Abstract

We present a study on the composition-dependent electron transport in ternary CdSxSe1x nanobelts at equilibrium and nonequilibrium conditions via THz spectroscopy. The measured spectra are analyzed using a Drude–Smith model combined with a harmonic oscillator. The physical origin of parameters in the Drude–Smith model is studied in detail. Under equilibrium conditions, the surface depletion region is the dominant factor to free-carrier backscattering. However, under nonequilibrium conditions, the influence of the surface depletion region is masked by the high bulk concentration and the free carriers are mainly localized by composition disorder. The contributions from different mechanisms to the carrier mobility are also explored. In equilibrium, alloy scattering is the most vital scattering mechanism for nanobelts with x=0.250.9 since composition disorder is significant in this range. On the other hand, the effect of electron–phonon interaction increases under photoexcitation.

© 2014 Optical Society of America

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  1. J. Lu, C. Sun, M. Zheng, N. Mathews, H. Liu, G. S. Chen, X. Zhang, M. G. Subodh, and C. H. Sow, J. Phys. Chem. C 115, 19538 (2011).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. J. W. Harrison and J. R. Hauser, Phys. Rev. B 13, 5347 (1976).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2012 (2)

H. Liu, J. Lu, H. F. Teoh, D. Li, Y. P. Feng, S. H. Tang, C. H. Sow, and X. Zhang, J. Phys. Chem. C 116, 26036 (2012).
[CrossRef]

X. Zhuang, C. Z. Ning, and A. Pan, Adv. Mater. 24, 13 (2012).
[CrossRef]

2011 (3)

R. Ulbricht, E. Hendry, J. Shan, T. F. Heinz, and M. Bonn, Rev. Mod. Phys. 83, 543 (2011).
[CrossRef]

J. Lu, C. Sun, M. Zheng, N. Mathews, H. Liu, G. S. Chen, X. Zhang, M. G. Subodh, and C. H. Sow, J. Phys. Chem. C 115, 19538 (2011).
[CrossRef]

X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).
[CrossRef]

2008 (1)

B. S. Simpkins, M. A. Mastro, J. C. R. Eddy, and P. E. Pehrsson, J. Appl. Phys. 103, 104313 (2008).
[CrossRef]

2007 (2)

E. Hendry, M. Koeberg, J. Pijpers, and M. Bonn, Phys. Rev. B 75, 233202 (2007).
[CrossRef]

A. Pan, X. Wang, P. He, Q. Zhang, Q. Wan, M. Zacharias, X. Zhu, and B. Zou, Nano Lett. 7, 2970 (2007).
[CrossRef]

2006 (1)

2003 (1)

S. Giordano, J. Electrost. 58, 59 (2003).
[CrossRef]

2002 (1)

J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager, E. E. Haller, H. Lu, and W. J. Schaff, Appl. Phys. Lett. 80, 4741 (2002).
[CrossRef]

2001 (1)

N. V. Smith, Phys. Rev. B 64, 155106 (2001).
[CrossRef]

1999 (1)

Z. F. Li, W. Lu, H. J. Ye, Z. H. Chen, X. Z. Yuan, H. F. Dou, S. C. Shen, G. Li, and S. J. Chua, J. Appl. Phys. 86, 2691 (1999).
[CrossRef]

1995 (1)

M. Bruening, E. Moons, D. Cahen, and A. Shanzer, J. Phys. Chem. 99, 8368 (1995).
[CrossRef]

1992 (1)

G. Mei, J. Phys-Condens. Mat. 4, 7521 (1992).

1976 (1)

J. W. Harrison and J. R. Hauser, Phys. Rev. B 13, 5347 (1976).
[CrossRef]

1968 (1)

I. F. Chang and S. S. Mitra, Phys. Rev. 172, 924 (1968).
[CrossRef]

1967 (1)

H. W. Verleur and A. S. Barker, Phys. Rev. 155, 750 (1967).
[CrossRef]

1958 (1)

P. W. Anderson, Phys. Rev. 109, 1492 (1958).
[CrossRef]

1900 (1)

P. Drude, Ann. Phys. 306, 566 (1900).
[CrossRef]

Ager, J. W.

