Physics of diodes-- question

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Regarding the four graphs (Figure 3.1) found in section 3.3, "3.3.
Full depletion analysis" -->

http://www.mtmi.vu.lt/pfk/funkc_dariniai/diod/schottky.htm

The four graphs alone -->

http://www.mtmi.vu.lt/pfk/funkc_dariniai/images/fig3_3_1.gif

The horizontal axis is distance. The center of the graph, X0, is where
the semiconductor and metal come in contact in the Schottky diode. Xd
is where the depletion zone ends. My question is by how much does the
electrical resistance change throughout the diode? IOW, lets say we
took 3 measurements of resistance; e.g., from X0 to X1, from X1 to X2,
from X2 to Xd. Of course there's no mention of X1, X2, X3 in the
graph, but lets say they are between X0 and Xd. By how much would our
three measurements of resistance vary?  I used to believe the
electrical resistance was nonlinear from X0 to Xd by an appreciable
amount, but now I am wondering if the resistance for the most part is
unchanging from X0 to Xd.

Thanks for any help,
Paul

Re: Physics of diodes-- question
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It might help to let go of the concept of 'resistance' when thinking
about diodes and other semiconductors. Its more about potential
differences. While these might look like a resistance at first glance
(voltage drop vs current flow) the underlying physics is different.

--
Paul Hovnanian    paul@hovnanian.com
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Re: Physics of diodes-- question
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I think potential is also important. I've seen diode graphs of
potential, but never seen any of resistance verses distance at various
locations throughout the diode. Such a graph would be interesting. It
seems to me that the resistance would be relative to how much the
specific area is depleted. I always thought depletion was relative to
the barrier height -->

http://www.mtmi.vu.lt/pfk/funkc_dariniai/images/image431.gif

If my assumption was correct then wouldn't that mean the resistance is
appreciably higher near where the metal-semiconductor come in contact?

Paul

Re: Physics of diodes-- question


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In the normal operation of a diode, the junction can be forward
biased (full conduction) or reverse biased (insulator condition
due to charge carrier depletion in the 'depletion region').   The
constant one calls 'resistance' does not have any
useful descriptive power,

And, it's not a constant in this case.

When current is low, the depletion region is a significant thickness
of insulator.  Actually probing that region (putting wires into it)
is disruptive in many ways, so the usual characterization is done
by determining the junction capacitance as a function of voltage
applied.  Study the C/V relation in a diode, and you can find lots
of data.  Try to study point-by-point resistance, and you're off
in no-data wilderness.

Re: Physics of diodes-- question
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Also a common calculation is for zero bias.


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The term "constant" could be referring to the diode in zero bias for
instance.


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Usually such diode parameters are calculated-- no wires. :-)  For
example Cjo is the capacitance at zero bias.



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What I'm thinking is that such a resistance graph could be calculated
just as the other graphs. Does anyone have a good book recommendation
on the physics (very detailed) of diodes?

Regards,
Paul

Re: Physics of diodes-- question

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What one would calculate, of course, would be resistivity
(the local property) as a function of axial distance, for
a PN diode junction.

Yes, of course, the space charge distribution of a planar
diode is well known, and one can use the known mobilities
of electrons and holes to calculate resistivity from that charge
distribution.    The easiest calculation would be for a so-called
abrupt junction.

The problem is, THOSE ARE EQUILIBRIUM CALCULATIONS.
Shockley, _Electrons and Holes in Semiconductors_ (1950)
 "The resistance of a p-n junction is much greater than the
integrated resistivity of the material composing the junction.
This point follows from the fact that the hole current, for
example, must flow a certain distance in regions where
the density of the carriers is much less than [equilibrium value]"


Re: Physics of diodes-- question
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Thanks for the info and book reference. I'll have to save up to
purchase that book. Amazon.com has a used version for $500. I'm
interested in small signals far below Vt, so equilibrium equations are
fine. Would you say a graph of the diodes point resistance throughout
the diodes depletion region is mostly constant in a Schottky diode
with an abrupt junction?

Regards,
Paul

Re: Physics of diodes-- question



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   Since it's out of print, only used copies are available. I did see
one for under $100. Enter the title at bookfinder.com.

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