Nature of the band gap of ${\mathrm{Tl}}_2\mathrm{O}{}_3$

The ground state electronic structure of thallic oxide has been a source of controversy in the literature, with Tl${}_2$O${}_3$ reported to be either a degenerate $n$-type semiconductor or an intrinsic semimetal with no band gap. Using a screened hybrid density functional theory (DFT) approach, we show that Tl${}_2$O${}_3$ is a semiconductor with a predicted band gap of 0.33 $\mathrm{eV}$. We rationalize the large optical band gaps reported in experimental studies and demonstrate that previous “standard” DFT approaches wrongly predict Tl${}_2$O${}_3$ to be a semimetal. Doubly ionized oxygen vacancies are shown to be the origin of the high carrier concentrations seen experimentally.

Figure 1

The total and partial density of states for Tl${}_2$O${}_3$ as calculated with (a) PBE and (b) HSE06. The scale on which the Tl 6$s$, 6$p$, and 5$d$ states are presented is increased by a factor of 5. The highest occupied state is set to $0\hspace{0.5em}\mathrm{eV}$.

Figure 2

The band structure of Tl${}_2$O${}_3$ as calculated with (a) PBE and (b) HSE06. The highest occupied state is set to $0\hspace{0.5em}\mathrm{eV}$.

Figure 3

(a) Calculated absorption spectrum of bulk Tl${}_2$O${}_3$. Note the onset of optical absorption is $~$1.2 $\mathrm{eV}$ above the fundamental band gap. (b) Band structure of Tl${}_2$O${}_3$ (along the H–$\Gamma$–N lines). The highest energy valence bands resulting in strong optical absorption to the conduction band are bold gray (red).

Figure 4

Schematic of the optical absorption of Tl${}_2$O${}_3$ seen experimentally. $E_{\mathrm{g}}$ represents the fundamental band gap as calculated with HSE06, $E_{\mathrm{g}}^{\mathrm{Opt},\mathrm{S}}$ represents the HSE06 calculated onset of optical absorption for stoichiometric Tl${}_2$O${}_3$, $E_{\mathrm{g}}^{\mathrm{F}}$ represents the distance of the $E_{\mathrm{F}}$ from the VBM reported in Ref. 6, and $E_{\mathrm{g}}^{\mathrm{Opt},\mathrm{NS}}$ represents the total optical absorption of a nonstoichiometric Tl${}_2$O${}_3$ sample.

Figure 5

HSE06 calculated formation energies for $V_{\mathrm{O}}$ under Tl-rich/O-poor conditions [dark gray (blue)] and Tl-poor/O-rich [light grey (green)] conditions. The solid dots denote the transition levels $\epsilon (q/q^{\prime })$. The HSE06 calculated CBM is indicated by the vertical (red) dashed line.