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Re: HOLES AS CARRIERS



At 04:03 PM 10/8/01 -0400, Michael Edmiston wrote:

It seems that John is trying to say holes as charge carriers is just a
viewpoint. It is just a way of viewing something just like we can choose
any coordinate system we want.

Yes. It's a good analogy, especially if we include the observation that in
some cases certain coordinate systems are verrrrry much more convenient
than others.

But how do we explain the Hall Effect? If "moving holes" is just an
artifact or just another way of viewing electrons in motion, why isn't the
Hall Effect the same sign for all materials?

Fact: If you work out the Hall effect in terms of electrons, the plain old
undressed electrons, you will get the right answer.

Homework (not easy): Convince yourself of that fact.

Hint: As a first step, do the following (vastly easier) warm-up
exercise: Convince yourself that a band that is 100% full contributes
nothing to the current or to the Hall voltage.

Hint, to help with previous hint: Take a completely full shampoo
bottle. Turn it upside down. There are no longer-term
consequences; nothing moves. It is like a completely empty bottle in this
regard! (But in contrast, the story is completely different for bottles
that are 10% or 90% full. There is a longer-term rearrangement of the
viscous contents.)

Huge hint: The second step of the argument involves superposition.

And what about semiconductor devices? The language we hear when people talk
about junctions includes "depleted of charge carriers" and similar wording.
People are referring to holes as something more than just a viewpoint,
aren't they? If so, is this wrong?

Holes are a viewpoint.
No, this is not wrong.
People make viewpoint-dependent statements all the time, and draw
physically-correct conclusions therefrom. For example, just the other day
I saw a sign "Speed Limit 55 MPH" which is obviously not invariant under
changes of reference frame (Galilean relativity). Everybody knows what it
means.

John says bubbles in shampoo is a good idea. I thought that was what I was
describing. When bubbles are rising in a shampoo bottle, the shampoo is
mostly everywhere. It is not localized. The bubbles are localized... not
diffuse... they are identifiable "objects"... and that is what we see
moving. An opposite example would be rain. The water vapor and air are
everywhere... not localized. The raindrops are localized entities,
identifiable objects that we see moving.

This is an unusual usage of "localized" that I had not conceived of. This
usage ruins an otherwise valid analogy, because it makes an invalid
correspondence between the shampoo (singular extensive entity) with the
undressed electrons (multiple individual entities). The correct
correspondence would be between small !parcels! of shampoo and individual
undressed electrons. It may be that the undressed electrons are annoyingly
numerous, but that does mean any particular electron is delocalized in any
physical sense.

The entire "localization" issue is a red herring. Go through all the
previous arguments in favor of the localization explanation, and replace
"localized" by "few" and similarly replace "non-localized" by
"annoyingly-numerous" and it will be easier to see why the arguments have
no physical validity.