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The feasibility of a fast, high-gain photodetector based on the phenomenon of avalanche multiplication in semiconductors has been investigated. Based on the process of carrier multiplication in a high electric field, criteria for the design of an optimized avalanche photodiode and for the choice of the best semiconductor material are developed. The device theory of an optimized, realizable avalanche photodiode is presented. A practical silicon device optimized for the detection of light with a wavelength of 9000Å is suggested and design parameters are presented. Details of the fabrication process are given and the performance of experimental devices is compared to the device theory presented. The results of the study indicate that it is possible to achieve a silicon photomultiplier with a quantum efficiency-bandwidth product of the order of 100 GHz for the detection of light up to a wavelength of over 9000Å.