SEMICONDUCTOR PHYSICS

Transition Gibbs free energy level cross section and formulation of carrier SRH recombination rate

Ken K. Chin

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 Corresponding author: Ken K. Chin,

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Abstract: The transition among multiple charging states of a semiconductor's localized intrinsic/impurity defects is considered as phase transitions, and the concept of transition Gibbs free energy level (TGFEL) is proposed. Dependence of the cross section of TGFEL on its charge state is discussed. Introduction of TGFEL to replace activation energy has fundamentally important consequences for semiconductor physics and devices. TGFEL involves entropy. What is to be included and not included in the entropy term consistently for all defect levels is an unresolved open question, related to correct interpretation of various experimental data associated with various defect levels. This work is a first step towards resolving this question.

Key words: transition Gibbs free energy levelShockley-Read-Hallsingle level defects



[1]
Kittel C, Kroemer H. Thermal physics. 2nd ed. New York:Freeman, 1980
[2]
Sze S. Physics of semiconductor devices. 2nd edition. New York:Wiley, 1981
[3]
Look D. Electrical characterization of GaAs materials and devices. Chapter 1. 4 and Appendix C. J Willey & Sons, 1989. The author argues that the degeneracy factors gD and gA are consisted with impurity states but not with band states. The two different attribution of the origin of the degeneracy factors does not affect the validity of the argument of this work.
[4]
Blood P, Orton J W. The Electrical characterization of semiconductors:majority carriers and electron states. Academic Press, 1992
[5]
Wang S. Solid state electronics. New York:McGraw-Hill, 1966:140
[6]
Smith R A. Semiconductors. 2nd ed. Cambridge, England:Cambridge University Press, 1978
[7]
Orton J W, Blood P. The electrical characterization of semiconductors:measurement of minority carrier properties. Academic Press, 1990
[8]
Wei S H, Zhang S B. Chemical trends of defect formation and doping limit in Ⅱ-Ⅵ semiconductors:the case of CdTe. Phys Rev B, 2002, 66:15521
[9]
Seymour F. Studies of electronic states controlling the performance of CdTe solar cells. PhD (Materials Science) Thesis, Colorado School of Mines, 2005:35
[10]
Wu X. High-efficiency polycrystalline thin-film solar cells. Solar Energy, 2004, 77:803 doi: 10.1016/j.solener.2004.06.006
[11]
Gessert T A, Metzger W K, Dippo P, et al. Dependence of carrier lifetime on copper-contacting temperature and ZnTe:Cu thickness in CdS/CdTe thin film solar cells. Thin Solid Films, 2009, 517:2370 doi: 10.1016/j.tsf.2008.11.008
[12]
Balcioglu A, Ahrenkiel R K, Hasoon F. Deep-level impurities in CdTe/CdS thin-film solar cells. J Appl Phys, 2000, 88(12):7175 doi: 10.1063/1.1326465
[13]
Meyer W, Neldel H Z. Z Tech Phys (Leipzig), 1937, 12: 588
[14]
Crandall R S. Meyer-Neldel rule in deep-level-transient-spectroscopy and its ramifications. MRS Symposium Proceedings, San Francisco, 2003:79 https://www.cambridge.org/core/journals/mrs-online-proceedings-library-archive/article/meyerneldel-rule-in-deepleveltransientspectroscopy-and-its-ramifications/2D77025AA923C6AEBFD30CD2D0499272
[15]
Yelon A, Movaghar B, Crandall R S. Multi-excitation entropy:its role in thermodynamics and kinetics. Rep Prog Phys, 2006, 69:1145 doi: 10.1088/0034-4885/69/4/R04
[16]
Macdonald D, Geerligs L J. Recombination activity of interstitial iron and other transition metal point defects in p-and n-type crystalline silicon. Appl Phys Lett, 2004, 85(18):4061 doi: 10.1063/1.1812833
[17]
Chin K K. Approximate graphical method for estimation of majority carrier compensation of semiconductors with multiple donors and multiple acceptors. Journal of Semiconductors, 2011, 32(6):062001 doi: 10.1088/1674-4926/32/6/062001
[18]
Chin K K. Local charge neutrality condition, Fermi level, and majority carrier density of semiconductors with multiple multi-level intrinsic/impurity defect states. Journal of Semiconductors, 2011, 32(11):112001 doi: 10.1088/1674-4926/32/11/112001
Fig. 1.  The relationship of donor ionization energy $E_{\rm D}$ and transition Gibbs free energy level $G_{\rm D}$ for an n-type semiconductor, and the relationship of $E_{\rm A}$ and $G_{\rm A}$ for a p-type semiconductor.

Fig. 2.  Coulomb interaction between the carrier and the SRH recombination center; the number of dashed arrows indicates the interaction between the carrier and the SRH center, with 4 arrows representing strong attraction, 3 representing attraction, 2 weak attraction, and 1 arrow repulsion. Superscripts (++/+), (+/0), (0/-), and (-/-) indicate double donor, donor, acceptor, and double acceptor transition level, respectively.

