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Research Papers: Radiative Heat Transfer

Absorption Spectra and Electron-Vibration Coupling of Ti:Sapphire From First Principles

[+] Author and Article Information
Hua Bao

Assistant Professor
University of Michigan-Shanghai Jiao Tong
University Joint Institute,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: hua.bao@sjtu.edu.cn

Xiulin Ruan

Associate Professor
School of Mechanical Engineering and
Birck Nanotechnology Center,
Purdue University,
West Lafayette, IN 47907
e-mail: ruan@purdue.edu

1Corresponding authors.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 25, 2015; final manuscript received November 30, 2015; published online January 12, 2016. Assoc. Editor: Zhuomin Zhang.

J. Heat Transfer 138(4), 042702 (Jan 12, 2016) (5 pages) Paper No: HT-15-1562; doi: 10.1115/1.4032177 History: Received August 25, 2015; Revised November 30, 2015

First-principles calculations are performed to study the absorption spectra and electron-vibration coupling of titanium-doped sapphire (Ti:Al2O3). Geometry optimization shows a local structure relaxation after the doping of Ti. Electronic band structure calculation shows that five additional dopant energy bands are observed around the band gap of Al2O3, and are attributed to the five localized d orbitals of the Ti dopant. The optical absorption spectra are then predicted by averaging the oscillator strength during a 4 ps first-principles molecular dynamics (MD) trajectory, and the spectra agree well with the experimental results. Electron-vibration coupling is further investigated by studying the response of the ground and excited states to the Eg vibrational mode, for which a configuration coordinate diagram is obtained. Stokes shift effect is observed, which confirms the red shift of emission spectra of Ti:sapphire. This work offers a quantitative understanding of the optical properties and crystal-field theory of Ti-doped sapphire. The first-principles calculation framework developed here can also be followed to predict the optical properties and study the electron-vibration coupling in other doped materials.

