# Questions on electron transport in metals

Discussion in 'Electronic Basics' started by Peter, Dec 16, 2004.

1. ### PeterGuest

Hello:

I have a couple of questions on electron transport (in metals):

1. Consider a metal wire connecting the two terminals of a power
source. What exactly happens? Is it correct to say that electrons
behave as particles and flow in the wire at the drift velocity (v)
amidst random thermal motion to produce the required current? [I =
n*(-e)*v*A; I: current, n: free electron density, e: electronic charge,
A: cross section of the wire]

2. What exactly "makes" the electrons to flow? If it is the electric
field, what causes the electric field? Would it be correct to say that
the electrons at one end of the terminal have a higher ionization
potential compared to the other end and that the electric field is just
a convenient way to express this difference in the "potential energy"?

3. Don't electrons themselves, being charged particles, create an
electric field? Shouldn't the electrons so rearrange themselves to
counteract this external field and so stop the flow of current?

4. Does one terminal keep supplying electrons steadily into the wire to
prevent the stagnation of current as mention in Q3 above? If so, is
there a concentration gradient of electrons along the wire from the
source terminal to the drain terminal?

5. What happens if there is a bend in the wire? Shouldn't that affect
the field created by the electrons? Shouldn't it affect the current
flow? In other words will the following two structures have the same
resistance (assume they have the same total length):

S________________D

S____/\______D
S: Source , D: Drain

What, in particular, if the wire dimensions are comparable to the
electron mean free path?

6. I know that the energy of the electron in a metal (or in any
periodic lattice) is related to its momentum through the band
structure. How does this actually affect the particle picture of
electron flow in a metallic wire?

7. I know that, for low electric fields, wave packets of electrons in a
band can be considered to behave as particles obeying Newtons laws to
describe the time dependence of their (crystal) momentum. Please
correct me if my understanding is incorrect/incomplete.
Any answers to enlighten me will be sincerely appreciated.

Peter

2. ### Guest

This paper answers several of your questions:

A unified treatment of electrostatics and circuits
Sherwood & Chabay
http://www4.ncsu.edu/~rwchabay/mi/circuit.pdf

((((((((((((((((((((((( ( ( (o) ) ) )))))))))))))))))))))))
William J. Beaty Research Engineer
UW Chem Dept, Bagley Hall RM74
Box 351700, Seattle, WA 98195-1700
ph206-543-6195 http//staff.washington.edu/wbeaty/

3. ### PeterGuest

Thank you so much for the reference.

Peter

4. ### Guest

In other words, "Why does a battery produce a potential difference,"
or "why does a generator produce a potential difference," or "why does
a solar cell produce a potential difference," or ...

The answer is different for each. The reason for the e-field depends
on the type of energy source.

energy"?

Yes, a few electrons at one end of the wire were originally in a low-
energy state, and these electrons were removed. Electrons in a high-
energy state are placed at the other end of the wire. In some
respects
the long copper wire behaves as a single gigantic atom: electrons
in a high-energy location will travel to a low-energy location,
emitting
phonons as they do (and the wire becomes warm.)

Correct. The current exists in the wire BECAUSE the electrons are
trying to rearrange themselves. But no matter what the electrons do,
there is a charge-pump device which scoops electrons out of one end
of the wire, pushes them up into a higher-energy state, and deposits
them into the other end of the wire.

Yes and yes. But note that, since electrons repel each other,
they will all move slightly in order to force the "region of electron-
imbalance" outwards. The electron-excess at the negative-charged
end of the wire will be found on the surface of the metal. The same
is true of the electron-deficeit on the positive-charged end.
Yes, this is a major issue. It is treated in the paper I referenced in
my earlier message.

In nano-sized semiconductors and in macro-sized vacuum tubes the
mean free path is long. The usual "circuit rules" break down in
both these situations. The electrons in a Klystron or in a CRT
behave very differently than in a resistor. The same is true of
"ballistic transistors."

Except for explaining how resistors work, this issue is mostly ignored
in circuitry explanations. The velocity of electrons during an
electric
current is very low (they move like a clock's minute-hand!)

