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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/">Transistor Loads for Inverters</name>
  <metadata xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
  <md:version xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">2.10</md:version>
  <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/">2007/08/14 13:18:41.463 GMT-5</md:revised>
  <md:authorlist xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
      <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>
    </md:author>
  </md:authorlist>

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      <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/">Liqun</md:firstname>
      
      <md:surname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Wang</md:surname>
      <md:email xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">liqun@rice.edu</md:email>
    </md:maintainer>
    <md:maintainer xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="lizzardg">
      <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>
    </md:maintainer>
    <md:maintainer xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="gerardw">
      <md:firstname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Gerard</md:firstname>
      
      <md:surname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Wysocki</md:surname>
      <md:email xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">gerardw@rice.edu</md:email>
    </md:maintainer>
  </md:maintainerlist>
  
  <md:keywordlist xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Inverters</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">transistor loads</md:keyword>
  </md:keywordlist>

  <md:abstract xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Discussing some other kinds of MOSFET's, and transistor loads for inverters.</md:abstract>
</metadata>

  <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">
      There are other kinds of MOSFET's besides the one we have
      studied so far. Strictly speaking, what we have seen up to now
      is called an <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/">n-channel enhancement mode MOSFET</term>. It
      turns out that you can build a MOSFET which looks just like a
      <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/" document="m1023" target="fig14">previous figure</cnxn>,
      except that by putting some additional impurities under the gate
      region, we can arrange it so that there is a channel formed,
      even with

      <m:math>
	<m:apply>
	  <m:eq/>
	  <m:ci>
	    <m:msub>
	      <m:mi>V</m:mi>
	      <m:mi>g</m:mi>
	    </m:msub>
	  </m:ci>
	  <m:cn>0</m:cn>
	</m:apply>
      </m:math>.

      The transistor now has a <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/">negative</emphasis>
      <m:math><m:ci><m:msub><m:mi>V</m:mi><m:mi>T</m:mi>
      </m:msub></m:ci></m:math>.  The process by which the additional
      impurities are added is called a <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/">
      <m:math><m:ci><m:msub><m:mi>V</m:mi><m:mi>T</m:mi>
      </m:msub></m:ci></m:math> adjust</term>.
    </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="para2">
      A MOSFET with a negative
      <m:math><m:ci><m:msub><m:mi>V</m:mi><m:mi>T</m:mi>
      </m:msub></m:ci></m:math> can be expected to have

      <m:math>
	<m:apply>
	  <m:minus/>
	  <m:ci>
	    <m:msub>
	      <m:mi>I</m:mi>
	      <m:mi>d</m:mi>
	    </m:msub>
	  </m:ci>
	  <m:ci>
	    <m:msub>
	      <m:mi>V</m:mi>
	      <m:mi>ds</m:mi>
	    </m:msub>
	  </m:ci>
	</m:apply>
      </m:math> curves similar to those for a positive
      <m:math><m:ci><m:msub><m:mi>V</m:mi><m:mi>T</m:mi>
      </m:msub></m:ci></m:math> device, except for one thing. For

