shang-Di Mo, and Lizhi Ouyang, “Electronic and optical properties of the cubic spinel phase of c-Si3N4, c-Ge3N4, c-SiGe2N4, and c-GeSi2N4,” Phys. Rev. B 63, 245110(2001). [CrossRef]

17.

S. Saha, T. P. Sinha, and A. Mookerjee, “Electronic structure, chemical bonding, and optical properties of paraelectric BaTiO3,” Phys. Rev. B 62, 8828 (2000). [CrossRef]

OCIS Codes
(160.0160) Materials : Materials
(300.6470) Spectroscopy : Spectroscopy, semiconductors

ToC Category:
Materials

Citation
Ming Xu, Songyou Wang, Gang Yin, Liangyao Chen, and Yu Jia, "Theoretical investigation of the electronic and optical properties of pseudocubic Si3P4, Ge3P4 and Sn3P4," Opt. Express 14, 710-716 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-2-710


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References

  1. M. L. Cohen, "Predicting useful materials," Science 261, 307(1993). [CrossRef] [PubMed]
  2. J. L. He, L. C. Guo, D. L. Yu, R. P. Liu, Y. J. Tian, and H. T. Wang, "Hardness of cubic spinel Si3N4," Appl. Phys. Lett. 85, 5571(2004). [CrossRef]
  3. B. Molina and L. E. Sansores, "Electronic structure of Ge3N4 possible structures," Int. J. Quantum Chem. 80, 249 (2000). [CrossRef]
  4. A. T. L. Lim, Y. P. Feng, and J. C. Zheng, "Stability of hypothetical carbon phosphide solids," Int. J. Mod. Phys. B 16, 1101 (2002). [CrossRef]
  5. A. T. L. Lim, Y. P. Feng, and J. C. Zheng, "Interesting electronic and structural properties of C3P4," Mater. Sci. Eng. B 99, 527 (2003). [CrossRef]
  6. M. Huang, Y. P. Feng, A. T. L. Lim, and J. C. Zheng, "Structural and electronic properties of Si3P4," Phys. Rev. B 69, 054112 (2004). [CrossRef]
  7. M. Huang and Y. P. Feng, "Stability and electronic properties of Sn3P4," Phys. Rev. B 70, 184116 (2004) [CrossRef]
  8. M. Huang and Y. P. Feng, "Theoretical prediction of the structure and properties of Sn3N4," J. Appl. Phys. 96, 4015 (2004). [CrossRef]
  9. P. Hohenberg and W. Kohn, "Inhomogeneous electron gas," Phys. Rev. 136, B864 (1964). [CrossRef]
  10. W. Kohn and L. J. Sham, "Self-consistent equations including exchange and correlation effects," Phys. Rev. 140, A1133 (1965). [CrossRef]
  11. J. P. Perdew, K. Burke, and M. Ernzerhof, "Generalized gradient approximation made simple," Phys. Rev. Lett. 77, 3865 (1996). [CrossRef] [PubMed]
  12. M. Segall, P. Lindan, M. Probert, C. Pickard, P. Hasnip, S. Clark, and M. Payne, "First-principles simulation: ideas, illustrations and the CASTEP code," J. Phys. Condens. Matter 14, 2717(2002). [CrossRef]
  13. M. S. Hybertsen and S. G. Louie, "Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies," Phys. Rev. B 34, 5390 (1986). [CrossRef]
  14. M. P. Surh, S. G. Louie, and M. L. Cohen, "Quasiparticle energies for cubic BN, BP, and BAs," Phys. Rev. B 43, 9126 (1991). [CrossRef]
  15. S. Saha, T. P. Sinha, and A. Mookerjee, "Electronic structure, chemical bonding, and optical properties of paraelectric BaTiO3," Phys. Rev. B 62, 8828 (2000). [CrossRef]

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