Abstract

Long-wavelength optical phonons in multinary mixed crystals are studied based on the Pseudo-Unit-Cell model. A unitary matrix method is developed to calculate the eigenfrequencies of optical phonons in multinary mixed crystals. The analytical expressions of oscillator strengths and dielectric constants of the multinary mixed crystals are obtained as a function of the phonon frequencies. The results indicate that the composition dependence of oscillator strengths shows clearly the phonon-mode behaviors of the mixed crystals. The theory and calculation method can be applied to any type of multinary mixed crystals. It is found that there is a composition independent point for the dielectric constant of quaternary mixed crystals.

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  1. I. F. Chang, Ph.D. dissertation, University of Rhode Island, (1968).
  2. I. F. Chang and S. S. Mitra, “Application of a modified Random-Element-Isodisplacement model to long-wavelength optic phonons of mixed crystals,” Phys. Rev. 172, 924–933 (1968).
    [CrossRef]
  3. I. F. Chang and S. S. Mitra, “Long wavelength optical phonons in mixed crystals,” Adv. Phys. 20, 359–404 (1971).
    [CrossRef]
  4. R. S. Zheng and M. Matsuura, “Electron-phonon interaction in mixed crystals”, Phys. Rev. B 59, 15422–15429 (1999).
    [CrossRef]
  5. R. S. Zheng and T. Taguchi, “Theory of long-wavelength optical lattice vibrations in multinary mixed crystals: Application to group-III nitride alloys,” Phys. Rev. B 66, 075327 (2002).
    [CrossRef]
  6. R. S. Zheng, “Properties of optical phonons in multinary phosphide mixed crystals,” J. Shenzhen University (Science and Engineering), 23(1), 10–15 (2006).
  7. F. Yang and R. S. Zheng, “Properties of optical phonons in Zn1-x-yMgyBexSe quaternary mixed crystal,” Solid State Commun. 141, 555–558 (2007).
    [CrossRef]
  8. M. A. Abid, H. Abu. Hassan, Z. Hassan, S. S. Ng, S. K. Mohd. Bakhori, and N. H. Abd. Raof, “Experimental investigation of long-wavelength optical lattice vibrations in quaternary AlxInyGa1-x-yN alloys and comparison with results from the pseudo-unit cell model,” Physica B 406, 1379–1384 (2011).
    [CrossRef]
  9. M. Romcevic and N. Romcevic, “Phonons in multicomponent alloys,” J. Alloys Compd. 416, 64–71 (2006).
    [CrossRef]
  10. L. Genzel, T. P. Martin, and C. H. Perry, “Model for long - wavelength optical-phonon modes of mixed crystals,” Phys. Status Solidi B 62, 83–92 (1974).
    [CrossRef]
  11. M. Born and K. Huang, Dynamical Theory of Crystal Lattices, (Oxford University, 1954).
  12. E. Oh, R. G. Alonso, J. Miotkowski, and A. K. Ramdas, “Raman scattering from vibrational and electronic excitations in a II–VI quaternary compound: Cd1-x-yZnxMnyTe,” Phys. Rev. B 45, 10934–10341 (1992).
    [CrossRef]
  13. M. Grynberg, R. Le Toullec, and M. Balkanski, “Dielectric function in HgTe between 8 and 300K,” Phys. Rev. B 9, 517–526 (1974).
    [CrossRef]
  14. A. Manabe and A. Mitsuishi, “Far-infrared reflection spectra of HgSe,” Solid State Commun. 16, 743–745 (1975).
    [CrossRef]
  15. W. Gebicki and W. Nazarewicz, “Long-wavelength optical phonons in MgxHg1-xTe mixed crystals,” Phys. Status Solidi B 80, 307–311 (1977).
    [CrossRef]
  16. M. Romcevic, V. A. Kulbachinskii, N. Romcevic, P. D. Maryanchuk, and L. A. Churilov, “Optical properties of Hg1-xMnxTe1-ySey,” Infrared Phys. Technol. 46, 379–387 (2005).
    [CrossRef]
  17. H. Makino, H. Sasaki, J. H. Chang, and T. Yao, “Raman investigation of Zn1-xMgxSe1-yTey quaternary alloys grown by molecular beam epitaxy,” J. Cryst. Growth 214–215, 359–363 (2000).
    [CrossRef]
  18. D. Huang, C. Jin, D. Wang, X. Liu, J. Wang, and X. Wang, “Crystal structure and Raman scattering in Zn1-xMgxSe alloys,” Appl. Phys. Lett. 67, 3611–3613 (1995).
    [CrossRef]
  19. C. S. Yang, W. C. Chou, D. M. Chen, C. S. Ro, and J. L. Shen, “Lattice vibration of ZnSe1-xTex epilayers grown by molecular-beam epitaxy,” Phys. Rev. B 59, 8128–8131 (1999).
    [CrossRef]
  20. O. Madelung, Semiconductors-Basic Data, 2nd revised ed., (Springer, 1996).

