What is a hole and how does it relate to electricity?

[I_am_learning]

My idea is this: the Lorenz force causes slightly more electrons to flow along the left of the conductor (ref post # 6). This would mean that more “holes” are formed at the left side, where now the probability of an electron knocking other electrons is higher. This way the fields of the static +ve holes at the left will dominate the Hall field generated by the electron current.

Can I understand what you said like this:
Considering figure post #6, right; Yes the current moves upwards, so due to Lorentz force/field more electrons flows in the left hand side than on the right. However for the more electrons to flow there must be more available holes (since in p-type materials the only way electrons move is my jumping from one hole to the other). So, in addition to more electrons on the left side there is also more holes.
But due to some * reasons, the holes dominate and hence we get the positive polarity!

If this summary is incorrect, you can entirely skip, what I have written below!

However one question has struck to me. Does the existence of hole makes the region spontaneously +ve? I mean to ask, suppose there are two blocks of silicon wafer. One is heavily doped with holes. One isn't doped. Is there a Voltage Deference between them? I guess no, because both are electrically neutral, although the p-type wafer has tendency to accept electrons in expense of its neutrality!
So, I think I got the answer, a Voltage develops after sometime if we connect them with a wire but not initially, is this correct?
If that's correct, then in above scenario, how can holes dominate and give positive polarity? Having holes in a region doesn't spontaneously makes that region +ve!

 

[Per Oni]

thecritic.
You are giving me a real hard time here.

The way I see it is that the slightly increased +ve lattice points at the left are fixed points and can’t go nowhere. Therefore it’s +ve field will stay locally. Conducting electrons on the other hand are infinitely more moveable and will spread their fields through the whole material, left as well as right.

This answer will perhaps still not satisfy you but you must remember that my classical explanation must at some point fail. It’s in a way the same as wondering “why doesn’t an electron slam into the nucleus” In the end the quantum people have the answers.

 

[I_am_learning]

Well, if the correct explanation (which won't evoke any contradictions) can't be provided based on the classical picture, I have no way but to go for Quantum Mechanics.
By the way, I am not too new at Quantum Mechanics (Know as much as the solution of Wave functions for hydrogen atom; but no further).
So, anyone interested at providing Quantum explanation is welcome! After all what I need is an answer that could explain what I have been question for so long!

 

[Studiot]

Here is a quantum explanation that sets out to avoid using holes (although they authors do mention them).

They also provide a basic explanation of Dr Du's comments about negative mass.

http://www.journal.lapen.org.mx/jan09/LAJPE%20225%20Lianxi%20Ma%20Preprint%20f.pdf

 

[I_am_learning]

http://www.journal.lapen.org.mx/jan09/LAJPE%20225%20Lianxi%20Ma%20Preprint%20f.pdf

Thanks for that, I hope that's what I had searching for.
Though I currently have no time to go through the details, one line struct me-

We discuss the details about two situations and point out that both quantum and classical mechanics give same current direction under external electric field. However, under the influence of external magnetic field, because the mass of electrons is negative at valence band, electrons move to the opposite direction of its Lorentz force, which behave like a positive charge and give positive RH.

So, the explanation in bulk is I think about showing that the electrons behave as having +ve Effective Mass for the electric Field but -ve Effective Mass for the Magnetic Field. Thats amazing! I will look at it this afternoon!
Thanks again.

 

[DrDu]

This is exactly my argumentation of post #24, only that I was arguing in terms of the electrons to be removed while in the article they consider the electrons that remain.
The effective mass is negative in both point of views for the reaction to both the electric and the magnetic field, but, if you argue in terms of the electrons that remain, dk/dt and the average k in the stationary state have different directions, here the relevant quote from the article:
"When electric field E is introduced, Eq. (5)
shows that k decreases (dk/dt is negative). But electrons
going out of -k border come back from +k border [3], and
so there are more electrons with +k, which means that
there are more electrons with negative velocity (opposite
to the electric field E)."

 

[I_am_learning]

This is exactly my argumentation of post #24,

O.K, I apologize for not getting you back then.