J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager, E. E. Haller, H. Lu, and W. J. Schaff, Appl. Phys. Lett. 80, 4741 (2002).
[CrossRef]

Anderson, P. W.

P. W. Anderson, Phys. Rev. 109, 1492 (1958).
[CrossRef]

Barker, A. S.

H. W. Verleur and A. S. Barker, Phys. Rev. 155, 750 (1967).
[CrossRef]

Bonn, M.

R. Ulbricht, E. Hendry, J. Shan, T. F. Heinz, and M. Bonn, Rev. Mod. Phys. 83, 543 (2011).
[CrossRef]

E. Hendry, M. Koeberg, J. Pijpers, and M. Bonn, Phys. Rev. B 75, 233202 (2007).
[CrossRef]

Bruening, M.

M. Bruening, E. Moons, D. Cahen, and A. Shanzer, J. Phys. Chem. 99, 8368 (1995).
[CrossRef]

Cahen, D.

M. Bruening, E. Moons, D. Cahen, and A. Shanzer, J. Phys. Chem. 99, 8368 (1995).
[CrossRef]

Chang, C.-F.

Chang, I. F.

I. F. Chang and S. S. Mitra, Phys. Rev. 172, 924 (1968).
[CrossRef]

Chen, G. S.

J. Lu, C. Sun, M. Zheng, N. Mathews, H. Liu, G. S. Chen, X. Zhang, M. G. Subodh, and C. H. Sow, J. Phys. Chem. C 115, 19538 (2011).
[CrossRef]

Chen, S.-J.

Chen, Z. H.

Z. F. Li, W. Lu, H. J. Ye, Z. H. Chen, X. Z. Yuan, H. F. Dou, S. C. Shen, G. Li, and S. J. Chua, J. Appl. Phys. 86, 2691 (1999).
[CrossRef]

Chi, C.-C.

Chua, S. J.

Z. F. Li, W. Lu, H. J. Ye, Z. H. Chen, X. Z. Yuan, H. F. Dou, S. C. Shen, G. Li, and S. J. Chua, J. Appl. Phys. 86, 2691 (1999).
[CrossRef]

Dou, H. F.

Z. F. Li, W. Lu, H. J. Ye, Z. H. Chen, X. Z. Yuan, H. F. Dou, S. C. Shen, G. Li, and S. J. Chua, J. Appl. Phys. 86, 2691 (1999).
[CrossRef]

Drude, P.

P. Drude, Ann. Phys. 306, 566 (1900).
[CrossRef]

Eddy, J. C. R.

B. S. Simpkins, M. A. Mastro, J. C. R. Eddy, and P. E. Pehrsson, J. Appl. Phys. 103, 104313 (2008).
[CrossRef]

Feng, Y. P.

H. Liu, J. Lu, H. F. Teoh, D. Li, Y. P. Feng, S. H. Tang, C. H. Sow, and X. Zhang, J. Phys. Chem. C 116, 26036 (2012).
[CrossRef]

Giordano, S.

S. Giordano, J. Electrost. 58, 59 (2003).
[CrossRef]

Haller, E. E.

J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager, E. E. Haller, H. Lu, and W. J. Schaff, Appl. Phys. Lett. 80, 4741 (2002).
[CrossRef]

Hane, J. K.

J. K. Hane, The Picosecond Dynamics of Electron-Hole Pairs in Graded and Homogeneous CdSxSe1−x Semiconductors (University of California, 1995).

Harrison, J. W.

J. W. Harrison and J. R. Hauser, Phys. Rev. B 13, 5347 (1976).
[CrossRef]

Hauser, J. R.

J. W. Harrison and J. R. Hauser, Phys. Rev. B 13, 5347 (1976).
[CrossRef]

He, P.

A. Pan, X. Wang, P. He, Q. Zhang, Q. Wan, M. Zacharias, X. Zhu, and B. Zou, Nano Lett. 7, 2970 (2007).
[CrossRef]

Heinz, T. F.

R. Ulbricht, E. Hendry, J. Shan, T. F. Heinz, and M. Bonn, Rev. Mod. Phys. 83, 543 (2011).
[CrossRef]

Hendry, E.