2011 (1)

M. A. Abid, H. Abu. Hassan, Z. Hassan, S. S. Ng, S. K. Mohd. Bakhori, and N. H. Abd. Raof, “Experimental investigation of long-wavelength optical lattice vibrations in quaternary AlxInyGa1-x-yN alloys and comparison with results from the pseudo-unit cell model,” Physica B 406, 1379–1384 (2011).
[CrossRef]

2007 (1)

F. Yang and R. S. Zheng, “Properties of optical phonons in Zn1-x-yMgyBexSe quaternary mixed crystal,” Solid State Commun. 141, 555–558 (2007).
[CrossRef]

2006 (2)

R. S. Zheng, “Properties of optical phonons in multinary phosphide mixed crystals,” J. Shenzhen University (Science and Engineering), 23(1), 10–15 (2006).

M. Romcevic and N. Romcevic, “Phonons in multicomponent alloys,” J. Alloys Compd. 416, 64–71 (2006).
[CrossRef]

2005 (1)

M. Romcevic, V. A. Kulbachinskii, N. Romcevic, P. D. Maryanchuk, and L. A. Churilov, “Optical properties of Hg1-xMnxTe1-ySey,” Infrared Phys. Technol. 46, 379–387 (2005).
[CrossRef]

2002 (1)

R. S. Zheng and T. Taguchi, “Theory of long-wavelength optical lattice vibrations in multinary mixed crystals: Application to group-III nitride alloys,” Phys. Rev. B 66, 075327 (2002).
[CrossRef]

2000 (1)

H. Makino, H. Sasaki, J. H. Chang, and T. Yao, “Raman investigation of Zn1-xMgxSe1-yTey quaternary alloys grown by molecular beam epitaxy,” J. Cryst. Growth 214–215, 359–363 (2000).
[CrossRef]

1999 (2)

C. S. Yang, W. C. Chou, D. M. Chen, C. S. Ro, and J. L. Shen, “Lattice vibration of ZnSe1-xTex epilayers grown by molecular-beam epitaxy,” Phys. Rev. B 59, 8128–8131 (1999).
[CrossRef]

R. S. Zheng and M. Matsuura, “Electron-phonon interaction in mixed crystals”, Phys. Rev. B 59, 15422–15429 (1999).
[CrossRef]

1995 (1)

D. Huang, C. Jin, D. Wang, X. Liu, J. Wang, and X. Wang, “Crystal structure and Raman scattering in Zn1-xMgxSe alloys,” Appl. Phys. Lett. 67, 3611–3613 (1995).
[CrossRef]

1992 (1)

E. Oh, R. G. Alonso, J. Miotkowski, and A. K. Ramdas, “Raman scattering from vibrational and electronic excitations in a II–VI quaternary compound: Cd1-x-yZnxMnyTe,” Phys. Rev. B 45, 10934–10341 (1992).
[CrossRef]

1977 (1)

W. Gebicki and W. Nazarewicz, “Long-wavelength optical phonons in MgxHg1-xTe mixed crystals,” Phys. Status Solidi B 80, 307–311 (1977).
[CrossRef]

1975 (1)

