How come it took two days before my message were posted?
You look for an opamp, it's not the bias current you worry because you
are only measuring 200nA lowest. Any opamp with bias current less than
10nA is plenty good. The most important thing you look for is input
capacitance. Most of the opamps have over 5pF of input capacitance and
that will increase the noise gain. You want to understand noise gain,
read the explanation in my Excel file. I explain each and every
component of the noise source and the relevant frequency range. I chose
LTC6268 because the input capacitance is about 0.5pF. For your
requirement, some BJT input opamp might be good enough, just look for
low input capacitance.
That said, you always see noise coupling into TIA circuits. I never saw a TIA circuit that dose not pick up all sort of noise.? All the noise calculation and the excel file I provided are ONLY for ideal theoretical noise limit. If you leave the bare circuit, you will see all the noise from around the surrounding.
FYI, our contractor designed another TIA that has only a 1M feedback resistor and it pick up all sort of noise. We have to re-layout the board to put in the shield. A ground plane is an absolute MUST. The other reason is people have long trace at the -ve input. That will pickup noise every time. Layout is everything. This is beyond the scope of this forum. Circuit is always simple, it's the layout and shielding. You need to look at your layout, put in the shielding, then talk more about it. LTSpice is NOT the place to talk about this, go to some electronic forum and ask question. I feel I already way out of bound here already.
You are only working with 50K feedback resistors. My circuit use 250M, and I designed with up to 2G resistors TIA circuits. Layout and shielding become the number one design. If you read my other post, 50K resistor will give you output range of 10mV to 5V( fit your 5V supply requirement). This is very easy signal to deal with. We deal with a lot lower signal successfully.