<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="9a4ff2454c3811ef857c16fffddbd97f" 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@4683ef1b84274dda8247652d782a8e71" data-graded="False">
<h2 class="hd hd-2 unit-title">Tutorial Overview</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITX+3.15.1x+2T2017+type@html+block@7140ee14403f4174a51e11436fda8cca">
<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="9a4ff2454c3811ef857c16fffddbd97f" 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@7140ee14403f4174a51e11436fda8cca" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<h2>TutorIal Overview</h2>
<p>In these tutorial sections, you will find overviews of many of the important topics covered in the week's lecture. Here, you will find:</p>
<ul>
<li>Summaries of important concepts and equations</li>
<li>Definitions of important terms and variables</li>
<li>Practice problems with worked solutions</li>
</ul>
<p></p>
<p>These tutorial sections are optional and are not graded, but are recommended if you would like extra practice with the material. The questions that you find here are generally simpler than those that you're encounter in the Homework and Quiz, but these problems should help to give you the fundamental skills that you will need to solve the graded problems </p>
<p></p>
</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="9a4ff2454c3811ef857c16fffddbd97f" 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@41e2ecb9323841c3b2e89bd32e65612c" data-graded="False">
<h2 class="hd hd-2 unit-title">Part 1.1</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITX+3.15.1x+2T2017+type@html+block@838a615d763346f4a4f0cca1c5d8ce11">
<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="9a4ff2454c3811ef857c16fffddbd97f" 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@838a615d763346f4a4f0cca1c5d8ce11" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<h2>Carrier Concentration</h2>
<p>(1) We define the charge carriers in a semiconductor material as follows:</p>
<p>\(n\) = number of electrons/cm<sup>3</sup></p>
<p>\(p\) = number of holes/cm<sup>3</sup></p>
<p></p>
<p>(2) In an intrinsic semiconductor under equilibrium conditions, the number of electrons and holes are equal:</p>
<p>\(n = p = n_i\)</p>
<p>where \(n_i\) is the intrinsic carrier concentration. Approximate intrinsic carrier concentrations for some important semiconductors at room temperature are given below:</p>
<table style="width: 50%;">
<tbody>
<tr>
<td>Silicon</td>
<td>\(1 \times 10^{10}/cm^3\)</td>
</tr>
<tr>
<td>GaAs</td>
<td>\(2 \times 10^6/cm^3\)</td>
</tr>
<tr>
<td>Germanium</td>
<td>\(2 \times 10^{13}/cm^3\)</td>
</tr>
</tbody>
</table>
<p></p>
<p>(3) The Law of Mass Action tells us that at equilibrium, the product of the electron concentration and the hole concentration are equal to the square of the intrinsic carrier concentration:</p>
<p>\(np = n_i^2\)</p>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@da531ff7cd394e2f85fb87c4d605f63c">
<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="9a4ff2454c3811ef857c16fffddbd97f" 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@da531ff7cd394e2f85fb87c4d605f63c" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_da531ff7cd394e2f85fb87c4d605f63c" class="problems-wrapper" role="group"
aria-labelledby="da531ff7cd394e2f85fb87c4d605f63c-problem-title"
data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@da531ff7cd394e2f85fb87c4d605f63c" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@da531ff7cd394e2f85fb87c4d605f63c/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="da531ff7cd394e2f85fb87c4d605f63c-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@da531ff7cd394e2f85fb87c4d605f63c-problem-progress" tabindex="-1">
Example 1.1A
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@da531ff7cd394e2f85fb87c4d605f63c-problem-progress"></div>
<div class="problem">
<div>
<p>Assume that a piece of silicon at room temperature is doped with \(10^{16}/cm^3\) phosphorus atoms. What is the hole concentration in the material?</p>
<p>\(p\) (in \(cm^{-3}\)):</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="formulaequationinput_da531ff7cd394e2f85fb87c4d605f63c_2_1" class="inputtype formulaequationinput">
<div class="unanswered">
<input type="text" name="input_da531ff7cd394e2f85fb87c4d605f63c_2_1" id="input_da531ff7cd394e2f85fb87c4d605f63c_2_1" data-input-id="da531ff7cd394e2f85fb87c4d605f63c_2_1" value="" aria-describedby="status_da531ff7cd394e2f85fb87c4d605f63c_2_1" size="20"/>
<span class="trailing_text" id="trailing_text_da531ff7cd394e2f85fb87c4d605f63c_2_1"/>
