I am really puzzled why the collector current is considered proportional to the base current in a bipolar NPN transitor, ie
$$ I_c = \beta I_b $$
Where I_c is the collector current, I_b the base current and below I_e the emitter current. I can't find any explanation in the books, it seems to be just stated as an empirical result. Is that how I should treat it, just an empirical result?
I know that it can be derived by assuming that the proportion of (conventional) current that enters the emitter from the base is a constant fraction of the collector current, ie
$$ I_c = \alpha I_e $$ and that $$I_b + I_e = I_c $$
but that begs the question why is the fraction of base current entering the emitter stream always assumed to be a fixed proportion?