A new approach for characterizing the avalanchebuildup-time-limited bandwidth of avalanche photodiodes (APD's) is introduced which relies on the direct knowledge of the statistics of the random response time. The random response time is the actual duration of the APD's finite buildup-limited random impulse response function. A theory is developed characterizing the probability distribution function (PDF) of the random response time. Recurrence equations are derived and numerically solved to yield the PDF of the random response time. The PDF is then used to compute the mean and the standard deviation of the bandwidth. The dependence of the mean and the standard deviation of the bandwidth on the APD mean gain and the ionization coefficient ratio is investigated. Exact asymptotics of the tail of the PDF of the response time are also developed to aid the computation efficiency. The technique can be readily applied to multiplication models which incorporate dead space and can be extended to cases for which the carrier ionization coefficient is position dependent. Index Terms-Avalanche buildup time, avalanche photodiode, bandwidth, dead space, impact ionization, impulse response, recurrence equations, time response. 0018-9383/00$10.00 © 2000 IEEE Majeed M. Hayat (S'89-M'92-SM'00) was born in Kuwait in 1963. He received the B.S. degree (summa cum laude) in 1985 from the University of the Pacific, Stockton, CA, and the M.S. and Ph.D. degrees in electrical and computer engineering from the University of Wisconsin in 1988 and 1992, respectively.From 1993 to 1996, he worked at the University of Wisconsin-Madison as the co-principal investigator of a major project on statistical modeling and detection of minefields, which was funded by the Office of Naval Research. He is currently a Tenure Track Assistant Professor of electro-optics and electrical and computer engineering at the University of Dayton, Dayton, OH. His research interests include noise in opto-electronic devices, optical and digital communications, image and signal processing, quantum imaging, detection and estimation of nonclassical light, and applied point processes.Guoquan Dong received the B. S. and M.S. degrees in physics from Zhejiang University, Hangzhou, China, in 1986 and 1991, respectively, and the MS. degree in electro-optics from the University of Dayton, Dayton, OH, in 1998. In 1991, he joined the Physics Department, Zhejiang University, where he became involved in research in hyper-spectral optical remote sensing. His research interests include fiber-optic communication systems and optical networks.