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Dark current, quantum efficiency, multiplication noise, and pulse response of germanium avalanche photodiodes with n+-p junction were studied to find an optimum structure. The dark current can be separated by graphical means into a leakage current component and a multiplied component which flows through the junction. The dark current components are also evaluated by using diodes with various diameters. The quantum efficiency and the multiplication noise are shown to be strongly affected by the n+ layer thickness. An n+ layer thickness optimized for signal-to-noise ratio is estimated from experimental and calculated results, using a figure of merit for avalanche photodiodes. The response waveform for mode-locked Nd:YAG laser shows a rise time of 100 ps and a half pulsewidth of less than 200 ps.