Silicon is doped with 2.0∗1016 arsenic atoms per cm3 . Assume an intrinsic carrier concentration equal to 1.7∗1010cm−3 at room temperature. What is the minority carrier concentration at room temperature ( T=300K ) in 104cm−3 ?
1.445
Silicon is doped with 2.0∗1016 arsenic atoms per cm3 . Assume an intrinsic carrier concentration equal to 1.7∗1010cm−3 at room temperature. What is the minority carrier concentration at room temperature ( T=300K ) in 104cm−3 ?
1.445*10^4
1.445
The free electron and hole concentrations, n and p respectively, are related with the intrinsic carrier concentration ni by the law of mass action:
n2i=np
Arsenic has one more valence electron than silicon. Therefore, each arsenic atom will contribute with one free electron, so the concentration of free electrons is n=2∗1016cm−3. Electrons are the majority charge carriers, while holes are the minority charge carriers. Since ni is given, we can calculate the concentration of free holes p as:
p=n2in=(1.7∗1010)22∗1016=1.45∗104cm−3