The energy which is being transferred by electric circuits is not
transferred by electrons, instead it is stored in the EM fields
surrounding the wires, and it does not travel within the metal.
There *is* some EM energy-flow within the metal, but it is directed
radially inwards as the external EM fields lose a bit of energy and
the metal is heated.

((((((((((((((((((((((( ( ( (o) ) ) )))))))))))))))))))))))
William J. Beaty Research Engineer
beaty(a)chem.washington.edu UW Chem Dept, Bagley Hall RM74
billb(a)eskimo.com Box 351700, Seattle, WA 98195-1700
ph206-543-6195 http//staff.washington.edu/wbeaty/

5. ### Bob MastaGuest

A good intuitive example is a pipe full of marbles. If you push
another marble into one end, a marble on the far end moves
out "instantly", even though it is a long way away.

Best regards,

Bob Masta
dqatechATdaqartaDOTcom

D A Q A R T A
Data AcQuisition And Real-Time Analysis
www.daqarta.com

6. ### John LarkinGuest

Not instantly, but at the speed of sound in marbles. Just like the
speed of light for electrons.

John

8. ### MikeGuest

Did you try that? Your intiition fails when the marbles get stuck. You
need a lot of lubrication to perform you 'intuitive' analogy for long
pipes. In contrast, while resistance of wires may increase depending on
dimensions, there is always a finite current flowing and electrons
never get 'stuck'. Thus, your analogy is false. It has no connection
whatsover to current generation and flowing, a phenomenon that its
causes are still subject to hypothesis whilst its effects are detected
experimentally.

Mike

9. ### John LarkinGuest

The "signal", a sudden push at the inlet side of the pipe, can't reach
the output end any faster than the speed of sound in the medium. A
compression wave flows down the pipe and zots the last marble out. For
electrons in a wire in free space, the compression wave flows at c.

Of course, a smooth steady slow flow of marbles will have a uniform
steady-state velocity, just like a steady current moves carriers
slowly.

When NASA first tested the Saturn S1B booster rocket, they
instrumented it with tons of accelerometers and fast telemetry. They
were surprised at first when they fired the main engines and
discovered that the bottom of the rocket accelerated right away, but
the top lagged behind. It took a measurable amount of time for the
force to propagate up the structure at the speed of sound (speed of
sound in the complex structure, of course.)

John

10. ### MikeGuest

No, that's a different situation. The delay is due to the non-rigidity
of the rocker composition, or any large structure for that purpose
which can be modelled in an approximate way by a complex arrangement of
spring-mass-damper systems. The delay in this case is due to the time
constants of those second order dynamical systems.

In the case of the electrons moving in a wire the time constant delay
is due to capacitance and inductance of the wire resulting in 2nd order
dynamics also.

Engineers were introduced to the 'analogies' in 70-80's in an attempt
to provide a unified way of modelling dynamical systems, whether
electrical, mechanical or hydraulic. However the physics behind each of
those systems are very different and any reference to analogies beyond
the concept of a 'model' are inappropriate IMO.

Mike

11. ### Franz HeymannGuest

Not quite instantly.
The pressure you apply at the input end is propagated at the speed of
sound in the marble column

Franz

12. ### John BäckstrandGuest

Not quite instantly.
It is? This seems very un-intuitive to me. Dont know why, it just seems
wrong. Sure, sound is vibration in a medium (?) so it kind-of makes
sense. I guess the speed of sound in very hard materials is very high?

13. ### John LarkinGuest

That speed will, I think, be lower than the speed of sound in an
equivalent solid cylinder of glass. The marbles only touch at small
places, so the coupling is low. Dispersion will be terrible because of
the many random-ish paths (unless they're nicely lined up) so the
pressure pulse at the outlet will be very sloppy. The waveform should
be interesting.

John

14. ### DougGuest

Speed of sound in various solids in m/s from a web stie. I made no attempt
to confirm

Diamond 12000
Pyrex glass 5640
Iron 5130
Aluminum 5100
Brass 4700
Copper 3560
Gold 3240
Lucite 2680
Lead 1322
Rubber 1600

15. ### AndroclesGuest

Yep.

