Extended Data Fig. 1: Modeling of electrical insulation performances of thin-film dielectrics in electrodes.

a, Schematic showing the transmission line model with conductive losses through the thin film dielectric encapsulation in a representative microelectrode structure. V_in, V_out, Z_elec, Z_amp, r_c, c_d, and r_d denote the input voltage at the electrode tip, the output voltage, the electrode tip electrochemical impedance, the amplifier’s input impedance, the sheet resistance of the conductive line, the capacitance per unit length of the dielectric, and the resistance per unit length of the dielectric, respectively. b, Stripline geometry for the electrode interconnect line insulated by a dielectric. L, h_c, and h_d denote the length of the electrode, the thickness of the conductor, and the thickness of dielectric encapsulation on each side, respectively. c, Signal attenuation at 10 kHz plotted as a function of h_d (for a dielectric constant ε_d = 3.2) for various thicknesses h_c of the metal line (with a conductivity σ_c = 4.5×10⁷ S/m). d, Signal attenuation as a function of frequency for various values of σ_c at the lossless (σ_d = 0) condition or lossy condition (σ_d = 5.18×10⁻⁸ S/m) due to ionic conduction within the dielectric encapsulation³⁷. L = 0.05 m in (c) and (d), h_c = 50 nm and h_d = 1 µm in (c).