<span class="status unanswered" id="status_da531ff7cd394e2f85fb87c4d605f63c_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_da531ff7cd394e2f85fb87c4d605f63c_2_1" class="answer"/>
<div id="input_da531ff7cd394e2f85fb87c4d605f63c_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_da531ff7cd394e2f85fb87c4d605f63c_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Example 1.1A" />
<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_da531ff7cd394e2f85fb87c4d605f63c" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_da531ff7cd394e2f85fb87c4d605f63c">
<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="da531ff7cd394e2f85fb87c4d605f63c-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="da531ff7cd394e2f85fb87c4d605f63c-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="da531ff7cd394e2f85fb87c4d605f63c-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@79a6420194a8455b80d02e82dd16fe28">
<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="9a4ff2454c3811ef857c16fffddbd97f" 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@79a6420194a8455b80d02e82dd16fe28" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_79a6420194a8455b80d02e82dd16fe28" class="problems-wrapper" role="group"
aria-labelledby="79a6420194a8455b80d02e82dd16fe28-problem-title"
data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@79a6420194a8455b80d02e82dd16fe28" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@79a6420194a8455b80d02e82dd16fe28/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="79a6420194a8455b80d02e82dd16fe28-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@79a6420194a8455b80d02e82dd16fe28-problem-progress" tabindex="-1">
Example 1.1B
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@79a6420194a8455b80d02e82dd16fe28-problem-progress"></div>
<div class="problem">
<div>
<p>As the temperature of the semiconductor increases, so does the intrinsic carrier concentration.</p>
<p>At \(50^{\circ}C\), the intrinsic carrier concentration in Si increases to approximately \(6 \times 10^{10}/cm^3\). What is the hole concentration in the material described above at \(50^{\circ}C\)?</p>
<p>\(p\) (in \(cm^{-3}\)):</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="formulaequationinput_79a6420194a8455b80d02e82dd16fe28_2_1" class="inputtype formulaequationinput">
<div class="unanswered">
<input type="text" name="input_79a6420194a8455b80d02e82dd16fe28_2_1" id="input_79a6420194a8455b80d02e82dd16fe28_2_1" data-input-id="79a6420194a8455b80d02e82dd16fe28_2_1" value="" aria-describedby="status_79a6420194a8455b80d02e82dd16fe28_2_1" size="20"/>
<span class="trailing_text" id="trailing_text_79a6420194a8455b80d02e82dd16fe28_2_1"/>
<span class="status unanswered" id="status_79a6420194a8455b80d02e82dd16fe28_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_79a6420194a8455b80d02e82dd16fe28_2_1" class="answer"/>
<div id="input_79a6420194a8455b80d02e82dd16fe28_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_79a6420194a8455b80d02e82dd16fe28_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Example 1.1B" />
<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_79a6420194a8455b80d02e82dd16fe28" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_79a6420194a8455b80d02e82dd16fe28">
<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="79a6420194a8455b80d02e82dd16fe28-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="79a6420194a8455b80d02e82dd16fe28-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="79a6420194a8455b80d02e82dd16fe28-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="9a4ff2454c3811ef857c16fffddbd97f" 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@1a9ff194e9304c2ab67d15e72c40a22b" data-graded="False">
<h2 class="hd hd-2 unit-title">Part 1.2</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITX+3.15.1x+2T2017+type@html+block@b5aa4f551305450a8a1cef20226f2b94">
<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="9a4ff2454c3811ef857c16fffddbd97f" 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@b5aa4f551305450a8a1cef20226f2b94" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<h2>CARRIER DISTRIBUTION</h2>
<p>To determine the distribution of carriers as a function of energy within a semiconductor, we need to know two things:</p>
<ol>
<li>The number of states that are found at a given energy level \(E\). This is given by the <em>density of states function</em> \(g(E)\). Typically, the density of states function has units of \(\#/eV \cdot cm^{3}\).<br /><br /></li>
<li>The probability that these states are occupied. This is given by the <em>Fermi function</em> \(f(E)\):</li>
</ol>
<p></p>
