Collector Doping Concentration and Current Gain
The reason the "collector" is called "collector" is it's main function is to collect the charge-carriers emitted by the emitter. More doping of a semiconductor, more charge-carriers it can generate. So we usually make emitter heavy doping, emitter emit, collector collect. The current gain mainly determined by how many carriers the emitter can generate.

And more doping, will lower the resistance as well the breakdown voltage. But if the doping level too low, it will limit the maximum current.