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Applications of Huang–Rhys theory in semiconductor optical spectroscopy

Yong Zhang

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 Corresponding author: Yong Zhang, yong.zhang@uncc.edu

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Abstract: A brief review of Huang–Rhys theory and Albrechtos theory is provided, and their connection and applications are discussed. The former is a first order perturbative theory on optical transitions intended for applications such as absorption and emission involving localized defect or impurity centers, emphasizing lattice relaxation or mixing of vibrational states due to electron–phonon coupling. The coupling strength is described by the Huang–Rhys factor. The latter theory is a second order perturbative theory on optical transitions intended for Raman scattering, and can in-principle include electron–phonon coupling in both electronic states and vibrational states. These two theories can potentially be connected through the common effect of lattice relaxation – non-orthonormal vibrational states associated with different electronic states. Because of this perceived connection, the latter theory is often used to explain resonant Raman scattering of LO phonons in bulk semiconductors and further used to describe the size dependence of electron–phonon coupling or Huang–Rhys factor in semiconductor nanostructures. Specifically, the A term in Albrechtos theory is often invoked to describe the multi-LO-phonon resonant Raman peaks in both bulk and nanostructured semiconductors in the literature, due to the misconception that a free-exciton could have a strong lattice relaxation. Without lattice relaxation, the A term will give rise to Rayleigh or elastic scattering. Lattice relaxation is only significant for highly localized defect or impurity states, and should be practically zero for either single particle states or free exciton states in a bulk semiconductor or for confined states in a semiconductor nanostructure that is not extremely small.

Key words: Huang–Rhys factorelectron–phonon couplingsemiconductor optical spectroscopyresonant Raman scattering



