Ionic current and polarization effect in TlBr

Thallium bromide (TlBr) is an ionic semiconductor that has shown great capacity for accurate radiation detection. Its application to this end, however, has been hampered by degradation of performance over time, in a process called polarization. This effect has been traditionally assigned to a build-up of ions at the electrodes, which would counteract an applied electrical bias field. Here, we estimate the ionic mobility in TlBr and its possible association with the polarization effect using parameter-free quantum simulations. Our results indicate that in samples with up to moderate levels of impurities, ions cannot traverse distances large enough to generate zones of accumulation and depletion in the crystal, suggesting different causes for the polarization effect.

Figure 1

Formation energies of intrinsic defects in TlBr: E${}_f$ of positively charged Br vacancies coincides with that of negatively charged Tl vacancies near the middle of the band-gap, pinning the Fermi level. Neutrally charged complexes of vacancies (Schottky pairs), Tl and Br antisites are also indicated. The vertical dashed lines indicate the positions of the calculated band edges.

Figure 2

Calculated migration barriers of charged Tl (blue squares) and Br (red circles) vacancies obtained using the nudged elastic band method. The lines are guides to the eye.

Figure 3

Ionic mobility, $\mu$, as a function of T${}^{-1}$ for Br${}^{-}$ (blue) and Tl${}^{+}$ (red) ions in TlBr. The solid lines are plotted for the case of intrinsic concentrations of vacancies, while the dotted and dashed lines correspond to cases with additional extrinsic concentrations of vacancies as indicated next to each line (in cm${}^{-3}$). These results were obtained using our calculated parameters, assuming that all vacancies are associated in pairs with oppositely charged defects. The binding energy assumed was the same as that of Schottky pairs. The dash-dotted curves correspond to the required extrinsic concentration of Tl vacancies so that Tl${}^{+}$ ions become the majority carriers at room temperature, given intrinsic concentrations of $V_{\text{Br}}^{+}$. The vertical dotted lines indicate room temperature and $-{20}^{\circ }$C.