<div class="xblock xblock-public_view xblock-public_view-vertical" data-block-type="vertical" data-runtime-class="LmsRuntime" data-runtime-version="1" data-has-score="False" data-request-token="ec7168dc4c3811ef857c16fffddbd97f" data-init="VerticalStudentView" data-course-id="course-v1:MITX+3.15.1x+2T2017" data-usage-id="block-v1:MITX+3.15.1x+2T2017+type@vertical+block@1ba5407ae8de4af1b27e8be498dd7587" data-graded="False">
<h2 class="hd hd-2 unit-title">Example 3.1</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@7de767f3c837413e885b1c0292cd34b8">
<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="ec7168dc4c3811ef857c16fffddbd97f" 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@7de767f3c837413e885b1c0292cd34b8" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_7de767f3c837413e885b1c0292cd34b8" class="problems-wrapper" role="group"
aria-labelledby="7de767f3c837413e885b1c0292cd34b8-problem-title"
data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@7de767f3c837413e885b1c0292cd34b8" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@7de767f3c837413e885b1c0292cd34b8/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="7de767f3c837413e885b1c0292cd34b8-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@7de767f3c837413e885b1c0292cd34b8-problem-progress" tabindex="-1">
problem
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@7de767f3c837413e885b1c0292cd34b8-problem-progress"></div>
<div class="problem">
<div>
<h2>The Unbiased pn-Junction</h2>
<p>First, we are going to consider an unbiased p-n junction.</p>
<h3 class="hd hd-2 problem-header">Exercise 3.1A</h3>
<p>Complete this exercise by drawing the following on a piece of paper. When you have completed your drawings, press the "Show Answer" button to check your work.</p>
<p>Begin by drawing the equilibrium energy diagram for a silicon step junction. Assume that the p-side has \(N_A = 10^{17}/cm^3\) and the n-side has \(N_D = 10^{18}/cm^3\).</p>
<div class="solution-span">
<span id="solution_7de767f3c837413e885b1c0292cd34b8_solution_1"/>
</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_7de767f3c837413e885b1c0292cd34b8" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_7de767f3c837413e885b1c0292cd34b8">
<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>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="7de767f3c837413e885b1c0292cd34b8-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="7de767f3c837413e885b1c0292cd34b8-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="7de767f3c837413e885b1c0292cd34b8-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITX+3.15.1x+2T2017+type@html+block@96f2f00e90344bf3a9e3987441c7b07e">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-block-type="html" data-runtime-class="LmsRuntime" data-runtime-version="1" data-has-score="False" data-request-token="ec7168dc4c3811ef857c16fffddbd97f" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITX+3.15.1x+2T2017" data-usage-id="block-v1:MITX+3.15.1x+2T2017+type@html+block@96f2f00e90344bf3a9e3987441c7b07e" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<h3>Exercise 3.1B</h3>
<p>Indicate the direction of the drift and diffusion of electrons and holes across the junction. Remember:</p>
<ul style="line-height: 25.6px;">
<li><span style="font-size: 1em; line-height: 1.6em;">Carriers diffuse from areas of high concentration to areas of low concentration.</span></li>
<li>Electrons drift down the band. </li>
<li>Holes drift up the band. </li>
</ul>
</div>
</div>
<div class="vert vert-2" data-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@7bc8f1adb9de479797ba5f0858232fe2">
<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="ec7168dc4c3811ef857c16fffddbd97f" 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@7bc8f1adb9de479797ba5f0858232fe2" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_7bc8f1adb9de479797ba5f0858232fe2" class="problems-wrapper" role="group"
aria-labelledby="7bc8f1adb9de479797ba5f0858232fe2-problem-title"
data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@7bc8f1adb9de479797ba5f0858232fe2" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@7bc8f1adb9de479797ba5f0858232fe2/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="4"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="7bc8f1adb9de479797ba5f0858232fe2-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@7bc8f1adb9de479797ba5f0858232fe2-problem-progress" tabindex="-1">
problem
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@7bc8f1adb9de479797ba5f0858232fe2-problem-progress"></div>
<div class="problem">
<div>
<p>What is the direction of electron diffusion?</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_7bc8f1adb9de479797ba5f0858232fe2_2_1">
<fieldset aria-describedby="status_7bc8f1adb9de479797ba5f0858232fe2_2_1">
<div class="field">
<input type="radio" name="input_7bc8f1adb9de479797ba5f0858232fe2_2_1" id="input_7bc8f1adb9de479797ba5f0858232fe2_2_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="7bc8f1adb9de479797ba5f0858232fe2_2_1-choice_0-label" for="input_7bc8f1adb9de479797ba5f0858232fe2_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_7bc8f1adb9de479797ba5f0858232fe2_2_1"> The electrons diffuse from left to right
</label>
</div>
<div class="field">
<input type="radio" name="input_7bc8f1adb9de479797ba5f0858232fe2_2_1" id="input_7bc8f1adb9de479797ba5f0858232fe2_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="7bc8f1adb9de479797ba5f0858232fe2_2_1-choice_1-label" for="input_7bc8f1adb9de479797ba5f0858232fe2_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_7bc8f1adb9de479797ba5f0858232fe2_2_1"> The electrons diffuse from right to left
</label>
</div>
<div class="field">
<input type="radio" name="input_7bc8f1adb9de479797ba5f0858232fe2_2_1" id="input_7bc8f1adb9de479797ba5f0858232fe2_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="7bc8f1adb9de479797ba5f0858232fe2_2_1-choice_2-label" for="input_7bc8f1adb9de479797ba5f0858232fe2_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_7bc8f1adb9de479797ba5f0858232fe2_2_1"> There is no net electron diffusion
</label>
</div>
<span id="answer_7bc8f1adb9de479797ba5f0858232fe2_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_7bc8f1adb9de479797ba5f0858232fe2_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<p>What is the direction of hole diffusion?</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div class="choicegroup capa_inputtype" id="inputtype_7bc8f1adb9de479797ba5f0858232fe2_3_1">
<fieldset aria-describedby="status_7bc8f1adb9de479797ba5f0858232fe2_3_1">
<div class="field">
<input type="radio" name="input_7bc8f1adb9de479797ba5f0858232fe2_3_1" id="input_7bc8f1adb9de479797ba5f0858232fe2_3_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="7bc8f1adb9de479797ba5f0858232fe2_3_1-choice_0-label" for="input_7bc8f1adb9de479797ba5f0858232fe2_3_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_7bc8f1adb9de479797ba5f0858232fe2_3_1"> The holes diffuse from left to right
</label>
</div>
<div class="field">
