4. Find the electron and hole concentrations, mobilities, and resistivities of silicon samples at 300 K, for each of the following impurity concentrations: (a) 5 x 1015 Boron atoms/cm3 . (b) 2 x 1016 Boron atoms/cm3 and 1.5 x 1016 Arsenic atoms/cm3 . (c) 5 x 1015 Boron atoms/cm3 , 1017 Arsenic atoms/cm3 , and 1017 Gallium atoms/cm3.
4. Find the electron and hole concentrations, mobilities, and resistivities of silicon samples at 300 K, for each of the following impurity concentrations: (a) 5 x 1015 Boron atoms/cm3 . (b) 2 x 1016 Boron atoms/cm3 and 1.5 x 1016 Arsenic atoms/cm3 . (c) 5 x 1015 Boron atoms/cm3 , 1017 Arsenic atoms/cm3 , and 1017 Gallium atoms/cm3.
(HINT: First, establish which are donors and which are acceptors. Assume complete ionization of all. The concentration of the majority carriers in each case will be given by the net of the ionized impurity concentrations (e.g. n=Σ[Nd-Na]). The concentration of the minority carriers is obtained from the relation np=ni2. The mobilities are controlled by the sum of the ionized impurities - all of which contribute the scattering (i.e. as the sum of the ionized impurities is increased, the mobilities are decreased !).
Refer to the following Figure. You now have all the concentrations and mobilities, from which you derive the resistivities.
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