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One of the biggest challenges in APD design and fabrication is to guarantee that the gain is highest and is uniform throughout the region where the photoinduced carriers flow. The consequences are severe if the gain is not uniform. If a small part of the diode has a breakdown voltage just slightly less than that of the active area, it may not be possible to get any useful gain in the active area at all. Even if the desired gain can be achieved, the undesired region will have a gain much larger than that of the active region and will contribute noise proportional to M3 as evident from Eqs.

For finite k, Shockley (9) and Muehlner (24) have both noted that the denominator in Eq. (9) goes smoothly through zero and should be well approximated by a Taylor expansion near the breakdown Vb, leading to the following simple expression: M= A Vb − V (11) The coefficient A has units of voltage and establishes the scale over which breakdown occurs. Shockley and Muehlner suggested plotting the reciprocal of the gain as a way of observing localized breakdown and other deviations from the expected linear behavior.

Numerically, this involves evaluating the inverse gain as a function of bias and iterating to find the zero. Figure 8 shows the result for uniformly doped one-sided abrupt junctions in Breakdown voltage (V) 10 20 169 1000 n+p GaAs p+n InP 100 n+p Si 10 1015 1016 Carrier concentration (cm–3) 1017 Figure 8. Calculated breakdown voltage versus doping for one-sided abrupt diodes in Si, GaAs, and InP using the ionization coefficients of Fig. 2. The type of the low doped side was chosen so that the predominant carrier has the higher ionization coefficient.

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20.Electron Devices by John G. Webster (Editor)

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