An apparatus capable of dispensing drops of material with volumes on the order of zeptoliters is described. In some embodiments of the inventive pipette the size of the droplets so dispensed is determined by the size of a hole, or channel, through a carbon shell encapsulating a reservoir that contains material to be dispensed. The channel may be formed by irradiation with an electron beam or other high-energy beam capable of focusing to a spot size less than about 5 nanometers. In some embodiments, the dispensed droplet remains attached to the pipette by a small thread of material, an atomic scale meniscus, forming a virtually free-standing droplet. In some embodiments the droplet may wet the pipette tip and take on attributes of supported drops. Methods for fabricating and using the pipette are also described.