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<h2 class="hd hd-2 unit-title">Exercise 4.1</h2>
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<h2>The Bipolar Junction Transistor</h2>
<p><span style="font-size: 1em; line-height: 1.6em;">1) The bipolar junction transistor is a three-terminal device. </span><span style="font-size: 1em; line-height: 1.6em;">In </span><em style="font-size: 1em; line-height: 1.6em;">Forward Active Mode</em><span style="font-size: 1em; line-height: 1.6em;">, the BJT acts as an amplifier.</span><br /><span style="line-height: 1.6;"></span></p>
<p><span style="line-height: 1.6;">2) The three terminals of the BJT are called the Emitter, the Base, and the Collector:</span></p>
<ul>
<li><span style="line-height: 1.6; font-size: 1em;">The Emitter emits majority carriers.</span></li>
<li><span style="line-height: 1.6; font-size: 1em;">A small Base current modulates the flow of carriers from the Emitter to the Collector. Small changes in Base current cause large changes in the E-C current.</span></li>
<li><span style="line-height: 1.6; font-size: 1em;">The Collector collects carriers from the depletion region.</span></li>
</ul>
<p>3) In Forward Active Mode:</p>
<ul>
<li>The E-B junction is forward biased</li>
<li>The B-C junction is reverse biased</li>
<li>The width of the Base \(w_B\) is much smaller than the minority carrier diffusion length \(L_p\) so that the minority carriers survive diffusion through the base. </li>
</ul>
<p>4) The gain \(\beta\) of a BJT is given as follows:</p>
<p>\(\beta = I_C/I_B \cong I_E/I_B = N_{A,E}/N_{D,B}\)</p>
<p>where \(I_C\) is the Collector current, \(I_E\) is the Emitter current (\(I_C \cong I_E\)), \(I_B\) is the Base current, \(N_{A,E}\) is the doping level of the Emitter, and \(N_{D,B}\) is the doping level of the Base.</p>
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Exercise 4.1A
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<p>For a BJT operating in forward-active mode, which of the following statements are correct?</p>
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Exercise 4.1B
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<p>Consider a pnp silicon bipolar junction transistor. The emitter has a doping level of \(5 \times 10^{18} cm^{-3}\), the base has a doping level of \(10^{17} cm^{-3}\), and the collector has a doping level of \(5 \times 10^{15} cm^{-3}\). What is the gain of the transistor in forward-active mode?</p>
<p>\(\beta\):</p>
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<h2 class="hd hd-2 unit-title">Exercise 4.2</h2>
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<h2>The MOS Capacitor</h2>
<p>The MOS Capacitor (Metal-Oxide-Semiconductor) plays an integral role in the MOS transistors that comprise modern electronics. Consider a p-type MOS Capacitor under the following conditions:</p>
<p><strong>Flat-Band Condition:</strong></p>
<p>An ideal MOS capacitor is one in which the work function \(\phi\) of the metal is equal to \(\chi_s + (E_c - E_f)\) in the semiconductor, where \(\chi_s\) is the electron affinity of the semiconductor.</p>
<p>For an ideal MOS capacitor, the flat-band condition occurs when the applied gate voltage \(V_G = 0\). A p-type MOS capacitor under flat-band condition is shown below:</p>
<p><img src="/assets/courseware/v1/2adb46169c2eba5620fd8b1cf3fd42ef/asset-v1:MITX+3.15.1x+2T2017+type@asset+block/315_Ex4_A.jpg" alt="p-type MOS Capacitor; Flat-Band Condition" type="saveimage" target="[object Object]" width="300" height="354" /></p>
<p><strong>Accumulation:</strong></p>
<p>In an ideal p-type MOS capacitor, accumulation occurs when \(V_G < 0\). In accumulation, majority carriers accumulate in the semiconductor near the oxide-semiconductor interface:</p>
<p><img src="/assets/courseware/v1/4bc299f0f9260b1f2f811800e88ee697/asset-v1:MITX+3.15.1x+2T2017+type@asset+block/315_Ex4_B.jpg" alt="p-type MOS capacitor in accumulation" width="300" type="saveimage" target="[object Object]" preventdefault="function (){r.isDefaultPrevented=n}" stoppropagation="function (){r.isPropagationStopped=n}" stopimmediatepropagation="function (){r.isImmediatePropagationStopped=n}" isdefaultprevented="function t(){return!1}" ispropagationstopped="function t(){return!1}" isimmediatepropagationstopped="function t(){return!1}" /></p>
<p><strong>Depletion:</strong></p>