<input type="radio" name="input_7bc8f1adb9de479797ba5f0858232fe2_3_1" id="input_7bc8f1adb9de479797ba5f0858232fe2_3_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="7bc8f1adb9de479797ba5f0858232fe2_3_1-choice_1-label" for="input_7bc8f1adb9de479797ba5f0858232fe2_3_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_7bc8f1adb9de479797ba5f0858232fe2_3_1"> The holes diffuse from right to left
</label>
</div>
<div class="field">
<input type="radio" name="input_7bc8f1adb9de479797ba5f0858232fe2_3_1" id="input_7bc8f1adb9de479797ba5f0858232fe2_3_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="7bc8f1adb9de479797ba5f0858232fe2_3_1-choice_2-label" for="input_7bc8f1adb9de479797ba5f0858232fe2_3_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_7bc8f1adb9de479797ba5f0858232fe2_3_1"> There is no net hole diffusion
</label>
</div>
<span id="answer_7bc8f1adb9de479797ba5f0858232fe2_3_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_7bc8f1adb9de479797ba5f0858232fe2_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<p>What is the direction of electron drift?</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 3" role="group"><div class="choicegroup capa_inputtype" id="inputtype_7bc8f1adb9de479797ba5f0858232fe2_4_1">
<fieldset aria-describedby="status_7bc8f1adb9de479797ba5f0858232fe2_4_1">
<div class="field">
<input type="radio" name="input_7bc8f1adb9de479797ba5f0858232fe2_4_1" id="input_7bc8f1adb9de479797ba5f0858232fe2_4_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="7bc8f1adb9de479797ba5f0858232fe2_4_1-choice_0-label" for="input_7bc8f1adb9de479797ba5f0858232fe2_4_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_7bc8f1adb9de479797ba5f0858232fe2_4_1"> The electrons drift from left to right
</label>
</div>
<div class="field">
<input type="radio" name="input_7bc8f1adb9de479797ba5f0858232fe2_4_1" id="input_7bc8f1adb9de479797ba5f0858232fe2_4_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="7bc8f1adb9de479797ba5f0858232fe2_4_1-choice_1-label" for="input_7bc8f1adb9de479797ba5f0858232fe2_4_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_7bc8f1adb9de479797ba5f0858232fe2_4_1"> The electrons drift from right to left
</label>
</div>
<div class="field">
<input type="radio" name="input_7bc8f1adb9de479797ba5f0858232fe2_4_1" id="input_7bc8f1adb9de479797ba5f0858232fe2_4_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="7bc8f1adb9de479797ba5f0858232fe2_4_1-choice_2-label" for="input_7bc8f1adb9de479797ba5f0858232fe2_4_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_7bc8f1adb9de479797ba5f0858232fe2_4_1"> There is no net electron ddrift
</label>
</div>
<span id="answer_7bc8f1adb9de479797ba5f0858232fe2_4_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_7bc8f1adb9de479797ba5f0858232fe2_4_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<p>What is the direction of hole drift?</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 4" role="group"><div class="choicegroup capa_inputtype" id="inputtype_7bc8f1adb9de479797ba5f0858232fe2_5_1">
<fieldset aria-describedby="status_7bc8f1adb9de479797ba5f0858232fe2_5_1">
<div class="field">
<input type="radio" name="input_7bc8f1adb9de479797ba5f0858232fe2_5_1" id="input_7bc8f1adb9de479797ba5f0858232fe2_5_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="7bc8f1adb9de479797ba5f0858232fe2_5_1-choice_0-label" for="input_7bc8f1adb9de479797ba5f0858232fe2_5_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_7bc8f1adb9de479797ba5f0858232fe2_5_1"> The holes drift from left to right
</label>
</div>
<div class="field">
<input type="radio" name="input_7bc8f1adb9de479797ba5f0858232fe2_5_1" id="input_7bc8f1adb9de479797ba5f0858232fe2_5_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="7bc8f1adb9de479797ba5f0858232fe2_5_1-choice_1-label" for="input_7bc8f1adb9de479797ba5f0858232fe2_5_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_7bc8f1adb9de479797ba5f0858232fe2_5_1"> The holes drift from right to left
</label>
</div>
<div class="field">
<input type="radio" name="input_7bc8f1adb9de479797ba5f0858232fe2_5_1" id="input_7bc8f1adb9de479797ba5f0858232fe2_5_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="7bc8f1adb9de479797ba5f0858232fe2_5_1-choice_2-label" for="input_7bc8f1adb9de479797ba5f0858232fe2_5_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_7bc8f1adb9de479797ba5f0858232fe2_5_1"> There is no net hole drift
</label>
</div>
<span id="answer_7bc8f1adb9de479797ba5f0858232fe2_5_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_7bc8f1adb9de479797ba5f0858232fe2_5_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<div class="solution-span">
<span id="solution_7bc8f1adb9de479797ba5f0858232fe2_solution_1"/>
</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_7bc8f1adb9de479797ba5f0858232fe2" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_7bc8f1adb9de479797ba5f0858232fe2">
<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>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="7bc8f1adb9de479797ba5f0858232fe2-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="7bc8f1adb9de479797ba5f0858232fe2-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="7bc8f1adb9de479797ba5f0858232fe2-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-3" data-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@00d703ca980f45e8ac2b76ef757b56f6">
<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="ec7168dc4c3811ef857c16fffddbd97f" 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@00d703ca980f45e8ac2b76ef757b56f6" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_00d703ca980f45e8ac2b76ef757b56f6" class="problems-wrapper" role="group"
aria-labelledby="00d703ca980f45e8ac2b76ef757b56f6-problem-title"
data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@00d703ca980f45e8ac2b76ef757b56f6" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@00d703ca980f45e8ac2b76ef757b56f6/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="00d703ca980f45e8ac2b76ef757b56f6-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@00d703ca980f45e8ac2b76ef757b56f6-problem-progress" tabindex="-1">
Exercise 3.1C
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@00d703ca980f45e8ac2b76ef757b56f6-problem-progress"></div>
<div class="problem">
<div>
<p>Now sketch the charge density profile, the electric field profile, and the potential inside the junction. Use the depletion approximation when answering this question. When you are finished, click the "Show Answer" button to check your work. </p>
<p>Remember:</p>
<p>\(E = \frac{1}{\epsilon_0 \epsilon_r}\int \rho (x) dx\)</p>
<p>where \(\rho (x)\) is the charge density profile, and:</p>
<p>\(V = - \int E (x) dx\)</p>
<div class="solution-span">
<span id="solution_00d703ca980f45e8ac2b76ef757b56f6_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Exercise 3.1C" />
<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_00d703ca980f45e8ac2b76ef757b56f6" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_00d703ca980f45e8ac2b76ef757b56f6">
