Question & Answer

The yield of good chips in multiprobe for a certain batch of wafers is 83%. The wafers have a

diameter of 150 mm with a processable area that is 140 mm in diameter. If the defects are all

assumed to be point defects, determine the density of point defects using the Bose-Einstein method

of estimating yield.

A 12-in wafer is processed over a circular area of diameter = 11.75 in. The density of point defects

in the surface area is 0.018 defects/in2. The chips to be fabricated are square with an area of 0.16 in2

each. Determine an estimate of the number of good chips using the Bose-Einstein yield

computation.

A silicon wafer with a diameter of 200 mm is processed over a circular area whose diameter = 190

mm. The chips to be fabricated are square with 10 mm on a side. The density of point defects in the

surface area is 0.0047 defects/cm2. Determine an estimate of the number of good chips using the

Bose-Einstein yield computation.

On a particular production line in a wafer fabrication facility, the crystal yield is 60%, the crystal-toslice

yield is 60%, wafer yield is 90%, multiprobe is 70%, and final test yield is 80%. (a) What isthe overall yield for the production line? (b) If wafer yield and multiprobe yield are combined into

the same reporting category, what overall yield for the two operations would be expected?

Given that crystal yield = 55%, crystal-to-slice yield = 60%, wafer yield = 75%, multiprobe yield =

65%, and final test yield = 95%, if a starting boule weighs 125 kg, what is the final weight of silicon

that is represented by the non-defective chips after final test?

A 250 mm diameter silicon wafer has a processable area that is circular with a diameter = 225

mm. The IC chips that will be fabricated on the wafer surface are square with 20 mm on a side.

However, the processable area on each chip is only 18 mm by 18 mm. The density of circuits

within each chip’s processable area is 465 circuits per mm^2. (a) How many IC chips can be placed

onto the wafer? (b) Using Rent’s Rule with C = 4.5 and m = 0.35, how many input/output

terminals (pins) will be needed for each chip package?

A 12-inch diameter silicon wafer has a processable area that is circular with a diameter = 11.4 in.

The IC chips that will be fabricated on the wafer surface are square with 0.75 in on a side,

including an allowance for subsequent chip separation. However, the processable area on each

chip is only 0.60 in by 0.60 in. The density of circuits within each chip’s processable area is

100,000 circuits per square inch. (a) How many IC chips can be placed onto the wafer? (b) Using

Rent’s Rule with C = 3.8 and m = 0.43, how many input/output terminals (pins) will be needed

for each chip package?

Suppose it is desired to produce a memory device that will be contained in a dual-in-line package

with 32 I/O leads. How many memory cells can be contained in the device, as estimated by (a)

Rent's rule with C = 6.0 and m = 0.12?

The first IBM personal computer was based on the Intel 8088 CPU, which was released in 1979.

The 8088 had 29,000 transistors and 40 I/O pins. The final version of the Pentium III (1 GHz) was

released in 2000. It contained 28,000,000 transistors and had 370 I/O pins. (a) Determine the Rent’s

rule coefficient values m and C assuming that a transistor can be considered a circuit. (b) Use the

value of m and C to predict the number of I/O pins required for the first Pentium 4 assuming that it

is manufactured with 42,000,000 transistors. (c) The first Pentium 4, released in 2001, used 423 I/O

pins. Comment on the accuracy of your prediction.

To produce a 10 megabit memory chip, how many I/O pins are predicted by Rent's rule (C = 6.0

and m = 0.12)?

A static memory device will have a two-dimensional array with 64 by 64 cells. Determine the

number of input/output pins required using Rent's rule with C = 6.0 and m = 0.12.

In the equation for Rent's rule with C = 4.5 and m = 0.5, determine the value of nio and nc at which

the number of logic gates equals the number of I/O terminals in the package.

An integrated circuit used in a memory module contains 224 memory circuits. Sixteen of these

integrated circuits are packaged onto a board to provide a 256 Mbyte memory module. Use Rent's

rule, Eq. (34.11), with C = 6.0 and m = 0.12 to determine the approximate number of input/output

pins required in each of the integrated circuits.

It is desired to determine the effect of package style on the number of circuits (logic gates) that can

be fabricated onto an IC chip to which the package is assembled. Using Rent's rule with C = 4.5 and

m = 0.5, compute the estimated number of devices (logic gates) that could be placed on the chip in

the following cases: (a) a DIP with 16 I/O pins on a side - a total of 32 pins; (b) a square chip carrierwith 16 pins on a side - a total of 64 I/O pins; and (c) a pin grid array with 16 by 16 pins - a total of

256 pins

A dual-in-line package has a total of 48 leads. Use Rent's rule with C = 4.5 and m = 0.5 to determine

the approximate number of logic gates that could be fabricated in the IC chip for this package.

An integrated circuit used in a microprocessor will contain 1000 logic gates. Use Rent's rule with C

= 3.8 and m = 0.6 to determine the approximate number of input/output pins required in the

package.

It is desired to etch out a region of a silicon dioxide film on the surface of a silicon wafer. The SiO2

film is 100 nm thick. The width of the etched-out area is specified to be 650 nm. (a) If the degree of

anisotropy for the etchant in the process is known to be 1.25, what should be the size of the opening

in the mask through which the etchant will operate? (b) If plasma etching is used instead of wet

etching, and the degree of anisotropy for plasma etching is infinity, what should be the size of the

mask opening?

The surface of a silicon wafer is thermally oxidized, resulting in a SiO2 film that is 100 nm thick. If

the starting thickness of the wafer was exactly 0.400 mm, what is the final wafer thickness after

thermal oxidation?

A silicon boule has been processed through grinding to provide a cylinder whose diameter = 285

mm and whose length = 900 mm. Next, it will be sliced into wafers 0.7 mm thick using a cut-off

saw with a kerf = 0.5 mm. The wafers thus produced will be used to fabricate as many IC chips as

possible for the personal computer market. Each IC has a market value to the company of $98. Each

chip is square with 15 mm on a side. The processable area of each wafer is defined by a diameter =

270 mm. Estimate the value of all of the IC chips that could be produced, assuming an overall yield

of 80% good product.

A 12-inch diameter silicon wafer has a processable area that is circular with a diameter = 11.4 in.

The IC chips that will be fabricated on the wafer surface are square with 0.75 in on a side,

including an allowance for subsequent chip separation. However, the processable area on each chip

is only 0.60 in by 0.60 in. The density of circuits within each chip’s processable area is 100,000

circuits per square inch. (a) How many IC chips can be placed onto the wafer? (b) Using Rent’s

Rule with C = 3.8 and m = 0.43, how many input/output terminals (pins) will be needed for each

chip package?

“The federal income tax scores very high on the economy criterion because the current IRS budget is relatively low compared to the costs of a typical collection agency.”  Explain why this statement may be considered wrong.

Many years ago a famous member of Congress proposed eliminating federal income tax withholding.  What criterion for evaluating tax systems did this proposal violate?  What would likely have been the result of eliminating withholding?

Many years ago a famous member of Congress proposed eliminating federal income tax withholding.  What criterion for evaluating tax systems did this proposal violate?  What would likely have been the result of eliminating withholding?

Compare the federal income tax to sales taxes using the “certainty” criterion.

Montel argues that a flat income tax rate system is vertically equitable.  Oprah argues that a progressive tax rate structure is vertically equitable.  How do their arguments differ?  Who is correct?