مرکز منطقه ای اطلاع رساني علوم و فناوري - The distribution of gains in uniformly multiplying avalanche photodiodes: Theory

Abstract :

Expressions are derived for the probability $P_{n,m}$ that a pulse initiated by $n$ electrons (or holes) in a uniformly multiplying semiconductor diode will result in a total number of electrons (or holes) $m$ , to give a gain $m/n$ , and for the probability $Q_{n,m}$ that the gain will be $m/n$ or greater. It is shown that the distributions are far from Gaussian. The gain distribution $P_{1,m}$ for a single photoelectron, for example, is shown to have a maximum value for $m = 1$ for any value of the average gain $M=m/n$ . The derivations are valid for any electric field distribution and assume only that the hole ionization coefficient $\\beta (E$ ) can be approximated by the relation $\\beta (E) =k\\alpha (E)$ , where $\\alpha (E)$ is the electron ionization coefficient and $k$ is a constant. A method of determining an effective value of $k$ , for cases where $\\beta =k\\alpha$ is not a good approximation, is presented. The results can be used to calculate the average gain and the mean square deviation from the average, giving results in agreement with previously published relations [1], [2]. The implications of this theory on the use of avalanche diodes for low-level photodetection are discussed. It is shown that in the near infrared, cooled avalanche photodiodes can compare favorably with the best available photomultiplier when used either in a photon-counting mode, or for the reliable detection of low-level laser pulses.