Re: Holes and the Hall effect

[Leigh Palmer <palmer@sfu.ca>]

Hugh Logan, in discussing the merit of calling the moving charges in
metallic conduction "holes" asks (after much uncontentious stuff):

[after observing that the Hall effect can not be interpreted as
arising from electrons moving through the metal]

>  But what is wrong with starting with a model like this and observing
> that it does not agree with experiment, thus requiring a better model
>  to replace it? Even using the Fermi speed instead of the mean speed
> of   the electrons doesn't give the correct result, a further correction
>  of the mean free path by Einstein being needed - hastily following
> the   discussion by Thornton and Rex on p. 324. Isn't this something
> like   the constructivist's approach -- replacing models with more
> viable   models? We never got to this chapter, and I don't think
> technology   students and their instructors would be interested in this
> kind of   theory. Perhaps they should be.

It's just a matter of taste. After the simpler model is rejected
one could merely say that deeper understanding requires the
application of more advanced techniques. Simply introducing the
naked concept of holes is not valuable, and it preempts using
that concept in semiconductors where it will be seen to
represent a very different animal*. One might equally well
ascribe the counterintuitive Hall result to the electrons'
negative mass, but without the theoretical backup that would be
an equally sterile concept.

As I stated before, I don't think this particular misconception
is nearly so malignant as some others that have become common.
It will likely do no lasting harm.

> > Another
> > related misconception is that the electron which emerges from
> > one end of a wire carrying a current is not the same electron
> > as the one that goes in at the other end, delayed only by
> > lightspeed. There is no way to tell any electron from any
> > other electron, and in a sense the statement is meaningless.
> > I never have understood why these factoids are inserted into
> > curricula.
> I hope you weren't referring to my battery example. I was only trying to
> explain in simplistic technician language what the direction of electron
> current in the external circuit of a battery would be if the charge sign
> convention were reversed. I haven't had much occasion to teach about
> metallic conduction in recent years, but when I taught AP Physics and
> E&M, I recall calculating the drift velocity of electrons in metallic
> conductors on the basis of the Drude model - a standard problem in
> general physics texts as I recall. It was a snail's pace compared with
> lightspeed. I wouldn't think of saying that one could track a single
> electron in going from one terminal of a battery to the other in the
> external circuit. But the students wouldn't know that fermions were
> indistinguishable at the general physics level.

I wasn't referring specifically to your battery example, and I
don't even recall it now; the misconception is widespread in our
culture. One factoid students can be usefully taught is that
electrons *are* indistinguishable; that is a truly remarkable
fact. Later (in college) they can be given the evidence which
supports this assertion, and the models which are built on it.

I think the simple picture of electrons drifting in a lattice of
positive ions is a good one on which to construct a mathematical
model and that it is valuable exercise for students to perform
the calculations on that model which are traditionally assigned.
Having said that, I will note that once the Bohr atom is
introduced, with the Pauli exclusion principle and the Heisenberg
uncertainty principle, it might be worthwhile to let the students
peek a little distance down the road to see why the simple
picture can't be right. You don't want any of them to go away
believing in the Truth of such models just because they achieved
high scores on an AP exam using them.

> Perhaps my comments are naive, but this discussion list keeps me on my
> toes.

Your comments and those of many other members of this list keep
me on my toes. I'm pleased to have such colleagues.

> > I got my lawn cut, and I think I've improved the high voltage
> > arcing behaviour of my monitor. Not a bad day.
> I keep my computer running 24 hours a day, because a virus or something
> makes it take many tries for it to detect both of my hard disk drives.
> Someday I will get an expert to look at it.

Experts just replace hardware until the problem disappears. If
you fix it yourself you'll save money, but you will also get a
tremendous rush from doing so. If you botch it, so what? It is
only a relatively small amount of money.

Leigh

* Holes in semiconductors are denizens of the valence band,
  not the conduction band, where metals conduct.