<p><span style="line-height: 25.6px;">In an ideal p-type MOS capacitor, depletion occurs when a small gate voltage \(V_G >0\) is applied to the gate. In depletion, the concentration of majority carriers decreases in the semiconductor near the oxide-semiconductor interface:</span><strong></strong></p>
<p><span style="line-height: 25.6px;"><img src="/assets/courseware/v1/ed3f495176d08c67dde0a2d2f39ed458/asset-v1:MITX+3.15.1x+2T2017+type@asset+block/315_Ex4_3C.jpg" alt="p-type MOS Capacitor under depletion condition" width="300" type="saveimage" target="[object Object]" preventdefault="function (){r.isDefaultPrevented=n}" stoppropagation="function (){r.isPropagationStopped=n}" stopimmediatepropagation="function (){r.isImmediatePropagationStopped=n}" isdefaultprevented="function t(){return!1}" ispropagationstopped="function t(){return!1}" isimmediatepropagationstopped="function t(){return!1}" /></span></p>
<p><strong>Inversion:</strong></p>
<p><span style="line-height: 25.6px;">In an ideal p-type MOS capacitor, inversion</span><span style="line-height: 25.6px;"> occurs when a large gate voltage \(V_G >>0\) is applied to the gate. Once all of the majority carriers have been depleted at the interface, carriers of the opposite type are attracted to this region. This creates a channel of the opposite charge type </span><span style="line-height: 25.6px;">:</span><strong></strong></p>
<p><span style="line-height: 25.6px;"><img src="/assets/courseware/v1/94667cfda9aed9ec63b887523010e8b1/asset-v1:MITX+3.15.1x+2T2017+type@asset+block/315_Ex4_2D.jpg" alt="p-type MOS capacitor under inversion condition" width="300" type="saveimage" target="[object Object]" preventdefault="function (){r.isDefaultPrevented=n}" stoppropagation="function (){r.isPropagationStopped=n}" stopimmediatepropagation="function (){r.isImmediatePropagationStopped=n}" isdefaultprevented="function t(){return!1}" ispropagationstopped="function t(){return!1}" isimmediatepropagationstopped="function t(){return!1}" /></span></p>
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<h3>Exercise 4.2</h3>
<p>Now consider an ideal n-type MOS capacitor. Indicate the applied gate voltage necessary to achieve each condition. </p>
<p>For additional practice, you should sketch out the band diagram for each condition given below. Once you have completed your sketches, click on the "Show Answer" button the check your work.</p>
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data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@37897ff4e9e64b51a542e5e40f4c0a0a" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@37897ff4e9e64b51a542e5e40f4c0a0a/handler/xmodule_handler"
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<h3 class="hd hd-3 problem-header" id="37897ff4e9e64b51a542e5e40f4c0a0a-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@37897ff4e9e64b51a542e5e40f4c0a0a-problem-progress" tabindex="-1">
Exercise 4.2A
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@37897ff4e9e64b51a542e5e40f4c0a0a-problem-progress"></div>
<div class="problem">
<div>
<ul>Depletion:</ul>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_37897ff4e9e64b51a542e5e40f4c0a0a_2_1" class="choicegroup capa_inputtype">
<fieldset aria-describedby="status_37897ff4e9e64b51a542e5e40f4c0a0a_2_1">
<div class="field">
<input id="input_37897ff4e9e64b51a542e5e40f4c0a0a_2_1_choice_0" type="radio" name="input_37897ff4e9e64b51a542e5e40f4c0a0a_2_1" class="field-input input-radio" value="choice_0"/><label id="37897ff4e9e64b51a542e5e40f4c0a0a_2_1-choice_0-label" class="response-label field-label label-inline" aria-describedby="status_37897ff4e9e64b51a542e5e40f4c0a0a_2_1" for="input_37897ff4e9e64b51a542e5e40f4c0a0a_2_1_choice_0"> \(V_G = 0\)
</label>
</div>
<div class="field">
<input id="input_37897ff4e9e64b51a542e5e40f4c0a0a_2_1_choice_1" type="radio" name="input_37897ff4e9e64b51a542e5e40f4c0a0a_2_1" class="field-input input-radio" value="choice_1"/><label id="37897ff4e9e64b51a542e5e40f4c0a0a_2_1-choice_1-label" class="response-label field-label label-inline" aria-describedby="status_37897ff4e9e64b51a542e5e40f4c0a0a_2_1" for="input_37897ff4e9e64b51a542e5e40f4c0a0a_2_1_choice_1"> \(V_G &gt; 0\)
</label>
</div>
<div class="field">
<input id="input_37897ff4e9e64b51a542e5e40f4c0a0a_2_1_choice_2" type="radio" name="input_37897ff4e9e64b51a542e5e40f4c0a0a_2_1" class="field-input input-radio" value="choice_2"/><label id="37897ff4e9e64b51a542e5e40f4c0a0a_2_1-choice_2-label" class="response-label field-label label-inline" aria-describedby="status_37897ff4e9e64b51a542e5e40f4c0a0a_2_1" for="input_37897ff4e9e64b51a542e5e40f4c0a0a_2_1_choice_2"> \(V_G &gt;&gt; 0\)