<p style="padding-left: 90px;">\(f(E) = 1/\{1 + exp[(E-E_F)/k_B T]\}\)</p>
<p style="padding-left: 90px;">where \(E_F\) is the Fermi energy, \(k_B\) is the Boltzmann constant, and \(T\) is temperature</p>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@826d4a4aa6c44f4e9d1e013c852c4b15">
<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="9a4ff2454c3811ef857c16fffddbd97f" 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@826d4a4aa6c44f4e9d1e013c852c4b15" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_826d4a4aa6c44f4e9d1e013c852c4b15" class="problems-wrapper" role="group"
aria-labelledby="826d4a4aa6c44f4e9d1e013c852c4b15-problem-title"
data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@826d4a4aa6c44f4e9d1e013c852c4b15" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@826d4a4aa6c44f4e9d1e013c852c4b15/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="826d4a4aa6c44f4e9d1e013c852c4b15-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@826d4a4aa6c44f4e9d1e013c852c4b15-problem-progress" tabindex="-1">
Example 1.2A
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@826d4a4aa6c44f4e9d1e013c852c4b15-problem-progress"></div>
<div class="problem">
<div>
<p>Let's assume that we have an impurity level that is located \(0.05 eV\) below the Fermi level in silicon. What is the probability that this state is occupied at \(300K\)?</p>
<p>P(occupation):</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="formulaequationinput_826d4a4aa6c44f4e9d1e013c852c4b15_2_1" class="inputtype formulaequationinput">
<div class="unanswered">
<input type="text" name="input_826d4a4aa6c44f4e9d1e013c852c4b15_2_1" id="input_826d4a4aa6c44f4e9d1e013c852c4b15_2_1" data-input-id="826d4a4aa6c44f4e9d1e013c852c4b15_2_1" value="" aria-describedby="status_826d4a4aa6c44f4e9d1e013c852c4b15_2_1" size="20"/>
<span class="trailing_text" id="trailing_text_826d4a4aa6c44f4e9d1e013c852c4b15_2_1"/>
<span class="status unanswered" id="status_826d4a4aa6c44f4e9d1e013c852c4b15_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_826d4a4aa6c44f4e9d1e013c852c4b15_2_1" class="answer"/>
<div id="input_826d4a4aa6c44f4e9d1e013c852c4b15_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_826d4a4aa6c44f4e9d1e013c852c4b15_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Example 1.2A" />
<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_826d4a4aa6c44f4e9d1e013c852c4b15" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_826d4a4aa6c44f4e9d1e013c852c4b15">
<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="826d4a4aa6c44f4e9d1e013c852c4b15-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="826d4a4aa6c44f4e9d1e013c852c4b15-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="826d4a4aa6c44f4e9d1e013c852c4b15-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@b70796b67a824170bb956ce394c32949">
<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="9a4ff2454c3811ef857c16fffddbd97f" 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@b70796b67a824170bb956ce394c32949" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_b70796b67a824170bb956ce394c32949" class="problems-wrapper" role="group"
aria-labelledby="b70796b67a824170bb956ce394c32949-problem-title"
data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@b70796b67a824170bb956ce394c32949" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@b70796b67a824170bb956ce394c32949/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="b70796b67a824170bb956ce394c32949-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@b70796b67a824170bb956ce394c32949-problem-progress" tabindex="-1">
Problem 1.2B
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@b70796b67a824170bb956ce394c32949-problem-progress"></div>
<div class="problem">
<div>
<p>Now assume that there are \(10^{17}/cm^3\) of these impurity atoms in silicon. What is the concentration of holes, \(p\) in the semiconductor under this doping condition (at room temperature)?</p>
<p>\(p\) (in \(cm^{-3}\)):</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="formulaequationinput_b70796b67a824170bb956ce394c32949_2_1" class="inputtype formulaequationinput">
<div class="unanswered">
<input type="text" name="input_b70796b67a824170bb956ce394c32949_2_1" id="input_b70796b67a824170bb956ce394c32949_2_1" data-input-id="b70796b67a824170bb956ce394c32949_2_1" value="" aria-describedby="status_b70796b67a824170bb956ce394c32949_2_1" size="20"/>
<span class="trailing_text" id="trailing_text_b70796b67a824170bb956ce394c32949_2_1"/>
<span class="status unanswered" id="status_b70796b67a824170bb956ce394c32949_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_b70796b67a824170bb956ce394c32949_2_1" class="answer"/>