<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>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="00d703ca980f45e8ac2b76ef757b56f6-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="00d703ca980f45e8ac2b76ef757b56f6-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="00d703ca980f45e8ac2b76ef757b56f6-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-block-type="vertical" data-runtime-class="LmsRuntime" data-runtime-version="1" data-has-score="False" data-request-token="ec7168dc4c3811ef857c16fffddbd97f" data-init="VerticalStudentView" data-course-id="course-v1:MITX+3.15.1x+2T2017" data-usage-id="block-v1:MITX+3.15.1x+2T2017+type@vertical+block@3a10c2603ce94c93a6539eb5bb134d74" data-graded="False">
<h2 class="hd hd-2 unit-title">Example 3.2</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITX+3.15.1x+2T2017+type@html+block@ab69803d4f9f4e55ab7dd0b1e0da5b41">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-block-type="html" data-runtime-class="LmsRuntime" data-runtime-version="1" data-has-score="False" data-request-token="ec7168dc4c3811ef857c16fffddbd97f" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITX+3.15.1x+2T2017" data-usage-id="block-v1:MITX+3.15.1x+2T2017+type@html+block@ab69803d4f9f4e55ab7dd0b1e0da5b41" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<h2>The Depletion Approximation</h2>
<p>The Depletion Approximation is an idealization of the pn-junction which allows us to derive an expression for the depletion region width \(d\) and the built-in voltage \(V_0\). The depletion approximation is an idealization of the charge distribution within the depletion region that assumes the following:</p>
<ul>
<li><span style="font-size: 1em; line-height: 1.6em;">The depletion region is fully depleted of majority carriers. </span></li>
<li><span style="font-size: 1em; line-height: 1.6em;">The majority carrier concentration outside of the depletion region is equal to the doping concentration (\(N_A\) or \(N_D\)).</span></li>
</ul>
<p><span style="font-size: 1em; line-height: 1.6em;">The built-in voltage (\(V_0\)) is given as follows:</span></p>
<p><span style="font-size: 1em; line-height: 1.6em;">\(V_0 = \frac{kT}{e}ln(\frac{N_A N_D}{n_i^2})\)</span></p>
<p><span style="font-size: 1em; line-height: 1.6em;">where \(k\) is the Boltzmann constant, \(T\) is temperature, \(e\) is the charge of an electron, and \(n_i\) is the intrinsic carrier concentration.</span></p>
<p>We can write the depletion region width \(d\) in terms of \(V_0\):</p>
<p>\(d = \sqrt{\frac{2 \epsilon_0\epsilon_r V_0}{e} \frac{N_D + N_A}{N_A N_D}}\)</p>
<p>where \(\epsilon_0\) is the permittivity of free space and \(\epsilon_r\) is the relative permittivity.</p>
<p></p>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@16aa0744ca694aad84601d30cdc8724b">
<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="ec7168dc4c3811ef857c16fffddbd97f" 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@16aa0744ca694aad84601d30cdc8724b" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_16aa0744ca694aad84601d30cdc8724b" class="problems-wrapper" role="group"
aria-labelledby="16aa0744ca694aad84601d30cdc8724b-problem-title"
data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@16aa0744ca694aad84601d30cdc8724b" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@16aa0744ca694aad84601d30cdc8724b/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="1"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="16aa0744ca694aad84601d30cdc8724b-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@16aa0744ca694aad84601d30cdc8724b-problem-progress" tabindex="-1">
Example 3.2A
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@16aa0744ca694aad84601d30cdc8724b-problem-progress"></div>
<div class="problem">
<div>
<p>For the pn-junction described in Example 3.1 (silicon homojunction with \(N_A = 10^{17}/cm^3\) and \(N_D = 10^{18}/cm^3\)), calculate the built-in voltage of the junction at \(300 \; K\).</p>
<p>\(V_0\) (in \(V\)):</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="formulaequationinput_16aa0744ca694aad84601d30cdc8724b_2_1" class="inputtype formulaequationinput">
<div class="unanswered">
<input type="text" name="input_16aa0744ca694aad84601d30cdc8724b_2_1" id="input_16aa0744ca694aad84601d30cdc8724b_2_1" data-input-id="16aa0744ca694aad84601d30cdc8724b_2_1" value="" aria-describedby="status_16aa0744ca694aad84601d30cdc8724b_2_1" size="20"/>
<span class="trailing_text" id="trailing_text_16aa0744ca694aad84601d30cdc8724b_2_1"/>
<span class="status unanswered" id="status_16aa0744ca694aad84601d30cdc8724b_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_16aa0744ca694aad84601d30cdc8724b_2_1" class="answer"/>
<div id="input_16aa0744ca694aad84601d30cdc8724b_2_1_preview" class="equation">
\(\)
<img src="/static/images/spinner.bc34f953403f.gif" class="loading" alt="Loading"/>
</div>
</div>
<div class="script_placeholder" data-src="/static/js/capa/src/formula_equation_preview.b1967ab28c31.js"/>
</div></div>
<div class="solution-span">
<span id="solution_16aa0744ca694aad84601d30cdc8724b_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Example 3.2A" />
<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_16aa0744ca694aad84601d30cdc8724b" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_16aa0744ca694aad84601d30cdc8724b">
<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>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="16aa0744ca694aad84601d30cdc8724b-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="16aa0744ca694aad84601d30cdc8724b-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="16aa0744ca694aad84601d30cdc8724b-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-2" data-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@d4de1fff7d10451dbc7f8c156907fa68">
<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="ec7168dc4c3811ef857c16fffddbd97f" 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@d4de1fff7d10451dbc7f8c156907fa68" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_d4de1fff7d10451dbc7f8c156907fa68" class="problems-wrapper" role="group"
aria-labelledby="d4de1fff7d10451dbc7f8c156907fa68-problem-title"
data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@d4de1fff7d10451dbc7f8c156907fa68" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@d4de1fff7d10451dbc7f8c156907fa68/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="1"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="d4de1fff7d10451dbc7f8c156907fa68-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@d4de1fff7d10451dbc7f8c156907fa68-problem-progress" tabindex="-1">
Example 3.2B
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@d4de1fff7d10451dbc7f8c156907fa68-problem-progress"></div>
<div class="problem">
<div>
<p>Now calculate the depletion region width for the junction described above:</p>
<p>\(d\) (in \(\mu m\)):</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="formulaequationinput_d4de1fff7d10451dbc7f8c156907fa68_2_1" class="inputtype formulaequationinput">
<div class="unanswered">
