Chapter 1, Problem 1.10.2E

Explanation of Solution

Given,

The diameter of the wafer is 15cm which costs Rs.12 and includes 84 dies with 0.020defects/cm².

The diameter of the wafer is 20cm which costs Rs.15 and includes 100 dies with 0.031defects/cm².

The radius of the wafer can be calculated using the formula $\text{r}\text{=}\frac{\text{d}}{\text{2}}$

Substitute, “15” for “d” is given below:

Radius $\begin{array}{c}{\text{r}}_{\text{15cm}}\text{=}\frac{\text{15}}{\text{2}}\\ \text{=}\text{7}\text{.5}\end{array}$

The radius of the wafer is 7.5cm.

Substitute, “20” for “d” is given below:

Radius $\begin{array}{c}{\text{r}}_{\text{20cm}}\text{=}\frac{\text{20}}{\text{2}}\\ \text{=}\text{10}\end{array}$

The radius of the wafer is 10cm.

The die area of the wafer can be calculated using the formula $\text{wafer}\text{area}\text{=}{\text{πr}}^{\text{2}}$

Substitute, “3.14” for “$\text{π}$” and “7.5” for “r” is given below:

$\begin{array}{c}\text{Wafer}{\text{area}}_{\text{15cm}}\text{=}\text{3}\text{.14}\text{×}{\text{(7}}^{\text{.5)}}\\ \text{=}\text{3}\text{.14}\text{×}\text{56}\text{.25}\\ \text{=}\text{176}\text{.625}\end{array}$

The area of the wafer with 15cm diameter is 176.625cm².

Substitute, “3.14” for “$\text{π}$” and “10” for “r” is given below:

$\begin{array}{c}\text{Wafer}{\text{area}}_{\text{20cm}}\text{=}\text{3}\text{.14}\text{×}{\text{(10)}}^{\text{2}}\\ \text{=}\text{3}\text{.14}\text{×}100\\ \text{=}314\end{array}$

The area of the wafer with 20cm diameter is 314cm².

The die area of the wafer can be calculated using the following formula

$\text{die}\text{area}\text{=}\frac{\text{wafer}\text{area}}{\text{dies}\text{per}\text{wafer}}$

Substitute, “176.625” for “wafer area” and “84” for “dies for wafer” is given below:

$\begin{array}{c}\text{die}{\text{area}}_{\text{15cm}}\text{=}\frac{\text{176}\text{.625}}{\text{84}}\\ \text{=}\text{2}\text{.10}\end{array}$

The die area of the wafer with 15cm is 2.10cm².

Substitute, “314” for “wafer area” and “100” for “dies for wafer” is given below:

$\begin{array}{c}\text{die}{\text{area}}_{\text{20cm}}\text{=}\frac{314}{100}\\ \text{=}3.14\end{array}$

The die area of the wafer with 20cm diameter is 3.14cm².

The yield of the wafer can be calculated using the following formula

$\text{yield}\text{=}\frac{\text{1}}{{\left(\text{1}\text{+}\left(\frac{\text{defects}\text{×}\text{die}\text{area}}{\text{2}}\right)\right)}^{\text{2}}}$

Substitute, “0