<div id="input_b70796b67a824170bb956ce394c32949_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_b70796b67a824170bb956ce394c32949_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Problem 1.2B" />
<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_b70796b67a824170bb956ce394c32949" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_b70796b67a824170bb956ce394c32949">
<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="b70796b67a824170bb956ce394c32949-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="b70796b67a824170bb956ce394c32949-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="b70796b67a824170bb956ce394c32949-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="9a4ff2454c3811ef857c16fffddbd97f" 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@a9f98faf39134676b3026e5016397fba" data-graded="False">
<h2 class="hd hd-2 unit-title">Part 1.3</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITX+3.15.1x+2T2017+type@html+block@89668001e8ad4a0687abe8d916752142">
<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="9a4ff2454c3811ef857c16fffddbd97f" 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@89668001e8ad4a0687abe8d916752142" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<h2>Equilibrium Carrier Concentrations</h2>
<p>We determine the equilibrium concentration of electrons and holes by integrating \(f(E)g(E)dE\) and making a few simplifying assumptions:</p>
<ul>
<li>\(n = n_i exp\{(E_F - E_i)/k_B T\}\)</li>
<li>\(p = n_i exp\{(E_i - E_F)/k_B T\}\)</li>
</ul>
<p>where \(E_F\) is the Fermi level, \(E_i\) is the Fermi level for the intrinsic semiconductor, \(k_B\) is the Boltzmann constant, and \(T\) is the temperature. </p>
<p>where the intrinsic carrier concentration \(n_i\) is given as:</p>
<ul>
<li>\(n_i = \sqrt{N_c N_v}e^{-E_G/2k_BT}\)</li>
</ul>
<p>where \(N_c\) is the effective density of states in the conduction band, and \(N_v\) is the effective density of states in the valence band. \(E_g\) is the band gap of the semiconductor.</p>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@50baa8d019464e1e9cd6d8a6eec6418d">
<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="9a4ff2454c3811ef857c16fffddbd97f" 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@50baa8d019464e1e9cd6d8a6eec6418d" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_50baa8d019464e1e9cd6d8a6eec6418d" class="problems-wrapper" role="group"
aria-labelledby="50baa8d019464e1e9cd6d8a6eec6418d-problem-title"
data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@50baa8d019464e1e9cd6d8a6eec6418d" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@50baa8d019464e1e9cd6d8a6eec6418d/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="50baa8d019464e1e9cd6d8a6eec6418d-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@50baa8d019464e1e9cd6d8a6eec6418d-problem-progress" tabindex="-1">
Example 1.3A
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@50baa8d019464e1e9cd6d8a6eec6418d-problem-progress"></div>
<div class="problem">
<div>
<p>Calculate the intrinsic carrier concentration for GaAs at \(40 ^{\circ} C\). (For GaAs, the band gap is \(1.42 \; eV\), the effective density of states in the conduction band is \(4\times 10^{17} cm^{-3}\), and the effective density of states in the valence band is \(9\times 10^{18} cm^{-3}\).</p>
<p>
\(n_i\) ( \(cm^{-3}\)) :</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="formulaequationinput_50baa8d019464e1e9cd6d8a6eec6418d_2_1" class="inputtype formulaequationinput">
<div class="unanswered">
<input type="text" name="input_50baa8d019464e1e9cd6d8a6eec6418d_2_1" id="input_50baa8d019464e1e9cd6d8a6eec6418d_2_1" data-input-id="50baa8d019464e1e9cd6d8a6eec6418d_2_1" value="" aria-describedby="status_50baa8d019464e1e9cd6d8a6eec6418d_2_1" size="20"/>
<span class="trailing_text" id="trailing_text_50baa8d019464e1e9cd6d8a6eec6418d_2_1"/>
<span class="status unanswered" id="status_50baa8d019464e1e9cd6d8a6eec6418d_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_50baa8d019464e1e9cd6d8a6eec6418d_2_1" class="answer"/>
<div id="input_50baa8d019464e1e9cd6d8a6eec6418d_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_50baa8d019464e1e9cd6d8a6eec6418d_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Example 1.3A" />
<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_50baa8d019464e1e9cd6d8a6eec6418d" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_50baa8d019464e1e9cd6d8a6eec6418d">
<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="50baa8d019464e1e9cd6d8a6eec6418d-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="50baa8d019464e1e9cd6d8a6eec6418d-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="50baa8d019464e1e9cd6d8a6eec6418d-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@d6396a860bdf48b380e30bf6b6b823f7">