[1]
Kittel C, Kroemer H. Thermal physics. 2nd ed. New York:Freeman, 1980
[2]
Sze S. Physics of semiconductor devices. 2nd edition. New York:Wiley, 1981
[3]
Look D. Electrical characterization of GaAs materials and devices. Chapter 1. 4 and Appendix C. J Willey & Sons, 1989. The author argues that the degeneracy factors gD and gA are consisted with impurity states but not with band states. The two different attribution of the origin of the degeneracy factors does not affect the validity of the argument of this work.
[4]
Blood P, Orton J W. The Electrical characterization of semiconductors:majority carriers and electron states. Academic Press, 1992
[5]
Wang S. Solid state electronics. New York:McGraw-Hill, 1966:140
[6]
Smith R A. Semiconductors. 2nd ed. Cambridge, England:Cambridge University Press, 1978
[7]
Orton J W, Blood P. The electrical characterization of semiconductors:measurement of minority carrier properties. Academic Press, 1990
[8]
Wei S H, Zhang S B. Chemical trends of defect formation and doping limit in Ⅱ-Ⅵ semiconductors:the case of CdTe. Phys Rev B, 2002, 66:15521
[9]
Seymour F. Studies of electronic states controlling the performance of CdTe solar cells. PhD (Materials Science) Thesis, Colorado School of Mines, 2005:35
[10]
Wu X. High-efficiency polycrystalline thin-film solar cells. Solar Energy, 2004, 77:803 doi: 10.1016/j.solener.2004.06.006
[11]
Gessert T A, Metzger W K, Dippo P, et al. Dependence of carrier lifetime on copper-contacting temperature and ZnTe:Cu thickness in CdS/CdTe thin film solar cells. Thin Solid Films, 2009, 517:2370 doi: 10.1016/j.tsf.2008.11.008
[12]
Balcioglu A, Ahrenkiel R K, Hasoon F. Deep-level impurities in CdTe/CdS thin-film solar cells. J Appl Phys, 2000, 88(12):7175 doi: 10.1063/1.1326465
[13]
Meyer W, Neldel H Z. Z Tech Phys (Leipzig), 1937, 12: 588
[14]
Crandall R S. Meyer-Neldel rule in deep-level-transient-spectroscopy and its ramifications. MRS Symposium Proceedings, San Francisco, 2003:79 https://www.cambridge.org/core/journals/mrs-online-proceedings-library-archive/article/meyerneldel-rule-in-deepleveltransientspectroscopy-and-its-ramifications/2D77025AA923C6AEBFD30CD2D0499272
[15]
Yelon A, Movaghar B, Crandall R S. Multi-excitation entropy:its role in thermodynamics and kinetics. Rep Prog Phys, 2006, 69:1145 doi: 10.1088/0034-4885/69/4/R04
[16]
Macdonald D, Geerligs L J. Recombination activity of interstitial iron and other transition metal point defects in p-and n-type crystalline silicon. Appl Phys Lett, 2004, 85(18):4061 doi: 10.1063/1.1812833
[17]
Chin K K. Approximate graphical method for estimation of majority carrier compensation of semiconductors with multiple donors and multiple acceptors. Journal of Semiconductors, 2011, 32(6):062001 doi: 10.1088/1674-4926/32/6/062001
[18]
Chin K K. Local charge neutrality condition, Fermi level, and majority carrier density of semiconductors with multiple multi-level intrinsic/impurity defect states. Journal of Semiconductors, 2011, 32(11):112001 doi: 10.1088/1674-4926/32/11/112001
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    Received: 01 June 2013 Revised: 05 August 2013 Online: Published: 01 December 2013

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      Ken K. Chin. Transition Gibbs free energy level cross section and formulation of carrier SRH recombination rate[J]. Journal of Semiconductors, 2013, 34(12): 122001. doi: 10.1088/1674-4926/34/12/122001 K K Chin. Transition Gibbs free energy level cross section and formulation of carrier SRH recombination rate[J]. J. Semicond., 2013, 34(12): 122001. doi:  10.1088/1674-4926/34/12/122001.Export: BibTex EndNote
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      Ken K. Chin. Transition Gibbs free energy level cross section and formulation of carrier SRH recombination rate[J]. Journal of Semiconductors, 2013, 34(12): 122001. doi: 10.1088/1674-4926/34/12/122001

      K K Chin. Transition Gibbs free energy level cross section and formulation of carrier SRH recombination rate[J]. J. Semicond., 2013, 34(12): 122001. doi:  10.1088/1674-4926/34/12/122001.
      Export: BibTex EndNote

      Transition Gibbs free energy level cross section and formulation of carrier SRH recombination rate

      doi: 10.1088/1674-4926/34/12/122001
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