- 1.
An IC designer worried about electromigration decides to increase the metal width of an aluminum-alloy conductor by 20 %. Assuming J_{crit} is negligibly small, how much of an increase in lifetime can the designer expect?

**Answer**: REF = 1.44 (or a 44 % increase in lifetime)

- 2.
If the conductor in Problem 1 is copper, how much lifetime improvement can be expected with an increase in conductor width by 20 %?

**Answer**: REF = 1.2 (or a 20 % increase in lifetime)

- 3.
If the temperature of the Al-alloy conductor in Problem 1 could be reduced from 105 to 95 °C by using a heat sink, how much longer would the conductor be expected to last?

**Answer**: REF = 1.87 (or a 87 % increase in lifetime)

- 4.
If the temperature of the copper conductor in Problem 2 could be reduced from 105 to 95 °C by using a heat sink, how much longer would the conductor be expected to last?

**Answer**: REF = 2.30 (or a 130 % increase in lifetime)

- 5.
A 45 Å gate oxide MOSFET operates in inversion with a gate voltage of 2.7 V. How much would the TDDB lifetime increase if gate voltage is reduced to 2.5 V?

**Answer**: REF = 5.92 (or a 492 % increase in lifetime)

- 6.
If the transistor described in Problem 5 is a p-channel MOSFET, how much would the NBTI lifetime increase if the gate voltage is reduced from 2.7 to 2.5 V?

**Answer**: REF = 4.15 (or a 315 % increase in lifetime)

- 7.
If the transistor described in Problem 5 is a n-channel MOSFET, how much would the HCI lifetime increase if the device operating voltage is reduced from 2.7 to 2.5 V?

**Answer**: REF = 9.23 (or a 823 % increase in lifetime)

- 8.
Assuming that a rotor’s arm is made of a strong metal and that the operational stress in the rotor’s arm is much greater than the materials yield point, what is the expected increase in creep lifetime if the length of the rotor’s arm *r* is reduced by 20 %?

**Answer**: REF = 2.44 (or 144 % increase in lifetime)

- 9.
Assuming that a thin-walled spherical storage vessel is made of a strong metal and that the operational stress is much greater than the materials yield point, what is the expected increase in creep lifetime if the thickness of the wall is increased by 30 %?

**Answer**: REF = 2.86 (or 186 % increase in lifetime)

- 10.
Assuming that a leaf spring is made of a strong metal and that the operational stress is much greater than the materials yield point, what is the expected increase in creep lifetime if the thickness of the spring is increased by 30 %?

**Answer**: REF = 8.16 (or 716 % increase in lifetime)

- 11.
Assuming that a nut and bolt type clamp is made of a strong metal and that the operational stress in the shaft of the bolt is much greater than the materials yield point, what is the expected increase in stress-relaxation lifetime if the radius of shaft is increased by 30 %?

**Answer**: REF = 4.83 (or 383 % increase in lifetime)

- 12.
Assuming that a thin-walled spherical storage vessel is made of a strong metal and that the operational stress is much greater than the materials yield point, what is the expected increase in fatigue lifetime if the allowed pressure range is decreased by 20 %?

**Answer**: REF = 2.44 (or 144 % increase in lifetime)

- 13.
Assuming that the elastic range is negligibly small and that a fatigue exponent of *n* = 4 can be used for a plastic molded integrated circuit, what is the expected increase in IC thermal-cycling lifetime if the operational thermal range is decreased by 20 %?

**Answer**: REF = 2.44 (or 144 % increase in lifetime)