The closest you can get is the equivalent SPICE model for transistor, but not for diode, to my knowledge. In this kind of data junction capacitance will be given explicitly.
Furthermore, doping profile is not uniform and depends on the tecnological process. You can saturate top layer with dopant and then heat the wafer to 900-1200*C to let dopants diffuse. Peak doping level will be at the surface then. You can do ion implantation instead, and peak of the doping level will be buried.
Technological processes differ very much indeed, because the ultimate goal is to make the device useful. In other words, you do not make some diode and then think about its applications, but rather make the diode with certain characteristics.
To some extent you can do "reverse engineering" mathematically.
- Frequency response is connected to junction capacitance and carrier mobility. The former is the largest when doping level is the highest, because you have enough impurities to screen electric field on small distances. Mobility is usually limited by scattering on impurities, so you can estimate it based on doping level.
- Tunnel breakdown voltage is connected to doping level, since the barrier thickness is important.
- Sometimes you can find injection efficiency parameter, which gives you the ration between direct and reverse injection (when you open the diode, the current flows both ways, but due to different doping level, i.e. different number of electrons and holes, it will be quite different).
In principle, resolving the above self-consistently could allow you to estimate doping levels and mobility. The only problem is the geometric sizes of the junction, but they are sometimes published. If not, you can roughly estimate them from the maximum current.
Sorry for not giving you the detailed formulas for each of these steps. They are pretty well summarized in "The Physics of Semiconductor Devices" by S. Sze. Please, feel free to ask for details if I have missed something.