Based on the assumption that the noise contribution of a semiconductor detector is due solely to the bulk properties of the semiconductor, equations are presented which indicate the theoretical limits of noise in detector-amplifier combinations. These equations show that an optimum amplifier time constant and detector bias voltage exist for which condition the minimum noise is independent of the semiconductor resistivity. The optimum performance of a detector-amplifier system is shown to depend only upon detector area, input capacity (less detector capacity), semiconductor minority carrier lifetime, and the transconductance of the amplifier input tube. A new detector structure including a guard-ring electrode as an integral part of the detector structure is described which largely eliminates noise due to surface leakage. Experimental results for detector leakage and energy resolution are presented which agree well with theory.