# In the Esaki diode, how do physicists measure/estimate the velocity of a would-be-tunneling electron?

Layman's explanation, please. Let's consider an Esaki diode.

How do physicists measure/obtain the velocity of a would-be-tunneling electron in order to justify the claim that the potential barrier is higher in energy in comparison with the tunneling electron?

And, a follow-up question: how can one be certain that the electron (on the other side of the barrier) is "the same" electron whose velocity one have measured before the quantum tunneling?

• that fellow helped make japan the major innovator it became in the 1960s. we had so little after the war. Commented Jan 3, 2023 at 15:40

This is a long comment.

At the level of diodes one is in the calculational range of quantum mechanics, the measuring the velocity of a single electron within the diode has no meaning. In quantum mechanics one deals with probabilities, which means the measurable quantities come from the accumulation of many events with the exact boundary conditions .

Now at the level of the diode, the velocities of the electrons are calculated from knowing the interactions they come from

Tunnel diodes have a heavily doped positive-to-negative (P-N) junction that is about 10 nm (100 Å) wide. The heavy doping results in a broken band gap, where conduction band electron states on the N-side are more or less aligned with valence band hole states on the P-side. They are usually made from germanium, but can also be made from gallium arsenide and silicon materials.

So there is no meaning to the "the same" electron whose velocity one have measured. It is all a matter of accumulating statistics biased with the quantum mechanical states.

See this for the tunneling effect.

• If measuring the velocity of a single electron within the diode has no meaning, then how can one meaningfully and reasonably hold that the electron actually crosses the PN-junction "without having sufficient energy to do so"?
– user352845
Commented Jan 3, 2023 at 15:17
• It is the statistical accumulation/distribution of the solid composing the diode, with enough energy to tunnel. think how large avogadro's number is, large, see how many atoms are in 6 grams of diamond here guidechem.com/question/… Commented Jan 3, 2023 at 15:40
• I don't have idea what is your point. Again, tunneling is phenomenon where a particle is able to penetrate through a potential energy barrier which is higher in energy than the particle's kinetic energy. If obtaining the velocity of an electron within the diode has no meaning, then how can we claim meaningfully that what we observe within the diode is actually QUANTUM TUNNELING of electrons?
– user352845
Commented Jan 3, 2023 at 15:46
• Also, "the velocities of the electrons are calculated from knowing the interactions they come from" What do you mean? Could you, please, elaborate more.
– user352845
Commented Jan 3, 2023 at 15:57
• Let me put the question in other words: at the level of the diode, how do one know that the "tunneling" electron's kinetic energy is lower than the barrier's energy?
– user352845
Commented Jan 3, 2023 at 16:09