In intrinsic Si, carrier concentration is of the order of . If we add both n and p type, it becomes a total of . So, if were true the highest doping we could have would not exceed the intrinsic doping and we could never have a low enough resistivity for this to work. Typical doping in semiconductors is . The reason np stays constant is because when you, e.g. dope the semiconductor with p-type dopant, it "eats up" or recombines with some of the electrons and electron density reduces, but the total product stays the same.
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