Accessible switching of electronic defect type in $\mathrm{SrTi}{\mathrm{O}}_3$ via biaxial strain

Elastic strain is used widely to alter the mobility of free electronic carriers in semiconductors, but a predictive relationship between elastic lattice strain and the extent of charge localization of electronic defects is still underdeveloped. Here we considered $\mathrm{SrTi}{\mathrm{O}}_3$, a prototypical perovskite as a model functional oxide for thin film electronic devices and nonvolatile memories. We assessed the effects of biaxial strain on the stability of electronic defects at finite temperature by combining density functional theory (DFT) and quasiharmonic approximation (QHA) calculations. We constructed a predominance diagram for free electrons and small electron polarons in this material, as a function of biaxial strain and temperature. We found that biaxial tensile strain in $\mathrm{SrTi}{\mathrm{O}}_3$ can stabilize the small polaron, leading to a thermally activated and slower electronic transport, consistent with prior experimental observations on $\mathrm{SrTi}{\mathrm{O}}_3$ and distinct from our prior theoretical assessment of the response of $\mathrm{SrTi}{\mathrm{O}}_3$ to hydrostatic stress. These findings also resolved apparent conflicts between prior atomistic simulations and conductivity experiments for biaxially strained $\mathrm{SrTi}{\mathrm{O}}_3$ thin films. Our computational approach can be extended to other functional oxides, and for the case of $\mathrm{SrTi}{\mathrm{O}}_3$ our findings provide concrete guidance for conditions under which strain engineering can shift the electronic defect type and concentration to modulate electronic transport in thin films.

Figure 1

Supercell containing (a) a free electron, and (b) a small electron polaron. Electron density of states of the (c) free electron structure, and the (d) small polaron structure. The yellow isosurface in (a) and (b) represents the spin density of free electrons and small polarons, respectively. For visualization purpose only, free electron structure (a) was generated with single $k$ point. Green, blue, and red spheres represent Sr, Ti, and O, respectively. VESTA [51] was used for visualization. Red dotted lines in (c) and (d) point to the highest occupied level of the system with a free electron and a small polaron, respectively, and zero energy was set to be the edge of the valence band.

Figure 2

Birch-Murnaghan equation of state fitting for a (a) free electron and (c) small polaron structure. Pressure obtained from the fitting of a (b) free electron and (d) small polaron structure. The legends in (a) and (b) also apply to (c) and (d), respectively. In (a) and (c) circular data points (red) are the total DFT 0 K energy, and triangular data points (blue) are the hydrostatic energy obtained by subtracting the deviatoric energy from DFT 0 K energy; dotted curves (red) and continuous curves (blue) are the Birch-Murnaghan equation of state fittings for circular data points (red) and triangular data points (blue), respectively. In (b) and (d) square data points (green) are the pressures obtained from DFT 0 K calculations, continuous curves (blue) and dotted curves (red) are fitted pressures obtained from the Birch-Murnaghan equation of state fitting from (a) and (c). (e) Self-trapping Gibbs free energy/enthalpy at 0 K for hydrostatic stress case from Ref. [2] (dotted curve, blue) and biaxial case obtained in this work (solid curve, red).

Figure 3

(a) The predominance diagram of the electronic defects in $\mathrm{SrTi}{\mathrm{O}}_3$ with respect to biaxial strain and temperature based on Helmholtz free energy of self-trapping. (b) $F_{\mathrm{self}\text{−}\mathrm{trapping}}$ contour plot in meV, and the predominance map in (a) is a result of the $F_{\mathrm{self}\text{−}\mathrm{trapping}}$ plotted in (b). (c) Predominance diagram based on internal energy. In (a) and (c), the orange area denotes the small polaron domination region, and the blue area denotes the free electron domination region. $l_{\mathrm{perfect}}$ represents the lattice parameter of defect-free $\mathrm{SrTi}{\mathrm{O}}_3$ as a function of temperature including the thermal expansion effect. Biaxial strain is calculated using $l_{\mathrm{perfect}}$ as the reference state. (d) Replotted carrier mobility versus temperature in Nb-$\mathrm{SrTi}{\mathrm{O}}_3$ from the experimental data reported in Ref. [29] under (i) compressive biaxial strain in temperature–carrier mobility space and (ii) tensile biaxial strain in $ln\left(\mu T^{1.5}\right)-1/T$ space, where $\mu$ is the carrier mobility. Migration barrier $E_a$ calculated in (d-ii) is 45 meV. Dotted lines are linear fittings for carrier mobility with respect to the corresponding temperature scales. The arrows in (a) represent the three different strain states and temperature ranges studied in the experiments of Ref. [29] replotted in (d).