</label>
</div>
<div class="field">
<input id="input_37897ff4e9e64b51a542e5e40f4c0a0a_2_1_choice_3" type="radio" name="input_37897ff4e9e64b51a542e5e40f4c0a0a_2_1" class="field-input input-radio" value="choice_3"/><label id="37897ff4e9e64b51a542e5e40f4c0a0a_2_1-choice_3-label" class="response-label field-label label-inline" aria-describedby="status_37897ff4e9e64b51a542e5e40f4c0a0a_2_1" for="input_37897ff4e9e64b51a542e5e40f4c0a0a_2_1_choice_3"> \(V_G &lt; 0\)
</label>
</div>
<div class="field">
<input id="input_37897ff4e9e64b51a542e5e40f4c0a0a_2_1_choice_4" type="radio" name="input_37897ff4e9e64b51a542e5e40f4c0a0a_2_1" class="field-input input-radio" value="choice_4"/><label id="37897ff4e9e64b51a542e5e40f4c0a0a_2_1-choice_4-label" class="response-label field-label label-inline" aria-describedby="status_37897ff4e9e64b51a542e5e40f4c0a0a_2_1" for="input_37897ff4e9e64b51a542e5e40f4c0a0a_2_1_choice_4"> \(V_G &lt; &lt; 0\)
</label>
</div>
<span id="answer_37897ff4e9e64b51a542e5e40f4c0a0a_2_1"/>
</fieldset>
<div class="indicator-container">
<span data-tooltip="Not yet answered." id="status_37897ff4e9e64b51a542e5e40f4c0a0a_2_1" class="status unanswered">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<div class="solution-span">
<span id="solution_37897ff4e9e64b51a542e5e40f4c0a0a_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Exercise 4.2A" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_37897ff4e9e64b51a542e5e40f4c0a0a" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_37897ff4e9e64b51a542e5e40f4c0a0a">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
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</div>
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<span class="icon fa fa-save" aria-hidden="true"></span>
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<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
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<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="37897ff4e9e64b51a542e5e40f4c0a0a-problem-title">Answers are displayed within the problem
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<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
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<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-block-type="problem" data-runtime-class="LmsRuntime" data-runtime-version="1" data-has-score="True" data-request-token="604ba3fe4c3811ef857c16fffddbd97f" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITX+3.15.1x+2T2017" data-usage-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@4ea2e071b59f44fb981c970bced4c06f" data-graded="False">
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aria-labelledby="4ea2e071b59f44fb981c970bced4c06f-problem-title"
data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@4ea2e071b59f44fb981c970bced4c06f" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@4ea2e071b59f44fb981c970bced4c06f/handler/xmodule_handler"
data-problem-score="0"
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<h3 class="hd hd-3 problem-header" id="4ea2e071b59f44fb981c970bced4c06f-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@4ea2e071b59f44fb981c970bced4c06f-problem-progress" tabindex="-1">
Exercise 4.2B
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@4ea2e071b59f44fb981c970bced4c06f-problem-progress"></div>
<div class="problem">
<div>
<ul>Accumulation:</ul>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_4ea2e071b59f44fb981c970bced4c06f_2_1" class="choicegroup capa_inputtype">
<fieldset aria-describedby="status_4ea2e071b59f44fb981c970bced4c06f_2_1">
<div class="field">
<input id="input_4ea2e071b59f44fb981c970bced4c06f_2_1_choice_0" type="radio" name="input_4ea2e071b59f44fb981c970bced4c06f_2_1" class="field-input input-radio" value="choice_0"/><label id="4ea2e071b59f44fb981c970bced4c06f_2_1-choice_0-label" class="response-label field-label label-inline" aria-describedby="status_4ea2e071b59f44fb981c970bced4c06f_2_1" for="input_4ea2e071b59f44fb981c970bced4c06f_2_1_choice_0"> \(V_G = 0\)
</label>
</div>
<div class="field">
<input id="input_4ea2e071b59f44fb981c970bced4c06f_2_1_choice_1" type="radio" name="input_4ea2e071b59f44fb981c970bced4c06f_2_1" class="field-input input-radio" value="choice_1"/><label id="4ea2e071b59f44fb981c970bced4c06f_2_1-choice_1-label" class="response-label field-label label-inline" aria-describedby="status_4ea2e071b59f44fb981c970bced4c06f_2_1" for="input_4ea2e071b59f44fb981c970bced4c06f_2_1_choice_1"> \(V_G &gt; 0\)
