Electronic – Opamp circuit problem

There are some point to keep in mid when asking a question like this. First there's no guarantee that transistor model that shipped with simulator X matches the datasheet from manufacturer Y, even for the same generic transistor type. If you need to operate in heavy saturation (hfe=10) then you can probably get by with using almost any model. If you want to operate in quasi-saturation (Vb>=Vc but hfe doesn't get close to 10) then you need to be careful what SPICE model you use.

Second, 2N3904 or 2N3906 are only good at most 200mA Ic in real life. So don't expect any SPICE model for them to be terribly useful at 1A. Usually some software like MODPEX [or similar] is used to generate the SPICE model by curve fitting from the traced curves; the derived parameters aren't necessarily much good beyond the window in which they were derived because the Gummel equation uses some parameters that pretty difficult to determine accurately. Here are the Gummel plots of two 2N3904 models I happen to have done already; first is the one that comes with LTspice (supposedly from NXP, but God knows where they pulled that data from) and second is the one actually downloaded by me from NXP.

There's a big difference between them in terms of how hfe varies and even what the max value is (in the active region) or how low it drops in saturation (Vbc was set to 0 in these plots). So before anyone can answer your question with more than a handwave we need to see the SPICE models that your sim uses for those transistors.

To get more to the point of your question, since you apparently using multisim (not exactly my favorite; I find the "virtual instruments" paradigm of having to modify the schematic to measure stuff on it incredibly clunky by design), I just imported their [NatSemi] 2N3904 model in LTspice. Basically you cannot saturate it at 1A collector current (for any base resistor), as you can see from the following sweeps:

The green curve is the power dissipation over the transistor. You can see that at 25 ohms load (corresponding to 200mA Ic, max allowed in datasheet), there's a pretty wide region for choosing the base resistor so that the transistor is in saturation. This margin gets smaller as we lower the load resistor. At 5 ohms load (top curve), you basically have nothing left; even with the optimal/minimum value it would dissipate nearly 1W. Never mind that it would burn the transistor in real life by exceeding the collector current alone. I'm not entirely sure what explains the massive difference we see with this model between 10-ohm and 5-ohm load, but it's probably caused by a combination of high-level injection dominating [Ikf, the forward knee current is 66mA] and the built-in collector package resistor (this is 1 ohm); the emitter resistor is not set in this model. If we set the load to 5 ohms but alter the built-in collector resistor to 0 we can see it would saturate to a more reasonable power dissipation level--the lower curve below:

The amplification and reaction speed of an APD depend on the current through it. It's a bad habit of the physics community to use APDs with a voltage source and a series resistor for biasing. As you have witnessed, this fails in high dynamic range applications. I suggest you change your biasing circuit to provide a constant current instead of constant voltage.

The ringing you see is from your opamp. You are using a variant that is not unity gain stable. The -10 in the part number denotes that it's a decompensated opamp for a gain of at least 10 (Linear's opamp numbering convention). But for this kind of circuit to work, you need unity gain stability.

I suggest you have a look at Linear Appnote 92 which discusses a few circuits for APDs.