A. Manabe and A. Mitsuishi, “Far-infrared reflection spectra of HgSe,” Solid State Commun. 16, 743–745 (1975).
[CrossRef]

1974 (2)

M. Grynberg, R. Le Toullec, and M. Balkanski, “Dielectric function in HgTe between 8 and 300K,” Phys. Rev. B 9, 517–526 (1974).
[CrossRef]

L. Genzel, T. P. Martin, and C. H. Perry, “Model for long - wavelength optical-phonon modes of mixed crystals,” Phys. Status Solidi B 62, 83–92 (1974).
[CrossRef]

1971 (1)

I. F. Chang and S. S. Mitra, “Long wavelength optical phonons in mixed crystals,” Adv. Phys. 20, 359–404 (1971).
[CrossRef]

1968 (1)

I. F. Chang and S. S. Mitra, “Application of a modified Random-Element-Isodisplacement model to long-wavelength optic phonons of mixed crystals,” Phys. Rev. 172, 924–933 (1968).
[CrossRef]

Abd. Raof, N. H.

M. A. Abid, H. Abu. Hassan, Z. Hassan, S. S. Ng, S. K. Mohd. Bakhori, and N. H. Abd. Raof, “Experimental investigation of long-wavelength optical lattice vibrations in quaternary AlxInyGa1-x-yN alloys and comparison with results from the pseudo-unit cell model,” Physica B 406, 1379–1384 (2011).
[CrossRef]

Abid, M. A.

M. A. Abid, H. Abu. Hassan, Z. Hassan, S. S. Ng, S. K. Mohd. Bakhori, and N. H. Abd. Raof, “Experimental investigation of long-wavelength optical lattice vibrations in quaternary AlxInyGa1-x-yN alloys and comparison with results from the pseudo-unit cell model,” Physica B 406, 1379–1384 (2011).
[CrossRef]

Alonso, R. G.

E. Oh, R. G. Alonso, J. Miotkowski, and A. K. Ramdas, “Raman scattering from vibrational and electronic excitations in a II–VI quaternary compound: Cd1-x-yZnxMnyTe,” Phys. Rev. B 45, 10934–10341 (1992).
[CrossRef]

Balkanski, M.

M. Grynberg, R. Le Toullec, and M. Balkanski, “Dielectric function in HgTe between 8 and 300K,” Phys. Rev. B 9, 517–526 (1974).
[CrossRef]

Born, M.

M. Born and K. Huang, Dynamical Theory of Crystal Lattices, (Oxford University, 1954).

Chang, I. F.

I. F. Chang and S. S. Mitra, “Long wavelength optical phonons in mixed crystals,” Adv. Phys. 20, 359–404 (1971).
[CrossRef]

I. F. Chang and S. S. Mitra, “Application of a modified Random-Element-Isodisplacement model to long-wavelength optic phonons of mixed crystals,” Phys. Rev. 172, 924–933 (1968).
[CrossRef]

I. F. Chang, Ph.D. dissertation, University of Rhode Island, (1968).

Chang, J. H.

H. Makino, H. Sasaki, J. H. Chang, and T. Yao, “Raman investigation of Zn1-xMgxSe1-yTey quaternary alloys grown by molecular beam epitaxy,” J. Cryst. Growth 214–215, 359–363 (2000).
[CrossRef]

Chen, D. M.

C. S. Yang, W. C. Chou, D. M. Chen, C. S. Ro, and J. L. Shen, “Lattice vibration of ZnSe1-xTex epilayers grown by molecular-beam epitaxy,” Phys. Rev. B 59, 8128–8131 (1999).
[CrossRef]

Chou, W. C.

C. S. Yang, W. C. Chou, D. M. Chen, C. S. Ro, and J. L. Shen, “Lattice vibration of ZnSe1-xTex epilayers grown by molecular-beam epitaxy,” Phys. Rev. B 59, 8128–8131 (1999).
[CrossRef]

Churilov, L. A.

M. Romcevic, V. A. Kulbachinskii, N. Romcevic, P. D. Maryanchuk, and L. A. Churilov, “Optical properties of Hg1-xMnxTe1-ySey,” Infrared Phys. Technol. 46, 379–387 (2005).
[CrossRef]

Gebicki, W.

