Effects of carrier concentration on the dielectric function of ZnO:Ga and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">In</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>:</mml:mo><mml:mi mathvariant="normal">Sn</mml:mi></mml:mrow></mml:math>studied by spectroscopic ellipsometry: Analysis of free-carrier and band-edge absorption

Abstract

We have determined the dielectric functions of ZnO:Ga and ${\mathrm{In}}_{2}{\mathrm{O}}_{3}:\mathrm{Sn}$ with different carrier concentrations by spectroscopic ellipsometry. The dielectric functions have been obtained from ellipsometry analyses using the Drude and Tauc-Lorentz models. With increasing Hall carrier concentration ${N}_{\text{Hall}}$ in a range from ${10}^{19}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}{10}^{21}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$, the dielectric functions of ZnO:Ga and ${\mathrm{In}}_{2}{\mathrm{O}}_{3}:\mathrm{Sn}$ show drastic changes due to increases in (i) free-carrier absorption in a low-energy region and (ii) the Burstein-Moss shift in a high-energy region. The analyses of the dielectric functions revealed reductions in high-frequency dielectric constant ${\ensuremath{\epsilon}}_{\ensuremath{\infty}}$ and increases in plasma energy ${E}_{\mathrm{p}}$ as ${N}_{\text{Hall}}$ in the films increases. From a set of the parameters $({N}_{\text{Hall}},\phantom{\rule{0.2em}{0ex}}{\ensuremath{\epsilon}}_{\ensuremath{\infty}},\phantom{\rule{0.2em}{0ex}}{E}_{\mathrm{p}})$ determined experimentally, effective mass ${m}^{*}$ of ZnO:Ga and ${\mathrm{In}}_{2}{\mathrm{O}}_{3}:\mathrm{Sn}$ is extracted. In contrast to previous studies, we found linear increases in ${m}^{*}$ with increasing ${N}_{\text{Hall}}$. When the variations of ${m}^{*}$ with carrier concentration are taken into account, carrier concentrations determined optically from spectroscopic ellipsometry show remarkable agreement with those estimated by Hall measurements. Nevertheless, the electron mobility obtained from spectroscopic ellipsometry and Hall measurements indicates rather poor agreement. We attributed this to the presence of grain boundaries in the films. In this article, we discuss various effects of carrier concentration on the optical properties of transparent conductive oxides.