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We present a novel design for a solid-state microrefrigerator using Normal-Insulator-Superconductor (NIS) tunnel junctions. Cooling of the normal electrode is achieved by electrons tunneling into the superconducting electrode, providing a means of continuous refrigeration at temperatures below 300 mK. The slow diffusion of quasiparticles away from the tunnel barrier limits the cooling power of thin film NIS microrefrigerators for two reasons. First, the efficiency of energy removal from the normal electrode is reduced as quasiparticles build up in the superconducting electrode. Second, phonons produced by quasiparticle recombination near the junction can enter and heat the normal electrode. Using single crystals as both the substrate and the superconducting electrode can prevent the accumulation of quasiparticles near the tunnel barrier. A large volume, high purity electrode will allow quasiparticles to rapidly move away from the junction, thereby eliminating the self-heating. We are developing a photolithographic process to fabricate NIS devices on single crystal Al substrates. Presented here are results from test devices with a 50 μm × 50 μm Al-Al2O3-Cu tunnel junction deposited on SiN substrates.