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  <name xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Introduction to Bipolar Transistors</name>
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  <md:created xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">2000/08/04</md:created>
  <md:revised xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">2008/05/28 15:56:46.125 GMT-5</md:revised>
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      <md:author xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="wlw">
      <md:firstname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Bill</md:firstname>
      
      <md:surname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Wilson</md:surname>
      <md:email xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">wlw@madriver.net</md:email>
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      <md:firstname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Elizabeth</md:firstname>
      
      <md:surname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Gregory</md:surname>
      <md:email xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">elizabeth.gregory@gmail.com</md:email>
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      <md:firstname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Jeffrey</md:firstname>
      <md:othername xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">M</md:othername>
      <md:surname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Silverman</md:surname>
      <md:email xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">JSilverman@astro.berkeley.edu</md:email>
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      <md:firstname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Gerard</md:firstname>
      
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      <md:firstname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Scott</md:firstname>
      <md:othername xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">W</md:othername>
      <md:surname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Kravitz</md:surname>
      <md:email xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">swkravitz@gmail.com</md:email>
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    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">bipolar</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">transistors</md:keyword>
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  <md:abstract xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Intro to Bipolar Transistors</md:abstract>
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  <content xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
    <para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="para1">
      Let's leave the world of two terminal devices (which are all
      called diodes by the way; diode just means two-terminals) and
      venture into the much more interesting world of three terminals.
      The first device we will look at is called the <term xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">bipolar
      transistor</term>.  Consider the structure shown in <cnxn xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" target="fig1"/>:
    </para>

    <figure xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="fig1">
      <name xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Bipolar Transistor Structure</name>
      <media xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" type="image/png" src="3_1.png"/>
      <caption xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Structure of an NPN bipolar transistor</caption>
    </figure>

    <para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="para2">
      The device consists of three layers of silicon, a heavily doped
      n-type layer called the emitter, a moderately doped p-type layer
      called the base, and third, more lightly doped layer called the
      collector.  In a biasing (applied DC potential) configuration
      called <term xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">forward active biasing</term>, the emitter-base
      junction is forward biased, and the base-collector junction is
      reverse biased. <cnxn xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" target="fig2"/> shows the biasing
      conventions we will use.  Both bias voltages are referenced to
      the base terminal.  Since the base-emitter junction is forward
      biased, and since the base is made of p-type material,

      <m:math>
	<m:ci><m:msub>
	    <m:mi>V</m:mi>
	    <m:mi>EB</m:mi>
	  </m:msub></m:ci>
      </m:math>

      must be negative.  On the other hand, in order to reverse bias
      the base-collector junction

      <m:math>
	<m:ci><m:msub>
	    <m:mi>V</m:mi>
	    <m:mi>CB</m:mi>
	  </m:msub></m:ci>
      </m:math>

      will be a positive voltage.
    </para>

    <figure xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="fig2"><name xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">forward_active_biasing</name><media xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" type="image/png" src="3_2.png">
<param name="print-width" value="4in"/>
</media><caption xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
	Forward active biasing of an npn bipolar transistor</caption></figure>

    <figure xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="fig3">
      <media xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" type="image/png" src="3_3.png"/>
      <caption xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
	Band diagram and carrier fluxes in a bipolar
	transistor</caption>
    </figure>

    <para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="para3">
      Now, let's draw the band-diagram for this device.  At first this
      might seem hard to do, but we know what forward and reverse
      biased band diagrams look like, so we'll just stick one of each
      together.  We show this in <cnxn xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" target="fig3"/>.  <cnxn xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" target="fig3"/> is a very busy figure, but it is also very
      important, because it shows all of the important features in the
      operation the transistor.  Since the base-emitter junction is
      forward biased, electrons will go from the (n-type) emitter into
      the base.  Likewise, some holes from the base will be injected
      into the emitter.
    </para>

    <para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="para4">
      In <cnxn xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" target="fig3"/>, we have two different kinds of arrows.
      The open arrows which are attached to the carriers, show us
      which way the carrier is moving.  The solid arrows which are
      labeled with some kind of subscripted <m:math><m:ci>I</m:ci>
      </m:math>, represent current flow.  We need to do this because
      for holes, motion and current flow are in the same direction,
      while for electrons, carrier motion and current flow are in
      opposite directions.
    </para>