W. Gebicki and W. Nazarewicz, “Long-wavelength optical phonons in MgxHg1-xTe mixed crystals,” Phys. Status Solidi B 80, 307–311 (1977).
[CrossRef]

Genzel, L.

L. Genzel, T. P. Martin, and C. H. Perry, “Model for long - wavelength optical-phonon modes of mixed crystals,” Phys. Status Solidi B 62, 83–92 (1974).
[CrossRef]

Grynberg, M.

M. Grynberg, R. Le Toullec, and M. Balkanski, “Dielectric function in HgTe between 8 and 300K,” Phys. Rev. B 9, 517–526 (1974).
[CrossRef]

Hassan, H. Abu.

M. A. Abid, H. Abu. Hassan, Z. Hassan, S. S. Ng, S. K. Mohd. Bakhori, and N. H. Abd. Raof, “Experimental investigation of long-wavelength optical lattice vibrations in quaternary AlxInyGa1-x-yN alloys and comparison with results from the pseudo-unit cell model,” Physica B 406, 1379–1384 (2011).
[CrossRef]

Hassan, Z.

M. A. Abid, H. Abu. Hassan, Z. Hassan, S. S. Ng, S. K. Mohd. Bakhori, and N. H. Abd. Raof, “Experimental investigation of long-wavelength optical lattice vibrations in quaternary AlxInyGa1-x-yN alloys and comparison with results from the pseudo-unit cell model,” Physica B 406, 1379–1384 (2011).
[CrossRef]

Huang, D.

D. Huang, C. Jin, D. Wang, X. Liu, J. Wang, and X. Wang, “Crystal structure and Raman scattering in Zn1-xMgxSe alloys,” Appl. Phys. Lett. 67, 3611–3613 (1995).
[CrossRef]

Huang, K.

M. Born and K. Huang, Dynamical Theory of Crystal Lattices, (Oxford University, 1954).

Jin, C.

D. Huang, C. Jin, D. Wang, X. Liu, J. Wang, and X. Wang, “Crystal structure and Raman scattering in Zn1-xMgxSe alloys,” Appl. Phys. Lett. 67, 3611–3613 (1995).
[CrossRef]

Kulbachinskii, V. A.

M. Romcevic, V. A. Kulbachinskii, N. Romcevic, P. D. Maryanchuk, and L. A. Churilov, “Optical properties of Hg1-xMnxTe1-ySey,” Infrared Phys. Technol. 46, 379–387 (2005).
[CrossRef]

Le Toullec, R.

M. Grynberg, R. Le Toullec, and M. Balkanski, “Dielectric function in HgTe between 8 and 300K,” Phys. Rev. B 9, 517–526 (1974).
[CrossRef]

Liu, X.

D. Huang, C. Jin, D. Wang, X. Liu, J. Wang, and X. Wang, “Crystal structure and Raman scattering in Zn1-xMgxSe alloys,” Appl. Phys. Lett. 67, 3611–3613 (1995).
[CrossRef]

Madelung, O.

O. Madelung, Semiconductors-Basic Data, 2nd revised ed., (Springer, 1996).

Makino, H.

H. Makino, H. Sasaki, J. H. Chang, and T. Yao, “Raman investigation of Zn1-xMgxSe1-yTey quaternary alloys grown by molecular beam epitaxy,” J. Cryst. Growth 214–215, 359–363 (2000).
[CrossRef]

Manabe, A.

A. Manabe and A. Mitsuishi, “Far-infrared reflection spectra of HgSe,” Solid State Commun. 16, 743–745 (1975).
[CrossRef]

Martin, T. P.

L. Genzel, T. P. Martin, and C. H. Perry, “Model for long - wavelength optical-phonon modes of mixed crystals,” Phys. Status Solidi B 62, 83–92 (1974).
[CrossRef]

Maryanchuk, P. D.

M. Romcevic, V. A. Kulbachinskii, N. Romcevic, P. D. Maryanchuk, and L. A. Churilov, “Optical properties of Hg1-xMnxTe1-ySey,” Infrared Phys. Technol. 46, 379–387 (2005).
[CrossRef]

Matsuura, M.

