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Question 4.1
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<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><p>Consider a pnp silicon bipolar junction transistor. Assume that the emitter has a doping level of \(10^{19} cm^{-3}\), the base has a doping level of \(10^{17} cm^{-3}\), and the collector has a doping level of \(10^{15} cm^{-3}\).</p>
<p>What is the gain of the transistor when operated in forward active mode?</p>
<p>\(\beta\)</p>
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<p>Now consider a pnp BJT in which the base contact is floating (i.e. not electrically connected to anything). We put the emitter at \(0 V\) and apply a negative voltage\( V_C\) to the collector. Which of the following statements are true:</p>
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<input type="checkbox" name="input_602afee2307f4329960381f7412e7aef_2_1[]" id="input_602afee2307f4329960381f7412e7aef_2_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="602afee2307f4329960381f7412e7aef_2_1-choice_0-label" for="input_602afee2307f4329960381f7412e7aef_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_602afee2307f4329960381f7412e7aef_2_1"> A very large current flows between the emitter and the collector.
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<input type="checkbox" name="input_602afee2307f4329960381f7412e7aef_2_1[]" id="input_602afee2307f4329960381f7412e7aef_2_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="602afee2307f4329960381f7412e7aef_2_1-choice_1-label" for="input_602afee2307f4329960381f7412e7aef_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_602afee2307f4329960381f7412e7aef_2_1"> A very small current flows between the emitter and the collector.
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<input type="checkbox" name="input_602afee2307f4329960381f7412e7aef_2_1[]" id="input_602afee2307f4329960381f7412e7aef_2_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="602afee2307f4329960381f7412e7aef_2_1-choice_2-label" for="input_602afee2307f4329960381f7412e7aef_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_602afee2307f4329960381f7412e7aef_2_1"> No current flows between the emitter and the collector.
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<input type="checkbox" name="input_602afee2307f4329960381f7412e7aef_2_1[]" id="input_602afee2307f4329960381f7412e7aef_2_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="602afee2307f4329960381f7412e7aef_2_1-choice_3-label" for="input_602afee2307f4329960381f7412e7aef_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_602afee2307f4329960381f7412e7aef_2_1"> The B-C junction is forward biased.
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<p>Now suppose that we shine visible light just on the base region of the BJT described in the previous question. Indicate which of the following statements are true of this phototransistor:</p>
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<input type="checkbox" name="input_602afee2307f4329960381f7412e7aef_3_1[]" id="input_602afee2307f4329960381f7412e7aef_3_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="602afee2307f4329960381f7412e7aef_3_1-choice_1-label" for="input_602afee2307f4329960381f7412e7aef_3_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_602afee2307f4329960381f7412e7aef_3_1"> A small current flows between the emitter and the collector.
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<input type="checkbox" name="input_602afee2307f4329960381f7412e7aef_3_1[]" id="input_602afee2307f4329960381f7412e7aef_3_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="602afee2307f4329960381f7412e7aef_3_1-choice_2-label" for="input_602afee2307f4329960381f7412e7aef_3_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_602afee2307f4329960381f7412e7aef_3_1"> No current flows between the emitter and the collector.
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<input type="checkbox" name="input_602afee2307f4329960381f7412e7aef_3_1[]" id="input_602afee2307f4329960381f7412e7aef_3_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="602afee2307f4329960381f7412e7aef_3_1-choice_3-label" for="input_602afee2307f4329960381f7412e7aef_3_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_602afee2307f4329960381f7412e7aef_3_1"> The photogenerated holes in the base flow into the emitter.
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<input type="checkbox" name="input_602afee2307f4329960381f7412e7aef_3_1[]" id="input_602afee2307f4329960381f7412e7aef_3_1_choice_4" class="field-input input-checkbox" value="choice_4"/><label id="602afee2307f4329960381f7412e7aef_3_1-choice_4-label" for="input_602afee2307f4329960381f7412e7aef_3_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_602afee2307f4329960381f7412e7aef_3_1"> The photogenerated holes in the base flow into the collector.
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<input type="checkbox" name="input_602afee2307f4329960381f7412e7aef_3_1[]" id="input_602afee2307f4329960381f7412e7aef_3_1_choice_5" class="field-input input-checkbox" value="choice_5"/><label id="602afee2307f4329960381f7412e7aef_3_1-choice_5-label" for="input_602afee2307f4329960381f7412e7aef_3_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_602afee2307f4329960381f7412e7aef_3_1"> The light has the effect of biasing the base because it provides the electrons that are normally provided by the base current.
