Silicon used in computer chips must have an impurity level below \(10^{-9}\) (that is, fewer than one impurity atom for every \(10^{9} \mathrm{Si}\) atoms \() .\) Silicon is prepared by the reduction of quartz \(\left(\mathrm{SiO}_{2}\right)\) with coke (a form of carbon made by the destructive distillation of coal) at about \(2000^{\circ} \mathrm{C}\) : $$\mathrm{SiO}_{2}(s)+2 \mathrm{C}(s) \longrightarrow \mathrm{Si}(I)+2 \mathrm{CO}(g)$$ Next, solid silicon is separated from other solid impurities by treatment with hydrogen chloride at \(350^{\circ} \mathrm{C}\) to form gaseous trichlorosilane \(\left(\mathrm{SiCl}_{3} \mathrm{H}\right)\) $$ \mathrm{Si}(s)+3 \mathrm{HCl}(g) \longrightarrow \mathrm{SiCl}_{3} \mathrm{H}(g)+\mathrm{H}_{2}(g) $$ Finally, ultrapure \(\mathrm{Si}\) can be obtained by reversing the above reaction at \(1000^{\circ} \mathrm{C}\) : $$ \mathrm{SiCl}_{3} \mathrm{H}(g)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{Si}(s)+3 \mathrm{HCl}(g) $$ (a) Trichlorosilane has a vapor pressure of 0.258 atm at \(-2^{\circ} \mathrm{C} .\) What is its normal boiling point? Is trichlorosilane's boiling point consistent with the type of intermolecular forces that exist among its molecules? (The molar heat of vaporization of trichlorosilane is \(28.8 \mathrm{~kJ} / \mathrm{mol} .\) ) (b) What types of crystals do Si and \(\mathrm{SiO}_{2}\) form? (c) Silicon has a diamond crystal structure (see Figure 11.28 ). Each cubic unit cell (edge length \(a=543 \mathrm{pm}\) ) contains eight Si atoms. If there are \(1.0 \times 10^{13}\) boron atoms per cubic centimeter in a sample of pure silicon, how many Si atoms are there for every \(\mathrm{B}\) atom in the sample? Does this sample satisfy the \(10^{-9}\) purity requirement for the electronic grade silicon?

Step by step solution

01

Finding Norming Boiling Point

For part (a), use the Clausius-Clapeyron equation: \[ln \left( \frac{P_1}{P_2} \right) = \frac{\Delta H_{vap}}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right)\] where \(P_1 = 1\) atm is the normal boiling point pressure, \(P_2 = 0.258\) atm is the initial pressure, \(T_2\) is the initial temperature in Kelvin \((-2 + 273.15 = 271.15 K)\), and \(\Delta H_{vap} = 28.8\) kJ/mol is the molar heat of vaporization. Solve for \(T_1\), the normal boiling point in Kelvin.

02

Analyzing Boiling Points

Discuss whether the calculated boiling point of trichlorosilane is consistent with the types of intermolecular forces. Since trichlorosilane is a polar molecule, it should have dipole-dipole interactions. If the calculated boiling point is relatively high, this is consistent with these forces.

03

Identifying Crystal Structures

For part (b), understand that silicon forms a diamond crystal structure and silicon dioxide forms a quartz crystal structure.

04

Calculating Atomic Ratios

For part (c), take into account that a cubic unit cell of edge length \(a = 543 \times 10^{-12} m\) contains 8 Si atoms. Compute the number of unit cells in a cubic cm: \((\frac{10^2}{5.43})^3\). This gives the total number of Si atoms in a cubic cm. Divide this number by \(1.0 \times 10^{13}\) to compute the ratio of Si to B atoms.

05

Evaluating Purity

Consider if the obtained ratio is adhering to the purity requirement of \(10^{9} : 1 \). If the Si:B ratio is at least \(10^9\), the sample passes the purity test.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Silicon Crystal Structure

Silicon, a pivotal element in modern electronics, crystallizes in a structure known as the diamond cubic crystal structure. This intricate configuration consists of each silicon atom covalently bonded to four neighboring atoms, forming a repeating lattice that extends in all directions.

This bond structure not only gives silicon its semiconductor properties but also contributes to its strength and stability. An interesting property of this crystal arrangement is the presence of semiconductor 'holes' — spots where an electron could be, which are integral to how semiconductors conduct electricity.

The diamond crystal structure has significant implications in the semiconductor industry, especially concerning the integration of impurity atoms, which can modify the electrical properties by either donating extra electrons or creating 'holes' in the structure.

The Importance of Trichlorosilane Vapor Pressure in Silicon Purification

When purifying silicon, the vapor pressure of trichlorosilane (SiCl₃H) plays a critical role. This pressure refers to the force exerted by the gaseous form of trichlorosilane in equilibrium with its liquid form at a given temperature.

Understanding the vapor pressure is crucial because it affects the efficiency of the chemical vapor deposition process used to create ultrapure silicon. High vapor pressure allows for trichlorosilane to be easily converted into a gas and subsequently distilled, removing impurities more effectively.

Engineers need to control the temperature carefully, as the vapor pressure can significantly alter the purification process's outcome. Maintaining the correct pressure is essential for achieving the high levels of purity required for the semiconductor industry.

How the Clausius-Clapeyron Equation Relates to Silicon Purification

The Clausius-Clapeyron equation provides a way to understand how the vapor pressure of a substance changes with temperature. In the context of silicon purification, this equation helps determine the boiling point of trichlorosilane based on its known vapor pressure at a certain temperature.

The equation indicates a logarithmic relationship between the vapor pressure and temperature, taking into account the heat of vaporization. By altering temperature, the vapor pressure changes, affecting the ability to separate silicon from its impurities through distillation.

With accurate calculations, one can tailor the conditions to precisely control the phases of trichlorosilane, ensuring the efficient extraction of high-purity silicon necessary for semiconductor applications. This efficient control of temperature and pressure directly impacts the quality of the silicon obtained.

Semiconductor Impurity Level and Its Impact on Silicon's Electrical Properties

In the world of semiconductors, the impurity level is a measure of how many foreign atoms are present within the silicon lattice. For semiconductor applications, particularly in computer chips, it's vital that this level is kept incredibly low, below 1 in a billion (less than one impurity atom for every 10⁹ Si atoms).

Impurities, such as boron or phosphorus, are deliberately added in controlled amounts during doping to modulate the electrical properties of silicon. These dopants can turn silicon into either a 'p-type' or 'n-type' semiconductor, essential for creating junctions that allow for diodes and transistors — the fundamental building blocks of electronic circuits.

However, too many impurities can disrupt the silicon crystal structure, negatively affecting its semiconductor properties. Therefore, maintaining impurity levels within strict limits is crucial for achieving the desired performance in electronic devices.