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InterviewSolution
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Predict effect on the electrical properties of a silicon crystal at room temperature if every millionth silver atom is replased by an atom of indium. Given, concentration of silicon atoms `=5xx10^(28) m^(-3)`, Intrinsic carrier concentration `=1.5xx10^(16) m^(-3), mue=0.135 m^(2)//Vs and mu_(h)=0.048m^(2)//Vs`. |
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Answer» Concentration of silicon atoms `=5xx10^(28)m^(-3)`. Doping of indium is 1 atoms in `10^(6)` atoms of Si. Indium has valence three. Each doped indium atom creates one hole in Si- crystal and hence acts as acceptor atom. `:.` Concentration of acceptor atoms, `n_(h)=5xx10^(28)xx10^(-6)m^(-3)=5xx10^(22)m^(-3)` Intrinsic carrier concentration, `n_(i)=1.5xx10^(16)m_(-3)` `:.` Hole concentration is increased by an amount `=n_(h)/n_(i)=(5xx10^(22))/(1.5xx10^(16))=3.33xx10^(6)` New electron concentration, `n_(e)=n_(i)^(2)/n_(h)=((1.5xx10^(16))^(2))/(5xx10^(22))=0.45xx10^(10)m^(-3)` It means the hole concentration has been increased over its intrinsic concentration by the same amount with the electron concentration has been decreased. The aonductivity of doped silicon is given by `sigma=e(n_(e)mu_(e)+n_(h)mu_(h)) =(1.6xx10^(-19))[(0.45xx10^(10))xx0.135+(5xx10^(22))xx0.048]` `=(9.72xx10^(-11)+384)Sm^(-1)=384Sm^(-1)` Resistivity, `rho=1/sigma=1/384=0.0026Omegam` Electrical conductivity of pure Si-crystal, `sigma=en_(i)(mu_(e)+mu_(h)) =(1.6xx10^(-19))xx(1.5xx10^(16))[0.135+0.048]` `=0.4392xx10^(-3)Sm^(-1)` Resistivity, `rho=1/sigma=(1)/(0.4392xx10^(-3))=2272Omegam` Thus we see that the conductivity of silicon doped with indium `(384Sm^(-1))` becomes much greater than its intrinsic conductivity `(0.4392xx10^(-3)Sm^(-1))` and the resistivity `(=0.0026Omega m )` has become much smaller than the instrinsic resistivity `(2272Omegam)`. |
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