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If you run a
cathode, emitting an electron
beam, with large electrical fields between
the cathode and the anode, you will find that your
workfunction
EA seems to change to smaller values as the field
strength increases. |
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This is called
Schottky
effect; it is observed at large field
values of (105 - 108)V/cm. |
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If you apply even higher field strengths (and
remember: E = U/d; you do not need high voltages
U, only small dimensions d),
EA seems to vanish altogether. |
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This effect is is called field emission. It works even at room temperature
and is barely temperature dependent, so it can not be a temperature activated
process. |
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Field emission is rather easy to obtain: all you
have to do, is to make a very fine tip with a curvature of the tip in the
nm - range as shown on the left. |
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Field emission might then occur with a few Volts
between the anode and the tip, because all the field lines will have to
converge on the small tip. |
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How can we understand these effects? Whereas the
Schottky effect is relatively straight
forward, field emission is a manifestation
of the tunnelling effect, a purely quantum
mechanical phenomenon. |
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Lets look at how the
free electron gas model must be
modified at high field strengths - and we will be able to account for both effects. |
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The potential energy E outside of
the material is such that electrons are to be extracted - it is not constant,
but varies with the field strength E
simply as |
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E, the
(constant) applied field strength (written in mauve to make
sure that we do not mix it up with the energy E). We have the
following situation: |
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Simply summing up the energies graphically yields
the qualitative energy curve for an electron at the edge of a crystal as shown
below. |
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Whichever way you superimpose the potential
energies, the potential barrier to the outside world will always be reduced.
This explains qualitatively the Schottky
effect. |
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The field
emission effect requires a somewhat different consideration. |
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Lets look at the extremes of the Schottky effect. For really high
field strengths the potential barrier gets even lower and thinner, it may look
somewhat like this: |
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Now the tunneling effect may occur. It is a
phenomenon inherent in quantum mechanics and allows electron "waves"
to "tunnel" through a potential
barrier. |
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In other words, the value of the
wave function
y for an electron does not got to zero abruptly at
a potential barrier, but decays exponentially. There is then a finite amplitude
for y on the
other side of the potential barrier, an effect that is felt if the
barrier is "thin" and low - as in the picture above. If the field
strength is high enough, large quantities of electrons can directly tunnel to
the outside world. More about tunnelling in the
link. |
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Field emission thus is a purely
quantum mechanical effect; there is no classical counterpart whatsoever. It is
used in a growing number of applications: |
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Electron microscopes for special
purposes (e.g. scanning electron microscopes with high resolution at low beam
voltage, a must for the chip industry) are usually equipped with
field emission "guns". |
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"Scanning Tunnelling
Microscopes" (STM) which are used to view
surfaces with atomic resolution, directly employ tunnelling effects. |
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Large efforts are being made to
construct flat panel displays with millions of miniature field emission
cathodes - at least one per pixel. |
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Some semiconductor devices (e.g. the
"tunnel diode") depend on
tunnelling effects through space charge regions. |
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In other contexts, tunnelling is not
useful, but may limit what you can do. Most
notorious, perhaps, is the effect that very
thin insulators - say 5 nm and below - are insulating no
more, a growing problem for the chip industry. |
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© H. Föll (Electronic Materials - Script)
