TECHNICAL NOTE

Noise limitations in solid state photodetectors: comment

Zhong Cao, Ling Li, and Peida Ye

In Ref. 1, on p. 1158, van Vliet writes which is different from Eq. (66). Only when

where m is the number of input particles, n is the number of output particles, and Pa is the probability that input particle α releases an output particle.

With Eq. (65), van Vliet gave

can we reduce Eq. (66') to

Here var m = m has been used in the second equality for m as a Poissonian variable.

Another error in quantum efficiency appears in Ref. 2. In that paper the fluctuations in the quan­tum efficiency are mentioned, but they are treated as a constant in Eq. (5) of Ref. 2:

and with

Equation (66) was reduced to [see the footnote on p. 1150 and explanation between Eqs. (66) and (67)]

Here van Vliet seemed to think that each input particle has its own probability of releasing an elec­tron. We suggest treating the input particles as Boson particles, which behave stochastically with the same statistical properties, and changing Eq. (65) to

where P is the quantum efficiency (a random variable independent of m). From Eq. (65'), one obtains

where n is the number of photons arriving at the detector surface per second, r is the reflection coeffi­cient of the surface, and N = ηn(l - r) is the number of electron-hole pairs generated per second. From Eq. (5) the authors inferred that a Poissonian n distribution gave a Poissonian N distribution.

If η is treated as a constant, from N = ηn(l — r), one can obtain only

which is different from Eq. (5). Treating η as a random variable, we still cannot obtain Eq. (5).

By the way, the experiments discussed in Ref. 2 showed no "enhancement of the shot noise" (Sec. IV, p. 5203) that should be attributed to the effect of η and r, i.e., η < 1.0, (1 - r) < 1.0.

The authors are with the Optical Communication Laboratory, Beijing University of Posts and Telecommunications, P.O. Box 66, Beijing 100088, China.

Received 21 May 1993. 0003-6935/93/285692-01$06.00/0. © 1993 Optical Society of America.

References 1. K. M. van Vliet, "Noise limitations in solid state photodetec­

tors," Appl. Opt. 6, 1145-1169 (1967). 2. L. He, Y. Lin, A. D. van Rheenen, A. van der Ziel, A. Young, and

J. P. van der Ziel, "Low-frequency noise in small InGaAs/InP p-i-n diodes under different bias and illumination conditions," J. Appl. Phys. 68, 5200-5204 (1990).

5692 APPLIED OPTICS / Vol. 32, No. 28 / 1 October 1993