This seems very un-intuitive to me.

Can't think why. If you hit one end of a rubber rod with a hammer
will the other end move instantaneously?
Androcles.

Dont know why, it just seems

16. ### Bob MastaGuest

Mike, it was an *intuitive* example, just to get across the
concept that the speed of information (energy) travel can
be much faster than the speed of the individual carriers.
In that respect it is a very good analogy, because the
reasons in both cases are the same: Each marble pushes
on the one ahead of it, and the force is transmitted
"instantly". (I used quotes to avoid getting into the speed
of sound issue.)

To demonstrate this to kids, I use a piece of PVC about
a foot long, filled with black marbles. A long rubber band runs
from end to end and holds in the marbles. When you
push a marble in one end, you have to overcome the
resistance of the rubber. That aspect may have no
particular analog, but it cause the marble on the far
end to "pop" out of the pipe like magic. When kids
first see this, it fits with the idea that electricity is
instantaneous. I repeat this a few times until they
expect to always see a black marble pop out, but
I've secretly put a white marble a few positions down
the pipe. So when they see a black marble go in
and a white marble pop out, they "get" the idea
that it's not the *same* marble coming out. That's
a very important concept, and leads to a discussion
of the amazing fact that they could *walk* faster
than the electrons move in most ordinary situations.
They can understand that after understanding the
pipe analogy.

Best regards,

Bob Masta
dqatechATdaqartaDOTcom

D A Q A R T A
Data AcQuisition And Real-Time Analysis
www.daqarta.com

17. ### Guest

Androcles wrote:
If you hit one end of a rubber rod with a hammer
No. The information propagates at the speed of sound, as others have
said. It is the same physical process as sound transmission: adjacent
atoms colliding or exerting force on each other.

As for electric signals, they propagate at the speed of light in the
medium. For a typical BNC cable, it's about 2/3 times c.

18. ### Guest

Probably right about the speed of sound being lower than for a solid
object. But, random paths don't necessarily make for sloppy waveforms.
Sound travels through randomized collections of molecules (like air)
just fine, as people are able to speak and hear each other clearly.

19. ### Guest

Simply use frictionless marbles in your thought-experiment.

Or, build a 20cm version, then pretend that no new effects will
arise when applied to a 20KM version.
Your argument is fallacious. If you try to prove that a model is
not an model, by showing that it's imperfect... instead you have
only proved that it's NOTHING BUT a model!

By definition, a model is different than the real-world phenomenon
being modeled. If in the situation where the model is used, the
differences are irrelevant, then the model works well.

If you don't like the "marbles" analogy, here is how to defeat
it. First look at the purpose of the model: to explain electric
circuits to children in a simple way. Then find places in which
the model fails at its task. If the "marbles" analogy gives
more misconceptions to children than it gives them understanding,
then the "marbles" model fails, and nobody should use it.

But if the model gives them major insights, yet gives little or
no misconceptions, then the model is EXCELLENT, and all its
imperfections are irrelevant.

On the other hand, if the same "marbles" analogy was being used
to teach physics grad students about the details of quantum
mechanics of metals, then it would be a bad model.

Yes. Your point? Sound is not an EM wave. That's what "analogy"
means.

20. ### MikeGuest

Bob, I understand your point but my point is that at the end of the day
this type of analogies have an adverse effect in the minds of those
people, the majority that is, who do not understand the purpose of
modelling. It has the potential to create ellusive connections in the
minds of people and eventually turn them into cranks.

I insist this whole approach is wrong although well motivated. There
are discussions going on on this recently and the need to change the
whole approach to teaching physics.

The model you described is problematic, I think highly. It does not
demonstrate how 'information' travels faster than individual carriers.
Simply because there is no indication in your example what kind of
information is transmitted. The information cannot be the carrier
itself. If you try to actually transmit information, you will find out
that dynamics enter into the picture and analogies start failing. As an
example, ask a student to paint the incoming ball a color of his
choice. What color is the ball coming out the other way? If it's not
the same, the information was not transmitted faster than the speed of
individual carriers but exactly at the speed of those carriers, as you
will have to push in several balls until you get the collor one out.
Mike

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