On the analytical formulation of excess noise in avalanche photodiodes with dead space

Abstract

Simple, approximate formulas are developed to calculate the mean gain and excess noise factor for avalanche photodiodes using the dead-space multiplication theory in the regime of small multiplication width and high applied electric field. The accuracy of the approximation is investigated by comparing it to the exact numerical method using recursive coupled integral equations and it is found that it works for dead spaces up to 15% of the multiplication width, which is substantial. The approximation is also tested for real materials such as GaAs, InP and Si for various multiplication widths, and the results found are accurate within ∼ 15% of the actual noise, which is a significant improvement over the local-theory noise formula. The results obtained for the mean gain also confirm the recently reported relationship between experimentally determined local ionization coefficients and the enabled non-local ionization coefficients.

Exact Analytical Formula for the Excess Noise Factor for Mixed Carrier Injection Avalanche Photodiodes

“…Note that the value of k for silicon is much larger at very high electric fields present in very thin multiplication regions (e.g., <400 nm [22] [27] than that for bulk silicon) as shown in Fig. 1 in [28]. Fig.…”

“…Moreover, the distributed-injection excess noise factor, ( ), with absorption profile is expressed as = < 2 > 2 , (28) which reduces to the formula as shown at the bottom of this page.…”

Analytical Formulas for Mean Gain and Excess Noise Factor in InAs Avalanche Photodiodes

“…While = 0.02 for silicon APDs with wide junctions and low electric field, for high-speed CMOS compatible silicon APDs [15]- [16][17] [18], k approaches 1 as we reach submicrometer thicknesses [19]. When compared with the case of ≈ 0, and for a given thickness of avalanche region, this leads to an increase in the buildup time (defined as the time required for all the impact ionizations to complete, due to additional chain of ionizations from the presence of holes) as well as the tunneling current.…”