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Thanks John, I totally get where you are coming form now and I always
appreciate learning the spots in my physics knowledge where I have been
trapped in some form of "introductory" knowledge without knowing there is a
deeper level. I'll have to do some reading on the question of insulators!
Back to my original question, if I may. There is a band gap for Sn, Ge, Si
and C which gets wider as you go down that list, but Pb has no band gap. I
have been told that this is due to the decreasing separation between atoms
in those solids. What I am still working at is where the split that comes
right after Pb comes from. What mechanism is responsible for taking mixed s
and p bands and splitting them when you get closer than roughly the
separation of lead atoms.
Thanks!
Jeff
On Tue, Mar 2, 2010 at 12:55 AM, John Denker<jsd@av8n.com> wrote:
Comparing carbon to silicon,_______________________________________________
On 03/01/2010 09:41 PM, Jeff Loats wrote:
Their bands are indeed carbon copies (nice pun!) but because of theiratomic
separations diamond ends up being an insulator while silicon is a
semiconductor. That is what I mean by similar configurations (same band
structure) but different conduction behaviors.
Aha! I know what the problem is here.
Consider the following statement:
"silicon is a semiconductor, but diamond is an insulator" [1]
I know that every textbook in the world makes such a statement
... but you shouldn't believe everything you read. They can
coerce that statement to be true by definition, but only by
using pathologically foolish definitions.
The main difference between the two is the magnitude of the
band gap.
Silicon: 1.12 eV
Carbon: 5.5 eV
In principle and in practice, it is better to think of carbon
as being a semiconductor with a large-ish band gap.
What matters is not so much the absolute size of the band gap
but rather the _ratio_ of band gap to kT. Specifically, making
a semiconductor device out of carbon is essentially the same
as making the corresponding device out of silicon and running
the latter at a 5x lower temperature. Liquid nitrogen is very
cheap and provides a temperature 4x below room temperature,
which is enough to illustrate the point; liquid helium is 75x
colder than room temperature, which makes the point with more
than an order of magnitude to spare.
Suppose you *wanted* to operate a semiconductor amplifier at
nitrogen temperature (or helium temperature) ... perhaps
because you wanted a really nice low noise temperature and/or
you were measuring a tiny thing inside a cryostat and you
wanted to amplify the signal so as to avoid the scenario where
it gets voltage-dividered into oblivion by the capacitance of
the cable that leads out of the cryostat.
Well, if you take a generic small-signal transistor (2N3904 or
2N3906) and cool it to nitrogen temperature, it doesn't work.
This is not surprising, because it is a _minority carrier_
device and there aren't gonna be any minority carriers when
the band gap is so large compared to kT.
So, in the immortal words of Henny Youngman: Don't do it that
way! Use a majority carrier device, such as a depletion-mode
FET.
http://www.google.com/search?q=cryogenic+transistor+amplifier
This is something sophomores can do with their own hands.
Once they see that silicon is a semiconductor at 77K, it's
obvious that diamond is a semiconductor at room temperature
... just not recommended for minority-carrier devices.
Here's another argument that leads to the same conclusion:
Suppose you wanted an _ultraviolet light emitting diode_.
What are you going to make it out of? Where are you going
to find something with a big enough band gap? You don't
need to guess; the answer is known:
http://www.google.com/search?q=%22n-type+diamond%22
http://www.google.com/search?q=%22p-type+diamond%22
There are about ten other arguments that lead to the same
conclusion. Diamond makes a perfectly terrible insulator.
If you want to know how to make an actual practical
insulator, a large band gap is neither necessary
nor sufficient. The physics of real insulators is
a bit tricky. It's related to the often-asked but
seldom-correctly-answered question of what makes
white things white.
http://www.av8n.com/physics/white.htm
So .... you have a choice.
a) You can try to explain why diamond is categorically
different from silicon, or
b) You can explain why diamond is closely analogous to
silicon, in principle and in practice.
Option (a) is for crazy people. Option (b) is lots easier,
more fun, and more useful.
This has been known for 40 years that I know of. Maybe in
another hundred years or so the textbooks will catch up.
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
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Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l