On the permittivity of titanium dioxide

Abstract

Conductive rutile TiO₂ has received considerable attention recently due to multiple applications. However, the permittivity in conductive, reduced or doped TiO₂ appears to cause controversy with reported values in the range 100-10,000. In this work, we propose a method for measurements of the permittivity in conductive, n-type TiO₂ that involves: (i) hydrogen ion-implantation to form a donor concentration peak at a known depth, and (ii) capacitance-voltage measurements for donor profiling. We cannot confirm the claims stating an extremely high permittivity of single crystalline TiO₂. On the contrary, the permittivity of conductive, reduced single crystalline TiO₂ is similar to that of insulating TiO₂ established previously, with a Curie-Weiss type temperature dependence and the values in the range 160-240 along with the c-axis.

Figure 1

Capacitance (a) of a TiO₂-N₂ sample (probing frequency 60 kHz) and the N(V)ε₀ε product (b) as functions of applied voltage. The red, dotted curve shows the as-prepared sample, i.e., after the N₂ heat treatment but prior to H⁺ implantation. The blue, solid curves are for the H-implanted sample measured at different temperatures (T_meas). The peaks in N(V)ε₀ε are indicated by the drop-down lines. The corresponding capacitance values, obtained at the same applied voltages, are also marked in (a).

Figure 2

Temperature dependence of the c-axis permittivity (ε) of conductive, n-type TiO₂ obtained after heat treatments in FG and N₂; and a modified Curie–Weiss dependence with the parameters determined by Samara and Peercy (solid curve).