Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: HOLES AS CARRIERS

On Sun, 7 Oct 2001, Ludwik Kowalski wrote:
In truth, a hole acts to "expose" the positive charge of the
silicon's protons which normally would be canceled out.
It's easy to concentrate on the emptiness of the "hole"
while forgetting that a hole is most definitely a positive
charge carrier.

After being satisfied with the explanation of the "positivity
of holes" I started thinking about it and I am less satisfied.

Well, let's take a semi-classical look at p-type semiconductor. (I hope I
have the following correct.)

Single-crystal silicon is a fairly good insulator because each silicon
atom has an outer filled electron shell after it bonds with four
neighboring atoms. There are almost no mobile charges available to support
a current.

Suppose I place a single dopant atom into a hunk of silicon, and the atom
is an "acceptor" type such as Boron, with only three outer electrons. In
that case everything is still neutral (the Boron atom still has equal
numbers of protons and electrons, as do all the silicon atoms.) However,
the Boron atom has an unfilled outer electron shell. There's a "hole" in
the crystal's electron bond lattice, and electrons from adjacent Silicon
atoms could move into this hole, although the hole is still neutral at
this point.

Now suppose that we jostle the crystal lattice with thermal vibrations.
One electron from an adjacent silicon atom is able to move into the
unfilled shell of the Boron atom, filling it. THIS CREATES AN ION PAIR.
The Boron atom has become a negative ion, but an ion having a filled outer
shell. The adjacent Silicon atom has become a positive ion, but one with
an unfilled outer shell. One would expect the electron to be attracted
back to the positively-charged Boron atom, and this does happen at low
temperatures. But at room temperature the forces caused by thermal motion
are fierce, and the electrical attraction is negligable.

Next, an electron from any neighboring neutral Silicon atom can fall into
the unfilled shell of our positive silicon ion we created above. A
distant observer would see a positive Silicon ion in one location vanish,
while a positive Silicon ion in an adjacent location suddenly appears.
This *looks* like a moving Silicon ion, but it actually is caused by
electrons leaving the filled shell of a neutral atom and falling into the
unfilled shell of an adjacent positive ion. To recap: a distant observer
at first would see a neutral Boron atom imbedded in neutral silicon, then
suddenly the Boron atom would become negative, and at the same time a
positive Silicon ion would go wandering off across the lattice.

All materials are made of atoms, systems containing
charged particles (electrons and protons). We learn that
there are no particles called holes, unless the "emptiness",
full of fields, is treated as a set of holes.

The "hole" is one unfilled outer electron shell in one crystal atom,
where all the other crystal atoms have filled shells. Note that this says
nothing about holes having a positive charge! It is only when the "hole"
moves away from its Boron atom that it appears to aquire a positive
charge.

Observed at the macro scale, P-type silicon appears to be made of mostly
neutral Silicon which contains an extremely sparse distrubution of
negative Boron ions and positive Silicon ions, and where the positive
Silicon ions are apparently wandering about.


A uniform semiconductor, n or p, is electrically neutral. It
remains neutral when a current flows through it due to an
applied difference of potentials. The same is true for metals.

Yep.

But we do not say that a free electron, drifting from point
A to point B, creates a positively charged region near A.

With metals we do not, but this is because the positive metal ion created
as the electron leaves point A is rapidly filled by a third electron. And
as the electron moves to point B, it must push a fourth electron out of
its way. In metals the mobile electrons are as dense as the lattice (one
mobile electron per metal atom.) In doped silicon, a typical doping
density creates only one mobile charge per 10^19 atoms. In other words:

IN METALS, THE MOBILE ELECTRONS ACT LIKE A LIQUID. IT'S NEARLY
INCOMPRESSIBLE, AND THE LINES OF FLUID-FLOW TAKE THE FORM OF CLOSED
LOOPS.

IN DOPED SEMICONDUCTORS, THE ELECTRON FLUID IS LIKE A GAS. IT'S
EASILY COMPRESSED BY SMALL DIFFERENCES IN POTENTIAL, AND LARGE
REGIONS OF "VACUUM" CAN BE CREATED AS DESIRED.


Why not? What we are saying is that the drift of electrons in
one direction is equivalent to the drift of positive charges.

The central difference is caused by the density of mobile charges; the
difference between "liquid" and "gas" behavior.


I am not able to make a good connection between the idea
of donors/acceptors and holes. Thermal transfers of trapped
electrons (from donor atoms or to acceptor atoms), and
reverse processes near-by, can probably be visualized as
random displacements. They occur even when the imposed
electric field is zero. Note that I am referring to uniform
materials, not to junctions.

If presence of acceptors is equivalent to holes then presence
of donors should also be equivalent to holes,

Close. Presence of donors is equivalent to positive ions. But these ions
are not mobile, just as the negative Boron ions are not mobile. When the
Phosphorus n-dopant atom loses its extra electron, it becomes a
non-moving positive ion, while the wandering electron temporarily creates
negative Silicon ions wherever it wanders.


unless a hole
is not simply a place in which neutrality is locally destroyed
for a short period of time. Clearly something is missing in
my mental image of reality. Is it because I am using the
semi-classical way of thinking about tiny particles (accepting
the QM band structure without abandoning the idea of
classical drifting) ?

It's the doping density that's the issue. Metal wires are like pipes
full of water, while silicon wires are like pipes full of gas.


In a message I already deleted Bill wrote that it is wrong to
identify a macroscopic current I (measured by an instrument)
with electrons drifting in metallic conductors. I do not agree.

Consider a wire element dL

Ah, but consider a *conductor* element dL. "Conductor" doesn't mean
"metal wire."

Suppose I have a plastic tube full of salt water with one ampere flowing
through it. Suppose I put a clamp-on ammeter around this tube. It
indicates one ampere. I can do the same with a neon sign tube, or a tube
with an electron beam, or a tube filled with liquid mercury. I can even
measure DC if I have one of those hall-sensor clampon ammeters. My point
is that ammeters cannot know the polarity of the particles or the
direction or their velocity. Ammeters only know the coulombs per second
and the [polarity * direction]. Or must we say that a clamp-on ammeter is
not really an ammeter?


((((((((((((((((((((( ( ( ( ( (O) ) ) ) ) )))))))))))))))))))))
William J. Beaty SCIENCE HOBBYIST website
billb@eskimo.com http://www.amasci.com
EE/programmer/sci-exhibits science projects, tesla, weird science
Seattle, WA 206-789-0775 freenrg-L taoshum-L vortex-L webhead-L