Usually you know what the doping is. If you do not, the Hall effect is used to determine the major carrier type. Then you measure the dimensions and resistance between opposite surfaces and back out the doping level. If it is a diffusion, you measure the surface resistivity in ohms/square with a 4 point probe measurement. You then remove a layer of the material by oxidizing it and then removing the oxide. You then measure the resistance. The difference is the sheet resistance of the layer removed. From the sheet resistance and the thickness removed you can back out the doping level.
Since the product of the n and p carriers is equal to the intrinsic number squared, you can back out the other polarity density.
Parameter extraction is a very big issue. I can help you if you define some parameters exactly. I don't have a "general" ebook. I know a couple of good books on the subject but not in ebook format.
Unfortunaly, I have the same problem, to get the parameters of a apd to simulate the behavior without destroy it.
What i could do now? God.
Maybe what i can do is just to test the output of apd under different bias voltage or temprature...