Question

Computer chips (Fig. 1–17) are etched on circular silicon wafers of thickness 0.300 mm that are sliced from a solid cylindrical silicon crystal of length 25 cm. If each wafer can hold 400 chips, what is the maximum number of chips that can be produced from one entire cylinder?

FIGURE 1-17 Problem 41. The wafer held by the hand is shown below, enlarged and illuminated by colored light. Visible are rows of integrated circuits (chips).

Short answer

A maximum $3.33\times {10}^5\mathrm{chips}/\mathrm{cylinder}$can be cut.

Step-by-step solution

Step 1. Formula for the number of wafers

The number of wafers that can be cut from the cylinder can be calculated by identifying the length of the silicon crystal and the thickness of the wafer.

The number of wavers that can be cut varies inversely with the thickness of the wafer.

Step 2. Given information

Length of the silicon crystal,$L=25\mathrm{cm}$

Thickness of the wafer,$t=0.300\mathrm{mm}$

Number of chips,$n=400\mathrm{chips}$

Step 3. Calculation of the number of wafers that can be cut from the cylinder

The number of wafers that can be cut from the cylinder can be calculated as:

$\begin{array}{c}N=\frac{L}{t}\\ N=\frac{\left(25\mathrm{cm}\times \frac{{10}^{-2}\mathrm{m}}{1\mathrm{cm}}\right)}{\left(0.300\mathrm{mm}\times \frac{{10}^{-3}\mathrm{m}}{1\mathrm{mm}}\right)}\\ N=833.33\end{array}$

Step 4. Calculation of the number of chips in the crystal cylinder

Themaximum number of chips that can be produced from one cylinder can be calculated as:

$\begin{array}{l}{N}_c=nN\\ N_c=\left(400\right)\left(833.33\right)\\ N_c=3.33\times {10}^5\mathrm{chips}/\mathrm{cylinder}\end{array}$

Thus, a maximum of $3.33\times {10}^5\mathrm{chips}/\mathrm{cylinder}$can be cut.