On July 1st, Toshiba Corporation's Semiconductor Company and Storage Products Company consolidated to form Semiconductor & Storage Products Company.This page describes reliability information of semiconductor products.

Temperature

[As of April, 2011]

Accelerated lifetime testing is closely associated with the physics of the failure. The physical and chemical reactions of device degradation are generally used as chemical kinetics. Chemical kinetics is a basic chemical reaction model that describes the temperature dependence of failures. The temperature dependence of failures are widely used with the Arrhenius model^{Note 1} in accelerated lifetime testing of semiconductor devices.
Given a chemical reaction speed K, the Arrhenius equation can be expressed as:

Ea: Activation energy (eV)
k: Boltzmann's constant (Where 8.617 × 10⁻⁵ [eV/K](1.380 × 10⁻²³ [J/K] in SI units))
T: Absolute temperature (K)
A: Constant

If the product's lifetime ends at a certain degradation B, then lifetime L can be expressed as L = B/K. Given B/A = A':

This equation expresses the relationship between temperature and lifetime. If the failure mechanism is uniform, lnL and 1/T can be plotted on a straight line as shown in Figure 1. That is, the acceleration from temperature T₁ to T₂ is lnL₁/lnL₂.

This is [Figure 1 Relationship between Lifetime and Temperature].

Figure 1 Relationship between Lifetime and Temperature

Given acceleration coefficient α and the lifetimetimes L₁ and L₂ at temperatures T₁ and T₂, respectively, the acceleration coefficient α can be found using the following formula:

This is [the equation for the acceleration coefficient, α].

Ea: Activation energy (eV)
k: Boltzmann's constant
T₁, T₂: Absolute temperature (K)

Figure 2 shows the relationship between the activation energy and the acceleration coefficient at each temperature.
It can be seen from the Arrhenius equation that the acceleration due to temperature changes drastically with the activation energy Ea. Figure 3 shows the relationship between each activation energy level and the accelerated coefficient when the temperature difference as a parameter.

This is [Figure 2 Relationship between Activation Energy and Acceleration Coefficient].

Figure 2 Relationship between Activation Energy and Acceleration Coefficient

This is [Figure 3 Relationship between Temperature and Acceleration Coefficient Using Activation Energy as a Parameter].

Figure 3 Relationship between Temperature and Acceleration Coefficient Using Activation Energy as a Parameter

Numerous sets of data have been disclosed regarding the relationship between temperature and lifetime or failure rate of semiconductor devices. Some examples of data from experiments conducted by Toshiba are as follows:

Temperature Acceleration of Intermetallic Formation of Bonding Wire
As temperature rises, intermetallic alloy begins to form at the junction of Au wire and the Al used on the pad, causing the contact resistance to increase and the contact to open. Figure 4 shows the relationship between the temperature and lifetime from the results of high-temperature storage testing.
From the lifetime values at different temperature conditions, it can be seen that the activation energy is approximately 1.0 eV.

Figure 4 Temperature Dependence of Formation of Intermetallic Alloy in Bonding Wire
Temperature Acceleration on Different Semiconductor Devices
Various data have been reported for the relationship between the temperature and failure rate of semiconductor devices. Figure 5 shows an example of data obtained from this type of experiment. The figure gives the acceleration rate for each device.

Figure 5 Example of Device Temperature Acceleration

The activation energy differs according to the failure mechanism. Table 1 shows typical failure mechanisms and activation energy values obtained from experiments performed by Toshiba and other organizations.

Table 1 Main Failure Mechanisms and Activation Energy Values (Examples)
Failure Mode	Failure Mechanism	Activation Energy (ev)
Metal wiring failure (open, short, corrosion)	Al metal electromigration	0.4 to 1.2
	Al metal stress migration	0.5 to 1.4
	Au-Al alloy growth	0.85 to 1.1
	Cu metal electromigration	0.8 to 1.0
	Al corrosion (moisture penetration)	0.6 to 1.2
Oxide film voltage breakdown (insulation breakdown, leakage current increase)	Oxide film breakdown	0.3 to0.9
h_FE degradation	Ion movement acceleration due to moisture	0.8
Characteristic value fluctuation	Degradation by NBTI	0.5 and up
	Na ion drive in SiO₂	1.0 to 1.4
	Slow trapping of Si-SiO₂ interface	1.0
Increased leakage current	Inversion layer formation	0.8 to 1.0

Note: The above-described obtained values differ according to the Si process generation and detailed structure. These values reflect results actually obtained as well as results from reported cases.

The model described so far was the Arrhenius model for temperature acceleration. Another failure model is the Eyring model. This model considers the effects of humidity, voltage and mechanical stress in addition to temperature. Given an average lifetime L, the relationship to temperature and stress can be expressed as:

L: Average lifetime
A, B, α: Constants
T: Temperature (K)
S: Stress other than temperature

Note 1: Bibliography. H. Shiomi; "Introduction to Failure Physics," published by the Japan Science and Technology Association (1970)