<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="9a4ff2454c3811ef857c16fffddbd97f" 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@d6396a860bdf48b380e30bf6b6b823f7" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_d6396a860bdf48b380e30bf6b6b823f7" class="problems-wrapper" role="group"
aria-labelledby="d6396a860bdf48b380e30bf6b6b823f7-problem-title"
data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@d6396a860bdf48b380e30bf6b6b823f7" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@d6396a860bdf48b380e30bf6b6b823f7/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="d6396a860bdf48b380e30bf6b6b823f7-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@d6396a860bdf48b380e30bf6b6b823f7-problem-progress" tabindex="-1">
Example 1.3B
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@d6396a860bdf48b380e30bf6b6b823f7-problem-progress"></div>
<div class="problem">
<div>
<p>Now assume that GaAs is doped with \(N_D = 10^{17} /cm^{3}\) donor atoms. What is the location of the Fermi Level at \(40^{\circ}C\), relative to the intrinsic Fermi level?</p>
<p>\((E_F - E_i)\) (in \( eV\)):</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="formulaequationinput_d6396a860bdf48b380e30bf6b6b823f7_2_1" class="inputtype formulaequationinput">
<div class="unanswered">
<input type="text" name="input_d6396a860bdf48b380e30bf6b6b823f7_2_1" id="input_d6396a860bdf48b380e30bf6b6b823f7_2_1" data-input-id="d6396a860bdf48b380e30bf6b6b823f7_2_1" value="" aria-describedby="status_d6396a860bdf48b380e30bf6b6b823f7_2_1" size="20"/>
<span class="trailing_text" id="trailing_text_d6396a860bdf48b380e30bf6b6b823f7_2_1"/>
<span class="status unanswered" id="status_d6396a860bdf48b380e30bf6b6b823f7_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_d6396a860bdf48b380e30bf6b6b823f7_2_1" class="answer"/>
<div id="input_d6396a860bdf48b380e30bf6b6b823f7_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_d6396a860bdf48b380e30bf6b6b823f7_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Example 1.3B" />
<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_d6396a860bdf48b380e30bf6b6b823f7" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_d6396a860bdf48b380e30bf6b6b823f7">
<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="d6396a860bdf48b380e30bf6b6b823f7-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="d6396a860bdf48b380e30bf6b6b823f7-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="d6396a860bdf48b380e30bf6b6b823f7-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="9a4ff2454c3811ef857c16fffddbd97f" 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@0a3d40fd4f524a0e9cd24367354a2898" data-graded="False">
<h2 class="hd hd-2 unit-title">Part 1.4</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITX+3.15.1x+2T2017+type@html+block@d21baf7f1d594c78a6f9c1a9f039a84d">
<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="9a4ff2454c3811ef857c16fffddbd97f" 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@d21baf7f1d594c78a6f9c1a9f039a84d" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<h2>POSITION OF \(E_i\)</h2>
<p>If we know the effective masses of electrons and holes in a semiconductor, we can determine the position of \(E_i\), the intrinsic Fermi level, relative to midgap:</p>
<p style="padding-left: 60px;">\(E_i = \frac{E_c + E_v}{2} + \frac{3}{4}k_BTln(\frac{m_p^*}{m_n^*})\)</p>
<p>where \(m_p^*\) is the effective mass of holes and \(m_n^*\) is the effective mass of electrons in the semiconductor.</p>
<p>Effective masses for some important semiconductors at \(300K\):</p>
<table style="width: 50%;">
<tbody>
<tr>
<td>Material</td>
<td>\(m_n^*/m_0\)</td>
<td>\(m_p^*/m_0\)</td>
</tr>
<tr>
<td>Si</td>
<td>1.18</td>
<td>0.81</td>
</tr>
<tr>
<td>Ge</td>
<td>0.55</td>
<td>0.36</td>
</tr>
<tr>
<td>GaAs</td>
<td>0.066</td>
<td>0.52</td>
</tr>
</tbody>
</table>
<p>where \(m_0\) is the rest mass of an electron.</p>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@6f5dd9e1ad94486687bb57fa7fc09980">
<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="9a4ff2454c3811ef857c16fffddbd97f" 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@6f5dd9e1ad94486687bb57fa7fc09980" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_6f5dd9e1ad94486687bb57fa7fc09980" class="problems-wrapper" role="group"
aria-labelledby="6f5dd9e1ad94486687bb57fa7fc09980-problem-title"
