The intrinsic level being constant does not mean that carrier concentrations stay the same when doping.
The rule you have to satisfy is that the product of hole concentration and electron concentration must be equal to the square of the intrinsic carrier concentration. When you dope the material, the concentration one type of carriers will increase, while the other will decrease. The net concentration of carrier will actually increase.
For example, in Si at room T, the intrinsic carrier concentration is around 10^10 cm^-3 . Without doping, the concentrations of holes and electrons are equally 10^10 cm^-3 . The product is 10^20.
Then I dope it with phosphorus and now the conducting electron concentration is 10^16 cm^-3. So, the concentration of holes must be 10^4 cm^-3 . The product is still 10^20 . But now you can see that you have many more conducting electrons even if the intrinsic concentration remains the same.
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The intrinsic level being constant does not mean that carrier concentrations stay the same when doping.
The rule you have to satisfy is that the product of hole concentration and electron concentration must be equal to the square of the intrinsic carrier concentration. When you dope the material, the concentration one type of carriers will increase, while the other will decrease. The net concentration of carrier will actually increase.
For example, in Si at room T, the intrinsic carrier concentration is around 10^10 cm^-3 . Without doping, the concentrations of holes and electrons are equally 10^10 cm^-3 . The product is 10^20.
Then I dope it with phosphorus and now the conducting electron concentration is 10^16 cm^-3. So, the concentration of holes must be 10^4 cm^-3 . The product is still 10^20 . But now you can see that you have many more conducting electrons even if the intrinsic concentration remains the same.