Nonlinear ion mobility at high electric field strengths in the perovskites <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>SrTiO</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>CH</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>NH</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>PbI</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>
Dennis Kemp, Roger A. De Souza
Abstract
As the characteristic dimensions of perovskite devices shrink to the nanoscale, operating voltages of a few volts lead to huge field strengths and, consequently, to the possibility of field-enhanced ion mobility. In this paper, the electrochemical mobility of $X$ anions (${u}_{X}$) along $\ensuremath{\langle}100\ensuremath{\rangle}$ in the $AB{X}_{3}$ perovskite structure was investigated as a function of electric field strength $E$ and temperature $T$ by means of classical molecular dynamics simulations. Two different cases were examined: one representative of inorganic perovskites, oxide-ion mobility (${u}_{\text{O}}$) in cubic ${\mathrm{SrTiO}}_{3}$; and the other representative of hybrid inorganic-organic perovskites, iodide-ion mobility (${u}_{\mathrm{I}}$) in cubic ${\mathrm{CH}}_{3}{\mathrm{NH}}_{3}{\mathrm{PbI}}_{3}$. In both cases, isothermal mobilities are, as expected, independent of field at low values ($E<{10}^{0}$ MV ${\mathrm{cm}}^{\ensuremath{-}1}$) but become field dependent at higher values. Data obtained for ${u}_{\text{O}}(E,T)$ can be described quantitatively with an analytical treatment incorporating a modified Haven ratio for a dilute solution. In contrast, ${u}_{\text{I}}(E,T)$ displays complex behavior. At high fields, the degree of field enhancement is underestimated by the analytical treatment, while in the field-independent regime, the data imply that moderate fields decrease ${u}_{\mathrm{I}}$. Our study thus demonstrates that for cubic, inorganic $AB{X}_{3}$ perovskites ${u}_{X}(E,T)$ along $\ensuremath{\langle}100\ensuremath{\rangle}$ can now be predicted quantitatively, but for hybrid perovskites substantially more complex models are required.