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Every phone and laptop runs on transistors, yet the first one came out of an experiment that did not work. John Bardeen's part in that story is a lesson in what to do with a failure: explain it properly. This post covers his life, how the point-contact transistor was found, a worked example on what "20 dB of gain" means, and what you can take from his way of working.
Who was John Bardeen?
Bardeen was born in Madison, Wisconsin, on 23 May 1908. His Nobel biography traces an unusual path. He took a degree in electrical engineering at the University of Wisconsin in 1928, then spent 1930 to 1933 at Gulf Research Laboratories in Pittsburgh, developing ways to interpret magnetic and gravitational surveys for oil prospecting. Feeling his interests lay in pure science, he left to study mathematical physics at Princeton under E.P. Wigner, where he first became interested in solid state physics, and received his PhD in 1936.
After posts at Harvard, the University of Minnesota and the Naval Ordnance Laboratory during the war, he joined the solid state research group at Bell Telephone Laboratories in late 1945. He moved to the University of Illinois in 1951.
How did a failed experiment lead to the transistor?
Bardeen's 1956 Nobel lecture tells the story in detail. Bell Labs began a basic research programme on semiconductors in early 1946, with William Shockley leading the group and Walter Brattain working on surface properties. There had long been hope of a semiconductor amplifier. Shockley suggested one based on the field effect: put a voltage on a plate next to a thin semiconductor film and change its conductance. His calculations said the effect should be large enough to amplify a signal.
The tests, Bardeen writes, "all gave negative results." In analysing why, he suggested that electrons were held in states localised at the surface, which soaked up most of the induced charge. The group decided to study these surface states directly.
That decision led to a chain of experiments:
Brattain and R.B. Gibney used electrolytes on the surface and saw large changes in the surface barrier.
Bardeen and Brattain used a drop of electrolyte around a point contact to control current, first on silicon, then on n-type germanium, and saw amplification, though only at very low frequencies.
Replacing the electrolyte with evaporated gold spots gave a surprise. The effect ran in the opposite direction: holes were flowing into the germanium from the gold and into the nearby point contact. Bardeen calls this "the first indication of the transistor effect."
They estimated that power amplification needed contacts about 0.005 cm (50 micrometres) apart. They evaporated gold onto a wedge and split it at the tip with a razor blade to make two very close contacts. It worked on the first attempt.
Their letter, The Transistor, A Semi-Conductor Triode, appeared in Physical Review in July 1948. Looking back, Bardeen wrote that much of the current at a germanium point contact is carried by minority carriers, holes in this case: "If this fact had been recognized earlier, the transistor might have come sooner."
Why did Bardeen win two Nobel Prizes?
The 1956 Nobel Prize in Physics went to Shockley, Bardeen and Brattain "for their researches on semiconductors and their discovery of the transistor effect". At Illinois, Bardeen then worked with Leon Cooper and Robert Schrieffer on superconductivity. Their 1957 paper, Theory of Superconductivity, earned the 1972 prize "for their jointly developed theory of superconductivity, usually called the BCS-theory". The Nobel Prize's list of multiple laureates shows he is the only person to have received the physics prize twice. For the discovery that started superconductivity research, see our post on Kamerlingh Onnes.
Worked example: what does a power gain of 20 dB mean?
Bardeen's lecture says the point-contact transistor gave "an overall power gain of 20 db. or more." Engineers measure gain in decibels:
gain in dB = 10 log₁₀(P_out / P_in)
Set 20 = 10 log₁₀(P_out / P_in), so log₁₀(P_out / P_in) = 2.
P_out / P_in = 10² = 100.
A 1 mW signal in gives 100 mW out.
Now chain two such stages. Decibels add, so the total is 40 dB, and the power ratio is 10⁴ = 10,000. The ratios multiply (100 × 100) while the decibel values add (20 + 20).
Common mistakes:
Adding power ratios. Two stages of ×100 give ×10,000, not ×200.
Using 20 log for power. The factor 20 is for voltage ratios, because power goes as voltage squared when the resistance is the same. A power ratio uses 10 log.
Losing units. 0.005 cm is 5 × 10⁻⁵ m, which is 50 micrometres, not 5 micrometres.
If you want the device physics behind the gain, our guide to transistor basics explains how a transistor works as a switch and an amplifier.
What can a student take from Bardeen's way of working?
Bardeen's lecture keeps returning to one point: the aim was to understand semiconductors "on the basis of atomic theory", not just to make a device. The device came from that understanding. Three habits follow:
Write down why it failed. When a problem goes wrong, a sentence on the cause, such as "I forgot the normal force changes on the curve", is worth more than the right answer copied from a key.
Pair theory with tests. Bardeen was the theorist; Brattain ran the experiments. Check a formula you derive against a quick limiting case or a measurement.
Follow surprises. The gold-spot effect went the wrong way, and that was the clue.
When a semiconductor idea will not form a picture in your head, try seeing it move. The Fermi Simulation Lab has interactive simulations for ideas that are easier to see than to read.
Next time a problem defeats you, write one line on why before you look at the solution.