R. Ulbricht, E. Hendry, J. Shan, T. F. Heinz, and M. Bonn, Rev. Mod. Phys. 83, 543 (2011).
[CrossRef]

E. Hendry, M. Koeberg, J. Pijpers, and M. Bonn, Phys. Rev. B 75, 233202 (2007).
[CrossRef]

Hsu, S.-H.

Koeberg, M.

E. Hendry, M. Koeberg, J. Pijpers, and M. Bonn, Phys. Rev. B 75, 233202 (2007).
[CrossRef]

Li, D.

H. Liu, J. Lu, H. F. Teoh, D. Li, Y. P. Feng, S. H. Tang, C. H. Sow, and X. Zhang, J. Phys. Chem. C 116, 26036 (2012).
[CrossRef]

Li, G.

Z. F. Li, W. Lu, H. J. Ye, Z. H. Chen, X. Z. Yuan, H. F. Dou, S. C. Shen, G. Li, and S. J. Chua, J. Appl. Phys. 86, 2691 (1999).
[CrossRef]

Li, Z. F.

Z. F. Li, W. Lu, H. J. Ye, Z. H. Chen, X. Z. Yuan, H. F. Dou, S. C. Shen, G. Li, and S. J. Chua, J. Appl. Phys. 86, 2691 (1999).
[CrossRef]

Lin, T.-Y.

Liu, H.

H. Liu, J. Lu, H. F. Teoh, D. Li, Y. P. Feng, S. H. Tang, C. H. Sow, and X. Zhang, J. Phys. Chem. C 116, 26036 (2012).
[CrossRef]

J. Lu, C. Sun, M. Zheng, N. Mathews, H. Liu, G. S. Chen, X. Zhang, M. G. Subodh, and C. H. Sow, J. Phys. Chem. C 115, 19538 (2011).
[CrossRef]

Lu, H.

J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager, E. E. Haller, H. Lu, and W. J. Schaff, Appl. Phys. Lett. 80, 4741 (2002).
[CrossRef]

Lu, J.

H. Liu, J. Lu, H. F. Teoh, D. Li, Y. P. Feng, S. H. Tang, C. H. Sow, and X. Zhang, J. Phys. Chem. C 116, 26036 (2012).
[CrossRef]

J. Lu, C. Sun, M. Zheng, N. Mathews, H. Liu, G. S. Chen, X. Zhang, M. G. Subodh, and C. H. Sow, J. Phys. Chem. C 115, 19538 (2011).
[CrossRef]

Lu, W.

Z. F. Li, W. Lu, H. J. Ye, Z. H. Chen, X. Z. Yuan, H. F. Dou, S. C. Shen, G. Li, and S. J. Chua, J. Appl. Phys. 86, 2691 (1999).
[CrossRef]

Mastro, M. A.

B. S. Simpkins, M. A. Mastro, J. C. R. Eddy, and P. E. Pehrsson, J. Appl. Phys. 103, 104313 (2008).
[CrossRef]

Mathews, N.

J. Lu, C. Sun, M. Zheng, N. Mathews, H. Liu, G. S. Chen, X. Zhang, M. G. Subodh, and C. H. Sow, J. Phys. Chem. C 115, 19538 (2011).
[CrossRef]

Mei, G.

G. Mei, J. Phys-Condens. Mat. 4, 7521 (1992).

Mitra, S. S.

I. F. Chang and S. S. Mitra, Phys. Rev. 172, 924 (1968).
[CrossRef]

Moons, E.

M. Bruening, E. Moons, D. Cahen, and A. Shanzer, J. Phys. Chem. 99, 8368 (1995).
[CrossRef]

Ning, C. Z.

X. Zhuang, C. Z. Ning, and A. Pan, Adv. Mater. 24, 13 (2012).
[CrossRef]

Pan, A.

X. Zhuang, C. Z. Ning, and A. Pan, Adv. Mater. 24, 13 (2012).
[CrossRef]

A. Pan, X. Wang, P. He, Q. Zhang, Q. Wan, M. Zacharias, X. Zhu, and B. Zou, Nano Lett. 7, 2970 (2007).
[CrossRef]

Pehrsson, P. E.

