Re: Conserving Q / space charge in insulators

["John S. Denker" <jsd@MONMOUTH.COM>]

At 09:08 PM 1/28/99 +0100, Ludwik Kowalski wrote:
> Thanks, John Denker, for an interesting message.

You're welcome.

> Was [Faraday] right or wrong by claiming the
> existence of "penetration of charges" into dielectric materials?

Answer:  Faraday was right about this.  (Is anybody surprised? :-)

To see how this works, let's consider the following perverted capacitor:

            DDD  P
              D  P
              D  P
   wwwwwwww>  D  Pwwwwwwww
              D  P
              D  P
            DDD  P

where "D" is a dielectric substance which is also a good insulator,  "w"
represents the wires, and "P" is an ordinary capacitor plate.  The
left-hand plate of the capacitor has been replaced by a sharp point.  In
air, it will produce a corona discharge.  In vacuum you could use a hot
cathode or rely on field emission.

You can use this apparatus to apply a monumental amount of charge to the
dielectric.

Good insulators -- the best insulators -- will carry charges not just on
their surfaces but also throughout their volume.  The buzzword is "space
charge".  By way of analogy, imagine pouring water into one of those trays
you use for making ice cubes.  If you incline the tray slightly, you can
fill the whole tray by pouring water into the top pocket only.  The pockets
in the tray are analogous to the *traps* in the insulator.  As the traps on
the surface get filled, the charge spills over into the traps deeper in the
material.

You see why I asked a couple of notes ago what physical processes or
principles you wanted to demonstrate.  When you slightly reword the
question about what you are looking for, it has a big effect on the choice
of apparatus used to capture the effect.

Now let's consider the case of an ordinary capacitor with two symmetric
capacitor plates, unlike the asymmetric thing diagrammed above.  If you run
the voltage up high enough, you can get charge injection.  You might get
symmetric injection: positive space charge penetrating the dielectric on
one side, plus negative space charge penetrating the other side;  this
would produce no *net* Q on the dielectric.  On the other hand, since the
physics of emission of electrons is different from the emission of anything
else, we can expect that even in a symmetric structure there will be
asymmetric injection, resulting in a net Q.  The following "capacitor"
(operated in vacuum) will put a negative charge on the dielectric every time:

            DDDDD
              D
              D
   wwwwwwww>  D  <wwwwwwww
              D
              D
            DDDDD

(It is amusing that although the initial process of charging the dielectric
is lossy, after it is sufficiently charged up this might be a reasonably
non-lossy capacitor.)

Obviously in practical capacitors, they try real hard to keep the fields
everywhere low enough that charges are not sprayed onto the dielectric, let
alone deeply injected into the dielectric.  Inside a capacitor there are
supposed to be displacement currents only, not long-distance movements of
free carriers.  Also note that in many materials, you'll get dielectric
breakdown before you get very much space charge.

By the way, folks, please do *not* blithely take an ordinary capacitor and
apply a large voltage to it just to see what happens.  At some point the
dielectric will break down.  Depending on the current-limit of your power
supply, and on the stored energy in the capacitor itself, it could well go
boom.

The story of how real insulators work is quite interesting: traps, charge
injection, Mott localization, Anderson localization, and all that.  But
it's a bit complicated.  Most elementary physics books say nothing about
any of this.  Most graduate-level solid state physics books cover only
metals and semiconductors, and tend to give the impression that "insulator"
is just the name we give to large-gap semiconductors ... which is horribly
far from being the whole story.

I don't think a vacuum or a large-gap semiconductor should be called an
insulator;  I suggest the term _semi-insulator_.  In the absence of
carriers it is a perfect insulator, but if you inject some charge it
becomes a perfect conductor.  A real, practical insulator insulates much
better than this, because it has traps.

I don't know of any references on how insulators work that would be
suitable for typical students or non-experts of any kind.  Back when I was
a student I actually traveled to the Xerox research lab in Rochester.  The
folks there *really* know about insulators.  They let me run around in
their library for a day, which I thought was pretty nice of them.

Cheers --- jsd