Question: A boron-doped crystal pulled by the Czochralski technique is required to have a resistivity of 10 Ω cm when half the crystal is grown. Assuming that a 100-gm pure silicon charge is used, how much 0.01 Ω cm boron-doped silicon must be added to the melt? For this crystal, plot resistivity as a function of the fraction of the melt solidified. Assume k0 = 0.8 and the hole mobility µp = 550 cm2 volt-1 sec-1.