B. S. Simpkins, M. A. Mastro, J. C. R. Eddy, and P. E. Pehrsson, J. Appl. Phys. 103, 104313 (2008).
[CrossRef]

Pijpers, J.

E. Hendry, M. Koeberg, J. Pijpers, and M. Bonn, Phys. Rev. B 75, 233202 (2007).
[CrossRef]

Qi, X.-L.

X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).
[CrossRef]

Schaff, W. J.

J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager, E. E. Haller, H. Lu, and W. J. Schaff, Appl. Phys. Lett. 80, 4741 (2002).
[CrossRef]

Shan, J.

R. Ulbricht, E. Hendry, J. Shan, T. F. Heinz, and M. Bonn, Rev. Mod. Phys. 83, 543 (2011).
[CrossRef]

Shanzer, A.

M. Bruening, E. Moons, D. Cahen, and A. Shanzer, J. Phys. Chem. 99, 8368 (1995).
[CrossRef]

Shen, S. C.

Z. F. Li, W. Lu, H. J. Ye, Z. H. Chen, X. Z. Yuan, H. F. Dou, S. C. Shen, G. Li, and S. J. Chua, J. Appl. Phys. 86, 2691 (1999).
[CrossRef]

Simpkins, B. S.

B. S. Simpkins, M. A. Mastro, J. C. R. Eddy, and P. E. Pehrsson, J. Appl. Phys. 103, 104313 (2008).
[CrossRef]

Smith, N. V.

N. V. Smith, Phys. Rev. B 64, 155106 (2001).
[CrossRef]

Sow, C. H.

H. Liu, J. Lu, H. F. Teoh, D. Li, Y. P. Feng, S. H. Tang, C. H. Sow, and X. Zhang, J. Phys. Chem. C 116, 26036 (2012).
[CrossRef]

J. Lu, C. Sun, M. Zheng, N. Mathews, H. Liu, G. S. Chen, X. Zhang, M. G. Subodh, and C. H. Sow, J. Phys. Chem. C 115, 19538 (2011).
[CrossRef]

Subodh, M. G.

J. Lu, C. Sun, M. Zheng, N. Mathews, H. Liu, G. S. Chen, X. Zhang, M. G. Subodh, and C. H. Sow, J. Phys. Chem. C 115, 19538 (2011).
[CrossRef]

Sun, C.

J. Lu, C. Sun, M. Zheng, N. Mathews, H. Liu, G. S. Chen, X. Zhang, M. G. Subodh, and C. H. Sow, J. Phys. Chem. C 115, 19538 (2011).
[CrossRef]

Tang, S. H.

H. Liu, J. Lu, H. F. Teoh, D. Li, Y. P. Feng, S. H. Tang, C. H. Sow, and X. Zhang, J. Phys. Chem. C 116, 26036 (2012).
[CrossRef]

Teoh, H. F.

H. Liu, J. Lu, H. F. Teoh, D. Li, Y. P. Feng, S. H. Tang, C. H. Sow, and X. Zhang, J. Phys. Chem. C 116, 26036 (2012).
[CrossRef]

Tsai, T.-R.

Ulbricht, R.

R. Ulbricht, E. Hendry, J. Shan, T. F. Heinz, and M. Bonn, Rev. Mod. Phys. 83, 543 (2011).
[CrossRef]

Verleur, H. W.

H. W. Verleur and A. S. Barker, Phys. Rev. 155, 750 (1967).
[CrossRef]

Walukiewicz, W.

J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager, E. E. Haller, H. Lu, and W. J. Schaff, Appl. Phys. Lett. 80, 4741 (2002).
[CrossRef]

Wan, Q.

A. Pan, X. Wang, P. He, Q. Zhang, Q. Wan, M. Zacharias, X. Zhu, and B. Zou, Nano Lett. 7, 2970 (2007).
[CrossRef]

Wang, X.

A. Pan, X. Wang, P. He, Q. Zhang, Q. Wan, M. Zacharias, X. Zhu, and B. Zou, Nano Lett. 7, 2970 (2007).
[CrossRef]

Wu, J.