    <para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="para5">
      Just as we saw in the last chapter, the electrons which are
      injected into the base diffuse away from the emitter-base
      junction towards the (reverse biased) base-collector junction.
      As they move through the base, some of the electrons encounter
      holes and recombine with them.  Those electrons which
      <emphasis xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">do</emphasis> get to the base-collector junction run
      into a large electric field which sweeps them out of the base
      and into the collector.  (They "fall" down the large potential
      drop at the junction.)
    </para>

    <para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="para6">
      These effects are all seen in <cnxn xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" target="fig3"/>, with arrows
      representing the various currents which are associated with each
      of the carriers fluxes.

      <m:math>
	<m:ci><m:msub>
	    <m:mi>I</m:mi>
	    <m:mi>Ee</m:mi>
	  </m:msub></m:ci>
      </m:math>

      represents the current associated with the electron injection
      into the base.  (It points in the opposite direction from the
      motion of the electrons, since electrons have a negative
      charge.)

      <m:math>
	<m:ci><m:msub>
	    <m:mi>I</m:mi>
	    <m:mi>Eh</m:mi> 
	  </m:msub></m:ci>
      </m:math>

      represents the current associated with holes injection into the
      emitter from the base.

      <m:math>
	<m:ci><m:msub>
	    <m:mi>I</m:mi>
	    <m:mi>Br</m:mi>
	  </m:msub></m:ci>
      </m:math>

      represents recombination current in the base, while

      <m:math>
	<m:ci><m:msub>
	    <m:mi>I</m:mi>
	    <m:mi>Ce</m:mi>
	  </m:msub></m:ci>
      </m:math>

      represents the electron current going into the collector.  It
      should be easy for you to see that:

      <equation xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="eqn1">
	<m:math>
	  <m:apply><m:eq/>
	    <m:ci><m:msub>
		<m:mi>I</m:mi>
		<m:mi>E</m:mi>
	      </m:msub></m:ci>
	    <m:apply><m:plus/>
	      <m:ci><m:msub>
		  <m:mi>I</m:mi>
		  <m:mi>Ee</m:mi>
		</m:msub></m:ci>
	      <m:ci><m:msub>
		  <m:mi>I</m:mi>
		  <m:mi>Eh</m:mi>
		</m:msub></m:ci>
	    </m:apply>
	  </m:apply>
	</m:math>
      </equation>

      <equation xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="eqn2">
	<m:math>
	  <m:apply><m:eq/>
	    <m:ci><m:msub>
		<m:mi>I</m:mi>
		<m:mi>B</m:mi>
	      </m:msub></m:ci>
	    <m:apply><m:plus/>
	      <m:ci><m:msub>
		  <m:mi>I</m:mi>
		  <m:mi>Eh</m:mi>
		</m:msub></m:ci>
	      <m:ci><m:msub>
		  <m:mi>I</m:mi>
		  <m:mi>Br</m:mi>
		</m:msub></m:ci>
	    </m:apply>
	  </m:apply>
	</m:math>
      </equation>

      <equation xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="eqn3">
	<m:math>
	  <m:apply><m:eq/>
	    <m:ci><m:msub>
		<m:mi>I</m:mi>
		<m:mi>C</m:mi>
	      </m:msub></m:ci>
	    <m:ci><m:msub>
		<m:mi>I</m:mi>
		<m:mi>Ce</m:mi>
	      </m:msub></m:ci>
	  </m:apply>
	</m:math>
      </equation>

    </para>

    <para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="para7">
      In a "good" transistor, almost all of the current across the
      base-emitter junction consists of electrons being injected into
      the base.  The transistor engineer works hard to design the
      device so that very little emitter current is made up of holes
      coming from the base into the emitter.  The transistor is also
      designed so that almost all of those electrons which are
      injected into the base make it across to the base-collector
      reverse-biased junction.  Some recombination is unavoidable, but
      things are arranged so as to minimize this effect.
    </para>
  </content>
  
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