Data looks perfect ... but the fitting was wrong.
Vn = Vdn + Z * sqrt( 2 e Idc ) ==> WRONG!!!
Dark noise and shot noise are not correlated. You need to take a quadratic sum!!!
Vn^2 = Vdn^2 + Z^2 *(2 e Idc)
And I was confused whether you need 2 in the sqrt, or not. Can you explain it?
Note that you are looking at the raw RF output of the PD and not using the demodulated output...
Also you should be able to fit Vdn. You should put your dark noise measurement at 10nA or 100nA and then make the fitting.
Here's another measurement of the noise of the REFL11 PD.
This time I made the fit constraining the Dark Noise. I realized that it didn't make much sense leaving it as a free coefficient: the dark noise is what it is.
Result: the transimpedance of REFL11at 11 MHz is about 4000 Ohm.