- 1.
During accelerated

*electromigration* (EM) TF testing of an aluminum-alloy at current density of

*J* = 2×9 10

^{6} A/cm

^{2} and a temperature of 150 °C, a lognormal distribution was obtained with the parameters:

*t*_{50} = 400 h and a

*σ* = 0.5. Assuming a current density power-law exponent of

*n* = 2 and an activation energy of

*Q* = 0.75 eV (and negligible Joule/self-heating):

- (a)
What is the AF from stress conditions to use conditions *(J*_{use} = 0.5× 10^{6} A/cm^{2}, *T*_{use} = 105 °C)?

- (b)
What is the expected TF for 1 % of the devices during use conditions?

**Answers**: (a) AF = 185, (b) TF(1 %) = 2.6 years

- 2.
During accelerated creep TF testing of a metal-alloy at tensile stress level of σ = 800 MPa and a temperature of 800 °C, a lognormal distribution was obtained with the parameters: t

_{50} = 250 h and a σ = 0.8. Assuming a creep power-law exponent of n = 4 and activation energy of Q = 1.3 eV:

- (a)
What is the AF from stress conditions to use conditions (*σ*_{use} = 500 MPa, *T*_{use} = 500 °C)?

- (b)
What is the expected TF for 1 % of the devices during use conditions?

**Answers**: (a) AF = 1,532, (b) TF (1 %) = 6.8 years

- 3.
During accelerated fatigue cycle-to-failure testing of a metal-alloy with a stress range of Δσ = 400 MPa and a temperature of 25°C, a lognormal distribution was obtained with the parameters: (CTF)

_{50} = 2,500 cycles and a σ = 0.7. Assuming a fatigue power-law exponent of n = 4:

- (a)
What is the AF from stress conditions to use conditions *(*Δ*σ*_{use} = 200MPa, *T*_{use} = 25 °C)?

- (b)
What is the expected cycles-to-failure for 1 % of the devices during use conditions?

**Answers**: (a) AF = 16 (b) TF(1 %) = 7,829 cycles

- 4.
During accelerated time-dependent dielectric breakdown (TDDB) testing of a silica-based dielectric, at an electric field of E = 10 MV/cm and a temperature of 105 °C, a Weibull distribution was obtained with the parameters: t

_{63} = 1.5 h and a β = 1.4. Assuming an exponential model with a field acceleration of γ = 4.0 cm/MV:

- (a)
What is the AF from stress conditions to use conditions (*E*_{use} = 5 MV/ cm, *T*_{use} = 105 °C?

- (b)
What is the expected TF for 1 % of the devices during use conditions?

**Answers**: (a) AF = 4.850 × 10

^{8} (b) TF = 3,107 years

- 5.
During accelerated corrosion TF testing at 90 % relative humidity (RH) and temperature of 121 °C, a lognormal distribution was obtained with the parameters: t

_{50} = 1,500 h and a σ = 0.7. Assuming an exponential TF model with a humidity acceleration parameter of γ = [0.12]/%RH and activation energy of 0.75 eV:

- (a)
What is the AF from stress conditions to use conditions (%RH)_{use} = 65 %, *T*_{use} = 85 °C)?

- (b)
What is the expected TF for 1 % of the devices during use conditions?

**Answers**: (a) AF = 185 (b) TF = 6.2 years

- 6.
During mobile-ions TF testing of MOSFET isolation devices at 7.5 V and 150 °C, a Weibull distribution was obtained with the parameters: t

_{63} = 1,200 h and a β = 1.6. Assuming a power-law TF model with n = 1 and activation energy of 1.0 eV:

- (a)
What is the AF from stress conditions to use conditions (*V*_{use} = 5.0 V, *T*_{use} = 85 °C)?

- (b)
What is the expected TF for 1 % of the devices during use conditions?

**Answers**: (a) AF = 218, (b) TF(1 %) = 1.7 years

- 7.
For the accelerated EM data given in Problem 1, perform a more conservative TF analysis by using n = 2 from J = 2.0 × 106 to 1.0 × 106 A/cm2 and n = 1.5 below 1.0 × 106 A/cm2.

- (a)
What is the AF from stress conditions to use conditions (*J*_{use} = 0.5 × 10^{6} A/cm^{2}, *T*_{use} = 105 °C)?

- (b)
What is the expected TF for 1 % of the devices during use conditions?

**Answers**: (a) AF = 131, (b) TF(1 %) = 1.9 years

- 8.
For the accelerated creep data given in Problem 2, perform a more conservative TF analysis by using n = 4 from σ = 800 to 600 MPa and n = 3 below 600 MPa

- (a)
What is the AF from stress conditions to use conditions (*σ* = 500 MPa, *T*_{use} = 500 °C)?

- (b)
What is the expected TF for 1 % of the devices during use conditions?

**Answers**: (a) AF = 1,279, (b) TF(1 %) = 5.7 years

- 9.
For the accelerated fatigue data given in Problem 3, perform a more conservative TF analysis by using n = 4 from Δσ = 400 to 300 MPa and n = 3 below Δσ = 300 MPa.

- (a)
What is the AF from stress conditions to use conditions (Δ*σ* = 200 MPa, *T*_{use} = 25 °C)?

- (b)
What is the expected cycles-to-failure for 1 % of the devices during use conditions?

**Answers**: (a) AF = 10.7, (b) TF(1 %) = 5,226 cycles

- 10.
For the accelerated TDDB data given in Problem 4, perform a more conservative TF analysis by using γ = 4 cm/MV from E = 10 to 7 MV/cm and γ = 3.5 cm/MV below 7 MV/cm.

- (a)
What is the AF from stress conditions to use conditions (*E*_{use} = 5 MV/ cm, *T*_{use} = 105 °C)?

- (b)
What is the expected TF for 1 % of the devices during use conditions?

**Answers**: (a) AF = 1.79 × 10

^{8}, (b) TF(1 %) = 1,142 years

- 11.
For the accelerated corrosion data given in Problem 5, perform a more conservative TF analysis by using γ = [0.12]/%RH from 90 to 80 %RH and γ = [0.1]/%RH below 80 %RH.

- (a)
What is the AF from stress conditions to use conditions (%RH)_{use} = 65 %, *T*_{use} = 85 °C?

- (b)
What is the expected TF for 1 % of the devices during use conditions?

**Answers**: (a) AF = 137, (b) TF = 4.6 years

- 12.
For the mobile-ions TF data given in Problem 6, perform a more conservative TF analysis by using Q = 1.0 eV from T = 150 to 100 °C and Q = 0.75 eV below 100 °C.

- (a)
What is the AF from stress conditions to use conditions (*V*_{use} = 5.0 V, *T*_{use} = 85 °C)?

- (b)
What is the expected TF for 1 % of the devices during use conditions?

**Answers**: (a) AF = 158, (b) TF = 1.22 years