J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager, E. E. Haller, H. Lu, and W. J. Schaff, Appl. Phys. Lett. 80, 4741 (2002).
[CrossRef]

Ye, H. J.

Z. F. Li, W. Lu, H. J. Ye, Z. H. Chen, X. Z. Yuan, H. F. Dou, S. C. Shen, G. Li, and S. J. Chua, J. Appl. Phys. 86, 2691 (1999).
[CrossRef]

Yu, K. M.

J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager, E. E. Haller, H. Lu, and W. J. Schaff, Appl. Phys. Lett. 80, 4741 (2002).
[CrossRef]

Yuan, X. Z.

Z. F. Li, W. Lu, H. J. Ye, Z. H. Chen, X. Z. Yuan, H. F. Dou, S. C. Shen, G. Li, and S. J. Chua, J. Appl. Phys. 86, 2691 (1999).
[CrossRef]

Zacharias, M.

A. Pan, X. Wang, P. He, Q. Zhang, Q. Wan, M. Zacharias, X. Zhu, and B. Zou, Nano Lett. 7, 2970 (2007).
[CrossRef]

Zhang, Q.

A. Pan, X. Wang, P. He, Q. Zhang, Q. Wan, M. Zacharias, X. Zhu, and B. Zou, Nano Lett. 7, 2970 (2007).
[CrossRef]

Zhang, S.-C.

X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).
[CrossRef]

Zhang, X.

H. Liu, J. Lu, H. F. Teoh, D. Li, Y. P. Feng, S. H. Tang, C. H. Sow, and X. Zhang, J. Phys. Chem. C 116, 26036 (2012).
[CrossRef]

J. Lu, C. Sun, M. Zheng, N. Mathews, H. Liu, G. S. Chen, X. Zhang, M. G. Subodh, and C. H. Sow, J. Phys. Chem. C 115, 19538 (2011).
[CrossRef]

Zheng, M.

J. Lu, C. Sun, M. Zheng, N. Mathews, H. Liu, G. S. Chen, X. Zhang, M. G. Subodh, and C. H. Sow, J. Phys. Chem. C 115, 19538 (2011).
[CrossRef]

Zhu, X.

A. Pan, X. Wang, P. He, Q. Zhang, Q. Wan, M. Zacharias, X. Zhu, and B. Zou, Nano Lett. 7, 2970 (2007).
[CrossRef]

Zhuang, X.

X. Zhuang, C. Z. Ning, and A. Pan, Adv. Mater. 24, 13 (2012).
[CrossRef]

Zou, B.

A. Pan, X. Wang, P. He, Q. Zhang, Q. Wan, M. Zacharias, X. Zhu, and B. Zou, Nano Lett. 7, 2970 (2007).
[CrossRef]

Adv. Mater. (1)

X. Zhuang, C. Z. Ning, and A. Pan, Adv. Mater. 24, 13 (2012).
[CrossRef]

Ann. Phys. (1)

P. Drude, Ann. Phys. 306, 566 (1900).
[CrossRef]

Appl. Phys. Lett. (1)

J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager, E. E. Haller, H. Lu, and W. J. Schaff, Appl. Phys. Lett. 80, 4741 (2002).
[CrossRef]

J. Appl. Phys. (2)

B. S. Simpkins, M. A. Mastro, J. C. R. Eddy, and P. E. Pehrsson, J. Appl. Phys. 103, 104313 (2008).
[CrossRef]

Z. F. Li, W. Lu, H. J. Ye, Z. H. Chen, X. Z. Yuan, H. F. Dou, S. C. Shen, G. Li, and S. J. Chua, J. Appl. Phys. 86, 2691 (1999).
[CrossRef]

J. Electrost. (1)

S. Giordano, J. Electrost. 58, 59 (2003).
[CrossRef]

J. Phys-Condens. Mat. (1)

G. Mei, J. Phys-Condens. Mat. 4, 7521 (1992).

J. Phys. Chem. (1)

M. Bruening, E. Moons, D. Cahen, and A. Shanzer, J. Phys. Chem. 99, 8368 (1995).
[CrossRef]

J. Phys. Chem. C (2)

H. Liu, J. Lu, H. F. Teoh, D. Li, Y. P. Feng, S. H. Tang, C. H. Sow, and X. Zhang, J. Phys. Chem. C 116, 26036 (2012).
[CrossRef]

