Summarizing the Arrhenius Model | How to Interpret Failure Modes and Activation Energy #15

Update: I have added a tool that can be used in practice.

Since publishing this article,
thankfully, it continues to receive traffic via search.

Determining that there is a demand for "I understand the formula, but I want something I can actually try by inputting numbers,"
I have created an
Arrhenius analysis tool that runs in the browser.

In reliability testing and material evaluation,
the Arrhenius model is a very commonly used analysis method for accelerated testing.

However, when it comes to actually using it, questions sometimes remain, such as "What is actually failing with this activation energy?".

In this article,

• The basics of the Arrhenius equation

• The relationship between failure modes and activation energy

• Pitfalls and points of caution in application

Focusing on these, I will organize interpretations from a field perspective and practical points as a memorandum.

1. What is the Arrhenius equation?

The basic formula for the Arrhenius model is as follows:

• MTTF: Mean Time To Failure

• Ea: Activation energy (eV)

• T: Absolute temperature (K)

• k: Boltzmann constant

• A: Constant (pre-exponential factor)

This model is based on the empirical rule that "as temperature rises, lifespan shortens exponentially," and

• oxidation

• Diffusion

• Dielectric breakdown
  , and many other temperature-dependent degradation phenomena are applied.

It is mainly applied to "phenomena where time-temperature dependence changes exponentially."
It holds true for many degradation reactions and failure processes (oxidation, diffusion, dielectric breakdown, etc.).

2. What are the "pitfalls" of the model?

❗ Understanding the mode is a prerequisite!

• The Arrhenius model assumes that "a single dominant failure mode remains constant" is a prerequisite

• If the mode switches depending on temperature conditions, it will not hold

In other words, if the mode switches, the activation energy (Ea) also becomes something else.

*Ranges vary depending on literature and products (refer to JEDEC, IEC, JEP122B, etc.)

Supplement: Things to know "before" using Arrhenius

Before estimating the activation energy (Ea)──
You need to understand "how exactly is it failing?" in the first place.

And what is important is,

• when you raise the temperature, the failure mode itself may change

• There are physical branching points (phase transformation temperature, glass transition, changes in charge transfer modes, etc.)

In other words, "it is not necessarily the case that the entire temperature range is governed by the same phenomenon." That is what it means.

📌 For example:

• For polymer materials, once it exceeds Tg (glass transition point), it becomes a different mode due to viscoelastic changes

• For Cu wiring, interface diffusion is dominant at low temperatures, while bulk diffusion is dominant at high temperatures

• Electrically, the mode switches by region, such as NBTI → TDDB → HCI

Therefore, it is important to
limit the Arrhenius plot to a 'meaningful range' after first understanding 'what happens in which temperature range'.

In that sense, inflection points of physical properties (state change temperatures, phase transformation temperatures, critical points, etc.) are
very effective clues as 'boundaries where failure modes change'.

3. Guidelines for Ea by Failure Mode

Activation energy can be called the fingerprint of the failure mechanism. In other words, by comparing the estimated Ea with these guidelines, you can infer
'what mechanism is causing the failure now'.

4. Practical Applications & Precautions

When using the Arrhenius model, the following prerequisites are important.

• Must be a single dominant failure mode
  If multiple degradation mechanisms coexist, the value will be averaged and ambiguous.

• Modes may switch depending on temperature
  → Need to be aware of inflection points (e.g., phase transformation temperature).

• Acceleration factor must be temperature only
  If humidity, voltage, current, etc., are also involved, complex models must be considered.

5. Recommended Combined Methods

• Physical observation (cross-section observation, SEM): Confirm the actual failure morphology

• Confirmation of state change points: Refer to phase transformation temperatures, molecular motion activation temperatures, etc.

• Non-linearity check: If the temperature-life plot is not a straight line, suspect a switch in the dominant mode

6. Summary: 'Interpretation' of Activation Energy is the Key to Physical Phenomena

Activation energy is not just a coefficient, but a key to deciphering 'what is breaking?'. However, to interpret it correctly,
it is essential to have:

• Test design (temperature range)

• Material knowledge (physical property change points)

• Combination with other methods (observation, other acceleration factors)

are indispensable.

7. Arrhenius Analyzer — Analysis Tool

▼ Click the image to jump to the page

The following three functions are integrated into one page.

7-1. Ea Estimation & Plot

When you input the MTTF (Mean Time To Failure) for multiple temperature conditions, it draws an Arrhenius plot (1/T vs ln MTTF) and automatically calculates Ea and R² from linear regression.

Furthermore, if R² < 0.95, it displays a warning that there may be a failure mode shift.

7-2. AF (Acceleration Factor) Calculator

By inputting Ea, usage temperature, and test temperature, you can calculate the
AF (Acceleration Factor) and equivalent lifetime in real-time.

Also, since you can
transfer the values calculated in the Ea estimation tab to the AF calculator with one click, you can prevent errors caused by manual input.

7-3. Ea Reference Table

When you input the estimated Ea, it highlights the row for the corresponding failure mode (oxidation, IM, TDDB, etc.), allowing you to check
“what this number physically means” on the spot.

📌 Calculations in this tool are based on the
Arrhenius model (linear regression by least squares method + acceleration factor model)
.

The prerequisites and scope of application for the calculations are clearly stated in the
“Usage & Notes” tab within the tool.

8. Arrhenius Analysis × AI Utilization Guide

▼ Click the image to jump to the page

This is a collection of
prompt templates
for throwing the next practical questions to AI, such as “Is this result physically valid?”

“How should I write this in the report?” after obtaining numerical values with the tool.

Using the division of roles where numerical calculation is done by the tool and interpretation, consideration, and documentation are done by
AI is quite efficient in practice.

🧪 Both the tool and guide can be used for free and without registration. Data is not sent to the server and is
completed entirely within the browser.

9. Related Articles

🧪 This article is a practical memorandum for those involved in reliability testing, material evaluation, quality assurance, etc. 📌 I look forward to your comments, feedback, and questions.

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