<input type="text" name="input_d4de1fff7d10451dbc7f8c156907fa68_2_1" id="input_d4de1fff7d10451dbc7f8c156907fa68_2_1" data-input-id="d4de1fff7d10451dbc7f8c156907fa68_2_1" value="" aria-describedby="status_d4de1fff7d10451dbc7f8c156907fa68_2_1" size="20"/>
<span class="trailing_text" id="trailing_text_d4de1fff7d10451dbc7f8c156907fa68_2_1"/>
<span class="status unanswered" id="status_d4de1fff7d10451dbc7f8c156907fa68_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_d4de1fff7d10451dbc7f8c156907fa68_2_1" class="answer"/>
<div id="input_d4de1fff7d10451dbc7f8c156907fa68_2_1_preview" class="equation">
\(\)
<img src="/static/images/spinner.bc34f953403f.gif" class="loading" alt="Loading"/>
</div>
</div>
<div class="script_placeholder" data-src="/static/js/capa/src/formula_equation_preview.b1967ab28c31.js"/>
</div></div>
<div class="solution-span">
<span id="solution_d4de1fff7d10451dbc7f8c156907fa68_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Example 3.2B" />
<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_d4de1fff7d10451dbc7f8c156907fa68" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_d4de1fff7d10451dbc7f8c156907fa68">
<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>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="d4de1fff7d10451dbc7f8c156907fa68-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="d4de1fff7d10451dbc7f8c156907fa68-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="d4de1fff7d10451dbc7f8c156907fa68-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-block-type="vertical" data-runtime-class="LmsRuntime" data-runtime-version="1" data-has-score="False" data-request-token="ec7168dc4c3811ef857c16fffddbd97f" data-init="VerticalStudentView" data-course-id="course-v1:MITX+3.15.1x+2T2017" data-usage-id="block-v1:MITX+3.15.1x+2T2017+type@vertical+block@0b11e76d6061442e8cdd414c776225d4" data-graded="False">
<h2 class="hd hd-2 unit-title">Example 3.3</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITX+3.15.1x+2T2017+type@html+block@59f8789da28846e996c5f1db7f78bb28">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-block-type="html" data-runtime-class="LmsRuntime" data-runtime-version="1" data-has-score="False" data-request-token="ec7168dc4c3811ef857c16fffddbd97f" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITX+3.15.1x+2T2017" data-usage-id="block-v1:MITX+3.15.1x+2T2017+type@html+block@59f8789da28846e996c5f1db7f78bb28" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<h2></h2>
<p>Now let's consider what happens when we forward bias the p-n junction described in Example 3.1 (\(N_A = 10^{17}/cm^3\) and \(N_D = 10^{18}/cm^3\)).</p>
<p>To achieve a forward bias condition:</p>
<ul>
<li>Apply a negative voltage to the n-side of the junction (or a positive voltage to the p-side).</li>
<li>This raises the energy level on the n-side (or lowers the energy level on the p-side).</li>
</ul>
<p></p>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@2da8a1fece6247a5b5dcc0fced6fffb5">
<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="ec7168dc4c3811ef857c16fffddbd97f" 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@2da8a1fece6247a5b5dcc0fced6fffb5" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_2da8a1fece6247a5b5dcc0fced6fffb5" class="problems-wrapper" role="group"
aria-labelledby="2da8a1fece6247a5b5dcc0fced6fffb5-problem-title"
data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@2da8a1fece6247a5b5dcc0fced6fffb5" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@2da8a1fece6247a5b5dcc0fced6fffb5/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="1"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="2da8a1fece6247a5b5dcc0fced6fffb5-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@2da8a1fece6247a5b5dcc0fced6fffb5-problem-progress" tabindex="-1">
Example 3.3A
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@2da8a1fece6247a5b5dcc0fced6fffb5-problem-progress"></div>
<div class="problem">
<div>
<p>Which of the following bias conditions would result in a forward-biased diode?</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_2da8a1fece6247a5b5dcc0fced6fffb5_2_1">
<fieldset aria-describedby="status_2da8a1fece6247a5b5dcc0fced6fffb5_2_1">
<div class="field">
<input type="checkbox" name="input_2da8a1fece6247a5b5dcc0fced6fffb5_2_1[]" id="input_2da8a1fece6247a5b5dcc0fced6fffb5_2_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="2da8a1fece6247a5b5dcc0fced6fffb5_2_1-choice_0-label" for="input_2da8a1fece6247a5b5dcc0fced6fffb5_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_2da8a1fece6247a5b5dcc0fced6fffb5_2_1"> \(+0.11 \; V\) on the p-side
</label>
</div>
<div class="field">
<input type="checkbox" name="input_2da8a1fece6247a5b5dcc0fced6fffb5_2_1[]" id="input_2da8a1fece6247a5b5dcc0fced6fffb5_2_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="2da8a1fece6247a5b5dcc0fced6fffb5_2_1-choice_1-label" for="input_2da8a1fece6247a5b5dcc0fced6fffb5_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_2da8a1fece6247a5b5dcc0fced6fffb5_2_1"> \(-0.12 \; V\) on the p-side
</label>
</div>
<div class="field">
<input type="checkbox" name="input_2da8a1fece6247a5b5dcc0fced6fffb5_2_1[]" id="input_2da8a1fece6247a5b5dcc0fced6fffb5_2_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="2da8a1fece6247a5b5dcc0fced6fffb5_2_1-choice_2-label" for="input_2da8a1fece6247a5b5dcc0fced6fffb5_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_2da8a1fece6247a5b5dcc0fced6fffb5_2_1"> \(+0.22 \; V\) on the n-side
</label>
</div>
<div class="field">
<input type="checkbox" name="input_2da8a1fece6247a5b5dcc0fced6fffb5_2_1[]" id="input_2da8a1fece6247a5b5dcc0fced6fffb5_2_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="2da8a1fece6247a5b5dcc0fced6fffb5_2_1-choice_3-label" for="input_2da8a1fece6247a5b5dcc0fced6fffb5_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_2da8a1fece6247a5b5dcc0fced6fffb5_2_1"> \(-0.25 \; V\) on the n-side
</label>
</div>
<span id="answer_2da8a1fece6247a5b5dcc0fced6fffb5_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_2da8a1fece6247a5b5dcc0fced6fffb5_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<div class="solution-span">
<span id="solution_2da8a1fece6247a5b5dcc0fced6fffb5_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Example 3.3A" />
<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_2da8a1fece6247a5b5dcc0fced6fffb5" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_2da8a1fece6247a5b5dcc0fced6fffb5">
<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>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="2da8a1fece6247a5b5dcc0fced6fffb5-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="2da8a1fece6247a5b5dcc0fced6fffb5-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="2da8a1fece6247a5b5dcc0fced6fffb5-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-2" data-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@190d069c96934f5abdaf7c6032d3cb3a">
<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="ec7168dc4c3811ef857c16fffddbd97f" 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@190d069c96934f5abdaf7c6032d3cb3a" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_190d069c96934f5abdaf7c6032d3cb3a" class="problems-wrapper" role="group"
