op amp preamp circuit for avalanche photodiode
Here is my proposal:
Make multistage:
Stage 1 is current to voltage (transimpedance), using feedback amplifier and small feedback resistor (5kohm?) to give good bandwidth, even with parasitic capacitance (10pf would give 3MHz).
Stage 2 is voltage to voltage amplifier. Use gain = 400 to acheive 2Megohms in combination with 5kohm in 1st stage. For gain of 400, bandwidth of 2MHz, you would need greater than 800MHz GBW in amp. If needed, this can be 2 gain stages, each of gain 20x, each with GBW greater than 40MHz.
Overall result should provide 2MegOhm transimpedance, >2MHz BW.
To obtain high frequency, it is likely that you would need op-amps with external compensation, or compensated for minimum gain greater than unity. This widebands the amplifier at a cost of unity gain stability, but, since you are not using unity gain configuration, your circuit does not need to be unity gain stable! If you use external compensation, you should be able to tailor your bandwidth for your necessary gain.
You will need to evaluate noise and drift performance, as the output of the 1st stage will be amplified by 400x. I am not sure if this approach will meet all your requirements, but it should be able to obtain your bandwidth.