A normal-metal/insulator/superconductor (NIS) tunnel junction can be applied to cool electrons by biasing the junction suitably with external voltage. Two NIS junctions in series can form an efficient microrefrigerator because of the symmetry with bias voltage. Our SINIS microrefrigerator has been capable of reaching electronic temperatures of about 100 mK starting from 300 mK. To achieve appreciable refrigeration of the underlying lattice, the microrefrigerator must be thermally decoupled from the bulk substrate. We have demonstrated experimentally the reduction of lattice temperature by 23 mK at 180 mK by extending the normal electrode on a thin dielectric membrane with four suspended bridges. Methods to improve the efficiency of refrigeration, e.g., by using a superconductor with a large energy gap and/or by increasing the number of tunnel junctions, are discussed.