Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 40

Silicon for computer chips is grown in large cylinders called aboules" that are 300 \(\mathrm{mm}\) in diameter and 2 \(\mathrm{m}\) in length, as shown. The density of silicon is 2.33 \(\mathrm{g} / \mathrm{cm}^{3} .\) Silicon wafers for making integrated circuits are sliced from a 2.0 -m boule and are typically 0.75 \(\mathrm{mm}\) thick and 300 \(\mathrm{mm}\) in diameter.(a) How many wafers can be cut from a single boule? (b) What is the mass of a silicon wafer? (The volume of a cylinder is given by \(\pi r^{2} h,\) where \(r\) is the radius and \(h\) is its height.)

Short Answer

Expert verified
(a) Approximately 2661 wafers can be cut from a single boule. (b) The mass of a single silicon wafer is approximately 123.7 grams.

Step by step solution

01

Finding the Volume of the Boule

Use the given formula for the volume of a cylinder: \(V = \pi r^{2}h\), where \(r\) is the radius and \(h\) is the height. The diameter of the boule is 300 mm, so the radius is half of that, 150 mm. The height is given as 2 m, which needs to be converted to millimeters (2000 mm). Now, plug in the values into the formula: \(V_{boule} = \pi (150 \,\mathrm{mm})^{2}(2000 \,\mathrm{mm}) \)
02

Calculate the Volume of the Boule

Calculate the volume of the boule: \(V_{boule} = \pi (150 \,\mathrm{mm})^{2}(2000 \,\mathrm{mm}) = \pi (22500 \,\mathrm{mm}^{2})(2000 \,\mathrm{mm})\) \(V_{boule} \approx 141372000 \, \mathrm{mm}^{3}\)
03

Finding the Volume of a Single Wafer

Use the same formula for the volume of a single wafer: \(V_{wafer} = \pi r^{2}h\) The diameter of the wafer is 300 mm, so the radius is 150 mm. The height (thickness) of the wafer is 0.75 mm. Plug in the values into the formula: \(V_{wafer} = \pi (150 \,\mathrm{mm})^{2}(0.75 \,\mathrm{mm}) \)
04

Calculating Volume of the Wafer

Calculate the volume of a single wafer: \(V_{wafer} = \pi (150 \,\mathrm{mm})^{2}(0.75 \,\mathrm{mm}) = \pi (22500 \,\mathrm{mm}^{2})(0.75 \,\mathrm{mm})\) \(V_{wafer} \approx 53093.374 \, \mathrm{mm}^{3}\)
05

Finding the Number of Wafers per Boule

Divide the volume of the boule by the volume of a single wafer to find the number of wafers that can be cut from the boule: (number of wafers) = \(\frac{V_{boule}}{V_{wafer}}\) (number of wafers) = \(\frac{141372000 \, \mathrm{mm}^{3}}{53093.374 \, \mathrm{mm}^{3}}\)
06

Calculate the Number of Wafers

Calculate the number of wafers: (number of wafers) ≈ 2661 So, approximately 2661 wafers can be cut from a single boule.
07

Calculate the Mass of a Single Wafer

To find the mass of a single wafer, use the density formula (mass = density × volume). The density of silicon is given as 2.33 g/cm³. First, we need to convert the volume of the wafer from mm³ to cm³: \(V_{wafer} \approx 53093.374 \, \mathrm{mm}^{3} = 53.093\, \mathrm{cm}^{3}\) Now, use the formula: mass of a wafer = (density of silicon) × (volume of a wafer) mass of a wafer = (2.33 g/cm³) × (53.093 cm³)
08

Finding the Mass of a Single Wafer

Calculate the mass of a single wafer: mass of a wafer = (2.33 g/cm³) × (53.093 cm³) mass of a wafer ≈ 123.707 g The mass of a single silicon wafer is approximately 123.7 grams.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The distance from Earth to the Moon is approximately \(240,000 \mathrm{mi.}\) (a) What is this distance in meters? (b) The peregrine falcon has been measured as traveling up to 350 \(\mathrm{km} /\) hr in a dive. If this falcon could fly to the Moon at this speed, how many seconds would it take? (c) The speed of light is \(3.00 \times 10^{8} \mathrm{m} / \mathrm{s} .\) How long does it take for light to travel from Earth to the Moon and back again? (\boldsymbol{d} ) ~ E a r t h ~ t r a v e l s ~ a r o u n d ~the Sun at an average speed of 29.783 \(\mathrm{km} / \mathrm{s} .\) Convert this speed to miles per hour.

In \(2009,\) a team from Northwestern University and Western Washington University reported the preparation of a new "spongy" material composed of nickel, molybdenum, and sulfur that excels at removing mercury from water. The density of this new material is 0.20 \(\mathrm{g} / \mathrm{cm}^{3}\) , and its surface area is 1242 \(\mathrm{m}^{2}\) per gram of material. (a) Calculate the volume of a 10.0 -mg sample of this material. (b) Calculate the surface area for a 10.0 -mg sample of this material. (c) A 10.0 -mL sample of contaminated water had 7.748 mg of mercury in it. After treatment with 10.0 \(\mathrm{mg}\) of the new spongy material, 0.001 \(\mathrm{mg}\) of mercury remained in the contaminated water. What percentage of the mercury was removed from the water? (d) What is the final mass of the spongy material after the exposure to mercury?

Round each of the following numbers to four significant figures and express the result in standard exponential notation: (a) \(102.53070,\) (b) \(656.980,\) (c) 0.008543210 ,(d) \(0.000257870 (\mathbf{e})-0.0357202\)

(a) Calculate the kinetic energy, in joules of a 1200 -kg automobile moving at 18 \(\mathrm{m} / \mathrm{s}\) . ( b ) Convert this energy to calories.(c) When the automobile brakes to a stop is the "lost" kinetic energy converted mostly to heat or to some form of potential energy?

Give the chemical symbol or name for each of the following elements, as appropriate: (a) carbon, (b) nitrogen, (c) titanium, \((\mathbf{d})\) zinc, \((\mathbf{e})\) iron, \((\mathbf{f}) \mathrm{P} (\mathrm{g}) \mathrm{Ca},(\mathbf{h}) \mathrm{He},(\mathbf{i}) \mathrm{Pb},(\mathbf{j}) \mathrm{Ag}\)
See all solutions

Recommended explanations on Chemistry Textbooks

Kinetics

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Chemistry Branches

Read Explanation

Chemical Analysis

Read Explanation

Making Measurements

Read Explanation

Nuclear Chemistry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free