R. S. Zheng and M. Matsuura, “Electron-phonon interaction in mixed crystals”, Phys. Rev. B 59, 15422–15429 (1999).
[CrossRef]

Miotkowski, J.

E. Oh, R. G. Alonso, J. Miotkowski, and A. K. Ramdas, “Raman scattering from vibrational and electronic excitations in a II–VI quaternary compound: Cd1-x-yZnxMnyTe,” Phys. Rev. B 45, 10934–10341 (1992).
[CrossRef]

Mitra, S. S.

I. F. Chang and S. S. Mitra, “Long wavelength optical phonons in mixed crystals,” Adv. Phys. 20, 359–404 (1971).
[CrossRef]

I. F. Chang and S. S. Mitra, “Application of a modified Random-Element-Isodisplacement model to long-wavelength optic phonons of mixed crystals,” Phys. Rev. 172, 924–933 (1968).
[CrossRef]

Mitsuishi, A.

A. Manabe and A. Mitsuishi, “Far-infrared reflection spectra of HgSe,” Solid State Commun. 16, 743–745 (1975).
[CrossRef]

Mohd. Bakhori, S. K.

M. A. Abid, H. Abu. Hassan, Z. Hassan, S. S. Ng, S. K. Mohd. Bakhori, and N. H. Abd. Raof, “Experimental investigation of long-wavelength optical lattice vibrations in quaternary AlxInyGa1-x-yN alloys and comparison with results from the pseudo-unit cell model,” Physica B 406, 1379–1384 (2011).
[CrossRef]

Nazarewicz, W.

W. Gebicki and W. Nazarewicz, “Long-wavelength optical phonons in MgxHg1-xTe mixed crystals,” Phys. Status Solidi B 80, 307–311 (1977).
[CrossRef]

Ng, S. S.

M. A. Abid, H. Abu. Hassan, Z. Hassan, S. S. Ng, S. K. Mohd. Bakhori, and N. H. Abd. Raof, “Experimental investigation of long-wavelength optical lattice vibrations in quaternary AlxInyGa1-x-yN alloys and comparison with results from the pseudo-unit cell model,” Physica B 406, 1379–1384 (2011).
[CrossRef]

Oh, E.

E. Oh, R. G. Alonso, J. Miotkowski, and A. K. Ramdas, “Raman scattering from vibrational and electronic excitations in a II–VI quaternary compound: Cd1-x-yZnxMnyTe,” Phys. Rev. B 45, 10934–10341 (1992).
[CrossRef]

Perry, C. H.

L. Genzel, T. P. Martin, and C. H. Perry, “Model for long - wavelength optical-phonon modes of mixed crystals,” Phys. Status Solidi B 62, 83–92 (1974).
[CrossRef]

Ramdas, A. K.

E. Oh, R. G. Alonso, J. Miotkowski, and A. K. Ramdas, “Raman scattering from vibrational and electronic excitations in a II–VI quaternary compound: Cd1-x-yZnxMnyTe,” Phys. Rev. B 45, 10934–10341 (1992).
[CrossRef]

Ro, C. S.

C. S. Yang, W. C. Chou, D. M. Chen, C. S. Ro, and J. L. Shen, “Lattice vibration of ZnSe1-xTex epilayers grown by molecular-beam epitaxy,” Phys. Rev. B 59, 8128–8131 (1999).
[CrossRef]

Romcevic, M.

M. Romcevic and N. Romcevic, “Phonons in multicomponent alloys,” J. Alloys Compd. 416, 64–71 (2006).
[CrossRef]

M. Romcevic, V. A. Kulbachinskii, N. Romcevic, P. D. Maryanchuk, and L. A. Churilov, “Optical properties of Hg1-xMnxTe1-ySey,” Infrared Phys. Technol. 46, 379–387 (2005).
[CrossRef]

Romcevic, N.

