مرکز منطقه ای اطلاع رساني علوم و فناوري - Frequency response of PIN avalanching photodiodes

Abstract :

The frequency response of a PIN avalanching photodiode has been analyzed without the usual assumption that the electrons and the holes have equal ionization rates ( $\\alpha _{n} = \\alpha _{p}$ ) and equal scattering-limited velocities ( $v_{n} = v_{p}$ ). A general formula for the frequency response is first derived for the case in which the photons are absorbed in the space charge region or $i$ region and the photon density decreases with penetration depth according to $e^{-\\alpha x}$ . The frequency response for the case of photon absorption in the $p$ or $n$ region is obtained simply by letting α approach infinity in the general formula and that for the case of uniform absorption of photons in the space charge region by allowing α to approach zero. The analysis, based on a model in which the photons come from the $p$ side, shows the following: 1) The dc multiplication factor does not depend on vnand vpin any manner. It does not depend on α if $\\alpha _{n} = \\alpha _{p}$ . When $\\alpha _{n} > \\alpha _{p}$ , the dc multiplication factor increases with increasing α according to $M_{A}(0)/M_{B}(0) = [1 - \\exp (-\\alpha w - \\alpha _{n}w +\\alpha _{p}w)]/[1 + (\\alpha _{n} - \\alpha _{p})/ \\alpha ] \\cdot [1 - \\exp (-\\alpha w)],$ where $M_{A}(0)$ and $M_{B}(0)$ are the dc multiplication factors for finite and infinite α, respectively, and $w$ is the space charge region width. $M_{B}(0)$ is given by $(1- \\alpha _{n}w)^{-1}$ when $\\alpha _{n} = \\alpha _{p}$ and by $[\\exp (-\\alpha _{n}w)-\\alpha _{p}/ \\alpha -{n}]^{-1}$ when $\\alpha _{n} \\gg \\alpha _{p}$ . 2) The cutoff frequency fcodoes not in any case depend on α but depends on αnand αpand on an "effective scattering-limited velocity" ve, defined as $v_{n}v_{p}/(v_{n}+v_{p})$ . For $\\alpha _{n} = \\alpha _{p}$ , the cutoff frequency is given by $f_{co}\\simeq 3v_{e}/[\\pi wM_{B}(0)]\\simeq 3\\alpha_{n}v_{e}/[\\pi M_{B}(0)]$ . For $\\alpha _{n} \\gg \\alpha _{p}, f_{co}$ is greatly improved and is given by $f_{co- }\\simeq \\alpha _{n}v_{e}/[2\\piw \\alpha _{p}M_{B}(0)]$ .