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In classical physics a ball that lacks the energy to roll over a hill stays on its side. In quantum physics an electron can sometimes appear on the other side anyway. This is called tunnelling. Leo Esaki was the first to show it clearly in a semiconductor device, and his tunnel diode was the result. This post explains what he found, estimates how sensitive tunnelling is to barrier width, and ends with what students can learn from his approach.
Who is Leo Esaki?
Esaki was born in Osaka, Japan, on 12 March 1925, according to his Nobel facts page. His Nobel biography records a BS in physics in 1947 and a PhD in 1959, both from the University of Tokyo. While working at Sony, his research on heavily doped germanium and silicon led to the tunnel diode, which the biography calls "the first quantum electron device". He joined IBM's Thomas J. Watson Research Center in 1960, where from 1969 he and colleagues pioneered semiconductor superlattices: stacks of ultra-thin layers designed to control electrons.
What problem was he working on?
In his Nobel lecture, Esaki explains that in 1956 he began studying how electrons might tunnel between bands in narrow p-n junctions. Earlier claims of tunnelling in diodes were disputed, because most junctions actually broke down by a different process, avalanche, in which fast carriers knock loose new ones.
His approach was to dope both sides so heavily that the junction became extremely thin. He calculated a junction width of about 200 Å (20 nm) at zero voltage and confirmed it with capacitance measurements. In such a thin junction, avalanche could be ruled out.
What did he see?
His first device conducted better in reverse than in forward bias, the opposite of an ordinary diode. Then, as he describes in the lecture, "When the unit was cooled, we saw, for the first time, a negative resistance." By narrowing the junction further with even heavier doping, the negative resistance appeared at all temperatures. He reported it in Physical Review in 1958 under the title "New Phenomenon in Narrow Germanium p-n Junctions".
Negative resistance means that over part of the voltage range, increasing the voltage makes the current fall. As the voltage rises, the filled electron states on one side stop lining up with the empty states on the other, so fewer electrons can tunnel across. The 1973 Nobel press release notes that Esaki's discovery showed the effect could be used in tunnel diodes and opened a new field of research.
Worked example: why does junction width matter so much?
For a simple rectangular barrier, the chance that an electron tunnels through is roughly
T ≈ e^(−2κd), with κ = √(2m(U − E)) / ħ
where d is the barrier width and U − E is how far the barrier rises above the electron's energy. This is a classroom estimate: real junctions have sloping barriers and electrons with an effective mass, so treat the numbers below as sample values.
Take a free electron (m = 9.11 × 10⁻³¹ kg) facing a barrier 1 eV high (1.60 × 10⁻¹⁹ J), with ħ = 1.055 × 10⁻³⁴ J s.
Step 1: κ. 2m(U − E) = 2 × 9.11 × 10⁻³¹ × 1.60 × 10⁻¹⁹ = 2.92 × 10⁻⁴⁹. Its square root is 5.40 × 10⁻²⁵. Divide by ħ: κ ≈ 5.12 × 10⁹ m⁻¹.
Step 2: d = 1 nm. 2κd = 2 × 5.12 × 10⁹ × 1 × 10⁻⁹ = 10.2. T ≈ e^(−10.2) ≈ 3.5 × 10⁻⁵.
Step 3: d = 2 nm. 2κd = 20.5. T ≈ e^(−20.5) ≈ 1.3 × 10⁻⁹.
Doubling the width did not halve the tunnelling chance. It squared it, making it nearly 30,000 times smaller. That is why Esaki needed extremely heavy doping: a thinner junction makes tunnelling enormously more likely.
Common mistakes:
Using eV directly in κ. Convert to joules first.
Forgetting the factor of 2 in 2κd.
Treating T as a fixed property of the electron. It depends on both barrier height and width.
Where does this sit in your syllabus?
The current NCERT Class 12 chapter on Semiconductor Electronics covers p-n junctions and diodes but does not include tunnelling, so the tunnel diode sits outside your NCERT course. It builds directly on what you do study; see our guide to p-n junction diode characteristics. The same tunnelling idea is at work in the instrument described in our post on Gerd Binnig and the scanning tunnelling microscope.
The 1973 prize was shared: a quarter to Esaki, a quarter to Ivar Giaever for tunnelling in superconductors, and half to Brian Josephson for his theoretical predictions about supercurrents through a tunnel barrier.
What can a student take from Leo Esaki?
Rule out the other explanation first. He designed junctions thin enough that avalanche breakdown could not be the cause.
Follow the anomaly. The negative resistance was not what he set out to find.
Push one variable hard. More doping meant thinner junctions and a clearer effect.
When a graph like the tunnel diode's current-voltage curve is hard to picture, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
Try it now: repeat the worked example for a 0.5 nm barrier and see how much larger the tunnelling chance becomes.
