Strong Electron‐Phonon Coupling Mediates Carrier Transport in BiFeO3

Abstract The electron‐phonon interaction is known as one of the major mechanisms determining electrical and thermal properties. In particular, it alters the carrier transport behaviors and sets fundamental limits to carrier mobility. Establishing how electrons interact with phonons and the resulting impact on the carrier transport property is significant for the development of high‐efficiency electronic devices. Here, carrier transport behavior mediated by the electron‐phonon coupling in BiFeO3 epitaxial thin films is directly observed. Acoustic phonons are generated by the inverse piezoelectric effect and coupled with photocarriers. Via the electron‐phonon coupling, doughnut shape carrier distribution has been observed due to the coupling between hot carriers and phonons. The hot carrier quasi‐ballistic transport length can reach 340 nm within 1 ps. The results suggest an effective approach to investigating the effects of electron‐phonon interactions with temporal and spatial resolutions, which is of great importance for designing and improving electronic devices.


Basic principles of transient absorption microscopy (TAM)
In pump-probe experiments, the pump pulse excites the sample into the excited states, and the delayed probe pulse monitors the carrier population. By scanning the pump and probe beams relative to each other and recording the corresponding relative changes in probe transmission or reflection, the time-dependent carrier and exciton density images are generated. These images can be used to monitor the carrier transport.
The solution to the diffusion equation with a Gaussian initial condition is given by , which is proportional to , where MSD is the mean-squared displacement, and is the diffusion exponent [1][2] . For normal diffusion, the diffusion coefficient is independent of time and equals to 1.
At 0 ps, the TAM image represents the initial photo-generated carrier population created by the pump pulse.  (1) At later delay times, the TAM curves reflect carrier diffusion away from the initial excitation volume. If the carrier transport is diffusive, the time and spatial dependent carrier density is given by, where ( ) is the carrier population as a function of position and time, D is the diffusion coefficient, and is the carrier lifetime. The solution to equation (2) dictates that the population follows a Gaussian distribution at any later delay time t given by, The TAM profiles are fitted by one-dimensional Gaussian functions with variances of , where the is the time-dependent variance of the Gaussian profiles at delay time t. The diffusion constant D is then given by , and the average diffusion distance L that excitons or charge travels in time t is given by .

Surface morphologies and ferroelectricity characterizations：
To confirm the quality of the growth thin films, the atomic force microscopy (AFM) topographies of (100), (110), and (111)-oriented BiFeO 3 were measured ( Figure S1). The morphologies show relatively uniform crystallinities and smooth surfaces. The average roughness (R a ) and the square root roughness (R q ) for the (100), (110), (111)-oriented BiFeO 3 epitaxial thin films are 2.2 and 3.5 nm, 1.85 and 5.25 nm, 1.11 and 1.41 nm, respectively. The ferroelectric property and domain structures of the (111)-oriented BiFeO 3 film were also characterized using piezo response force microscopy (PFM) ( Figure S2). The PFM measurements were carried out in a glovebox under an argon atmosphere at room temperature and ambient pressure (Icon, Bruker). A platinum/iridium (Pt/Ir) coated Si tip (SCM-PIT-V2) was used for PFM measurements. The amplitude and phase hysteresis loops confirm the ferroelectricity of the BiFeO 3 films. The in-plane (IP) piezo response force microscopy (IP-PFM) images, however, show that the domain structures are small (smaller than 50 nm) and randomly arranged. In our setup configuration, the pump and probe beams are about 1 m, which is much larger than the domain size. The small domain area and the disordered domain structures are the main reasons for the isotropic response of the transient dynamics. The conventional X-ray diffraction and reciprocal space mapping were also measured to confirm the single-crystallinity and epitaxial growth ( Figure S3). The sharp peaks ( ) of the rocking curves ( Figure S3B) indicate the good single-crystalline properties of the BiFeO 3 thin films. The diffraction peaks of the BiFeO 3 layers follow that of the SrTiO 3 in both conventional X-ray diffractions ( Figure S3A) and reciprocal space mappings ( Figure S3C-E). Therefore, the BiFeO 3 thin films have good epitaxy stack structures and single crystalline. The small peaks apart from the diffraction peaks of BiFeO 3 and SrTiO 3 in the scans and RSM images arise from the diffractions of unfiltered and X-rays. The elongated diffraction spots of the RSM images arise from the stripe-like X-ray beam.

Optical characterization：
The absorption and photoluminescence (PL) were also measured using home-built microscopy ( Figure S4). For better understanding, the band structure is also marked out by blue and red-shaded areas according to results from previous works [3][4][5] . The spectra show a sharp increase in absorbance and a strong peak in photoluminescence at about 2.66 eV. This indicates that the bandgap is about 2.66 eV, which is consistent with previous experimental results. [3] However, the absorptance onset occurs at a much lower energy of about 1.65 eV. In addition, the absorptance spectrum exhibits a broad shoulder centered at about 2 eV and a small absorbance feature below 1.5 eV. These absorption bands can be assigned to the 6 4 (below 1.5 eV) and 6 4 (between 1.65 and 2.2 eV) transitions of the Fe 3+ ions [4][5] . These broad absorption bands are named magnon sidebands and are associated with the reduced symmetry in BiFeO 3 [4][5] . The small PL peak at about 1.65 eV can be attributed to the recombination of carriers in magnon sidebands.

Transient properties of photoexcited carriers probed in (100) and (110) planes
To further elucidate the role of electron-phonon coupling in the transport properties, the decay dynamics and transport properties are investigated in (100) and (110) BiFeO 3 thin films. The decay dynamics and corresponding FFT results are shown in Figure S13. Both the carrier decay dynamics in (100) and (110)