M. Romcevic and N. Romcevic, “Phonons in multicomponent alloys,” J. Alloys Compd. 416, 64–71 (2006).
[CrossRef]

M. Romcevic, V. A. Kulbachinskii, N. Romcevic, P. D. Maryanchuk, and L. A. Churilov, “Optical properties of Hg1-xMnxTe1-ySey,” Infrared Phys. Technol. 46, 379–387 (2005).
[CrossRef]

Sasaki, H.

H. Makino, H. Sasaki, J. H. Chang, and T. Yao, “Raman investigation of Zn1-xMgxSe1-yTey quaternary alloys grown by molecular beam epitaxy,” J. Cryst. Growth 214–215, 359–363 (2000).
[CrossRef]

Shen, J. L.

C. S. Yang, W. C. Chou, D. M. Chen, C. S. Ro, and J. L. Shen, “Lattice vibration of ZnSe1-xTex epilayers grown by molecular-beam epitaxy,” Phys. Rev. B 59, 8128–8131 (1999).
[CrossRef]

Taguchi, T.

R. S. Zheng and T. Taguchi, “Theory of long-wavelength optical lattice vibrations in multinary mixed crystals: Application to group-III nitride alloys,” Phys. Rev. B 66, 075327 (2002).
[CrossRef]

Wang, D.

D. Huang, C. Jin, D. Wang, X. Liu, J. Wang, and X. Wang, “Crystal structure and Raman scattering in Zn1-xMgxSe alloys,” Appl. Phys. Lett. 67, 3611–3613 (1995).
[CrossRef]

Wang, J.

D. Huang, C. Jin, D. Wang, X. Liu, J. Wang, and X. Wang, “Crystal structure and Raman scattering in Zn1-xMgxSe alloys,” Appl. Phys. Lett. 67, 3611–3613 (1995).
[CrossRef]

Wang, X.

D. Huang, C. Jin, D. Wang, X. Liu, J. Wang, and X. Wang, “Crystal structure and Raman scattering in Zn1-xMgxSe alloys,” Appl. Phys. Lett. 67, 3611–3613 (1995).
[CrossRef]

Yang, C. S.

C. S. Yang, W. C. Chou, D. M. Chen, C. S. Ro, and J. L. Shen, “Lattice vibration of ZnSe1-xTex epilayers grown by molecular-beam epitaxy,” Phys. Rev. B 59, 8128–8131 (1999).
[CrossRef]

Yang, F.

F. Yang and R. S. Zheng, “Properties of optical phonons in Zn1-x-yMgyBexSe quaternary mixed crystal,” Solid State Commun. 141, 555–558 (2007).
[CrossRef]

Yao, T.

H. Makino, H. Sasaki, J. H. Chang, and T. Yao, “Raman investigation of Zn1-xMgxSe1-yTey quaternary alloys grown by molecular beam epitaxy,” J. Cryst. Growth 214–215, 359–363 (2000).
[CrossRef]

Zheng, R. S.

F. Yang and R. S. Zheng, “Properties of optical phonons in Zn1-x-yMgyBexSe quaternary mixed crystal,” Solid State Commun. 141, 555–558 (2007).
[CrossRef]

R. S. Zheng, “Properties of optical phonons in multinary phosphide mixed crystals,” J. Shenzhen University (Science and Engineering), 23(1), 10–15 (2006).

R. S. Zheng and T. Taguchi, “Theory of long-wavelength optical lattice vibrations in multinary mixed crystals: Application to group-III nitride alloys,” Phys. Rev. B 66, 075327 (2002).
[CrossRef]

R. S. Zheng and M. Matsuura, “Electron-phonon interaction in mixed crystals”, Phys. Rev. B 59, 15422–15429 (1999).
[CrossRef]

Adv. Phys. (1)

I. F. Chang and S. S. Mitra, “Long wavelength optical phonons in mixed crystals,” Adv. Phys. 20, 359–404 (1971).
[CrossRef]

Appl. Phys. Lett. (1)

D. Huang, C. Jin, D. Wang, X. Liu, J. Wang, and X. Wang, “Crystal structure and Raman scattering in Zn1-xMgxSe alloys,” Appl. Phys. Lett. 67, 3611–3613 (1995).
[CrossRef]

