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In physics, quantum tunnelling, barrier penetration, or simply tunnelling is a quantum mechanical phenomenon in which an object such as an electron or atom passes through a potential energy barrier that, according to classical mechanics, should not be passable due to the object not having sufficient energy to pass or surmount the barrier.
In quantum mechanics, the rectangular (or, at times, square) potential barrier is a standard one-dimensional problem that demonstrates the phenomena of wave-mechanical tunneling (also called "quantum tunneling") and wave-mechanical reflection.
Schematic representation of an electron tunneling through a barrier. In electronics, a tunnel junction is a barrier, such as a thin insulating layer or electric potential, between two electrically conducting materials. Electrons (or quasiparticles) pass through the barrier by the process of quantum tunnelling. Classically, the electron has zero ...
Tunneling ionization is a quantum mechanical phenomenon since in the classical picture an electron does not have sufficient energy to overcome the potential barrier of the atom. When the atom is in a DC external field, the Coulomb potential barrier is lowered and the electron has an increased, non-zero probability of tunnelling through the ...
In nonrelativistic quantum mechanics, electron tunneling into a barrier is observed, with exponential damping. However, Klein's result showed that if the potential is at least of the order of the electron mass (where V is the electric potential, e is the elementary charge, m is the electron mass and c is the speed of light), the barrier is ...
Proton tunneling is a type of quantum tunneling involving the instantaneous disappearance of a proton in one site and the appearance of the same proton at an adjacent site separated by a potential barrier. The two available sites are bounded by a double well potential of which its shape, width and height are determined by a set of boundary ...
As the name ferroelectric tunnel junction suggests, the devices operate based on quantum tunneling through a barrier. As electrons tunnel through the barrier, the resulting movement can be measured as current. The amplitude of the current is determined by the tunneling probability. On the interface of the insulating potential barrier, when the ...
The delta potential is the potential = (), where δ(x) is the Dirac delta function. It is called a delta potential well if λ is negative, and a delta potential barrier if λ is positive. The delta has been defined to occur at the origin for simplicity; a shift in the delta function's argument does not change any of the following results.