Silicon for computer chips is grown in large cylinders called “boules” that are 300 mm in diameter and 2 m in length,as shown.(Figure 1) The density of silicon is 2.33 g/cm3. Silicon wafers for making integrated circuits are sliced from a 2.0 m boule and are typically 0.75 mm thick and 300. mm in diameter. How many wafers can be cut from a single boule
To determine the number of wafers that can be cut from a single boule, we need to calculate the volume of the boule and the volume of each wafer.
First, let's calculate the volume of the boule using the given diameter and length. The formula for the volume of a cylinder is:
Volume = π * (radius^2) * height
The diameter of the boule is 300 mm, so the radius (r) is half of that, which is 150 mm (or 15 cm). The length (height) of the boule is given as 2 m, which is 200 cm.
Therefore, the volume of the boule is:
Volume = π * (15^2) * 200 cm3
Volume ≈ 141,371 cm3
Next, let's calculate the volume of each wafer. The wafer is a cylindrical disk, so the formula for the volume of a cylinder can be used again.
The diameter of the wafer is given as 300 mm, so the radius (r) is half of that, which is 150 mm (or 15 cm). The thickness (height) of the wafer is given as 0.75 mm (or 0.075 cm).
Therefore, the volume of each wafer is:
Volume = π * (15^2) * 0.075 cm3
Volume ≈ 105.68 cm3
To find how many wafers can be cut from a single boule, we divide the volume of the boule by the volume of each wafer:
Number of wafers = Volume of boule / Volume of each wafer
Number of wafers ≈ 141,371 cm3 / 105.68 cm3
Number of wafers ≈ 1,337
Therefore, approximately 1,337 wafers can be cut from a single boule.