Summary: Measurement and plot of shot-noise-intercept-current for PDA255.
Motivation:It is to measure the shot noise intercept current for PDA255 - the MC transmission RF photodiode to get an idea for the noise current for the detector
Result: The final plot is attached here. The plot suggests that the value of shot-noise-intercept current is 3.06mA
The plot is for the measured data of Noise voltage (V/sqrt(Hz)) vs DCcurrent(A). The fitted plot to this measured data follows the noise equation
Vnoise = gdet* sqrt[ 2e (iDC+idet)] , where gdet= transimpedance of the PD in RF region as described in manual of PDA255 (i.e. 5e3 when it is not in High-impedance region).
On the other hand for DCcurrent calculation we must use the high-impedance value for the transimpedance i.e. 1e4 Ohm. idet is the shot noise intercept current.
For the rough calculation of the noise level we may use the following formulae:
Vnoise = gdet*sqrt[2e (iDC+idet)] = gdet*sqrt(2e in), when in=iDC+idet;
For say, in1=1mA; Vnoise1=gdet*sqrt(2e *in1)
and sqrt(2e *in1)~18pA/sqrt(Hz)
In current case dark noise is ~1.5e-7 V/sqrt(Hz)
Therefore dark current(in2) ~dark noise voltage/RF transimpedance = 30pA/sqrt(Hz)
i.e. sqrt(2e *in2)=30pA/sqrt(Hz)
therefore, in2~3mA (since in1=1mA)
For, iDC=0, in=idet.
Therefore the shot-noise-intercept current will be ~3mA
Then Vdc = in2*1e4 = 30V
According to the experiment and also from the PDA255 manual the DC voltage level never goes beyond ~10V. Therefore following the photodiode characteristics(we work in reverse bias) we may infer that it can never become shot noise limited.
Also, from PDA255 manual, at 1650nm the dark noise is 30pW/sqrt(Hz) and the responsivity is 0.9A/W. Therefore the noise current level will be = noise power* responsivity ~27pA/sqrt(Hz). The value matches well with our expectation.