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References

Moulton, P. , 1982, “ Ti-Doped Sapphire Tunable Solid-State Laser,” Opt. News, 8(6), p. 9. [CrossRef]
Powell, R. , 1998, Physics of Solid-State Laser Materials, Springer-Verlag, New York.
Kikoin, K. , and Fleurov, V. , 1994, Transition Metal Impurities in Semiconductors, World Scientific Publishing, Singapore.
Grinberg, M. , and Mandelis, A. , 1994, “ Photopyroelectric-Quantum-Yield Spectroscopy and Quantum-Mechanical Photoexcitation-Decay Kinetics of the Ti3+ Ion in Al2O3,” Phys. Rev. B, 49(18), pp. 12496–12506. [CrossRef]
Bao, H. , and Ruan, X. L. , 2010. “ Ab Initio Calculations of Thermal Radiative Properties: The Semiconductor GaAs,” Int. J. Heat Mass Transfer, 53(7–8), pp. 1308–1312. [CrossRef]
Yang, J. , Liu, L. , and Tan, J. , 2014, “ First-Principles Molecular Dynamics Study on Temperature-Dependent Dielectric Function of Bulk 3C and 6H SiC in the Energy Range 3-8 eV,” Physica B, 436, pp. 182–187. [CrossRef]
Bao, H. , Habenicht, B. F. , Prezhdo, O. V. , and Ruan, X. L. , 2009, “ Temperature Dependence of Hot Carrier Relaxation in a PbSe Nanocrystal: An Ab Initio Study,” Phys. Rev. B, 79(23), p. 235306. [CrossRef]
Sisto, A. , Ruan, X. , and Fisher, T. S. , 2014, “ First Principles and Finite Element Predictions of Radiative Properties of Nanostructure Arrays: Single-Walled Carbon Nanotube Arrays,” ASME J. Heat Transfer, 136(6), p. 062702. [CrossRef]
Yang, J. , Liu, L. , and Tan, J. , 2015, “ First-Principles Study on Dielectric Function of Isolated and Bundled Carbon Nanotubes,” J. Quant. Spectrosc. Radiat. Transfer, 158, pp. 78–83. [CrossRef]
Ruan, X. L. , and Kaviany, M. , 2008, “ Ab Initio Calculations of the Photon-Electron-Phonon Interactions in Laser Cooling of Ion-Doped Solids,” J. Comput. Theor. Nanosci., 5, pp. 221–229.
Ching, W. , Xu, Y.-N. , and Brickeen, B. , 1999, “ Ab-Initio Calculation of Excited State Absorption of Cr4+ in Y3Al5O12,” Appl. Phys. Lett., 74(25), pp. 3755–3757. [CrossRef]
Xu, Y.-N. , Gu, Z.-Q. , Zhong, X.-F. , and Ching, W. Y. , 1997, “ Ab Initio Calculations for the Neutral and Charged o Vacancy in Sapphire,” Phy. Rev. B, 56(12), pp. 7277–7284. [CrossRef]
Matsunaga, K. , Nakamura, A. , Yamamoto, T. , and Ikuhara, Y. , 2003, “ First-Principles Study of Defect Energetics in Titanium-Doped Alumina,” Phys. Rev. B, 68(21), p. 214102. [CrossRef]
Bao, H. , Qiu, B. , Zhang, Y. , and Ruan, X. L. , 2012, “ A First-Principles Molecular Dynamics Approach for Predicting Optical Phonon Lifetimes and Far-Infrared Reflectance of Polar Materials,” J. Quant. Spectrosc. Radiat. Transfer, 113(13), pp. 1683–1688. [CrossRef]
Yang, J. Y. , Liu, L. H. , and Tan, J. Y. , 2014, “ Temperature-Dependent Dielectric Function of Germanium in the UV-vis Spectral Range: A First-Principles Study,” J. Quant. Spectrosc. Radiat. Transfer, 141, pp. 24–31. [CrossRef]
Perdew, J. P. , and Zunger, A. , 1981, “ Self-Interaction Correction to Density-Functional Approximations for Many-Electron Systems,” Phys. Rev. B, 23, pp. 5048–5079. [CrossRef]
Kresse, G. , and Furthmuller, J. , 1996, “ Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set,” Comput. Mater. Sci., 6(1), pp. 15–50. [CrossRef]
Vanderbilt, D. , 1990, “ Soft Self-Consistent Pseudopotentials in a Generalized Eigenvalue Formalism,” Phys. Rev. B, 41, pp. 7892–7895. [CrossRef]
Rappe, A. M. , Rabe, K. M. , Kaxiras, E. , and Joannopoulos, J. D. , 1990, “ Optimized Pseudopotentials,” Phys. Rev. B, 41(2), pp. 1227–1230. [CrossRef]
Lewis, J. , Schwarzenbach, D. , and Flack, H. , 1982, “ Electric Field Gradients and Charge Density in Corundum, α-Al2O3,” Acta Cryst., A38, pp. 733–739. [CrossRef]
Matsunaga, K. , Yamamoto, T. , and Ikuhara, Y. , 2003, “ First-Principles Calculations of Intrinsic Defects in Al2O3,” Phys. Rev. B, 68(8), p. 085110. [CrossRef]
Ching, W. , and Xu, Y.-N. , 1994, “ First-Principles Calculation of Electronic, Optical, and Structural Properties of α-Al2O3,” J. Am. Ceram. Soc., 77(2), pp. 404–411. [CrossRef]
Bortz, M. , and French, R. , 1989, “ Optical Reflectivity Measurements Using a Laser Plasma Light Source,” Appl. Phys. Lett., 55(19), pp. 1955–1957. [CrossRef]
Pulci, O. , Onida, G. , Sole, R. D. , and Reining, L. , 1998, “ Ab Initio Calculation of Self-Energy Effects on Optical Properties of GaAs(110),” Phys. Rev. Lett., 81(24), pp. 5374–5377. [CrossRef]
Momma, K. , and Izumi, F. , 2006, “ An Integrated Three-Dimensional Visualization System Vesta Using wxWidgets,” Commision Crystallogr. Comput., IUCr Newslett., No. 7, pp. 106–119.
Mohapatra, S. , and Kröger, F. , 1977, “ Defect Structure of α-Al2O3 Doped With Titanium,” J. Am. Ceram. Soc., 60(9–10), pp. 381–387. [CrossRef]
Hilborn, R. , 1982, “ Einstein Coefficients, Cross Sections, f Values, Dipole Moments, and All That,” Am. J. Phys., 50(11), pp. 982–986. [CrossRef]
Gonze, X. , 1997, “ First-Principles Responses of Solids to Atomic Displacements and Homogeneous Electric Fields: Implementation of a Conjugate-Gradient Algorithm,” Phys. Rev. B, 55(16), pp. 10337–10354. [CrossRef]
Aggarwal, R. L. , Sanchez, A. , Fahey, R. E. , and Strauss, A. J. , 1986, “ Magnetic and Optical Measurements on Ti:Al2O3 Crystals for Laser Applications: Concentration and Absorption Cross Section of Ti3+ Ions,” Appl. Phys. Lett., 48(20), pp. 1345–1347. [CrossRef]
Rapoport, W. R. , and Khattak, C. P. , 1988, “ Titanium Sapphire Laser Characteristics,” Appl. Opt., 27(13), pp. 2677–2684. [CrossRef] [PubMed]
Kilina, S. V. , Craig, C. F. , Kilin, D. S. , and Prezhdo, O. V. , 2007, “ Ab Initio Time-Domain Study of Phonon-Assisted Relaxation of Charge Carriers in PbSe Quantum Dot,” J. Phys. Chem. C, 111(12), pp. 4871–4878. [CrossRef]
Bernasconi, L. , Tomić, S. , Ferrero, M. , Rérat, M. , Orlando, R. , Dovesi, R. , and Harrison, N. M. , 2011, “ First-Principles Optical Response of Semiconductors and Oxide Materials,” Phys. Rev. B, 83(19), p. 195325. [CrossRef]
Bernasconi, L. , 2015, “ Chaotic Soliton Dynamics in Photoexcited Trans-Polyacetylene,” J. Phys. Chem. Lett., 6(5), pp. 908–912. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

The optimized structure for a doped 120 ion Ti:Al2O3 supercell

Grahic Jump Location
Fig. 2

Electronic energy levels for the Ti-doped alumina supercell. The lower Ti 3d level is three-fold degenerate (D1, D2, and D3 denoted by the three circles) and the upper Ti 3d level is two-fold degenerate (D4 and D5 denoted by the two circles).

Grahic Jump Location
Fig. 3

Charge density isosurfaces where the magnitude of the charge density is 3.4×10−10 e per unit cell. (a) The charge distribution of the D1 orbital. (b) The charge distribution of D4 orbital. It can be seen that these states are highly localized around the Ti dopant. The shape of the lobes around the Ti dopant resembles the typical d orbital.

Grahic Jump Location
Fig. 4

Calculated absorption spectra at 300 K in this work (black solid line) and the experimental absorption spectra at room temperature [29] (dotted line) and emission spectra from Ref. [30] (dashed line)

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Fig. 5

The five different local vibrational modes of Ti octahedra

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Fig. 6

Configuration coordinate diagram for Eg vibrational mode

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Fig. 7

Fourier transform of transition energy during a 4 ps trajectory

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