engineering

Johnson's figure of merit

Johnson's figure of merit is a engineering topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Johnson's figure of merit rather than just read about it. In short: Johnson's figure of merit is a measure of suitability of a semiconductor material for high frequency power transistor applications and requirements. More specifically, it is the product of the charge carrier saturation velocity in the material and the electric breakdown field under same conditions, first proposed by Edward O.

Key takeaways

Johnson's figure of merit belongs to engineering; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Johnson's figure of merit to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Johnson's figure of merit from memory before moving on to harder problems.

Reference excerpt

Johnson's figure of merit is a measure of suitability of a semiconductor material for high frequency power transistor applications and requirements. More specifically, it is the product of the charge carrier saturation velocity in the material and the electric breakdown field under same conditions, first proposed by Edward O. Johnson of RCA in 1965. Note that this figure of merit (FoM), sometimes referred to as JFoM, is applicable to both field-effect transistors (FETs), and with proper interpretation of the parameters, also to bipolar junction transistors (BJTs). JFoM is meant to identify the relative suitability of a bulk semiconductor material for high power and high speed applications. There are variations on this FoM for evaluating relative merit specifically at high frequencies by including the cut-off frequency of a transistor made of the specific material. There are FoMs used for particular power applications like switching for example.

Example materials Note that both saturation velocity and breakdown voltage are temperature and doping/impurity level dependent

JFoM figures may vary significantly between different sources mainly due to temperature effects and sensitivity to material purity and other conditions such as crystal orientation and the measurement technique used. Breakdown field also shows some dependency on the field value itself, and somewhat to the frequency of the field also if it is not a static one. For this reason, high field electron velocities should be used for this estimation. Also, note that semiconductors GaAs and InP, belonging to two-valley family of Group III-V materials, have peak electron velocities greater than the high field saturation velocities used here.

External links Gallium Nitride as an Electromechanical Material. R-Z. IEEE 2014 Table IV (p. 5) lists JFM (relative to Si) : Si: 1, GaAs: 2.7, SiC: 20, InP: 0.33, GaN: 27.5, also shows Vsat and Ebreakdown.

References

Worked examples

Example 1 — a first encounter with Johnson's figure of merit

Start with the simplest possible case. Write down what Johnson's figure of merit claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In engineering, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Johnson's figure of merit before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Johnson's figure of merit ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Johnson's figure of merit

In research: Johnson's figure of merit appears in engineering research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Johnson's figure of merit in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Johnson's figure of merit is common in secondary-school and first-year university syllabi. It links to neighbouring topics Materials science stubs, Microwave technology, Semiconductors, so understanding it makes those chapters shorter.
In everyday life: Look for Johnson's figure of merit outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Johnson's figure of merit in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Johnson's figure of merit means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Johnson's figure of merit out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Johnson's figure of merit in simple terms?

Why does Johnson's figure of merit matter?

Because it connects several engineering ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Johnson's figure of merit?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Johnson's figure of merit.