</label>
</div>
<div class="field">
<input id="input_4ea2e071b59f44fb981c970bced4c06f_2_1_choice_2" type="radio" name="input_4ea2e071b59f44fb981c970bced4c06f_2_1" class="field-input input-radio" value="choice_2"/><label id="4ea2e071b59f44fb981c970bced4c06f_2_1-choice_2-label" class="response-label field-label label-inline" aria-describedby="status_4ea2e071b59f44fb981c970bced4c06f_2_1" for="input_4ea2e071b59f44fb981c970bced4c06f_2_1_choice_2"> \(V_G &gt;&gt; 0\)
</label>
</div>
<div class="field">
<input id="input_4ea2e071b59f44fb981c970bced4c06f_2_1_choice_3" type="radio" name="input_4ea2e071b59f44fb981c970bced4c06f_2_1" class="field-input input-radio" value="choice_3"/><label id="4ea2e071b59f44fb981c970bced4c06f_2_1-choice_3-label" class="response-label field-label label-inline" aria-describedby="status_4ea2e071b59f44fb981c970bced4c06f_2_1" for="input_4ea2e071b59f44fb981c970bced4c06f_2_1_choice_3"> \(V_G &lt; 0\)
</label>
</div>
<div class="field">
<input id="input_4ea2e071b59f44fb981c970bced4c06f_2_1_choice_4" type="radio" name="input_4ea2e071b59f44fb981c970bced4c06f_2_1" class="field-input input-radio" value="choice_4"/><label id="4ea2e071b59f44fb981c970bced4c06f_2_1-choice_4-label" class="response-label field-label label-inline" aria-describedby="status_4ea2e071b59f44fb981c970bced4c06f_2_1" for="input_4ea2e071b59f44fb981c970bced4c06f_2_1_choice_4"> \(V_G &lt; &lt; 0\)
</label>
</div>
<span id="answer_4ea2e071b59f44fb981c970bced4c06f_2_1"/>
</fieldset>
<div class="indicator-container">
<span data-tooltip="Not yet answered." id="status_4ea2e071b59f44fb981c970bced4c06f_2_1" class="status unanswered">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<div class="solution-span">
<span id="solution_4ea2e071b59f44fb981c970bced4c06f_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Exercise 4.2B" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_4ea2e071b59f44fb981c970bced4c06f" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_4ea2e071b59f44fb981c970bced4c06f">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
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<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
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<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="4ea2e071b59f44fb981c970bced4c06f-problem-title">Answers are displayed within the problem
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data-graded="False">
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<span class="sr">Loading…</span>
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aria-labelledby="aa04cfb799434c91b79e1b9238b9360c-problem-title"
data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@aa04cfb799434c91b79e1b9238b9360c" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@aa04cfb799434c91b79e1b9238b9360c/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="1"
data-attempts-used="0"
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<h3 class="hd hd-3 problem-header" id="aa04cfb799434c91b79e1b9238b9360c-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@aa04cfb799434c91b79e1b9238b9360c-problem-progress" tabindex="-1">
Exercise 4.2C
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@aa04cfb799434c91b79e1b9238b9360c-problem-progress"></div>
<div class="problem">
<div>
<ul>Flat-Band:</ul>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_aa04cfb799434c91b79e1b9238b9360c_2_1" class="choicegroup capa_inputtype">
<fieldset aria-describedby="status_aa04cfb799434c91b79e1b9238b9360c_2_1">
<div class="field">
<input id="input_aa04cfb799434c91b79e1b9238b9360c_2_1_choice_0" type="radio" name="input_aa04cfb799434c91b79e1b9238b9360c_2_1" class="field-input input-radio" value="choice_0"/><label id="aa04cfb799434c91b79e1b9238b9360c_2_1-choice_0-label" class="response-label field-label label-inline" aria-describedby="status_aa04cfb799434c91b79e1b9238b9360c_2_1" for="input_aa04cfb799434c91b79e1b9238b9360c_2_1_choice_0"> \(V_G = 0\)
</label>
</div>
<div class="field">
<input id="input_aa04cfb799434c91b79e1b9238b9360c_2_1_choice_1" type="radio" name="input_aa04cfb799434c91b79e1b9238b9360c_2_1" class="field-input input-radio" value="choice_1"/><label id="aa04cfb799434c91b79e1b9238b9360c_2_1-choice_1-label" class="response-label field-label label-inline" aria-describedby="status_aa04cfb799434c91b79e1b9238b9360c_2_1" for="input_aa04cfb799434c91b79e1b9238b9360c_2_1_choice_1"> \(V_G &gt; 0\)