J. Lu, C. Sun, M. Zheng, N. Mathews, H. Liu, G. S. Chen, X. Zhang, M. G. Subodh, and C. H. Sow, J. Phys. Chem. C 115, 19538 (2011).
[CrossRef]

Nano Lett. (1)

A. Pan, X. Wang, P. He, Q. Zhang, Q. Wan, M. Zacharias, X. Zhu, and B. Zou, Nano Lett. 7, 2970 (2007).
[CrossRef]

Opt. Express (1)

Phys. Rev. (3)

H. W. Verleur and A. S. Barker, Phys. Rev. 155, 750 (1967).
[CrossRef]

I. F. Chang and S. S. Mitra, Phys. Rev. 172, 924 (1968).
[CrossRef]

P. W. Anderson, Phys. Rev. 109, 1492 (1958).
[CrossRef]

Phys. Rev. B (3)

J. W. Harrison and J. R. Hauser, Phys. Rev. B 13, 5347 (1976).
[CrossRef]

N. V. Smith, Phys. Rev. B 64, 155106 (2001).
[CrossRef]

E. Hendry, M. Koeberg, J. Pijpers, and M. Bonn, Phys. Rev. B 75, 233202 (2007).
[CrossRef]

Rev. Mod. Phys. (2)

R. Ulbricht, E. Hendry, J. Shan, T. F. Heinz, and M. Bonn, Rev. Mod. Phys. 83, 543 (2011).
[CrossRef]

X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).
[CrossRef]

Other (1)

J. K. Hane, The Picosecond Dynamics of Electron-Hole Pairs in Graded and Homogeneous CdSxSe1−x Semiconductors (University of California, 1995).

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Figures (5)

Fig. 1.
Fig. 1.

(a) XRD patterns and (b) PL spectra of six CdSxSe1x nanobelt samples with x=0 (wine), 0.29 (olive), 0.65 (blue), 0.75 (orange), 0.87 (red), and 1 (magenta).

Fig. 2.
Fig. 2.

Observed (a) real and (b) imaginary parts of frequency-dependent static conductivity of six CdSxSe1x nanobelt samples. The symbols are raw data and the solid lines are fits, including both DS and a harmonic oscillator.

Fig. 3.
Fig. 3.

(a) TO frequencies and (b) corresponding oscillator strength of CdSxSe1x nanobelts as a function of composition x. The solid lines are fitted by the modified random-element-isodisplacement model.

Fig. 4.
Fig. 4.

(a) Schematic diagram of the energy band of CdSxSe1x nanobelts with a depleted surface region. (b) Observed mobility (green dots), optical phonon mobility (red triangles) and calculated alloy scattering mobility (blue circles) as a function of composition x.

Fig. 5.
Fig. 5.

(a) Real and (b) imaginary parts of frequency-dependent excited conductivity of six CdSxSe1x nanobelts. The symbols are raw data and the solid lines are fits by Eq. (2).

Tables (3)

Tables Icon

Table 1. Phonon Parameters of CdSxSe1x Nanobelts Obtained from the Fitting of Complex Conductivity Spectra

Tables Icon

Table 2. Best Fit Parameters Obtained using DS Model

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Table 3. Calculated Carrier Concentration and Mobility with and without Photoexcitation

Equations (7)

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ε˜(ω)=εr(ω)+iεi(ω)=ε+iσ˜(ω)ωε0=n˜(ω)2,
σ˜(ω)=ε0τ0ωp21iωτ0(1+ici(1iωτ0)i)jiωε0AjωTO,j2ωTO,j2ω2iγjω.
ϕ(r)=eN(Rw)22εε0[ln(rRw)r22(Rw)2+12],
w=2εε0VdeN,
μ=[i1μi]1.
μi=eτim*,
τalloy=8NA4z1/232πx(1x)(ΔU)2(m*)2/3(kBT)1/2,

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