*2.1. Film Fabrication*

Firstly, the flexible mica substrate coated with bottom electrode was provided for depositing dielectric thin film. The fluorophlogopite mica [KMg3(AlSi3O10)F2] was purchased from Changchun Taiyuan Fluorophlogopite Co., Ltd. (Changchun, China). The mica sheet was washed with ethanol and water to get a cleaned surface. Then, a 20 nm thick Pt layer was sputtered onto the surface under a 30 mA current in Ar atmosphere of 0.05 mbar, to be used as the bottom electrode.

The multilayer BST/0.4BFO-0.6STO thin film was fabricated on Pt/mica substrate by sol-gel. Precursor solutions of BFO, BTO and STO were prepared, respectively, with the use of bismuth nitrate pentahydrate, iron nitrate nonahydrate, strontium acetate, barium acetate and tetrabutyl titanate. Ethylene glycol and acetic acid were selected as solvents to dissolve the solid raw materials. Here, 5 mol% excess bismuth was added to compensate for element volatilization during the high temperature treatment. Subsequently, the tetrabutyl titanate and acetylacetone were added into the solution. Meanwhile, 2 mol% manganese acetate tetrahydrate was added to each solution to improve the electrical resistivity of the film. The final concentration of each precursor solution was 0.15 M. Then, we used proportionable BFO and BTO solutions, separately mixed with STO, to form solutions of 0.4BFO-0.6STO and BST. The solutions were stirred with a magnetic stirrer for 12 h and further aged for another 48 h. The BST layer was first spin-coated on the substrate, and 0.4BFO-0.6STO layers were then deposited in situ on top of the BST layer. Both layers were dried at 200 ◦C for 2 min, successively. Subsequently, each layer was pyrolyzed on a hot plate at 300 ◦C for 5 min and annealed in a mini tubular furnace at 700 ◦C for 10 min. Both components (0.4BFO-0.6STO and BST) were spin coated alternately 10 times, with the ultimate sample consisting of twenty dielectric layers. For electrical measurements, Au top electrodes with a diameter of about 200 μm were sputtered through a shadow mask to form the capacitor structure. Finally, a simple mechanical peeling process was conducted

to realize flexibility in the film by tearing off the bottom mica layer to reduce the thickness to ~10 μm.