</label>
</div>
<div class="field">
<input id="input_aa04cfb799434c91b79e1b9238b9360c_2_1_choice_2" type="radio" name="input_aa04cfb799434c91b79e1b9238b9360c_2_1" class="field-input input-radio" value="choice_2"/><label id="aa04cfb799434c91b79e1b9238b9360c_2_1-choice_2-label" class="response-label field-label label-inline" aria-describedby="status_aa04cfb799434c91b79e1b9238b9360c_2_1" for="input_aa04cfb799434c91b79e1b9238b9360c_2_1_choice_2"> \(V_G &gt;&gt; 0\)
</label>
</div>
<div class="field">
<input id="input_aa04cfb799434c91b79e1b9238b9360c_2_1_choice_3" type="radio" name="input_aa04cfb799434c91b79e1b9238b9360c_2_1" class="field-input input-radio" value="choice_3"/><label id="aa04cfb799434c91b79e1b9238b9360c_2_1-choice_3-label" class="response-label field-label label-inline" aria-describedby="status_aa04cfb799434c91b79e1b9238b9360c_2_1" for="input_aa04cfb799434c91b79e1b9238b9360c_2_1_choice_3"> \(V_G &lt; 0\)
</label>
</div>
<div class="field">
<input id="input_aa04cfb799434c91b79e1b9238b9360c_2_1_choice_4" type="radio" name="input_aa04cfb799434c91b79e1b9238b9360c_2_1" class="field-input input-radio" value="choice_4"/><label id="aa04cfb799434c91b79e1b9238b9360c_2_1-choice_4-label" class="response-label field-label label-inline" aria-describedby="status_aa04cfb799434c91b79e1b9238b9360c_2_1" for="input_aa04cfb799434c91b79e1b9238b9360c_2_1_choice_4"> \(V_G &lt; &lt; 0\)
</label>
</div>
<span id="answer_aa04cfb799434c91b79e1b9238b9360c_2_1"/>
</fieldset>
<div class="indicator-container">
<span data-tooltip="Not yet answered." id="status_aa04cfb799434c91b79e1b9238b9360c_2_1" class="status unanswered">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<div class="solution-span">
<span id="solution_aa04cfb799434c91b79e1b9238b9360c_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Exercise 4.2C" />
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Exercise 4.2D
</h3>
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<div class="field">
<input id="input_1b527b77f29041f4af273b645b210503_2_1_choice_4" type="radio" name="input_1b527b77f29041f4af273b645b210503_2_1" class="field-input input-radio" value="choice_4"/><label id="1b527b77f29041f4af273b645b210503_2_1-choice_4-label" class="response-label field-label label-inline" aria-describedby="status_1b527b77f29041f4af273b645b210503_2_1" for="input_1b527b77f29041f4af273b645b210503_2_1_choice_4"> \(V_G &lt; &lt; 0\)
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<span id="answer_1b527b77f29041f4af273b645b210503_2_1"/>
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<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
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<h2 class="hd hd-2 unit-title">Exercise 4.3</h2>
<div class="vert-mod">
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<h2>The MOSFET</h2>
<p>Complete the following information about MOSFETs.</p>
<h3>Exercise 4.3A</h3>
<p>Begin by identifying the following components of the MOSFET:</p>
<p><img src="/assets/courseware/v1/eea79a145b5b2c8786540fa0d2742d31/asset-v1:MITX+3.15.1x+2T2017+type@asset+block/315_TransistorSchematic.jpg" alt="MOSFET Schematic" type="saveimage" target="[object Object]" width="500" height="323" /></p>
</div>
</div>
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problem
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@63d3d0f60b394e2da1460d61acb140df-problem-progress"></div>
<div class="problem">
<div>
<p>A:</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="inputtype option-input ">
<select name="input_63d3d0f60b394e2da1460d61acb140df_2_1" id="input_63d3d0f60b394e2da1460d61acb140df_2_1" aria-describedby="status_63d3d0f60b394e2da1460d61acb140df_2_1">
<option value="option_63d3d0f60b394e2da1460d61acb140df_2_1_dummy_default">Select an option</option>
<option value="oxide"> oxide</option>
<option value="depletion region"> depletion region</option>
<option value="n-channel"> n-channel</option>
<option value="metal"> metal</option>
<option value="source"> source</option>
<option value="gate"> gate</option>
<option value="drain"> drain</option>
</select>
<div class="indicator-container">
<span class="status unanswered" id="status_63d3d0f60b394e2da1460d61acb140df_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
<p class="answer" id="answer_63d3d0f60b394e2da1460d61acb140df_2_1"/>