      <m:math>
	<m:apply>
	  <m:eq/>
	  <m:ci>
	    <m:msub>
	      <m:mi>V</m:mi>
	      <m:mi>gs</m:mi>
	    </m:msub>
	  </m:ci>
	  <m:cn>0</m:cn>
	</m:apply>
      </m:math>, the device is already turned on, and so we get a
      usual MOSFET-type curve.  <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/">Positive</emphasis> gate
      voltage turns it on even more, while negative
      <m:math><m:ci><m:msub><m:mi>V</m:mi><m:mi>gs</m:mi>
      </m:msub></m:ci></m:math> tends to reduce the drain current. It
      takes a <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/">negative</emphasis> gate voltage to turn the
      thing off. <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="fig40"/> shows comparative
      characteristic curves for an enhancement and depletion mode
      devices.
    </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="fig40">
      <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="4.40.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/">Enhancement and depletion characteristic curves</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">
      For an enhancement mode transistor, you have to get
      <m:math>
	<m:apply>
	  <m:gt/>
	  <m:ci>
	    <m:msub>
	      <m:mi>V</m:mi>
	      <m:mi>g</m:mi>
	    </m:msub>
	  </m:ci>
	  <m:ci>
	    <m:msub>
	      <m:mi>V</m:mi>
	      <m:mi>T</m:mi>
	    </m:msub>
	  </m:ci>
	</m:apply>
      </m:math> (-1 Volt in this example) to
      <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/">enhance</emphasis> the conductivity or channel to make
      it conduct. For a depletion mode device, a gate voltage Vgs of
      0, still finds the device conducting. You have to put some
      negative voltage on the gate to <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/">deplete</emphasis> the
      channel, in order to turn it off. We now have a <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/">depletion
      mode n-channel MOSFET</term>.
    </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">
      How would we use a depletion mode device in an inverter gate?
      The answer is fairly straight-forward. In the schematic 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="fig41"/>, we indicate a depletion mode MOSFET by adding
      a second line, under the gate, to suggest that a channel already
      exists in the device, even with no
      <m:math><m:ci><m:msub><m:mi>V</m:mi><m:mi>g</m:mi>
      </m:msub></m:ci></m:math>.  Note that the gate of the depletion
      mode transistor (also sometimes 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/">pull up</term>
      transistor) is connected to its source, so, in fact,
      <m:math><m:ci><m:msub><m:mi>V</m:mi><m:mi>gs</m:mi>
      </m:msub></m:ci></m:math> does equal 0 for this device. The
      input transistor (or 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/">pull down</term> transistor) is
      just an enhancement mode MOSFET like we had before. It is not
      hard to choose appropriate <m:math><m:ci>W</m:ci></m:math> and
      <m:math><m:ci>L</m:ci></m:math> so that
      <m:math><m:ci><m:msub><m:mi>I</m:mi><m:mi>dsat</m:mi>
      </m:msub></m:ci></m:math> for the pull up transistor is on the
      order of the 500 μA that we need to get our 1 ns rise time
      on the capacitive load.
    </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="fig41">
      <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="4.41.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/">Depletion mode load</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="para5">
      In order to get the transfer characteristic for this circuit,
      we first note 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="eqn55">
	<m:math>
	  <m:apply>
	    <m:eq/>
	    <m:ci>
	      <m:msub>
		<m:mi>V</m:mi>
		<m:mi>sdd</m:mi>
	      </m:msub>
	    </m:ci>

	    <m:apply>
	      <m:minus/>
	      <m:ci>
		<m:msub>
		  <m:mi>V</m:mi>
		  <m:mi>dd</m:mi>
		</m:msub>
	      </m:ci>
	      <m:ci>
		<m:msub>
		  <m:mi>V</m:mi>
		  <m:mi>sde</m:mi>
		</m:msub>
	      </m:ci>
	    </m:apply>
	  </m:apply>
	</m:math>
      </equation>

      where <m:math><m:ci><m:msub><m:mi>V</m:mi><m:mi>sde</m:mi>
      </m:msub></m:ci></m:math> is the source-drain voltage for the
      pull-down, or enhancement transistor, and
      <m:math><m:ci><m:msub><m:mi>V</m:mi><m:mi>sdd</m:mi>
      </m:msub></m:ci></m:math>, is the source-drain voltage for the
      depletion-mode transistor. If we want to plot 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/">load-line</term> for the pull-down transistor that is
      created by the pull-up or depletion mode transistor, we should
      take its
      <m:math>
	<m:apply>
	  <m:eq/>
	  <m:ci>
	    <m:msub>
	      <m:mi>V</m:mi>
	      <m:mi>gs</m:mi>
	    </m:msub>
	  </m:ci>
	  <m:cn>0</m:cn>
	</m:apply>
      </m:math> characteristic curve, shift it over by an amount
      <m:math><m:ci><m:msub><m:mi>V</m:mi><m:mi>dd</m:mi>
      </m:msub></m:ci></m:math>, and then reverse its polarity. When
      we do this we get the following 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="fig42"/>. Noting the intersection points of 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/">load line</term> and the characteristic curves allows us
      the opportunity for drawing the <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="fig43">transfer
      characteristic</cnxn>. This is a better looking curve. It is
      symmetric around the mid-voltage point, and gets closer to zero
      for its output "low" condition. The transition from "high" to
      "low" is also somewhat more abrupt, which is advantageous. Can
      you figure out why?
    </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="fig42">
      <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="4.42.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/">Characteristic curve and load line for a depletion MOS
	load</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="fig43">
      <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="4.43.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/">Transfer characteristics for a depletion load
	inverter</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="para6">
      Well, we solved one problem. At least we have a pull up
      structure that we can manufacture. It turns out not to be too hard to
      build an enhancement MOSFET that has an equivalent resistance in the
      range we need without taking up too much chip area. We have not
      solved the other problem however. We are still looking at a
      <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/">huge</emphasis> current draw for large circuits. Since on
      average, half of the inverter gates will be "on" in a
      logic circuit, we still have a large current sink to ground. This is
      something that would be completely prohibitive in a modern-day VLSI
      integrated circuit.
    </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">
      Fortunately, we have not run out of options for <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/" document="m1029">MOS structures</cnxn> yet.
    </para>
  </content>
  
</document>