aria-labelledby="190d069c96934f5abdaf7c6032d3cb3a-problem-title"
data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@190d069c96934f5abdaf7c6032d3cb3a" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@190d069c96934f5abdaf7c6032d3cb3a/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="190d069c96934f5abdaf7c6032d3cb3a-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@190d069c96934f5abdaf7c6032d3cb3a-problem-progress" tabindex="-1">
Example 3.3B
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@190d069c96934f5abdaf7c6032d3cb3a-problem-progress"></div>
<div class="problem">
<div>
<p>Sketch the p-n junction under a forward bias condition. Make sure to indicate the position of the quasi-Fermi levels \(E_{F,n} \) and \(E_{F,p}\). When you are done, click on the "Show Answer" button to check your work.</p>
<div class="solution-span">
<span id="solution_190d069c96934f5abdaf7c6032d3cb3a_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Example 3.3B" />
<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_190d069c96934f5abdaf7c6032d3cb3a" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_190d069c96934f5abdaf7c6032d3cb3a">
<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>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="190d069c96934f5abdaf7c6032d3cb3a-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="190d069c96934f5abdaf7c6032d3cb3a-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="190d069c96934f5abdaf7c6032d3cb3a-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-3" data-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@030b1a305b13431883fbfa3719e54cce">
<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="ec7168dc4c3811ef857c16fffddbd97f" 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@030b1a305b13431883fbfa3719e54cce" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_030b1a305b13431883fbfa3719e54cce" class="problems-wrapper" role="group"
aria-labelledby="030b1a305b13431883fbfa3719e54cce-problem-title"
data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@030b1a305b13431883fbfa3719e54cce" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@030b1a305b13431883fbfa3719e54cce/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="3"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="030b1a305b13431883fbfa3719e54cce-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@030b1a305b13431883fbfa3719e54cce-problem-progress" tabindex="-1">
Example 3.3C
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@030b1a305b13431883fbfa3719e54cce-problem-progress"></div>
<div class="problem">
<div>
<p>Which of the following occur when we forward bias the junction?</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_030b1a305b13431883fbfa3719e54cce_2_1">
<fieldset aria-describedby="status_030b1a305b13431883fbfa3719e54cce_2_1">
<div class="field">
<input type="checkbox" name="input_030b1a305b13431883fbfa3719e54cce_2_1[]" id="input_030b1a305b13431883fbfa3719e54cce_2_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="030b1a305b13431883fbfa3719e54cce_2_1-choice_0-label" for="input_030b1a305b13431883fbfa3719e54cce_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_030b1a305b13431883fbfa3719e54cce_2_1"> The diffusion current increases
</label>
</div>
<div class="field">
<input type="checkbox" name="input_030b1a305b13431883fbfa3719e54cce_2_1[]" id="input_030b1a305b13431883fbfa3719e54cce_2_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="030b1a305b13431883fbfa3719e54cce_2_1-choice_1-label" for="input_030b1a305b13431883fbfa3719e54cce_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_030b1a305b13431883fbfa3719e54cce_2_1"> The diffusion current remains the same
</label>
</div>
<div class="field">
<input type="checkbox" name="input_030b1a305b13431883fbfa3719e54cce_2_1[]" id="input_030b1a305b13431883fbfa3719e54cce_2_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="030b1a305b13431883fbfa3719e54cce_2_1-choice_2-label" for="input_030b1a305b13431883fbfa3719e54cce_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_030b1a305b13431883fbfa3719e54cce_2_1"> The diffusion current decreases
</label>
</div>
<span id="answer_030b1a305b13431883fbfa3719e54cce_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_030b1a305b13431883fbfa3719e54cce_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div class="choicegroup capa_inputtype" id="inputtype_030b1a305b13431883fbfa3719e54cce_3_1">
<fieldset aria-describedby="status_030b1a305b13431883fbfa3719e54cce_3_1">
<div class="field">
<input type="checkbox" name="input_030b1a305b13431883fbfa3719e54cce_3_1[]" id="input_030b1a305b13431883fbfa3719e54cce_3_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="030b1a305b13431883fbfa3719e54cce_3_1-choice_0-label" for="input_030b1a305b13431883fbfa3719e54cce_3_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_030b1a305b13431883fbfa3719e54cce_3_1"> The drift current increases
</label>
</div>
<div class="field">
<input type="checkbox" name="input_030b1a305b13431883fbfa3719e54cce_3_1[]" id="input_030b1a305b13431883fbfa3719e54cce_3_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="030b1a305b13431883fbfa3719e54cce_3_1-choice_1-label" for="input_030b1a305b13431883fbfa3719e54cce_3_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_030b1a305b13431883fbfa3719e54cce_3_1"> The drift current remains the same
</label>
</div>
<div class="field">
<input type="checkbox" name="input_030b1a305b13431883fbfa3719e54cce_3_1[]" id="input_030b1a305b13431883fbfa3719e54cce_3_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="030b1a305b13431883fbfa3719e54cce_3_1-choice_2-label" for="input_030b1a305b13431883fbfa3719e54cce_3_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_030b1a305b13431883fbfa3719e54cce_3_1"> The drift current decreases
</label>
</div>
<span id="answer_030b1a305b13431883fbfa3719e54cce_3_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_030b1a305b13431883fbfa3719e54cce_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 3" role="group"><div class="choicegroup capa_inputtype" id="inputtype_030b1a305b13431883fbfa3719e54cce_4_1">
<fieldset aria-describedby="status_030b1a305b13431883fbfa3719e54cce_4_1">
<div class="field">
<input type="checkbox" name="input_030b1a305b13431883fbfa3719e54cce_4_1[]" id="input_030b1a305b13431883fbfa3719e54cce_4_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="030b1a305b13431883fbfa3719e54cce_4_1-choice_0-label" for="input_030b1a305b13431883fbfa3719e54cce_4_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_030b1a305b13431883fbfa3719e54cce_4_1"> The total current increases
</label>
</div>
<div class="field">
<input type="checkbox" name="input_030b1a305b13431883fbfa3719e54cce_4_1[]" id="input_030b1a305b13431883fbfa3719e54cce_4_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="030b1a305b13431883fbfa3719e54cce_4_1-choice_1-label" for="input_030b1a305b13431883fbfa3719e54cce_4_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_030b1a305b13431883fbfa3719e54cce_4_1"> The total current remains the same