</div></div>
<p>B:</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div class="inputtype option-input ">
<select name="input_63d3d0f60b394e2da1460d61acb140df_3_1" id="input_63d3d0f60b394e2da1460d61acb140df_3_1" aria-describedby="status_63d3d0f60b394e2da1460d61acb140df_3_1">
<option value="option_63d3d0f60b394e2da1460d61acb140df_3_1_dummy_default">Select an option</option>
<option value="oxide"> oxide</option>
<option value="depletion region"> depletion region</option>
<option value="n-channel"> n-channel</option>
<option value="metal"> metal</option>
<option value="source"> source</option>
<option value="gate"> gate</option>
<option value="drain"> drain</option>
</select>
<div class="indicator-container">
<span class="status unanswered" id="status_63d3d0f60b394e2da1460d61acb140df_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
<p class="answer" id="answer_63d3d0f60b394e2da1460d61acb140df_3_1"/>
</div></div>
<p> </p>
<p>C:</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 3" role="group"><div class="inputtype option-input ">
<select name="input_63d3d0f60b394e2da1460d61acb140df_4_1" id="input_63d3d0f60b394e2da1460d61acb140df_4_1" aria-describedby="status_63d3d0f60b394e2da1460d61acb140df_4_1">
<option value="option_63d3d0f60b394e2da1460d61acb140df_4_1_dummy_default">Select an option</option>
<option value="oxide"> oxide</option>
<option value="depletion region"> depletion region</option>
<option value="n-channel"> n-channel</option>
<option value="metal"> metal</option>
<option value="source"> source</option>
<option value="gate"> gate</option>
<option value="drain"> drain</option>
</select>
<div class="indicator-container">
<span class="status unanswered" id="status_63d3d0f60b394e2da1460d61acb140df_4_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
<p class="answer" id="answer_63d3d0f60b394e2da1460d61acb140df_4_1"/>
</div></div>
<p>D:</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 4" role="group"><div class="inputtype option-input ">
<select name="input_63d3d0f60b394e2da1460d61acb140df_5_1" id="input_63d3d0f60b394e2da1460d61acb140df_5_1" aria-describedby="status_63d3d0f60b394e2da1460d61acb140df_5_1">
<option value="option_63d3d0f60b394e2da1460d61acb140df_5_1_dummy_default">Select an option</option>
<option value="oxide"> oxide</option>
<option value="depletion region"> depletion region</option>
<option value="n-channel"> n-channel</option>
<option value="metal"> metal</option>
<option value="source"> source</option>
<option value="gate"> gate</option>
<option value="drain"> drain</option>
</select>
<div class="indicator-container">
<span class="status unanswered" id="status_63d3d0f60b394e2da1460d61acb140df_5_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
<p class="answer" id="answer_63d3d0f60b394e2da1460d61acb140df_5_1"/>
</div></div>
<p>E:</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 5" role="group"><div class="inputtype option-input ">
<select name="input_63d3d0f60b394e2da1460d61acb140df_6_1" id="input_63d3d0f60b394e2da1460d61acb140df_6_1" aria-describedby="status_63d3d0f60b394e2da1460d61acb140df_6_1">
<option value="option_63d3d0f60b394e2da1460d61acb140df_6_1_dummy_default">Select an option</option>
<option value="oxide"> oxide</option>
<option value="depletion region"> depletion region</option>
<option value="n-channel"> n-channel</option>
<option value="metal"> metal</option>
<option value="source"> source</option>
<option value="gate"> gate</option>
<option value="drain"> drain</option>
</select>
<div class="indicator-container">
<span class="status unanswered" id="status_63d3d0f60b394e2da1460d61acb140df_6_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
<p class="answer" id="answer_63d3d0f60b394e2da1460d61acb140df_6_1"/>
</div></div>
<p>F:</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 6" role="group"><div class="inputtype option-input ">
<select name="input_63d3d0f60b394e2da1460d61acb140df_7_1" id="input_63d3d0f60b394e2da1460d61acb140df_7_1" aria-describedby="status_63d3d0f60b394e2da1460d61acb140df_7_1">
<option value="option_63d3d0f60b394e2da1460d61acb140df_7_1_dummy_default">Select an option</option>
<option value="oxide"> oxide</option>
<option value="depletion region"> depletion region</option>
<option value="n-channel"> n-channel</option>
<option value="metal"> metal</option>
<option value="source"> source</option>
<option value="gate"> gate</option>
<option value="drain"> drain</option>
