[sdiy] Charge diffusion conceptual confusion

[ASSI]

On Thursday 31 March 2011, David wrote:
> Now, my problem. In an N type, there are literally free electrons which
> can move and drift and that's easy for me to conceptualize.

No, they are not free electrons in the same sense they are free in metals.  
Forget this picture of the electrons if you want to really understand how a 
semiconductor works.  The n-type electrons can only move when put into the 
conduction band by thermal energy (the donors need to be ionized).  How many 
of them do depends on temperature (shape of the Fermi-Dirac distribution 
folded with the the density of states in the conduction band) and doping 
level (where in the bandgap that distribution is centered).

> But, in a P
> type, the holes are derived from the doping element which is bound in
> the lattice. These holes can be filled/emptied, but they can't move.
> Lastly, I can grasp the concept of electrons flowing in a conductor or
> semi-conductor. But, holes don't "flow" in a conductor, right? So, don't
> the holes just stay in the semiconductor?

They do, but you seem to confuse the defect bonds of the p-dopant for the 
actual holes (just as you seemed to confuse the defect bonds of an n-type 
dopant for a free electron).  I don't blame you, you'll find these 
illustrations in just about any textbook on that subject, but at a certain 
point this gets in the way of understanding what really happens.  So, these 
are not the electrons and holes you are looking for (waves hand in hope to 
complete Jedi mind trick).

You also must not forget that current is a macroscopic quantity (how much 
charge goes through a given cut surface averaged over a certain amount of 
time), or in other words a statistical moment of the actual movement of many 
charges.  If your current is 1A through some wire, that doesn't mean you 
have 6.241e18 electrons coming through per second like peas through a tube, 
it means that of the many more that went back and forth during one second 
6.241e18 more went one direction than the other.  

Same thing with holes on the microscopic level: "hole" is a convenient 
moniker for the (statistical) lack of an electron, which when subjected to 
an electrical field behaves like a positive charge.  If you look at this 
from the Fermi level perspective again, the distribution is shifted towards 
the valence band edge or electrons that are bound to the crystal lattice. 
Since there are more electrons "in demand" than the crystal can offer, this 
will look like a lack of electrons overall.  As with the n-type 
semiconductor you need thermal energy to actually create these movable 
charges, respectively ionize the acceptors.  What is really moving is still 
electrons (between valence states), but they don't move like electrons do in 
an n-type semiconductor (the structure of valence and conduction bands is 
different).  Instead of talking about "those unfilled places for the sort of 
electrons that are moving differently than the other sort of electrons", you 
just say "holes".

If you do the math you'll never be sure about how electrons move either, 
because each "moving" electron actually has a finite probability to be 
_anywhere_ in the whole crystal (periodic infinite boundary conditions...) 
and in that sense it actually is _everywhere_ at the same time.  At that 
point most people are perfectly willing to go back to that picture of 
electrons as little blue balls with a "-" stamped onto them rolling around 
in some dark alleys in the crystal, since that seems to make more sense.  It 
is somewhat disconcerting that they are going uphill on the potential 
slopes, but that seemingly comes with the "-".

> Maybe I should stick to Lagrangian mechanics...

Well, if you know that, you shouldn't have problems wrapping your head 
around the semiconductor equations.  Just avoid to picture charges as 
objects, or if you must, at least as really, really squishy (but not fuzzy) 
ones. :-)


Now you must be confused even more.  Sorry.
Achim.
-- 
+<[Q+ Matrix-12 WAVE#46+305 Neuron microQkb Andromeda XTk Blofeld]>+

Factory and User Sound Singles for Waldorf Blofeld:
http://Synth.Stromeko.net/Downloads.html#WaldorfSounds