Tunnel Effect in Quantum Science Alexander Gabovich ,

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Tunnel Effect in Quantum Science Alexander Gabovich ,  KPI ,  Lecture 1 Tunnel Effect in Quantum Science Alexander Gabovich , KPI , Lecture

Tunnel effect is one of the most important manifestations of quantum mechanics Tunnel effect is one of the most important manifestations of quantum mechanics

Classic analogy: full internal reflection In the geometric optics sin(r) starts to exceed 1 when nClassic analogy: full internal reflection In the geometric optics sin(r) starts to exceed 1 when n 2 is low enough. Thus, refraction becomes impossible. Actually, electromagnetic wave penetrates into the optically more dense medium at a distance of the wave length λ. It can be found by the indicated set-up when δ ≤ λ. Hence, a massive particle (electron, proton, etc. ) directly reveals its wave properties!

Classic analogy: full internal reflection Classic analogy: full internal reflection

Examples of tunnel phenomena:  -decay of heavy nuclei  Potential energy of the particle insideExamples of tunnel phenomena: -decay of heavy nuclei Potential energy of the particle inside and outside the atomic nucleus: is the probability of the -particle escape during the time unit

Scientists, who discovered the tunnel effect Scientists, who discovered the tunnel effect

Scientists, who discovered the tunnel effect Scientists, who discovered the tunnel effect

Cold emission of metal electrons Cold emission current E is the external electrostatic field Cold emission of metal electrons Cold emission current E is the external electrostatic field

Cold emission of metal electrons Cold emission of metal electrons

Oscillation of a particle between two potential wells Separate wells Coupled wells. Initially the particle isOscillation of a particle between two potential wells Separate wells Coupled wells. Initially the particle is in the left well

Oscillation of a particle between two potential wells Results of calculation: W ( t ) isOscillation of a particle between two potential wells Results of calculation: W ( t ) is a probability of the particle to occur in the left well at the moment t Limiting cases: The particle spends equal times in both wells The particle is predominately in the left well

Tunneling in the periodic lattice;  electron band formation One-dimensional periodic lattice potential E k 0Tunneling in the periodic lattice; electron band formation One-dimensional periodic lattice potential E k 0 is the bandwidth

Franz-Keldysh effect Tunneling probability W (B C) from the valence band AB into the conductance bandFranz-Keldysh effect Tunneling probability W (B C) from the valence band AB into the conductance band CD is proportional to exp{- c [ ε g ] 3/2 / E }, where ε g is the forbidden-gap width. This is Zener effect. It changes the coefficient E of the light absorption in a semiconductor in the homogeneous electric field E. This is Franz-Keldysh effect.

Tunneling in chemistry Tunneling in chemistry

Tunneling in chemistry Tunneling in chemistry

Tunneling in chemistry Tunneling in chemistry

Tunneling in chemistry Tunneling in chemistry

Single-electron tunneling Single-electron tunneling

Single-electron tunneling (4) (2) Δ E = e ( e /2± Q )/ CCorrect formula: Single-electron tunneling (4) (2) Δ E = e ( e /2± Q )/ CCorrect formula:

Single-electron tunneling Single-electron tunneling

Single-electron tunneling Single-electron tunneling