</select>
<div class="indicator-container">
<span class="status unanswered" id="status_63d3d0f60b394e2da1460d61acb140df_7_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
<p class="answer" id="answer_63d3d0f60b394e2da1460d61acb140df_7_1"/>
</div></div>
<p>G:</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 7" role="group"><div class="inputtype option-input ">
<select name="input_63d3d0f60b394e2da1460d61acb140df_8_1" id="input_63d3d0f60b394e2da1460d61acb140df_8_1" aria-describedby="status_63d3d0f60b394e2da1460d61acb140df_8_1">
<option value="option_63d3d0f60b394e2da1460d61acb140df_8_1_dummy_default">Select an option</option>
<option value="oxide"> oxide</option>
<option value="depletion region"> depletion region</option>
<option value="n-channel"> n-channel</option>
<option value="metal"> metal</option>
<option value="source"> source</option>
<option value="gate"> gate</option>
<option value="drain"> drain</option>
</select>
<div class="indicator-container">
<span class="status unanswered" id="status_63d3d0f60b394e2da1460d61acb140df_8_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
<p class="answer" id="answer_63d3d0f60b394e2da1460d61acb140df_8_1"/>
</div></div>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="problem" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_63d3d0f60b394e2da1460d61acb140df" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_63d3d0f60b394e2da1460d61acb140df">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
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is-hidden"
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<h3 class="hd hd-3 problem-header" id="69cbbfc53f7b4cdd831908ccf63ee74b-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@69cbbfc53f7b4cdd831908ccf63ee74b-problem-progress" tabindex="-1">
Exercise 4.3B
</h3>
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<p>
Again consider the n-channel MOSFET shown above. Complete the following statements by selecting the correct terms from the dropdown menus below: </p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="multi-inputs-group" role="group"><p style="display:inline">1) The source and the substrate of the MOSFET are grounded. When a gate voltage </p>
<div class="inputtype option-input inline">
<select name="input_69cbbfc53f7b4cdd831908ccf63ee74b_2_1" id="input_69cbbfc53f7b4cdd831908ccf63ee74b_2_1" aria-describedby="status_69cbbfc53f7b4cdd831908ccf63ee74b_2_1">
<option value="option_69cbbfc53f7b4cdd831908ccf63ee74b_2_1_dummy_default">Select an option</option>
<option value="less than 0"> less than 0</option>
<option value="greater than 0"> greater than 0</option>
<option value="less than the threshold voltage"> less than the threshold voltage</option>
<option value="greater than the threshold voltage"> greater than the threshold voltage</option>
</select>
<div class="indicator-container">
<span class="status unanswered" id="status_69cbbfc53f7b4cdd831908ccf63ee74b_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
<p class="answer" id="answer_69cbbfc53f7b4cdd831908ccf63ee74b_2_1"/>
</div><p style="display:inline">is applied, an n-channel forms, which conducts current from the source to the drain.</p>
<br/>
<br/>
<p style="display:inline">2) If the drain voltage \(V_D\)</p>
<div class="inputtype option-input inline">
<select name="input_69cbbfc53f7b4cdd831908ccf63ee74b_2_2" id="input_69cbbfc53f7b4cdd831908ccf63ee74b_2_2" aria-describedby="status_69cbbfc53f7b4cdd831908ccf63ee74b_2_2">
<option value="option_69cbbfc53f7b4cdd831908ccf63ee74b_2_2_dummy_default">Select an option</option>
<option value="is equal to 0"> is equal to 0</option>
<option value="is less than 0"> is less than 0</option>
<option value="is greater than 0"> is greater than 0</option>
</select>
<div class="indicator-container">
<span class="status unanswered" id="status_69cbbfc53f7b4cdd831908ccf63ee74b_2_2" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
<p class="answer" id="answer_69cbbfc53f7b4cdd831908ccf63ee74b_2_2"/>
</div><p style="display:inline">, then the channel will have uniform width.</p>
<br/>
<br/>
<p style="display:inline">3) When the drain voltage \(V_D\) is greater than zero </p>
<div class="inputtype option-input inline">
<select name="input_69cbbfc53f7b4cdd831908ccf63ee74b_2_3" id="input_69cbbfc53f7b4cdd831908ccf63ee74b_2_3" aria-describedby="status_69cbbfc53f7b4cdd831908ccf63ee74b_2_3">