</label>
</div>
<div class="field">
<input type="checkbox" name="input_030b1a305b13431883fbfa3719e54cce_4_1[]" id="input_030b1a305b13431883fbfa3719e54cce_4_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="030b1a305b13431883fbfa3719e54cce_4_1-choice_2-label" for="input_030b1a305b13431883fbfa3719e54cce_4_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_030b1a305b13431883fbfa3719e54cce_4_1"> The total current decrease
</label>
</div>
<span id="answer_030b1a305b13431883fbfa3719e54cce_4_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_030b1a305b13431883fbfa3719e54cce_4_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<div class="solution-span">
<span id="solution_030b1a305b13431883fbfa3719e54cce_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Example 3.3C" />
<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_030b1a305b13431883fbfa3719e54cce" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_030b1a305b13431883fbfa3719e54cce">
<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>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="030b1a305b13431883fbfa3719e54cce-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="030b1a305b13431883fbfa3719e54cce-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="030b1a305b13431883fbfa3719e54cce-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-block-type="vertical" data-runtime-class="LmsRuntime" data-runtime-version="1" data-has-score="False" data-request-token="ec7168dc4c3811ef857c16fffddbd97f" data-init="VerticalStudentView" data-course-id="course-v1:MITX+3.15.1x+2T2017" data-usage-id="block-v1:MITX+3.15.1x+2T2017+type@vertical+block@70e7963678d945e1a20d4d8c0442a11d" data-graded="False">
<h2 class="hd hd-2 unit-title">Example 3.4</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITX+3.15.1x+2T2017+type@html+block@8ff1315f375c49dc9e5326d7584c578d">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-block-type="html" data-runtime-class="LmsRuntime" data-runtime-version="1" data-has-score="False" data-request-token="ec7168dc4c3811ef857c16fffddbd97f" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITX+3.15.1x+2T2017" data-usage-id="block-v1:MITX+3.15.1x+2T2017+type@html+block@8ff1315f375c49dc9e5326d7584c578d" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<h2><span>Reverse Biased pn-Junction</span></h2>
<p><span style="line-height: 25.6px;">Finally consider what happens when we reverse bias the p-n junction described in Example 3.1 (\(N_A = 10^{17}/cm^3\) and \(N_D = 10^{18}/cm^3\)).</span></p>
<p></p>
<p></p>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@37e547008446450abbbcbfd957d7e156">
<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="ec7168dc4c3811ef857c16fffddbd97f" 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@37e547008446450abbbcbfd957d7e156" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_37e547008446450abbbcbfd957d7e156" class="problems-wrapper" role="group"
aria-labelledby="37e547008446450abbbcbfd957d7e156-problem-title"
data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@37e547008446450abbbcbfd957d7e156" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@37e547008446450abbbcbfd957d7e156/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="37e547008446450abbbcbfd957d7e156-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@37e547008446450abbbcbfd957d7e156-problem-progress" tabindex="-1">
Exercise 3.4A
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@37e547008446450abbbcbfd957d7e156-problem-progress"></div>
<div class="problem">
<div>
<p>Begin by sketching the energy band diagram for the p-n junction under a moderate reverse bias. When you are done, click on the "Show Answer" button to check your work.</p>
<div class="solution-span">
<span id="solution_37e547008446450abbbcbfd957d7e156_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Exercise 3.4A" />
<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_37e547008446450abbbcbfd957d7e156" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_37e547008446450abbbcbfd957d7e156">
<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>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="37e547008446450abbbcbfd957d7e156-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="37e547008446450abbbcbfd957d7e156-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="37e547008446450abbbcbfd957d7e156-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-2" data-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@6d98d19fd15b4c6baf4a09615d37a59f">
<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="ec7168dc4c3811ef857c16fffddbd97f" 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@6d98d19fd15b4c6baf4a09615d37a59f" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_6d98d19fd15b4c6baf4a09615d37a59f" class="problems-wrapper" role="group"
aria-labelledby="6d98d19fd15b4c6baf4a09615d37a59f-problem-title"
data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@6d98d19fd15b4c6baf4a09615d37a59f" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@6d98d19fd15b4c6baf4a09615d37a59f/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="1"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="6d98d19fd15b4c6baf4a09615d37a59f-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@6d98d19fd15b4c6baf4a09615d37a59f-problem-progress" tabindex="-1">
Exercise 3.4B
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@6d98d19fd15b4c6baf4a09615d37a59f-problem-progress"></div>
<div class="problem">
<div>
<p>Which of the following bias conditions would result in a reverse-biased diode?</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_6d98d19fd15b4c6baf4a09615d37a59f_2_1">
<fieldset aria-describedby="status_6d98d19fd15b4c6baf4a09615d37a59f_2_1">
<div class="field">
<input type="checkbox" name="input_6d98d19fd15b4c6baf4a09615d37a59f_2_1[]" id="input_6d98d19fd15b4c6baf4a09615d37a59f_2_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="6d98d19fd15b4c6baf4a09615d37a59f_2_1-choice_0-label" for="input_6d98d19fd15b4c6baf4a09615d37a59f_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_6d98d19fd15b4c6baf4a09615d37a59f_2_1"> \(+0.11 \; V\) on the p-side
</label>
</div>
<div class="field">
<input type="checkbox" name="input_6d98d19fd15b4c6baf4a09615d37a59f_2_1[]" id="input_6d98d19fd15b4c6baf4a09615d37a59f_2_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="6d98d19fd15b4c6baf4a09615d37a59f_2_1-choice_1-label" for="input_6d98d19fd15b4c6baf4a09615d37a59f_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_6d98d19fd15b4c6baf4a09615d37a59f_2_1"> \(-0.12 \; V\) on the p-side
</label>
</div>
<div class="field">
<input type="checkbox" name="input_6d98d19fd15b4c6baf4a09615d37a59f_2_1[]" id="input_6d98d19fd15b4c6baf4a09615d37a59f_2_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="6d98d19fd15b4c6baf4a09615d37a59f_2_1-choice_2-label" for="input_6d98d19fd15b4c6baf4a09615d37a59f_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_6d98d19fd15b4c6baf4a09615d37a59f_2_1"> \(+0.2 \; V\) on the n-side
