Re: Transistorized

[William Beaty <billb@ESKIMO.COM>]

On Wed, 10 Nov 1999, Chuck Britton wrote:

> I remember 'learning' that the beta or hfe rating of a junction
> transistor was the 'current amplification' ratio. The collector
> current was typically 50 to 100 times larger than the base current.
> The Ebers-Moll model goes a bit further by including the (almost
> constant) base-collector voltage drop.
>
> Please let us know when you get a better conceptual model figured out.


Thought you'd never ask!   :)  I've long been meaning to get some ideas
down on paper, and now I have an excuse.


The hfe certainly is the ratio of Ib/Ic, but correlation is not causation.
For example, we could measure the (tiny) current in the gate of Vacuum
Tube and then decide that VTs amplify current.  Yet the operation of a
Vaccum Tube actually employs a voltage to control a current, and a VT is
not a "current amplifier."  If we wished to understand the internal
workings of Vacuum Tubes, it would be foolish to pay attention to the Gate
current or to the I(out)/I(in) ratio.

My problems with Bipolar transistors began when I tried to understand them
as a kid.  I was about 11, and was building a "Thermal IR sensor"  from a
book I'd found.  (Junior Science Projects, Arco publishing.)  I read the
explanations over and over, but they simply would not sink in.
Explanations in more advanced books did no better.  My big "Aha" regarding
Bipolar transistors occurred decades later when I attempted to explain
them to children, and I realized that textbooks do not explain them at
all.  Textbooks show where the design equations originate, but a
disjointed collection of microscopic phenomena and mathematical
connections is not an "explanation."

Once I began to regard the typical transistor explanation with suspicion,
clues started appearing which made great sense to me.  The first one is in
the name itself:  "Transistor."  This name was coined by the inbentors as
a contraction of the words "Transfer Resistor," and it means that a
voltage over HERE can control a current over THERE.  I heard the story
behind the word "transistor" long ago.  However, since it implies that the
Base voltage controls the Collector current, I dismissed it.  I knew that
the inventors of the transistor had it wrong, and that they had been
misled by vacuum-tube concepts . In vacuum tubes the gate potential
controls the anode current.  I thought that the name "Transfer Resistor"
was screwy, since everyone knows that BJTs amplify current.  It turns out
that I was wrong.  The transistor's inventors understood their device
better than I, and they were NOT biased by "vacuum tube" thinking.

Another clue: the "sea of charge" in metals does not resemble the one
within semiconductors.  In metals the "charge-fluid" resembles a nearly
incompressible liquid.  Every metal atom supplies at least one electron,
therefor the particle density of the "liquid" is similar to the particle
density of the metal.  The "liquid" is difficult to compress: if we wished
to sweep the electrons out of a small portion of the metal, staggering
huge voltages would be required.  A doped semiconductor is different.  In
a semiconductor, ideally only the dopant atoms supply mobile charges.  At
typical levels of doping, only one of many billions of atoms supplies an
electron or hole.  As a result, the "fluid charge stuff" inside a
semiconductor resembles a sparse, very compressible gas.  If we wished to
remove all of the charges from a small bit of semiconductor, only a small
voltage is required.  And a semiconductor without mobile charges is not a
conductor.  Because the "electric gas" within semiconductors is
compressible, a semiconductor can be converted from "metal" to "glass"
using electrical signals.  Apply a voltage to doped silicon, and the
electrostatic field compresses the "gas" out of the way and makes part of
the material become nonconductive.  Very weird.  However, things are
starting to fall into place.

Now look at FET operation.  (Those Bell Labs scientists were actually in
pursuit of FETs when they stumbled across the BJT concept.)  In a Field
Effect transistor, the Gate potential controls the width of an insulating
region in the semiconductor.  The Gate potential repels charges, which
sweeps the charges away, which converts part of the silicon from "metal"
(meaning conductive) to "glass" (meaning insulating.)  As this glass-like
region grows in size, it intrudes on a metal-like conducting channel, and
the narrow conducting channel becomes narrower.  Simple.  It's like
squeezing a rubber hose between thumb and finger.  Might there be a crude
fluid analogy for the Bipolar transistor as well?  Yes.