data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@6f5dd9e1ad94486687bb57fa7fc09980" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@6f5dd9e1ad94486687bb57fa7fc09980/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="6f5dd9e1ad94486687bb57fa7fc09980-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@6f5dd9e1ad94486687bb57fa7fc09980-problem-progress" tabindex="-1">
Example 1.4A
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@6f5dd9e1ad94486687bb57fa7fc09980-problem-progress"></div>
<div class="problem">
<div>
<p>What is the position of \(E_i\) relative to midgap for GaAs at room temperature?</p>
<p>\((E_i - midgap\)) (in \(eV\)):</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="formulaequationinput_6f5dd9e1ad94486687bb57fa7fc09980_2_1" class="inputtype formulaequationinput">
<div class="unanswered">
<input type="text" name="input_6f5dd9e1ad94486687bb57fa7fc09980_2_1" id="input_6f5dd9e1ad94486687bb57fa7fc09980_2_1" data-input-id="6f5dd9e1ad94486687bb57fa7fc09980_2_1" value="" aria-describedby="status_6f5dd9e1ad94486687bb57fa7fc09980_2_1" size="20"/>
<span class="trailing_text" id="trailing_text_6f5dd9e1ad94486687bb57fa7fc09980_2_1"/>
<span class="status unanswered" id="status_6f5dd9e1ad94486687bb57fa7fc09980_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_6f5dd9e1ad94486687bb57fa7fc09980_2_1" class="answer"/>
<div id="input_6f5dd9e1ad94486687bb57fa7fc09980_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_6f5dd9e1ad94486687bb57fa7fc09980_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Example 1.4A" />
<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_6f5dd9e1ad94486687bb57fa7fc09980" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_6f5dd9e1ad94486687bb57fa7fc09980">
<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="6f5dd9e1ad94486687bb57fa7fc09980-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="6f5dd9e1ad94486687bb57fa7fc09980-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="6f5dd9e1ad94486687bb57fa7fc09980-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@75dbf2b1bc2e40798c61629e7de93fff">
<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="9a4ff2454c3811ef857c16fffddbd97f" 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@75dbf2b1bc2e40798c61629e7de93fff" data-graded="False">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_75dbf2b1bc2e40798c61629e7de93fff" class="problems-wrapper" role="group"
aria-labelledby="75dbf2b1bc2e40798c61629e7de93fff-problem-title"
data-problem-id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@75dbf2b1bc2e40798c61629e7de93fff" data-url="/courses/course-v1:MITX+3.15.1x+2T2017/xblock/block-v1:MITX+3.15.1x+2T2017+type@problem+block@75dbf2b1bc2e40798c61629e7de93fff/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="75dbf2b1bc2e40798c61629e7de93fff-problem-title" aria-describedby="block-v1:MITX+3.15.1x+2T2017+type@problem+block@75dbf2b1bc2e40798c61629e7de93fff-problem-progress" tabindex="-1">
Example 1.4B
</h3>
<div class="problem-progress" id="block-v1:MITX+3.15.1x+2T2017+type@problem+block@75dbf2b1bc2e40798c61629e7de93fff-problem-progress"></div>
<div class="problem">
<div>
<p>Assume that we have a semiconductor where \(m_n^* = 2 m_p^*\). What is the position of \(E_i\) relative to midgap at \(300K\)?</p>
<p>\((E_i - midgap\)) (in \(eV\)):</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="formulaequationinput_75dbf2b1bc2e40798c61629e7de93fff_2_1" class="inputtype formulaequationinput">
<div class="unanswered">
<input type="text" name="input_75dbf2b1bc2e40798c61629e7de93fff_2_1" id="input_75dbf2b1bc2e40798c61629e7de93fff_2_1" data-input-id="75dbf2b1bc2e40798c61629e7de93fff_2_1" value="" aria-describedby="status_75dbf2b1bc2e40798c61629e7de93fff_2_1" size="20"/>
<span class="trailing_text" id="trailing_text_75dbf2b1bc2e40798c61629e7de93fff_2_1"/>
<span class="status unanswered" id="status_75dbf2b1bc2e40798c61629e7de93fff_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_75dbf2b1bc2e40798c61629e7de93fff_2_1" class="answer"/>
<div id="input_75dbf2b1bc2e40798c61629e7de93fff_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_75dbf2b1bc2e40798c61629e7de93fff_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Example 1.4B" />
<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_75dbf2b1bc2e40798c61629e7de93fff" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_75dbf2b1bc2e40798c61629e7de93fff">
<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="75dbf2b1bc2e40798c61629e7de93fff-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="75dbf2b1bc2e40798c61629e7de93fff-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="75dbf2b1bc2e40798c61629e7de93fff-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