</label>
</div>
<div class="field">
<input type="checkbox" name="input_6d98d19fd15b4c6baf4a09615d37a59f_2_1[]" id="input_6d98d19fd15b4c6baf4a09615d37a59f_2_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="6d98d19fd15b4c6baf4a09615d37a59f_2_1-choice_3-label" for="input_6d98d19fd15b4c6baf4a09615d37a59f_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_6d98d19fd15b4c6baf4a09615d37a59f_2_1"> \(-0.25 \; V\) on the n-side
</label>
</div>
<span id="answer_6d98d19fd15b4c6baf4a09615d37a59f_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_6d98d19fd15b4c6baf4a09615d37a59f_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<div class="solution-span">
<span id="solution_6d98d19fd15b4c6baf4a09615d37a59f_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Exercise 3.4B" />
<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_6d98d19fd15b4c6baf4a09615d37a59f" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_6d98d19fd15b4c6baf4a09615d37a59f">
<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>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="6d98d19fd15b4c6baf4a09615d37a59f-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="6d98d19fd15b4c6baf4a09615d37a59f-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="6d98d19fd15b4c6baf4a09615d37a59f-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-3" data-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@92825896c40e49db8ec017646c6efc31">
<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="ec7168dc4c3811ef857c16fffddbd97f" 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@92825896c40e49db8ec017646c6efc31" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_92825896c40e49db8ec017646c6efc31" class="problems-wrapper" role="group"
aria-labelledby="92825896c40e49db8ec017646c6efc31-problem-title"
data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@92825896c40e49db8ec017646c6efc31" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@92825896c40e49db8ec017646c6efc31/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="2"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="92825896c40e49db8ec017646c6efc31-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@92825896c40e49db8ec017646c6efc31-problem-progress" tabindex="-1">
Exercise 3.4C
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@92825896c40e49db8ec017646c6efc31-problem-progress"></div>
<div class="problem">
<div>
<div>
<p>Which of the following occur when we reverse bias the junction, compared with the unbiased case?</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_92825896c40e49db8ec017646c6efc31_2_1">
<fieldset aria-describedby="status_92825896c40e49db8ec017646c6efc31_2_1">
<div class="field">
<input type="checkbox" name="input_92825896c40e49db8ec017646c6efc31_2_1[]" id="input_92825896c40e49db8ec017646c6efc31_2_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="92825896c40e49db8ec017646c6efc31_2_1-choice_0-label" for="input_92825896c40e49db8ec017646c6efc31_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_92825896c40e49db8ec017646c6efc31_2_1"> The diffusion current increases
</label>
</div>
<div class="field">
<input type="checkbox" name="input_92825896c40e49db8ec017646c6efc31_2_1[]" id="input_92825896c40e49db8ec017646c6efc31_2_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="92825896c40e49db8ec017646c6efc31_2_1-choice_1-label" for="input_92825896c40e49db8ec017646c6efc31_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_92825896c40e49db8ec017646c6efc31_2_1"> The diffusion current remains the same
</label>
</div>
<div class="field">
<input type="checkbox" name="input_92825896c40e49db8ec017646c6efc31_2_1[]" id="input_92825896c40e49db8ec017646c6efc31_2_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="92825896c40e49db8ec017646c6efc31_2_1-choice_2-label" for="input_92825896c40e49db8ec017646c6efc31_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_92825896c40e49db8ec017646c6efc31_2_1"> The diffusion current decreases
</label>
</div>
<span id="answer_92825896c40e49db8ec017646c6efc31_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_92825896c40e49db8ec017646c6efc31_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div class="choicegroup capa_inputtype" id="inputtype_92825896c40e49db8ec017646c6efc31_3_1">
<fieldset aria-describedby="status_92825896c40e49db8ec017646c6efc31_3_1">
<div class="field">
<input type="checkbox" name="input_92825896c40e49db8ec017646c6efc31_3_1[]" id="input_92825896c40e49db8ec017646c6efc31_3_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="92825896c40e49db8ec017646c6efc31_3_1-choice_0-label" for="input_92825896c40e49db8ec017646c6efc31_3_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_92825896c40e49db8ec017646c6efc31_3_1"> The drift current increases
</label>
</div>
<div class="field">
<input type="checkbox" name="input_92825896c40e49db8ec017646c6efc31_3_1[]" id="input_92825896c40e49db8ec017646c6efc31_3_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="92825896c40e49db8ec017646c6efc31_3_1-choice_1-label" for="input_92825896c40e49db8ec017646c6efc31_3_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_92825896c40e49db8ec017646c6efc31_3_1"> The drift current remains the same
</label>
</div>
<div class="field">
<input type="checkbox" name="input_92825896c40e49db8ec017646c6efc31_3_1[]" id="input_92825896c40e49db8ec017646c6efc31_3_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="92825896c40e49db8ec017646c6efc31_3_1-choice_2-label" for="input_92825896c40e49db8ec017646c6efc31_3_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_92825896c40e49db8ec017646c6efc31_3_1"> The drift current decreases
</label>
</div>
<span id="answer_92825896c40e49db8ec017646c6efc31_3_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_92825896c40e49db8ec017646c6efc31_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<div class="solution-span">
<span id="solution_92825896c40e49db8ec017646c6efc31_solution_1"/>
</div></div>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Exercise 3.4C" />
<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_92825896c40e49db8ec017646c6efc31" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_92825896c40e49db8ec017646c6efc31">
<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>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="92825896c40e49db8ec017646c6efc31-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="92825896c40e49db8ec017646c6efc31-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="92825896c40e49db8ec017646c6efc31-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-block-type="vertical" data-runtime-class="LmsRuntime" data-runtime-version="1" data-has-score="False" data-request-token="ec7168dc4c3811ef857c16fffddbd97f" data-init="VerticalStudentView" data-course-id="course-v1:MITX+3.15.1x+2T2017" data-usage-id="block-v1:MITX+3.15.1x+2T2017+type@vertical+block@d9d29fb3127944f7925948303c21080c" data-graded="False">
