A new approach for computing the bandwidth statistics of avalanche photodiodes

Abstract

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.

Effect of dead space on avalanche speed [APDs]

“…For comparison, the RPL techniques and the recurrence equations described in [14] and [17] are used to calculate the mean impulse response and the pdf of avalanche duration. In this work, dead space is included in the method proposed in [17].…”

“…In this work, dead space is included in the method proposed in [17]. In all temporal calculations, a constant velocity of 10 ms is assumed for both electrons and holes, although different velocities for electrons and holes can be readily incorporated in the RPL model.…”

“…Using mean current impulse response and its standard deviation Hayat et al have also investigated the effects of dead space on the bit-error-rate of optical communication systems [16]. Using a different recurrence technique, Hayat and Dong showed how to calculate the probability distribution of the avalanche duration of an APD [17]. Although the inclusion of dead space in their model is straightforward, these authors investigated only the local case.…”

Exponential Time Response in Analogue and Geiger Mode Avalanche Photodiodes

“…These include Monte Carlo calculations of varying degrees of sophistication [3]- [7] and a recurrence equation technique [8] which allows for arbitrary carrier speeds to ionization and also for random fluctuations about these mean speeds, corresponding to diffusion. Hayat and Dong [9] showed how to calculate the pdf of avalanche duration, the distribution in times for the last avalanche carrier to exit the multiplication region, under the same restrictive conditions as used in [1]. Ng et al [10] generalized this technique by relaxing the conditions to those used in [8].…”

Simulation of dynamic characteristics of GaN p-i-n avalanche diode operating as particle detector with internal gain

“…Majority of papers devoted to APD are addressing the analysis of these characteristics. However, dynamic characteristics of APD [24][25][26][27][28][29][30][31][32], especially based on GaN, are less examined. A pulsed response of APD shows [25,27,29] that the rise-time of the APD current is rather short, while the fall-time is longer by several orders of time-scales.…”