<option value="option_69cbbfc53f7b4cdd831908ccf63ee74b_2_3_dummy_default">Select an option</option>
<option value="the channel has uniform depth between the source and the drain."> the channel has uniform depth between the source and the drain.</option>
<option value="the channel is deeper near the drain."> the channel is deeper near the drain.</option>
<option value="the channel is less deep near the drain."> the channel is less deep near the drain.</option>
</select>
<div class="indicator-container">
<span class="status unanswered" id="status_69cbbfc53f7b4cdd831908ccf63ee74b_2_3" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
<p class="answer" id="answer_69cbbfc53f7b4cdd831908ccf63ee74b_2_3"/>
</div><br/>
<br/>
<p style="display:inline">4) Additionally, when \(V_D &gt; 0\), </p>
<div class="inputtype option-input inline">
<select name="input_69cbbfc53f7b4cdd831908ccf63ee74b_2_4" id="input_69cbbfc53f7b4cdd831908ccf63ee74b_2_4" aria-describedby="status_69cbbfc53f7b4cdd831908ccf63ee74b_2_4">
<option value="option_69cbbfc53f7b4cdd831908ccf63ee74b_2_4_dummy_default">Select an option</option>
<option value="the depletion region is wider near the drain."> the depletion region is wider near the drain.</option>
<option value="the depletion region is wider near the source."> the depletion region is wider near the source.</option>
</select>
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<span class="status unanswered" id="status_69cbbfc53f7b4cdd831908ccf63ee74b_2_4" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
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<p class="answer" id="answer_69cbbfc53f7b4cdd831908ccf63ee74b_2_4"/>
</div><br/>
<br/>
<p style="display:inline">5) When the drain voltage \(V_D\)</p>
<div class="inputtype option-input inline">
<select name="input_69cbbfc53f7b4cdd831908ccf63ee74b_2_5" id="input_69cbbfc53f7b4cdd831908ccf63ee74b_2_5" aria-describedby="status_69cbbfc53f7b4cdd831908ccf63ee74b_2_5">
<option value="option_69cbbfc53f7b4cdd831908ccf63ee74b_2_5_dummy_default">Select an option</option>
<option value="approaches zero"> approaches zero</option>
<option value="is very low"> is very low</option>
<option value="is very high"> is very high</option>
</select>
<div class="indicator-container">
<span class="status unanswered" id="status_69cbbfc53f7b4cdd831908ccf63ee74b_2_5" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
<p class="answer" id="answer_69cbbfc53f7b4cdd831908ccf63ee74b_2_5"/>
</div><p style="display:inline">pinch-off will occur.</p>
<br/>
<br/>
<p style="display:inline">6) At pinch-off </p>
<div class="inputtype option-input inline">
<select name="input_69cbbfc53f7b4cdd831908ccf63ee74b_2_6" id="input_69cbbfc53f7b4cdd831908ccf63ee74b_2_6" aria-describedby="status_69cbbfc53f7b4cdd831908ccf63ee74b_2_6">
<option value="option_69cbbfc53f7b4cdd831908ccf63ee74b_2_6_dummy_default">Select an option</option>
<option value="the source-drain current can no longer increase."> the source-drain current can no longer increase.</option>
<option value="the source-drain current grows rapidly."> the source-drain current grows rapidly.</option>
<option value="the source-drain current goes to zero."> the source-drain current goes to zero.</option>
</select>
<div class="indicator-container">
<span class="status unanswered" id="status_69cbbfc53f7b4cdd831908ccf63ee74b_2_6" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
<p class="answer" id="answer_69cbbfc53f7b4cdd831908ccf63ee74b_2_6"/>
</div><br/>
<br/>
<p style="display:inline">7) As the gate voltage \(V_G\) increases,</p>
<div class="inputtype option-input inline">
<select name="input_69cbbfc53f7b4cdd831908ccf63ee74b_2_7" id="input_69cbbfc53f7b4cdd831908ccf63ee74b_2_7" aria-describedby="status_69cbbfc53f7b4cdd831908ccf63ee74b_2_7">
<option value="option_69cbbfc53f7b4cdd831908ccf63ee74b_2_7_dummy_default">Select an option</option>
<option value="pinch-off occurs at a lower V_D"> pinch-off occurs at a lower V_D</option>
<option value="pinch-off occurs at a higher V_D"> pinch-off occurs at a higher V_D</option>
<option value="pinch-off no longer occcurs"> pinch-off no longer occcurs</option>
</select>
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<span class="status unanswered" id="status_69cbbfc53f7b4cdd831908ccf63ee74b_2_7" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
<p class="answer" id="answer_69cbbfc53f7b4cdd831908ccf63ee74b_2_7"/>
</div></div></div>
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