Question

Extremely high-purity silicon is required to manufacture semiconductors such as the memory chips found in calculators and computers. If a silicon wafer is \(99.99999999 \%\) pure, approximately how many atoms of some other element are present per gram of high-purity silicon?

Short answer

Approximately \(2.14 \times 10^{12}\) impurity atoms per gram of silicon.

Step-by-step solution

Understanding the Purity Percentage

First, we need to understand that the silicon wafer has a purity of \(99.99999999\%\). This implies that out of every 100 atoms, 99.99999999 are silicon, and the rest are impurities.

Calculate Impurity Percentage

The impurity percentage is \(100\% - 99.99999999\% = 0.00000001\%\). This percentage represents how many atoms of other elements are present in silicon.

Find the Number of Impurity Atoms per 100 Atoms

With 0.00000001% impurity, we first calculate how many non-silicon atoms are there when we consider a base of 100 atoms. This is \( \frac{0.00000001}{100} = 0.0000000001 \) atoms per 100 atoms. Since impurity per atom is very small, we scale up to find per gram of silicon.

Calculate Moles of Silicon per Gram

Silicon's atomic mass is approximately 28.09 g/mol, so 1 gram of silicon is \( \frac{1}{28.09} \approx 0.0356 \) moles.

Calculate Total Atoms in 1 Gram of Silicon

Avogadro's number, \(6.022 \times 10^{23}\), tells us the number of atoms per mole. Therefore, 0.0356 moles of silicon contain \( 0.0356 \times 6.022 \times 10^{23} \) atoms, which is approximately \( 2.14 \times 10^{22} \) atoms.

Calculate Impurity Atoms in 1 Gram

Since 0.0000000001% of these atoms are impurities, there are \( 0.0000000001 \times \frac{1}{100} \times 2.14 \times 10^{22} \approx 2.14 \times 10^{12} \) impurity atoms per gram of silicon.

Key concepts

Semiconductor manufacturing

Semiconductors are materials that conduct electricity under certain conditions, making them essential for electronic devices like computers and calculators. Silicon is a primary material used in semiconductor manufacturing due to its excellent electrical properties and abundance. High-purity silicon is crucial because impurities can significantly affect the performance and reliability of the semiconductor.

During manufacturing:

• Silicon is extracted from quartz or sand, then refined using processes like the Czochralski method to achieve high purity.
• Extreme purity levels—often referred to as electronic-grade silicon—are necessary to minimize electrical resistance and defects.
• Even tiny amounts of impurities can alter electrical behavior, making precise impurity control essential.

By maintaining a high standard of purity, manufacturers ensure the functionality and longevity of semiconductor components.

Impurity calculation

Impurity calculation involves determining how many unwanted atoms are present in a substance—in this case, silicon wafers. Calculating impurity levels is vital to maintaining the quality of semiconductors.

Given in silicon:

• The purity level is 99.99999999%, meaning only 0.00000001% of the composition consists of impurities.
• This minuscule percentage can still result in a significant number of impurity atoms when considering the vast number of atoms in a gram.
• To find impurity atoms per gram, calculate the total atoms (using Avogadro's number) and apply the impurity percentage.

These calculations help in assessing and ensuring the silicon's suitability for semiconductor use.

Avogadro's number

Avogadro's number, approximately \(6.022 \times 10^{23}\), is a fundamental constant in chemistry. It represents the number of atoms or molecules in one mole of a substance, providing a bridge between the microscopic and macroscopic worlds.

In practical application, Avogadro's number allows us to calculate:

• The total number of atoms in a given mass of material.
• For one gram of silicon, which has a molar mass of 28.09 g/mol, you have approximately 0.0356 moles.
• Using Avogadro's number, this translates to \(0.0356 \times 6.022 \times 10^{23}\), or approximately \(2.14 \times 10^{22}\) atoms.

Through this concept, we can determine the number of impurity atoms, critical in high-precision fields like semiconductor manufacturing.