Quantum Mechanics:
Tunneling Effect and Its
Applications
Discovery of Tunneling Effect
Quantum mechanical tunneling works in
the cold emission of electrons,
semiconductor devices
superconductor devices
Applications: flash memory, RTD (resonance tunneling diodes)
Scanning Tunneling Microscope
The current leakage in MOSFETs (and Very-Large-Scale Integrated circuits, VLSIs)
is due to tunneling through the supernarrow oxide barriers.
It has been found that quantum tunneling may be the mechanism used by enzymes
to speed up reactions in live cells to millions of times their normal speed
Discovery of Tunneling Effect
1904-1968, George Gamow
1926-28 - PhD in St.Petersburg University
1928 - discovered beta-decay
1929-31 - in Bohr and Rutherford labs
1931-33 - Staff Fellow at Ioffe Institute
1932 - elected to the Academy of Sciences
since 1934 - worked in U.S.
predicted the Cosmic Microwave Background Radiation
1948 - "The Origin of Chemical Elements" with Alpher (and Bethe)
Gamow was a student of Alexander Friedman (1988-1925): in 1922 he found new
solutions to the Einstein theory (general relativity field equations). Which is known
nowadays as the expanding-universe solution.
Discovery of Tunneling Effect
1928, George Gamow
the theory of the alpha decay: decay of a
nucleus via tunneling.
Classically, the particle is confined to the
nucleus because of the high energy
requirement to escape the very strong
potential.
In quantum mechanics, however, there is a
probability the particle can tunnel through
the potential and escape.
Then the half-life of the particle becomes
finite and the energy of the emission is
broadened.
Ψ
Max Born (1882-1970)
Influenced by Gamow, Born developed a theory of quantum-mechanical tunneling.
Modern Understanding of Tunneling Effect
1905, the photoelectric effect,
Albert Einstein
1924, Louis de Broglie
hypothesis
Using relation between the wave length,
wave vector, frequency etc
we obtain that the energy
and momentum
in 1925 Schrödinger suggested wave function,
the quantum phase or the probability wave
Modern Understanding of Tunneling Effect
in 1925 Schrödinger suggested wave function, we obtain that the energy
the quantum phase or the probability wave
and momentum
If we take derivative of the phase we get
...or we get another derivative of the phase as
...which can be rewritten using the concepts of energy and momentum
...with the last step of making the second derivative...
... we arrive to the Schrödinger equation
Modern Understanding of Tunneling Effect
Solving 1D Schrödinger equation is
almost trivial:
Less trivial is the generalization to
the case of the "negative" kinetic
energy: the forbidden state
Tunneling Through a Barrier
For a classical particle the energy barrier
is impenetrable: the particle coming from
the left must be reflected
Ar = Al
A quantum particle, however, has a tail
of the wave function under the barrier
(non-zero probability) : then the particle
coming from the left can be reflected OR
transmitted
Ar = Al + Br
with the probability
Discovery of Tunneling Diode
the 1973 Nobel Prize in Physics
Leo Esaki, Ivar Giaever
"for their experimental discoveries regarding
tunneling phenomena in semiconductors and
superconductors, respectively"
and Brian David Josephson
for the Josephson effect
Tunneling Diode: Principles
Double Barrier Tunneling Diode