Gain changes in the APS due to diode bias voltage

intrinsic density

donor density in the n tub

acceptor density in the epi layer

acceptor density in the adjacent p tub

Diode self bias voltage

Measured gain of APS under bias

approximate capacitance of the diode under bias assuming that half of the capacitance is traces and source follower gate

reverse bias voltage from scope trace for rail to rail of the chip output

Capacitance per unit area bottom

Capacitance per unit area for side

Side area assuming tub depth of one micron

bottom area

So not so far off considering there is a guess about 1/2 of capacitance being non diode and guessing that tub depth is 1 micron

So go with the calculated area estimate for capacitance.

Find capacitance for self bias only

Capacitance per unit area bottom, self bias

Capacitance per unit area side, self bias

Gain change from reset bias to self bias:

We have assumed that the output voltage on the chip is limited by the bias range on the diode. It could be that the source follower or the output buffer is really the limitation. If we assume that the bias on the diode is actually 1.6 volts instead of 0.8 the gain reduction drops to 0.7, so this assumption does not seem to be too important.

Apparent gain from slopes in Fig. 1

Fig. 1 Output from a single pixel on APS-3 with injected LED at 3 points in time.

slope before avalanche

slope in the avalanche region

crudely this is the apparent gain ratio for avalanche region vs standard

It has been suggested that since we don't see a gain with light injection that the capacitance has increased in the avalanche region thus actually reducing gain.

Taking this into account:

So predicted effective gain is still much larger (factor of 10) than the observed light gain of only 0.91