Temperature Dependent Strain Relaxation in LaAlO$_{3}$ Thin Films on SrTiO$_{3}$ Substrates

LaAlO$_{3}$/SrTiO$_{3}$ interface has attracted great interest due to discoveries of rich interfacial properties. Strain and strain relaxation in LaAlO$_{3}$ films on SrTiO$_{3}$ substrates directly impact the lattice distortions and defects at the interface and therefore will influence the interfacial properties. Combining grazing incident x-ray diffraction and reciprocal space mapping, we directly measured the in-plane lattice constants of LaAlO$_{3}$ films on SrTiO$_{3}$ with thickness ranging from 4 u.c. to 250 u.c. We found a strong relationship between the strain relaxation behavior and the growth temperature of the LaAlO$_{3}$ films. Cracks were observed when the strain relaxed rapidly, consistent with the fracture theory. The processing temperature-dependent strain relaxation significantly affects the LaAlO$_{3}$/SrTiO$_{3}$ interface properties.