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This paper presents the energy conversion theory of radioisotope battery and analyzes the effects of a three-dimensional (3-D) silicon p-n diode with cylindrical hole array on the electrical-output parameters. An equivalent circuit model for direct radioisotope-energy conversion battery has been established. We derive the mathematical equations of short-circuit current, open-circuit voltage and maximum output power of silicon radioisotope battery in the case that a plane solid radioactive source is put on the surface of 3-D silicon p-n diode with cylindrical hole array structure. The simulated results show that for a 3-D silicon p-n diode with cylindrical hole array, the short-circuit current rise but open-circuit voltage decrease with the hole radius increasing. Therefore, the maximum output power is not significantly improved in comparison with the 2-D plane p-n diode without cylindrical hole array.