   In bipolar transistors, the Base/Emitter potential controls the
   thickness of a very thin layer of insulator, and the main path
   for the Collector current is THROUGH this thin layer.

That was my big 'Aha.' A bipolar transistor is like a membrane of porus
balsa wood stretched across an air hose, and the thickness of the membrane
is controlled by a low-energy signal.  Or if you prefer an optical
analogy, a BJT is like a neutral-density filter placed in a light beam,
where the opacity of the filter plate can be varied from zero to infinity.

In FETs, the layer of insulator intrudes into the current path FROM THE
SIDE, which narrows the conducting channel.  In BJTs the layer of
insulator appears ACROSS the conducting channel, and by varying its
thickness, the main current is controlled.

So, where exactly is this insulating layer?  It's the "depletion region"
of the diode formed by the Base/Emitter junction.  As with any diode, the
thickness of the depletion region is inversely proportional to the forward
voltage applied across the junction.  The higher the voltage, the thinner
the depletion region, and the higher the output current.  The central idea
behind the transistor is that the forward voltage of one tiny diode can
control the current through a second independant pathway.  Change the
diode voltage, and a huge current can be controlled, yet the "input signal
voltage" draws almost no current itself.  Voltage controls current.

Obviously the above explanation is quite different from the "current
amplification" concept found in most textbooks.  How do we get
conceptually from the "voltage controlled" viewpoint to the "current
amplifier" viewpoint?  If the ratio between the input voltage and the
output current of a Bipolar transistor was linear, then we could mentally
model them as vaccum tubes or FETs, and we could think in terms of
"transimpedance", where the central concept was the ratio of V(in)  to
I(out).  Fortunately there is a trick we can pull which makes circuit
calculations much simpler.

When we apply a control voltage across the Base junction of a Bipolar
transistor, there is a leakage current in the base lead as well as a large
"output current" in the collector lead.  The leakage current in the Base
is directly proportional to the main current in the Collector.  This makes
perfect sense, since both currents pass through the same junction and obey
V/I graphs which have similar shape.  IT'S AS IF THE BASE CURRENT WAS
CONTROLLING THE COLLECTOR CURRENT.

That was the second half of my big "aha."  The "current amplifier" concept
is derived from a convenient method for simplifying transistor
calculations.  If we want to design a Bipolar transistor circuit, we
should imagine that the Vbe is constant at 0.7Vdc, while the Collector
current is proportional to the Base current.  However, if we want to
UNDERSTAND the internal workings of a Bipolar transistor, this mental
model is wrong. Even though Ib is proportional to Ic, Ib does not CAUSE Ic
to vary.  Instead, Vbe is the input signal, and Ib is not important.  Vbe
affects the thickness of the insulating Depletion Layer, and the Depletion
Layer affects the collector current.  A bipolar transistor resembles a
vacuum tube!  And... the term "transfer resistor"  is totally appropriate
after all.

In conclusion, if we teach that Ic is caused by Ib, and that Vbe remains
constant and can usually be ignored, then we are teaching an engineer's
mental model.  This mental model only applies to the large-scale behavior
of Bipolar transistors in circuits.  However, if we try to use this model
to understand what goes on inside that little grain of silicon, then we
are up the wrong creek without a paddle.  The internal workings of BJTs
require a "physicists' model" where Vbe is the input signal, and where the
ratio of Ic/Ib is just an interesting mathematical artifact which has
little bearing on what makes transistors "transist."


All of the above is just a basic mental model.  There are many other
aspects of Bipolar transistor which require explaining, and some are hard
to ignore.  For example, when a transistor is in the normal operating
mode, we can apply a relatively large voltage across the Collector and
Emitter leads, yet this does not affect the Collector current.  Strange!
On the other hand, changing the Vbe by 1/100 of a volt would have a
massive effect upon the depletion layer and upon the Collector current.
Somehow the depletion layer is shielded from the Collector voltage which
is thousands of times higher.


So, does all of this make any more sense than other explanations?


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