Superconducting Transition Temperatures of Semiconducting SrTi${\mathrm{O}}_3$

The superconducting transition temperature $T_c$ of SrTi${\mathrm{O}}_3$ has been measured for specimens having electron carrier concentrations $n_c$ from 6.9×${10}^{18}$ to 5.5×${10}^{20}$ ${\mathrm{cm}}^{-3\mathrm{}}$. The curve exhibits a maximum in $T_c$ for $n_c$ near 9×${10}^{19}$ ${\mathrm{cm}}^{-3\mathrm{}}$. The transition temperature has also been calculated using one adjustable parameter $\xi$, the intervalley deformation potential, in addition to the known normal-state properties of SrTi${\mathrm{O}}_3$. A good fit to the experimental curve is obtained.