Infrared dielectric anisotropy and phonon modes of sapphire M. Schubert* Center for Microelectronic and Optical Materials Research, and Department of Electrical Engineering, University of Nebraska-Lincoln, Lincoln, Nebraska 68588 and Abteilung Halbleiterphysik, Institut fu ¨r Experimentelle Physik II, Universita ¨t Leipzig, Vor dem Hospitaltor 1, D-04103 Leipzig, Germany T. E. Tiwald Center for Microelectronic and Optical Materials Research, and Department of Electrical Engineering, University of Nebraska-Lincoln, Lincoln, Nebraska 68588 C. M. Herzinger J. A. Woollam Co., Inc., 645 M Street, Suite 102, Lincoln, Nebraska 68508 Received 17 June 1999 Spectroscopic ellipsometry in the infrared spectral range is used for comprehensive analysis of the aniso- tropic dielectric response of sapphire. We determine the ordinary and extraordinary infrared complex dielectric functions as well as all infrared-active phonon modes of single crystal  -Al 2 O 3 for wavelengths from 3 to 30 m. Data were acquired from high-symmetry orientations of a-plane and c-plane surfaces cut from bulk crystals. A simple classification scheme is developed, which allows identification of the total reflection bands for p- and s-polarized light in anisotropic materials with multiple phonon branches. We employ a factorized form of the dielectric function for superior best-fit calculation of the infrared ellipsometry spectra adjusting frequencies and damping parameters of the transverse and longitudinal phonon modes with A 2u and E u symmetry separately. A generalized Lowndes condition for the damping parameters is derived and found satisfied for the A 2u and E u branches. Excellent agreement with phonon mode literature values is obtained, and improper use of selection rules reported previously for calculation of the sapphire dielectric functions is revised Harman, Ninomiya, and Adachi, J. Appl. Phys. 76, 8032 1994. The dielectric function model will become useful for infrared ellipsometry investigation of multiple-layer structures grown on  -Al 2 O 3 substrates such as group-III nitride heterostructures. I. INTRODUCTION Sapphire is an excellent insulator with high thermal conductivity. 1,2 Due to its wide band gap the material is highly transparent for photons with energies from the far infrared IR to the deep ultraviolet, i.e., from the lattice reststrahlen band 0.12 eV to the onset of the electronic band-to-band transitions 9 eV. 3–5 Sapphire (  -Al 2 O 3 ) consists of a hexagonal closely packed hcp lattice of alu- minum atoms with oxygen atoms at octahedral sites Fig. 1; Al atoms at 12( c ) sites point symmetry C 2 , O atoms at 18( e ) sites ( C 3 )]. 1,2 Because of its rombohedral structure, sapphire exhibits a uniaxial optical anisotropic character. Spectroscopic ellipsometry SE is known as an excellent technique for determination of the complex dielectric func- tions of materials, and avoids inaccuracies due to extrapola- tion into experimentally inaccessible spectral regions as nec- essary for Kramers-Kronig analysis of reflectivity data. 6 Applications within the near-IR NIR, visible VIS, and ultraviolet UV spectral range include optical characteriza- tion of electronic band-structure properties in compound semiconductor materials, such as band-to-band transitions, and related critical point information. 7 Recent development of polarization sensitive spectrophotometers in the middle- and far-IR spectral range now enable feasible SE application for photon energies that match the phonon energies of many group-III-V semiconductor thin-film materials. 8–16 Resonant excitation of phonons by the IR-SE probe beam strongly affects the state of polarization of the reflected beam, thereby providing high sensitivity to the thin-film and substrate opti- cal lattice properties. Analysis of IR-SE data follows the same line as for those acquired within the NIR-VIS-UV spectral range. Model calculations are performed by varia- tion of significant parameters until simulated and experimen- tal data match as closely as possible. 17 High-quality synthetic sapphire is widely used as sub- strate material for solid-state device applications. Because of FIG. 1. Crystal structure of  -Al 2 O 3 ( , Al; , O). PHYSICAL REVIEW B 15 MARCH 2000-II VOLUME 61, NUMBER 12 PRB 61 0163-1829/2000/6112/818715/$15.00 8187 ©2000 The American Physical Society