Interplay between intrinsic defects, doping, and free carrier concentration in SrTiO${}_3$ thin films

Using both computational and experimental analysis, we demonstrate a rich point-defect phase diagram in doped strontium titanate as a function of thermodynamic variables such as oxygen partial pressure and electronic chemical potential. Computational modeling of point-defect energetics demonstrates that a complex interplay exists between dopants, thermodynamic parameters, and intrinsic defects in thin films of SrTiO${}_3$ (STO). We synthesize STO thin films via pulsed laser deposition and explore this interplay between intrinsic defects, doping, compensation, and carrier concentration. Our point-defect analysis (i) demonstrates that careful control over growth conditions can result in the tunable presence of anion and cation vacancies, (ii) suggests that compensation mechanisms will pose intrinsic limits on the dopability of perovskites, and (iii) provides a guide for tailoring the properties of doped perovskite thin films.

Figure 1

Chemical potential phase space: each point in the triangle satisfies $\Delta {\mu }_{\text{Sr}}+\Delta {\mu }_{\text{Ti}}+3\Delta {\mu }_{\text{O}}=\Delta {\mu }_{\text{STO}}$. In the white region, STO is stable; in the shaded regions, formation of different phases (indicated) is favorable.

Figure 2

Finite size extrapolation to estimate the energy of charged defect-defect interactions for the singly charged oxygen vacancy V${}_{\text{O}}^{+1}$. The line is the fit to the data based on Eq. (3).

Figure 3

Defect formation energy as a function of the Fermi energy $E_F$ for vacancies and vacancy complexes in STO. Defect formation energies are shown at three points along the path ${\lambda }^1$ in Fig. 1. $\Delta {\mu }_o={\lambda }_{\text{min}}^1,{\lambda }_{\text{min}}^1/2,0$ corresponds to low, midranged, and high oxygen pressures, respectively. The circles correspond to defect transition levels. Two trends are evident. As the oxygen pressure increases, the most favorable defect changes from oxygen vacancies/vacancy complexes to strontium/titanium vacancies. As the Fermi level increases, the most favorable defect changes from oxygen vacancies/vacancy complexes (compensating donors) to strontium/titanium vacancies (compensating acceptors).

Figure 4

Plots showing the most favorable vacancy/vacancy complex for normal, Sr-poor, and Ti-poor prevailing thermodynamic conditions, as a function of chemical potential $\lambda =\Delta {\mu }_{\text{O}}$ and Fermi energy $E_F$. The La concentration is estimated from the charge neutrality constraint and the mass-action law.

Figure 5

Carrier density, obtained from Hall effect measurements, of PLD-grown STO films vs La content for growth at different oxygen partial pressures. Dashed line: carrier density predicted by La concentration in otherwise stoichiometric films. Measured carrier concentrations exhibit a large sensitivity to the oxygen partial pressure.

Figure 6

Time-of-flight ion scattering and recoil spectroscopy measurements on pure and La-doped STO thin films indicate Sr deficiency (or O excess) when films are synthesized at high $P_{{\text{O}}_2}$. (a) Counts registered by the MSRI detector, normalized to the scattered potassium signal, for La-doped STO grown at high and low $P_{{\text{O}}_2}$. Although the La signal is similar for both cases, the Sr signal is notably lower for films synthesized at high $P_{{\text{O}}_2}$. (The experimental setup is shown in the inset.) (b) and (c) Counts registered by the MSRI detector, normalized to the scattered potassium signal, for pure STO grown at high and low $P_{{\text{O}}_2}$ for beam incident at 15${}^{\circ }$ and 30${}^{\circ }$ incident angles, respectively. Again, while Ti count is similar for high and low $P_{{\text{O}}_2}$, Sr count is smaller at high $P_{{\text{O}}_2}$ and larger at low $P_{{\text{O}}_2}$.