<h2 class="hd hd-2 unit-title">Example 3.5</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITX+3.15.1x+2T2017+type@html+block@0f430a0968e54f2e9ddb9e1384265e2c">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-block-type="html" data-runtime-class="LmsRuntime" data-runtime-version="1" data-has-score="False" data-request-token="ec7168dc4c3811ef857c16fffddbd97f" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITX+3.15.1x+2T2017" data-usage-id="block-v1:MITX+3.15.1x+2T2017+type@html+block@0f430a0968e54f2e9ddb9e1384265e2c" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<h2>The Ideal Diode Equation</h2>
<p>The ideal diode equation allows us to model the current-voltage characteristics of a pn-junction diode. In terms of current density (\(J\)), we can write:</p>
<p>\(J = J_0(exp(\frac{eV_A}{kT}) -1 \))</p>
<p>where \(J_0\) is the reverse saturation current density (dark current density), \(e\) is the charge on an electron, \(k\) is the Boltzmann constant, and \(T\) is temperature, and \(V_A\) is the applied voltage. Current density \(J\) is typically given in units of \(A/cm^2\).</p>
<p></p>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@40ecd67261c843969fa60b277a95a879">
<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="ec7168dc4c3811ef857c16fffddbd97f" 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@40ecd67261c843969fa60b277a95a879" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_40ecd67261c843969fa60b277a95a879" class="problems-wrapper" role="group"
aria-labelledby="40ecd67261c843969fa60b277a95a879-problem-title"
data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@40ecd67261c843969fa60b277a95a879" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@40ecd67261c843969fa60b277a95a879/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="1"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="40ecd67261c843969fa60b277a95a879-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@40ecd67261c843969fa60b277a95a879-problem-progress" tabindex="-1">
Exercise 3.5A
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@40ecd67261c843969fa60b277a95a879-problem-progress"></div>
<div class="problem">
<div>
<p>Calculate the current density through a silicon diode at room temperature when a voltage of \(+0.1 V\) is applied to the p-side of the junction. Assume the the dark current density \(J_0 = 10^{-12} A/cm^2\).</p>
<p>\(J\) (in \(A/cm^2\)):</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="formulaequationinput_40ecd67261c843969fa60b277a95a879_2_1" class="inputtype formulaequationinput">
<div class="unanswered">
<input type="text" name="input_40ecd67261c843969fa60b277a95a879_2_1" id="input_40ecd67261c843969fa60b277a95a879_2_1" data-input-id="40ecd67261c843969fa60b277a95a879_2_1" value="" aria-describedby="status_40ecd67261c843969fa60b277a95a879_2_1" size="20"/>
<span class="trailing_text" id="trailing_text_40ecd67261c843969fa60b277a95a879_2_1"/>
<span class="status unanswered" id="status_40ecd67261c843969fa60b277a95a879_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_40ecd67261c843969fa60b277a95a879_2_1" class="answer"/>
<div id="input_40ecd67261c843969fa60b277a95a879_2_1_preview" class="equation">
\(\)
<img src="/static/images/spinner.bc34f953403f.gif" class="loading" alt="Loading"/>
</div>
</div>
<div class="script_placeholder" data-src="/static/js/capa/src/formula_equation_preview.b1967ab28c31.js"/>
</div></div>
<div class="solution-span">
<span id="solution_40ecd67261c843969fa60b277a95a879_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Exercise 3.5A" />
<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_40ecd67261c843969fa60b277a95a879" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_40ecd67261c843969fa60b277a95a879">
<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>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="40ecd67261c843969fa60b277a95a879-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="40ecd67261c843969fa60b277a95a879-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="40ecd67261c843969fa60b277a95a879-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-2" data-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@f12d494955dc494f8501e6476fb3ee20">
<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="ec7168dc4c3811ef857c16fffddbd97f" 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@f12d494955dc494f8501e6476fb3ee20" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_f12d494955dc494f8501e6476fb3ee20" class="problems-wrapper" role="group"
aria-labelledby="f12d494955dc494f8501e6476fb3ee20-problem-title"
data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@f12d494955dc494f8501e6476fb3ee20" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@f12d494955dc494f8501e6476fb3ee20/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="1"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="f12d494955dc494f8501e6476fb3ee20-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@f12d494955dc494f8501e6476fb3ee20-problem-progress" tabindex="-1">
Exercise 3.5B
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@f12d494955dc494f8501e6476fb3ee20-problem-progress"></div>
<div class="problem">
<div>
<p>Now calculate the current density through a silicon diode at room temperature when a voltage of \(-0.1 V\) is applied to the p-side of the junction. Assume the the dark current density \(J_0 = 10^{-12} A/cm^2\).</p>
<p>\(J\) (in \(A/cm^2\)):</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="formulaequationinput_f12d494955dc494f8501e6476fb3ee20_2_1" class="inputtype formulaequationinput">
<div class="unanswered">
<input type="text" name="input_f12d494955dc494f8501e6476fb3ee20_2_1" id="input_f12d494955dc494f8501e6476fb3ee20_2_1" data-input-id="f12d494955dc494f8501e6476fb3ee20_2_1" value="" aria-describedby="status_f12d494955dc494f8501e6476fb3ee20_2_1" size="20"/>
<span class="trailing_text" id="trailing_text_f12d494955dc494f8501e6476fb3ee20_2_1"/>
<span class="status unanswered" id="status_f12d494955dc494f8501e6476fb3ee20_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_f12d494955dc494f8501e6476fb3ee20_2_1" class="answer"/>
<div id="input_f12d494955dc494f8501e6476fb3ee20_2_1_preview" class="equation">
\(\)
<img src="/static/images/spinner.bc34f953403f.gif" class="loading" alt="Loading"/>
</div>
</div>
<div class="script_placeholder" data-src="/static/js/capa/src/formula_equation_preview.b1967ab28c31.js"/>
</div></div>
<div class="solution-span">
<span id="solution_f12d494955dc494f8501e6476fb3ee20_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Exercise 3.5B" />
<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_f12d494955dc494f8501e6476fb3ee20" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_f12d494955dc494f8501e6476fb3ee20">
<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>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="f12d494955dc494f8501e6476fb3ee20-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="f12d494955dc494f8501e6476fb3ee20-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="f12d494955dc494f8501e6476fb3ee20-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
© All Rights Reserved