[1]
Huang K, Rhys A, Mott N F. Theory of light absorption and non-radiative transitions in F-centres. Proc Royal Soc London A, 1950, 204, 406 doi: 10.1098/rspa.1950.0184
[2]
Permogorov S. Excitons. North-Holland Publishing Company, 1982, 177
[3]
Cardona M. Light Scattering in Solids II. Springer Berlin Heidelberg, 1982, 19
[4]
Karazhanov S Z, Yong Z, Wang L W, et al. Resonant defect states and strong lattice relaxation of oxygen vacancies in WO3. Phys Rev B, 2003, 68, 233204 doi: 10.1103/PhysRevB.68.233204
[5]
Albrecht A C. On the theory of Raman intensities. J Chem Phys, 1961, 34, 1476 doi: 10.1063/1.1701032
[6]
Zhang Y, Ge W K, Sturge M D, et al. Phonon side-band of excitons bound to isoelectronic impurities in semiconductors. Phys Rev B, 1969, 47 doi: 10.1103/PhysRevB.47.6330
[7]
Zhang Y, Ge W K. Behavior of nitrogen impurities in III–V semiconductors. J Lumin, 2000, 85, 247 doi: 10.1016/S0022-2313(99)00193-3
[8]
Imbusch G F. Luminescence spectroscopy. New York: Academic Press, 1978, 1
[9]
Bassani F, Parravicini G P. Electronic states and optical transitions in solids. Oxford: Pergamon, 1975, 190 doi: 10.1063/1.3023374
[10]
Yu P Y, Cardona M. Fundamentals of semiconductors. Heidelberg: Springer-Verlag, 1996
[11]
Pekar S I. Theory of F-centers. Zh Eksp Teor Fiz, 1950, 20, 510
[12]
Dean P J, Herbert D C. Excitons. New York: Springer, 1979
[13]
Huang K. Lattice relaxation and theory of multiphonon transitions. Prog Phys, 1981, 1, 31
[14]
Balkanski M. Effects of electron–phonon interaction in luminescence and light scattering. J Lumin, 1981, 24/25, 381 doi: 10.1016/0022-2313(81)90294-5
[15]
Snyder P G, Myles C W, Dai H H, et al. Model for phonon-assisted indirect recombination at impurity sites in semiconductors: A test of impurity wave-function theories. Phys Rev B, 1985, 32, 2685 doi: 10.1103/PhysRevB.32.2685
[16]
Ridley B K. Quantum processes in semiconductors. Oxford: Oxford Science Publications, 1999
[17]
Wang Y L, Gu Z Q, Huang K. A disorder induced lattice relaxation mechanism in alloys. Chin Sci Bull, 1981, 26, 531 doi: 10.1360/csb1981-26-9-531
[18]
Schmitt-Rink S, Miller D A B, Chemla D S. Theory of the linear and nonlinear optical properties of semiconductor microcrystallites. Phys Rev B, 1987, 35, 8113 doi: 10.1103/PhysRevB.35.8113
[19]
Nomura S, Kobayashi T. Exciton--LO-phonon couplings in spherical semiconductor microcrystallites. Phys Rev B, 1992, 45, 1305 doi: 10.1103/PhysRevB.45.1305
[20]
Merlin R, Güntherodt G, Humphreys R, et al. Multiphonon processes in YbS. Phys Rev B, 1987, 17, 4951 doi: 10.1103/PhysRevB.17.4951
[21]
Heitz R, Mukhametzhanov I, Stier O, et al. Enhanced polar exciton-LO-phonon interaction in quantum dots. Phys Rev Lett, 1999, 83, 4654 doi: 10.1103/PhysRevLett.83.4654
[22]
Alivisatos A P, Harris T D, Carroll P J, et al. Electron–vibration coupling in semiconductor clusters studied by resonance Raman spectroscopy. J Chem Phys, 1989, 90, 3463 doi: 10.1063/1.455855
[23]
Zhang Q, Zhang J, Utama M I B, et al. Exciton–phonon coupling in individual ZnTe nanorods studied by resonant Raman spectroscopy. Phys Rev B, 2012, 85, 085418 doi: 10.1103/PhysRevB.85.085418
[24]
Klein M C, Hache F, Ricard D, et al. Size dependence of electron–phonon coupling in semiconductor nanospheres: The case of CdSe. Phys Rev B, 1990, 42, 11123 doi: 10.1103/PhysRevB.42.11123
[25]
Faulkner R A. Toward a theory of isoelectronic impurities in semiconductors. Phys Rev, 1968, 175, 991 doi: 10.1103/PhysRev.175.991
[26]
Zhang Y. Acceptor-like bound excitons in semiconductors. Phys Rev B, 1992, 45, 9025 doi: 10.1103/PhysRevB.45.9025
[27]
Zhang Y, Mascarenhas A, Wang L W. Systematic approach to distinguishing a perturbed host state from an impurity state in a supercell calculation for a doped semiconductor: Using GaP:N as an example. Phys Rev B, 2006, 74, 041201 doi: 10.1103/PhysRevB.74.041201
[28]
Shi L, Wang L W. Ab initio calculations of deep-level carrier nonradiative recombination rates in bulk semiconductors. Phys Rev Lett, 2012, 109, 245501 doi: 10.1103/PhysRevLett.109.245501
[29]
Champion P M, Albrecht A C. Investigations of Soret excited resonance Raman excitation profiles in cytochrome c. J Chem Phys, 1979, 71, 1110 doi: 10.1063/1.438455
[30]
Scamarcio G, Spagnolo V, Ventruti G, et al. Size dependence of electron–LO-phonon coupling in semiconductor nanocrystals. Phys Rev B, 1996, 53, R10489 doi: 10.1103/PhysRevB.53.R10489
[31]
Kelley A M. Resonance Raman overtone intensities and electron–phonon coupling strengths in semiconductor nanocrystals. J Phys Chem A, 2013, 117, 6143 doi: 10.1021/jp400240y
[32]
Rodríguez-Suárez R, Menéndez-Proupin E, Trallero-Giner C, et al. Multiphonon resonant Raman scattering in nanocrystals. Phys Rev B, 2000, 62, 11006 doi: 10.1103/PhysRevB.62.11006
[33]
Yi Y, Marmon J K, Chen Y, et al. unpublished
[34]
Dos Santos M P, Hirlimann C, Balkanski M. Local induced activity in resonant Raman scattering of GaP:N. Phys B + C, 1983, 117/118, 108 doi: 10.1016/0378-4363(83)90454-0
[35]
Frommer A, Cohen E, Ron A. Resonant Raman-scattering induced by excitons bound to nitrogen impurities in GaP:N. Phys Rev B, 1993, 47, 1823 doi: 10.1103/physrevb.47.1823
[36]
Tan P H, Xu Z Y, Luo X D, et al. Resonant Raman scattering with the E+ band in a dilute GaAs1–xNx alloy (x = 0.1%). Appl Phys Lett, 2006, 89, 101912 doi: 10.1063/1.2345605
Fig. 1.  (Color online) Illustration of a configuration coordinate model. (a) Energy levels before and after taking into account the lattice relaxation. (b) Transition energies in relaxed configuration coordinates.

