Dielectric electrostatic capacitors1, because of their ultrafast charge-discharge, are desirable for high-power energy storage applications. Along with ultrafast operation, on-chip integration can enable miniaturized energy storage devices for emerging autonomous microelectronics and microsystems2-5. Moreover, state-of-the-art miniaturized electrochemical energy storage systems-microsupercapacitors and microbatteries-currently face safety, packaging, materials and microfabrication challenges preventing on-chip technological readiness2,3,6, leaving an opportunity for electrostatic microcapacitors. Here we report record-high electrostatic energy storage density (ESD) and power density, to our knowledge, in HfO2-ZrO2-based thin film microcapacitors integrated into silicon, through a three-pronged approach. First, to increase intrinsic energy storage, atomic-layer-deposited antiferroelectric HfO2-ZrO2 films are engineered near a field-driven ferroelectric phase transition to exhibit amplified charge storage by the negative capacitance effect7-12, which enhances volumetric ESD beyond the best-known back-end-of-the-line-compatible dielectrics (115 J cm-3) (ref. 13). Second, to increase total energy storage, antiferroelectric superlattice engineering14 scales the energy storage performance beyond the conventional thickness limitations of HfO2-ZrO2-based (anti)ferroelectricity15 (100-nm regime). Third, to increase the storage per footprint, the superlattices are conformally integrated into three-dimensional capacitors, which boosts the areal ESD nine times and the areal power density 170 times that of the best-known electrostatic capacitors: 80 mJ cm-2 and 300 kW cm-2, respectively. This simultaneous demonstration of ultrahigh energy density and power density overcomes the traditional capacity-speed trade-off across the electrostatic-electrochemical energy storage hierarchy1,16. Furthermore, the integration of ultrahigh-density and ultrafast-charging thin films within a back-end-of-the-line-compatible process enables monolithic integration of on-chip microcapacitors5, which can unlock substantial energy storage and power delivery performance for electronic microsystems17-19.