The merits and limitations of local impact ionization theory [APDs]

Abstract

Abstract-Multiplication measurements onIt is suggested that these should therefore be thought of as effective coefficients which, despite the presence of dead-space effects, can be still be used with the existing local theory for efficiently quantifying multiplication and breakdown voltages.

Avalanche multiplication in Al/sub x/Ga/sub 1-x/As (x=0 to 0.60)

“…The ionization softness factor is another fitting parameter to experiment which is in the range from 3.6 10 /s to 4.2 10 /s in reasonable agreement with ab initio ionization rate calculations [19]. In [16], we report this model's ability to accurately simulate the avalanche process by it closely fitting the measured multiplication curves in GaAs p -i-n s with w as thin as 0.025 m and p -n junctions doped to 2.2 10 cm…”

“…Since experimentalists have not used this recursive technique to analyze their results to date, no reliable data exists which can be used for calculations of the avalanche multiplication process in sub-micron devices. Moreover, it is apparent that these differences between the "local" and "microscopic" ionization coefficients and their applicability to different models has led to some confusion in the literature as described in [13], [16].…”

“…Therefore, we use an MC model described previously in [16] where the transport is described using effective dispersion relations which take the form where is kinetic energy, is a nonparabolicity factor, is wavevector and is the mass at the valley minima for both electrons and holes. (This model is different to the one we reported in [30] which used parabolic effective dispersion curves and, consequently, slightly overestimated the increase in multiplication with bias.)…”

Extremely Low Excess Noise in InAs Electron Avalanche Photodiodes

“…In this case, it is necessary to offer an explanation as to how for InAs APDs can fall below the lower boundary condition for excess noise in the local model, usually considered to be approximately accurate for APDs like P2 with thick multiplication regions. It has been shown [10] that where and have similar magnitudes, the local model is reasonable because the deadspace , not taken into account by the local model and equal to the distance traveled by a carrier while it obtains the threshold energy required before it can potentially undergo impact ionization, is relatively small compared with the mean ionization path length . Since there is less than one ionization event on average per carrier transit of the multiplication region in such cases below breakdown, the deadspace introduces little determinism into the ionization probability distribution within the multiplication width and hence has little effect on the excess noise.…”

The InAs Electron Avalanche Photodiode

“…This increased determinism leads to a reduction in the excess noise factor. It is noted that deadspace is typically only considered to be of significance in conventional APDs with thin multiplication regions, less than a few hundred nanometres wide (Plimmer et al, 2000). However it has been found that even in e-APDs with thick multiplication regions, such as the ones reported in figure 7, the deadspace can become significant with respect to the mean ionisation path length of electrons, -1 , and hence noticeably affect the excess noise factor.…”