# Introduction to semiconductor quality and reliability—Part I

**Factors of Semiconductor Device Failure**

Package related factors:

- Thermal and Mechanical Stress
- Moisture Induced Corrosion
- Alpha Radiation
- Aging

The pictures below shows package related failure – Lifted Bond Balls

- Sensitive towards thermal and voltage stress
- Particle contamination
- Silicon Lattice defect
- Thin film oxide integrity
- Static Electricity

Figures below shows the Particle contamination and Silicon Defect respectively

**Indicators of Reliability:**

Reliability function: The reliability function “R(t)” represents the probability of survival of any device. This can be indicated as the ratio of conforming products that can function properly when time “t” elapses after starting use. The following formula expresses the reliability function:

Unreliability function (failure distribution function):- The unreliability function “F(t)” indicates the total number of failures (number of cumulative failures) that are detected by time “t” after starting use. The following formula expresses the unreliability function:

Figure 1 shows relationship between R(t) and F(t)

Failure density function: The failure density function “F(t)” indicates the failure occurrence rate in the unit time for all samples at time “t” after starting use. The following formula expresses the failure density function.

Failure rate function (also referred to as hazard rate function): The failure rate function “λ(t)” indicates the possible failure occurrence rate in the next unit time for any samples still operating properly at time “t” after starting use. The following formula expresses the failure rate function:

The failure rate function is also referred to as the instantaneous failure rate, and is frequently used to express the reliability of semiconductor devices.

Cumulative hazard function: The failure rate function “λ(t)” is accumulated to express the cumulative hazard function “H(t)” as follows:

Mean time to failure (MTTF): Like the failure rate, the time to failure is also frequently used. The time to failure is defined as the time required for a semiconductor device to fail after starting use. The mean value of the time to failure is referred to as the mean time to failure (MTTF). The following formula expresses the mean time to failure:

Semiconductor device failure distribution: The failure occurrence condition of an electronic part or an electronic device is generally illustrated as shown in Figure 2. The curve shown in Figure 2.2 is referred to as the BATH TUB curve because of its shape.