Fig. 2.  (Color online) Photoluminescence spectrum of the isolated nitrogen bound exciton in GaP:N (4.2 K, [N] = 1016 cm-3, A line at 2.317 eV)[6].

Fig. 3.  (Color online) Resonant Raman spectra of ZnTe measured by a 532 nm laser at room temperature for one high quality single crystal sample and a thin-film sample grown on a Si (211) substrate. Strong PL background of the single crystal sample has been removed.

[1]
Huang K, Rhys A, Mott N F. Theory of light absorption and non-radiative transitions in F-centres. Proc Royal Soc London A, 1950, 204, 406 doi: 10.1098/rspa.1950.0184
[2]
Permogorov S. Excitons. North-Holland Publishing Company, 1982, 177
[3]
Cardona M. Light Scattering in Solids II. Springer Berlin Heidelberg, 1982, 19
[4]
Karazhanov S Z, Yong Z, Wang L W, et al. Resonant defect states and strong lattice relaxation of oxygen vacancies in WO3. Phys Rev B, 2003, 68, 233204 doi: 10.1103/PhysRevB.68.233204
[5]
Albrecht A C. On the theory of Raman intensities. J Chem Phys, 1961, 34, 1476 doi: 10.1063/1.1701032
[6]
Zhang Y, Ge W K, Sturge M D, et al. Phonon side-band of excitons bound to isoelectronic impurities in semiconductors. Phys Rev B, 1969, 47 doi: 10.1103/PhysRevB.47.6330
[7]
Zhang Y, Ge W K. Behavior of nitrogen impurities in III–V semiconductors. J Lumin, 2000, 85, 247 doi: 10.1016/S0022-2313(99)00193-3
[8]
Imbusch G F. Luminescence spectroscopy. New York: Academic Press, 1978, 1
[9]
Bassani F, Parravicini G P. Electronic states and optical transitions in solids. Oxford: Pergamon, 1975, 190 doi: 10.1063/1.3023374
[10]
Yu P Y, Cardona M. Fundamentals of semiconductors. Heidelberg: Springer-Verlag, 1996
[11]
Pekar S I. Theory of F-centers. Zh Eksp Teor Fiz, 1950, 20, 510
[12]
Dean P J, Herbert D C. Excitons. New York: Springer, 1979
[13]
Huang K. Lattice relaxation and theory of multiphonon transitions. Prog Phys, 1981, 1, 31
[14]
Balkanski M. Effects of electron–phonon interaction in luminescence and light scattering. J Lumin, 1981, 24/25, 381 doi: 10.1016/0022-2313(81)90294-5
[15]
Snyder P G, Myles C W, Dai H H, et al. Model for phonon-assisted indirect recombination at impurity sites in semiconductors: A test of impurity wave-function theories. Phys Rev B, 1985, 32, 2685 doi: 10.1103/PhysRevB.32.2685
[16]
Ridley B K. Quantum processes in semiconductors. Oxford: Oxford Science Publications, 1999
[17]
Wang Y L, Gu Z Q, Huang K. A disorder induced lattice relaxation mechanism in alloys. Chin Sci Bull, 1981, 26, 531 doi: 10.1360/csb1981-26-9-531
[18]
Schmitt-Rink S, Miller D A B, Chemla D S. Theory of the linear and nonlinear optical properties of semiconductor microcrystallites. Phys Rev B, 1987, 35, 8113 doi: 10.1103/PhysRevB.35.8113
[19]
Nomura S, Kobayashi T. Exciton--LO-phonon couplings in spherical semiconductor microcrystallites. Phys Rev B, 1992, 45, 1305 doi: 10.1103/PhysRevB.45.1305
[20]
Merlin R, Güntherodt G, Humphreys R, et al. Multiphonon processes in YbS. Phys Rev B, 1987, 17, 4951 doi: 10.1103/PhysRevB.17.4951
[21]
Heitz R, Mukhametzhanov I, Stier O, et al. Enhanced polar exciton-LO-phonon interaction in quantum dots. Phys Rev Lett, 1999, 83, 4654 doi: 10.1103/PhysRevLett.83.4654
[22]
Alivisatos A P, Harris T D, Carroll P J, et al. Electron–vibration coupling in semiconductor clusters studied by resonance Raman spectroscopy. J Chem Phys, 1989, 90, 3463 doi: 10.1063/1.455855
[23]
Zhang Q, Zhang J, Utama M I B, et al. Exciton–phonon coupling in individual ZnTe nanorods studied by resonant Raman spectroscopy. Phys Rev B, 2012, 85, 085418 doi: 10.1103/PhysRevB.85.085418
[24]
