Final answer:
The intrinsic carrier concentration of silicon is represented by the equation ni = BT^3/2e^(-(Eg)/(2kT)), which is important for the manufacturing of semiconductor devices and relies on the purity of silicon.
Step-by-step explanation:
The intrinsic carrier concentration of silicon is a measure of the number of electron-hole pairs generated within the material due to thermal energy in the absence of any impurity doping. The intrinsic carrier concentration is temperature-dependent and can be determined using the equation ni = BT3/2e-(Eg)/(2kT), where B is a material-dependent constant, T is the absolute temperature in Kelvin, Eg is the band-gap energy of silicon, and k is the Boltzmann constant. This formula is crucial as extremely pure silicon is necessary for the manufacture of semiconductor electronic devices, which are fabricated after converting impure silicon into highly pure forms such as silicon tetrahalides or silane (SiH4). The process for purifying silicon often involves chemical reactions with materials like carbon and magnesium as indicated by the chemical equations SiO2(s) + 2C(s) → Si(s) + 2CO(g) or SiO2(s) + 2Mg(s) → Si(s) + 2MgO(s).