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<!DOCTYPE document PUBLIC "-//CNX//DTD CNXML 0.5 plus MathML//EN" "http://cnx.rice.edu/cnxml/0.5/DTD/cnxml_mathml.dtd">
<document xmlns="http://cnx.rice.edu/cnxml" 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="new53">
  <name>Transistor Loads for Inverters</name>
  <metadata>
  <md:version>2.10</md:version>
  <md:created>2000/08/04</md:created>
  <md:revised>2007/08/14 13:18:41.463 GMT-5</md:revised>
  <md:authorlist>
      <md:author id="wlw">
      <md:firstname>Bill</md:firstname>
      
      <md:surname>Wilson</md:surname>
      <md:email>wlw@madriver.net</md:email>
    </md:author>
  </md:authorlist>

  <md:maintainerlist>
    <md:maintainer id="wlw">
      <md:firstname>Bill</md:firstname>
      
      <md:surname>Wilson</md:surname>
      <md:email>wlw@madriver.net</md:email>
    </md:maintainer>
    <md:maintainer id="liqun">
      <md:firstname>Liqun</md:firstname>
      
      <md:surname>Wang</md:surname>
      <md:email>liqun@rice.edu</md:email>
    </md:maintainer>
    <md:maintainer id="lizzardg">
      <md:firstname>Elizabeth</md:firstname>
      
      <md:surname>Gregory</md:surname>
      <md:email>elizabeth.gregory@gmail.com</md:email>
    </md:maintainer>
    <md:maintainer id="jsilv">
      <md:firstname>Jeffrey</md:firstname>
      <md:othername>M</md:othername>
      <md:surname>Silverman</md:surname>
      <md:email>JSilverman@astro.berkeley.edu</md:email>
    </md:maintainer>
    <md:maintainer id="gerardw">
      <md:firstname>Gerard</md:firstname>
      
      <md:surname>Wysocki</md:surname>
      <md:email>gerardw@rice.edu</md:email>
    </md:maintainer>
  </md:maintainerlist>
  
  <md:keywordlist>
    <md:keyword>Inverters</md:keyword>
    <md:keyword>transistor loads</md:keyword>
  </md:keywordlist>

  <md:abstract>Discussing some other kinds of MOSFET's, and transistor loads for inverters.</md:abstract>
</metadata>

  <content>
    <para 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>n-channel enhancement mode MOSFET</term>. It
      turns out that you can build a MOSFET which looks just like a
      <cnxn 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>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>
      <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 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>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>negative</emphasis> gate voltage to turn the
      thing off. <cnxn target="fig40"/> shows comparative
      characteristic curves for an enhancement and depletion mode
      devices.
    </para>


    <figure id="fig40">
      <media type="image/png" src="4.40.png"/>
      <caption>Enhancement and depletion characteristic curves</caption></figure>


    <para 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>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>deplete</emphasis> the
      channel, in order to turn it off. We now have a <term>depletion
      mode n-channel MOSFET</term>.
    </para>


    <para 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 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>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>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 id="fig41">
      <media type="image/png" src="4.41.png"/>
      <caption>Depletion mode load</caption>
    </figure>


    <para id="para5">
      In order to get the transfer characteristic for this circuit,
      we first note that

      <equation 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>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 target="fig42"/>. Noting the intersection points of the
      <term>load line</term> and the characteristic curves allows us
      the opportunity for drawing the <cnxn 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 id="fig42">
      <media type="image/png" src="4.42.png"/>
      <caption>Characteristic curve and load line for a depletion MOS
	load</caption>
    </figure>


    <figure id="fig43">
      <media type="image/png" src="4.43.png"/>
      <caption>Transfer characteristics for a depletion load
	inverter</caption>
    </figure>


    <para 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>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 id="para7">
      Fortunately, we have not run out of options for <cnxn document="m1029">MOS structures</cnxn> yet.
    </para>
  </content>
  
</document>
