Evaporated Sn-doped In2O3 films: Basic optical properties and applications to energy-efficient windows

Abstract

We review work on In₂O₃:Sn films prepared by reactive e‐beam evaporation of In₂O₃ with up to 9 mol % SnO₂ onto heated glass. These films have excellent spectrally selective properties when the deposition rate is ∼0.2 nm/s, the substrate temperature is ≳150 °C, and the oxygen pressure is ∼5×10⁻⁴ Torr. Optimized coatings have crystallite dimensions ≳50 nm and a C‐type rare‐earth oxide structure. We cover electromagnetic properties as recorded by spectrophotometry in the 0.2–50‐μm range, by X‐band microwave reflectance, and by dc electrical measurements. Hall‐effect data are included. An increase of the Sn content is shown to have several important effects: the semiconductor band gap is shifted towards the ultraviolet, the luminous transmittance remains high, the infrared reflectance increases to a high value beyond a certain wavelength which shifts towards the visible, phonon‐induced infrared absorption bands vanish, the microwave reflectance goes up, and the dc resisitivity drops to ∼2×10⁻⁴ Ω cm. The corresponding mobility is ∼30 cm²/V s. The complex dielectric function ε is reported. These data were obtained from carefully selected combinations of spectrophotometric transmittance and reflectance data. It is found that ε can be reconciled with the Drude theory only by assuming a strongly frequency‐dependent relaxation energy between the plasma energy and the band gap. We review a recently formulated quantitative theoretical model for the optical properties which explicitly includes the additive contributions to ε from valence electrons, free electrons, and phonons. The theory embodies an effective‐mass model for n‐doped semiconductors well above the Mott critical density. Because of the high doping, the Sn impurities are singly ionized and the associated electrons occupy the bottom of the conduction band in the form of an electron gas. The Sn ions behave approximately as point scatterers, which is consistent with pseudopotential arguments. Screening of the ions is described by the random phase approximation. This latter theory works well as a consequence of the small effective electron radii. Exchange and correlation in the electron gas are represented by the Hubbard and Singwi–Sjölander schemes. Phonon effects are included by three empirically determined damped Lorentz oscillators. Free‐electron properties are found to govern the optical performance in the main spectral range. An analysis of the complex dynamic resistivity (directly related to ε) shows unambiguously that Sn ions are the most important scatterers, although grain‐boundary scattering can play some role in the midvisible range. As a result of this analysis one concludes that the optical properties of the best films approach the theoretical limit. Band‐gap shifts can be understood as the net result of two competing mechanisms: a widening due to the Burstein–Moss effect, and a narrowing due to electron‐electron and electron‐ion scattering. The transition width—including an Urbach tail—seems to be consistent with these notions. Window applications are treated theoretically from detailed computations of integrated luminous, solar, and thermal properties. It is found that In₂O₃:Sn films on glass can yield∼78% normal solar transmittance and ∼20% hemispherical thermal emittance. Substrate emission is found to be insignificant. Antireflection with evaporated MgF₂ or high‐rate sputtered aluminum oxyfluoride can give ∼95% normal luminous transmittance, ∼5% normal luminous reflectance, little perceived color and little increase in emittance. A color purity <1% in normal transmission and <10% in normal reflection is achievable for a daylight illuminant within extended ranges of film thickness.