Ferroelectric Ordering in Colloidal Nanocrystals
The size-stability and fundamental nature of ferroelectric ordering in low-dimensional nanomaterials are explored using colloidal nanocrystals of the ferroelectric semiconductor germanium telluride (GeTe) and the archetypal perovskite ferroelectric barium titanate (BaTiO3). The synthesis of size-controlled colloidal GeTe nanocrystals is first explored, and the evolution of a polarization domain structure with increasing size is examined with transmission electron microscopy (TEM) and electron diffraction. The size-dependent ferroelectric ordering in ensembles of GeTe nanocrystals is then examined using a combination of temperature-dependent synchrotron x-ray diffraction, Raman scattering, and aberration-corrected TEM. Finally, the polarization state in individual nanocrystals of GeTe and BaTiO3 is elucidated using atomic-resolution TEM, off-axis electron holography, and piezoresponse force microscopy (PFM). The nature of the polar state and the correlations among local ferroelectric distortions are compared for the cases of GeTe and BaTiO3, the former a highly conductive semiconductor and the latter an electrical insulator, to deconvolute the influences of surface-induced strains and depolarization fields on the nature of the polar state.
GeTe nanocrystals with sizes ranging from 8 nm to 500 nm and size distributions of approximately 10-20 percent are prepared using divalent germanium (Ge) precursors and trioctylphosphine-tellurium (TOP-Te). GeTe nanocrystals with widely varying sizes are prepared using Ge precursors with different reduction kinetics. Particles of all sizes are confirmed to exist in the rhombohedral phase characteristic of the ferroelectric state.
The evolution of a polarization domain structure is examined in GeTe nanocrystals with average sizes of 8, 100, and 500 nm. Dark-field TEM and electron diffraction experiments indicate a monodomain state for the 8 nm particles, a transition to a bidomain state for the 100 nm particles, and the emergence of a polydomain state for the largest (500 nm) particles.
The size-dependent ferroelectric ordering in 8, 17, 100, and 500 nm average diameter GeTe nanocrystals is examined using synchrotron x-ray diffraction, Raman scattering, and atomic-resolution TEM. Rietveld refinement of room-temperature synchrotron diffraction patterns indicates a monotonic decrease in the lattice constant and the rhombohedral angular distortion of the unit cell with decreasing particle size, and temperature-resolved synchrotron diffraction experiments demonstrate a reversible rhombohedral-cubic ferroelectric phase transition. Raman scattering confirms the broken inversion symmetry of particles of all sizes and indicates a substantial displacive component of the phase transition down to the smallest sizes studied. In addition, analysis with atomic-resolution TEM suggests the preservation of a substantial linear component of the ferroelectric polarization.
Individual nanocrystals of GeTe with an average diameter of 8 nm and nanocubes of BaTiO3 with an average side length of 10 nm are then imaged with aberration-corrected TEM and off-axis electron holography. These experiments suggest that the polarization exists in a largely linear, monodomain state, in contrast with theoretical reports indicating a transition towards a toroidal polarization state. In addition, analysis with PFM demonstrates the preservation of polarization switching at room temperature in BaTiO3 nanocubes smaller than 10 nm in size and indicates a transition to a superparaelectric state below a critical length scale of approximately 5-10 nm.
These studies of individual GeTe and BaTiO3 nanocrystals are complimented with atomic pair distribution function analyses, which indicate correlations among ferroelectric dipoles that are stronger in the case of GeTe, but reduced relative to bulk material. Comparisons between GeTe and BaTiO3 nanomaterials of comparable size and between BaTiO3 nanocrystals with varying morphologies indicate strong contributions to ferroelectric size effects due to both electrostatics and internal strain and demonstrate a shape-dependence of the stability of the ferroelectric state.
Overall, these experiments demonstrate the surprising stability of a coherent, linear, and monodomain polarization state in the smallest ferroelectric nanomaterials ever characterized. The overall polarization is weakened significantly due to a combination of both surface-induced strains and depolarization effects, although the local ferroelectric distortions in both GeTe and BaTiO3 nanocrystals remain close to the bulk values. Although limited evidence for a rotational tendency of the polarization is observed in the atomic-resolution TEM studies, no clear evidence for a vortex polarization state was found, in contrast with theoretical expectations.