Klein M C, Hache F, Ricard D, et al. Size dependence of electron–phonon coupling in semiconductor nanospheres: The case of CdSe. Phys Rev B, 1990, 42, 11123 doi: 10.1103/PhysRevB.42.11123
[25]
Faulkner R A. Toward a theory of isoelectronic impurities in semiconductors. Phys Rev, 1968, 175, 991 doi: 10.1103/PhysRev.175.991
[26]
Zhang Y. Acceptor-like bound excitons in semiconductors. Phys Rev B, 1992, 45, 9025 doi: 10.1103/PhysRevB.45.9025
[27]
Zhang Y, Mascarenhas A, Wang L W. Systematic approach to distinguishing a perturbed host state from an impurity state in a supercell calculation for a doped semiconductor: Using GaP:N as an example. Phys Rev B, 2006, 74, 041201 doi: 10.1103/PhysRevB.74.041201
[28]
Shi L, Wang L W. Ab initio calculations of deep-level carrier nonradiative recombination rates in bulk semiconductors. Phys Rev Lett, 2012, 109, 245501 doi: 10.1103/PhysRevLett.109.245501
[29]
Champion P M, Albrecht A C. Investigations of Soret excited resonance Raman excitation profiles in cytochrome c. J Chem Phys, 1979, 71, 1110 doi: 10.1063/1.438455
[30]
Scamarcio G, Spagnolo V, Ventruti G, et al. Size dependence of electron–LO-phonon coupling in semiconductor nanocrystals. Phys Rev B, 1996, 53, R10489 doi: 10.1103/PhysRevB.53.R10489
[31]
Kelley A M. Resonance Raman overtone intensities and electron–phonon coupling strengths in semiconductor nanocrystals. J Phys Chem A, 2013, 117, 6143 doi: 10.1021/jp400240y
[32]
Rodríguez-Suárez R, Menéndez-Proupin E, Trallero-Giner C, et al. Multiphonon resonant Raman scattering in nanocrystals. Phys Rev B, 2000, 62, 11006 doi: 10.1103/PhysRevB.62.11006
[33]
Yi Y, Marmon J K, Chen Y, et al. unpublished
[34]
Dos Santos M P, Hirlimann C, Balkanski M. Local induced activity in resonant Raman scattering of GaP:N. Phys B + C, 1983, 117/118, 108 doi: 10.1016/0378-4363(83)90454-0
[35]
Frommer A, Cohen E, Ron A. Resonant Raman-scattering induced by excitons bound to nitrogen impurities in GaP:N. Phys Rev B, 1993, 47, 1823 doi: 10.1103/physrevb.47.1823
[36]
Tan P H, Xu Z Y, Luo X D, et al. Resonant Raman scattering with the E+ band in a dilute GaAs1–xNx alloy (x = 0.1%). Appl Phys Lett, 2006, 89, 101912 doi: 10.1063/1.2345605
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    Received: 07 August 2019 Revised: Online: Accepted Manuscript: 16 August 2019Uncorrected proof: 16 August 2019Published: 01 September 2019

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      Yong Zhang. Applications of Huang–Rhys theory in semiconductor optical spectroscopy[J]. Journal of Semiconductors, 2019, 40(9): 091102. doi: 10.1088/1674-4926/40/9/091102 Y Zhang, Applications of Huang–Rhys theory in semiconductor optical spectroscopy[J]. J. Semicond., 2019, 40(9): 091102. doi: 10.1088/1674-4926/40/9/091102.Export: BibTex EndNote
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      Yong Zhang. Applications of Huang–Rhys theory in semiconductor optical spectroscopy[J]. Journal of Semiconductors, 2019, 40(9): 091102. doi: 10.1088/1674-4926/40/9/091102

      Y Zhang, Applications of Huang–Rhys theory in semiconductor optical spectroscopy[J]. J. Semicond., 2019, 40(9): 091102. doi: 10.1088/1674-4926/40/9/091102.
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      Applications of Huang–Rhys theory in semiconductor optical spectroscopy

      doi: 10.1088/1674-4926/40/9/091102
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      • Corresponding author: yong.zhang@uncc.edu
      • Received Date: 2019-08-07
      • Published Date: 2019-09-01

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