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Transistor Equations

There are several "figures of merit" for the operation of the transistor. The first of these is called the emitter injection efficiency , γ . The emitter injection efficiency is just the ratio of the electron current flowing in the emitter to the totalcurrent across the emitter base junction:

γ I e I Ee I Eh

If you go back and look at the diode equation you will note that the electron forward current across a junction is proportional to N d the doping on the n-side of the junction. Clearly the hole current will be proportional to N a , the acceptor doping on the p-side of the junction. Thus, atleast to first order

γ N d E N d E N a B

(There are some other considerations which we are ignoring in obtaining this expression, but to first order, and for most"real" transistors, is a very good approximation.)

The second "figure of merit" is the base transport factor, α T . The base transport factor tells us what fraction of the electroncurrent which is injected into the base actually makes it to collector junction. This turns out to be given, to a very goodapproximation, by the expression

α T 1 1 2 W B L e 2

Where W B is the physical width of the base region, and L e is the electron diffusion length, defined in the electron diffusion length equation .

L e D e τ r

Clearly, if the base is very narrow compared to the diffusion length, and since the electron concentration is falling off like x L e the shorter the base is compared to L e the greater the fraction of electrons who will actually make it across. We saw before that a typical value for L e might be on the order of 0.005 cm or 50 μm. In a typical bipolar transistor, the base width, W B is usually only a few μm and so α can be quite close to unity as well.

Looking back at this figure , it should be clear that, so long as the collector-base junction remains reverse-biased, the collectorcurrent I Ce , will only depend on how much of the total emitter current actually gets collected by thereverse-biased base-collector junction. That is, the collector current IC is just some fraction of the total emitter current I E . We introduce yet one more constant which reflects the ratio between these two currents, and call it simply" α ." Thus we say

I C α I E

Since the electron current into the base is just γ I E and α T of that current reaches the collector, we can write:

I C α I E α T γ I E

Looking back at the structure of an npn bipolar transistor , we can use Kirchoff's current law for the transistor and say:

I B I E I C I C α I C

This can be re-written to express I C in terms of I B as:

I C α 1 α I B β I B

This is the fundamental operational equation for the bipolar equation. It says that the collector current is dependent onlyon the base current. Note that if α is a number close to (but still slightly less than) unity, then β which is just given by

β α 1 α
will be a fairly large number. Typical values for a will be on the order of 0.99 or greater, which puts β , the current gain, at around 100 or more! This means that we can control, or amplifythe current going into the collector of the transistor with a current 100 times smaller going into the base. This all occursbecause the ratio of the collector current to the base current is fixed by the conditions across the emitter-base junction, andthe ratio of the two, I C to I B is always the same.

Questions & Answers

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In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
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Source:  OpenStax, Introduction to physical electronics. OpenStax CNX. Sep 17, 2007 Download for free at http://cnx.org/content/col10114/1.4
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