A MEMS-fabricated microvacuum pump assembly is provided. The pump assembly is designed to operate in air and can be easily integrated into MEMS-fabricated microfluidic systems. The pump assembly includes a series of pumping cavities with electrostatically-actuated membranes interconnected by electrostatically-actuated microvalves. A large deflection electrostatic actuator has a curved fixed drive electrode and a flat movable polymer electrode. The curved electrodes are fabricated by buckling the electrode out-of-plane using compressive stress, and the large deflection parallel-plane electrostatic actuators are formed by using the curved electrode. The curved electrode allows the movable electrode to travel over larger distances than is possible using a flat electrode, with lower voltage. The movable electrode is a flat parylene membrane that is placed on top of the curved electrode using a wafer-level transfer and parylene bonding process. Using this approach, large out-of-plane deflection of the parylene membrane is achieved using a voltage smaller than is achievable using flat parallel-plate electrodes.