The effective mass is negative in both point of views for the reaction to both the electric and the magnetic field, but, if you argue in terms of the electrons that remain, dk/dt and the average k in the stationary state have different directions, here the relevant quote from the article:
"When electric field E is introduced, Eq. (5)
shows that k decreases (dk/dt is negative). But electrons
going out of -k border come back from +k border [3], and
so there are more electrons with +k, which means that
there are more electrons with negative velocity (opposite
to the electric field E)."

I followed the whole text but I am no further in position than in my previous post.
Is it that the effective Mass of electrons for electric and magnetic is different because they act along different directions??
Otherwise I have even read that there is not a absolute distinction between electric and magnetic field, what appears as electric field may appear as magnetic field for some other frame of reference!

 

[DrDu]

I again thought about the problem and now I am convinced, that most of the mind boggling effects are due to the utilization of the reduced zone scheme. In an extended zone scheme, we are talking about electrons (or holes) living in a region where the velocity decreases with increasing momentum, but with force and momentum being always parallel. This decrease of velocity is due to increased scattering of the electrons from the lattice with increasing momentum. As a classical analog, think of pulling a parachute behind you. As long as you pull weakly, the parachute is closed and its velocity does increase the stronger you pull. But then there is a region where the parachute starts to open and it gets slower with increasing force and momentum due to its increasing air resistance. A magnetic field would only change the direction of the momentum, but not its absolute value, so the velocity would increase normally with momentum in case of the parachute for a force tangential to the velocity.
This would only describe a differential hall effect. It becomes a true Hall effect if we go over to the reduced zone scheme.

I would like to predict a new kind of Hall effect ( which probably has been observed and described one hundred years ago): Take a light bulb. The current is known to be higher at low voltages when the filament is cold than at higher voltages when the filament is hot. So there is a region where the current gets smaller with increasing temperature. However, this should have no effect on the reaction of the charge carriers to an applied magnetic field. So there is some kind of a negative Hall effect, at least a differential Hall effect, in that system. Obviously, the true Hall effect is defined under isothermal conditions.

 

[Per Oni]

I followed the whole text but I am no further in position than in my previous post.
Is it that the effective Mass of electrons for electric and magnetic is different because they act along different directions??
Otherwise I have even read that there is not a absolute distinction between electric and magnetic field, what appears as electric field may appear as magnetic field for some other frame of reference!

I read the article in post #54 as well and now in addition to thecritc’s valid point I want to add another equally valid objection.

Take the quote from top left of the last page:

Rather, they accelerate toward the direction opposite to the Lorentz force!

I explain my objection:
With the strip of material on right side of the picture in post #6 in mind, imagine underneath this strip of +ve doped material run 2 fixed parallel conducting rails in the x-direction. (Current is in the y and magnetic field in the z direction as shown). Say the distance between these rails is L. The set up is such that the rails and strip are in good electrical contact but the strip can slide, say over a small film of mercury.

Now I can take any material I like to replace the strip but the force F on the strip is always BIL and the direction of this force is always to the left (for the picture shown). So if I make F big enough the strip starts to slide to the left and not right. Therefore the assertion made in this article that the Lorentz force is now in the opposite direction is false!

 

[Per Oni]

Therefore the assertion made in this article that the Lorentz force is now in the opposite direction is false!

Sorry folks, I have clouded this issue. After reading the article again a bit more careful this time I realize I should not have made that claim. Their Lorenz is in the correct direction although the electrons end up on the opposite site they would normally end up. It ‘s very confusing but I still support thecritic in his claims.

 

[Studiot]

I would just like to point out the the Left Hand Rule is predicated upon the use of the direction of conventional current. It is the motor rule and will give the correct direction for force or motion only when the direction of the second finger is aligned with the direction of conventional current.

The Right Hand Rule is the generator rule and gives correct (voltage) polarity, regardless of charge carriers because it defines a voltage, not a current.

When considering the vector cross products the right hand rule should be used in any case.