Question

A silicon ingot, which should contain 10^16 boron atoms/cm3, is to be grown by the Czochralski technique. What
concentration of boron atoms should be in the melt to give the required concentration in the ingot ? If the initial load of Si in the crucible is 60 kg, how many grams of boron (atomic weight 10.8) should be added ? The density of molten silicon is 2.53 gm/cm3 and segregation co-eff ko for boron is 0.8.

Answer 1

To determine the concentration of boron atoms in the melt, we can use the segregation coefficient (ko) formula:

Concentration in ingot = ko × Concentration in melt
10^16 atoms/cm3 = 0.8 × Concentration in melt
Concentration in melt = (10^16 atoms/cm3) / 0.8
Concentration in melt = 1.25 × 10^16 atoms/cm3

Now we need to find the number of moles of silicon and boron. First, let's find the volume of molten silicon:

60 kg = 60000 g
Volume = mass / density
Volume = 60000 g / 2.53 g/cm3
Volume = 23715.42 cm3

Now, let's find the number of silicon atoms and their molar quantity:

Silicon atoms volume = Volume × density
Silicon atoms = 23715.42 cm3 × 5.0 × 10^22 atoms/cm3(Avogadro constant)
Silicon atoms = 1.1857 × 10^28 atoms

Number of Moles (silicon) = Number of atoms / (Avogadro constant)
Number of Moles (silicon) = 1.1857 × 10^28 atoms / (6.022 × 10^23 atoms/mol)
Number of Moles (silicon) = 196,938.19 moles

Now we find the amount of boron atoms in the molten silicon:
Boron atoms = Volume × Concentration in melt
Boron atoms = 23715.42 cm3 × 1.25 × 10^16 atoms/cm3
Boron atoms = 2.9644 × 10^21 atoms

Now, let's find the molar quantity of boron:
Number of Moles (boron) = Number of atoms / (Avogadro constant)
Number of Moles (boron) = 2.9644 × 10^21 atoms / (6.022 × 10^23 atoms/mol)
Number of Moles (boron) = 4,920.96 moles

Now we have the molar quantities of silicon and boron, and we can find the amount of boron in grams that should be added:

Grams (boron) = Number of moles × atomic weight
Grams (boron) = 4,920.96 moles × 10.8 g/mol
Grams (boron) = 53,146.36 g

Therefore, to achieve the desired concentration of boron atoms in the silicon ingot, 53,146.36 grams of boron should be added to the initial load of 60 kg silicon in the crucible.