Infrared Phys. Technol. (1)

M. Romcevic, V. A. Kulbachinskii, N. Romcevic, P. D. Maryanchuk, and L. A. Churilov, “Optical properties of Hg1-xMnxTe1-ySey,” Infrared Phys. Technol. 46, 379–387 (2005).
[CrossRef]

J. Alloys Compd. (1)

M. Romcevic and N. Romcevic, “Phonons in multicomponent alloys,” J. Alloys Compd. 416, 64–71 (2006).
[CrossRef]

J. Cryst. Growth (1)

H. Makino, H. Sasaki, J. H. Chang, and T. Yao, “Raman investigation of Zn1-xMgxSe1-yTey quaternary alloys grown by molecular beam epitaxy,” J. Cryst. Growth 214–215, 359–363 (2000).
[CrossRef]

J. Shenzhen University (Science and Engineering) (1)

R. S. Zheng, “Properties of optical phonons in multinary phosphide mixed crystals,” J. Shenzhen University (Science and Engineering), 23(1), 10–15 (2006).

Phys. Rev. (1)

I. F. Chang and S. S. Mitra, “Application of a modified Random-Element-Isodisplacement model to long-wavelength optic phonons of mixed crystals,” Phys. Rev. 172, 924–933 (1968).
[CrossRef]

Phys. Rev. B (5)

R. S. Zheng and M. Matsuura, “Electron-phonon interaction in mixed crystals”, Phys. Rev. B 59, 15422–15429 (1999).
[CrossRef]

R. S. Zheng and T. Taguchi, “Theory of long-wavelength optical lattice vibrations in multinary mixed crystals: Application to group-III nitride alloys,” Phys. Rev. B 66, 075327 (2002).
[CrossRef]

C. S. Yang, W. C. Chou, D. M. Chen, C. S. Ro, and J. L. Shen, “Lattice vibration of ZnSe1-xTex epilayers grown by molecular-beam epitaxy,” Phys. Rev. B 59, 8128–8131 (1999).
[CrossRef]

E. Oh, R. G. Alonso, J. Miotkowski, and A. K. Ramdas, “Raman scattering from vibrational and electronic excitations in a II–VI quaternary compound: Cd1-x-yZnxMnyTe,” Phys. Rev. B 45, 10934–10341 (1992).
[CrossRef]

M. Grynberg, R. Le Toullec, and M. Balkanski, “Dielectric function in HgTe between 8 and 300K,” Phys. Rev. B 9, 517–526 (1974).
[CrossRef]

Phys. Status Solidi B (2)

W. Gebicki and W. Nazarewicz, “Long-wavelength optical phonons in MgxHg1-xTe mixed crystals,” Phys. Status Solidi B 80, 307–311 (1977).
[CrossRef]

L. Genzel, T. P. Martin, and C. H. Perry, “Model for long - wavelength optical-phonon modes of mixed crystals,” Phys. Status Solidi B 62, 83–92 (1974).
[CrossRef]

Physica B (1)

M. A. Abid, H. Abu. Hassan, Z. Hassan, S. S. Ng, S. K. Mohd. Bakhori, and N. H. Abd. Raof, “Experimental investigation of long-wavelength optical lattice vibrations in quaternary AlxInyGa1-x-yN alloys and comparison with results from the pseudo-unit cell model,” Physica B 406, 1379–1384 (2011).
[CrossRef]

Solid State Commun. (2)

A. Manabe and A. Mitsuishi, “Far-infrared reflection spectra of HgSe,” Solid State Commun. 16, 743–745 (1975).
[CrossRef]

F. Yang and R. S. Zheng, “Properties of optical phonons in Zn1-x-yMgyBexSe quaternary mixed crystal,” Solid State Commun. 141, 555–558 (2007).
[CrossRef]

Other (3)

M. Born and K. Huang, Dynamical Theory of Crystal Lattices, (Oxford University, 1954).

I. F. Chang, Ph.D. dissertation, University of Rhode Island, (1968).

O. Madelung, Semiconductors-Basic Data, 2nd revised ed., (Springer, 1996).

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