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<h2 class="hd hd-2 unit-title">Question 4.2</h2>
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<h2>Question 4.2</h2>
<p>An ideal MOS junction is shown below. Band bending has caused the Fermi level to touch the intrinsic level at the Si/SiO<sub>2</sub> interface. </p>
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<div class="problem">
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<p>Which of the following equations describes the electric field in the device described above?</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_c0ccd8f6a0674c8e9160a5f0a5ec2152_2_1">
<fieldset aria-describedby="status_c0ccd8f6a0674c8e9160a5f0a5ec2152_2_1">
<div class="field">
<input type="radio" name="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_2_1" id="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_2_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="c0ccd8f6a0674c8e9160a5f0a5ec2152_2_1-choice_0-label" for="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_c0ccd8f6a0674c8e9160a5f0a5ec2152_2_1"> \(E=\int{\rho}(x)dx\)
</label>
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<div class="field">
<input type="radio" name="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_2_1" id="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="c0ccd8f6a0674c8e9160a5f0a5ec2152_2_1-choice_1-label" for="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_c0ccd8f6a0674c8e9160a5f0a5ec2152_2_1"> \(E=-\int{\rho}(x)dx\)
</label>
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<div class="field">
<input type="radio" name="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_2_1" id="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="c0ccd8f6a0674c8e9160a5f0a5ec2152_2_1-choice_2-label" for="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_c0ccd8f6a0674c8e9160a5f0a5ec2152_2_1"> \(E=\frac{1}{\epsilon_{0}\epsilon_{r}}\int{\rho}(x)dx\)
</label>
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<div class="field">
<input type="radio" name="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_2_1" id="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_2_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="c0ccd8f6a0674c8e9160a5f0a5ec2152_2_1-choice_3-label" for="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_c0ccd8f6a0674c8e9160a5f0a5ec2152_2_1"> \(E=-\frac{1}{\epsilon_{0}\epsilon_{r}}\int{\rho}(x)dx\)
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<span id="answer_c0ccd8f6a0674c8e9160a5f0a5ec2152_2_1"/>
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<p>Which of the following equations describes the potential in the device described above?</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div class="choicegroup capa_inputtype" id="inputtype_c0ccd8f6a0674c8e9160a5f0a5ec2152_3_1">
<fieldset aria-describedby="status_c0ccd8f6a0674c8e9160a5f0a5ec2152_3_1">
<div class="field">
<input type="radio" name="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_3_1" id="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_3_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="c0ccd8f6a0674c8e9160a5f0a5ec2152_3_1-choice_0-label" for="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_3_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_c0ccd8f6a0674c8e9160a5f0a5ec2152_3_1"> \(V=\int{E}(x)dx\)
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<input type="radio" name="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_3_1" id="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_3_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="c0ccd8f6a0674c8e9160a5f0a5ec2152_3_1-choice_1-label" for="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_3_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_c0ccd8f6a0674c8e9160a5f0a5ec2152_3_1"> \(V=-\int{E}(x)dx\)
</label>
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<div class="field">
<input type="radio" name="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_3_1" id="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_3_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="c0ccd8f6a0674c8e9160a5f0a5ec2152_3_1-choice_2-label" for="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_3_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_c0ccd8f6a0674c8e9160a5f0a5ec2152_3_1"> \(V=\frac{1}{\epsilon_{0}\epsilon_{r}}\int{E}(x)dx\)
</label>
</div>
<div class="field">
<input type="radio" name="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_3_1" id="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_3_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="c0ccd8f6a0674c8e9160a5f0a5ec2152_3_1-choice_3-label" for="input_c0ccd8f6a0674c8e9160a5f0a5ec2152_3_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_c0ccd8f6a0674c8e9160a5f0a5ec2152_3_1"> \(V=-\frac{1}{\epsilon_{0}\epsilon_{r}}\int{E}(x)dx\)
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<p>Indicate if the following statements are true or false:</p>
<p>The semiconductor is under equillibrium:</p>
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<p>The entire device is under equillibrium:</p>
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<p>Right next to the junction, the electron concentration is equal to the intrinsic carrier concentration:</p>
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<p>Far from the junction, the electron concentration is equal to the intrinsic carrier concentration:</p>
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<h2 class="hd hd-2 unit-title">Question 4.3</h2>
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<h2>question 4.3</h2>
<p>A semiconductor-oxide-semicondutor (SOS) structure can be built similar to a MOS structure. You can assume that all the bands are flat in the SOS structure when the semiconductor is intrinsic, so it looks like this: <img alt="" src="/assets/courseware/v1/a1ea6d519ea6e7a6be7d7cf19aa6a216/asset-v1:MITX+3.15.1x+2T2017+type@asset+block/315PS4Ex3_4.jpg" width="500" /></p>
<p>Now suppose that one layer is p-type and the other is n-type. The SOS band structure is shown below under a variety of different conditions. Answer the questions below pertaining to the SOS structure.</p>
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<p>
<b> Figure 1: </b>
</p>
<img alt="" src="/assets/courseware/v1/59138719b6b5e579877e362c83ce0206/asset-v1:MITX+3.15.1x+2T2017+type@asset+block/315PS4Ex3_2.jpg" width="500"/>
<p>Figure 1 represents the SOS band structure under what condition?</p>
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<option value="option_ab24a17bc93c49c586b59d2ddcc110e7_2_1_dummy_default">Select an option</option>
<option value="Equillibrium"> Equillibrium</option>
<option value="The p-side is positively biased"> The p-side is positively biased</option>
<option value="The p-side is negatively biased"> The p-side is negatively biased</option>
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<b> Figure 2: </b>
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<img alt="" src="/assets/courseware/v1/ee2e6b6e8bc8d8850128a6ffe1173ca0/asset-v1:MITX+3.15.1x+2T2017+type@asset+block/315PS4Ex3_1.jpg" width="500"/>
<p>Figure 2 represents the SOS band structure under what condition?</p>
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<b> Figure 3: </b>
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<img alt="" src="/assets/courseware/v1/c41c5fe8d568176de885b42b14d203c2/asset-v1:MITX+3.15.1x+2T2017+type@asset+block/315PS4Ex3_3.jpg" width="500"/>
<p>Figure 3 represents the SOS band structure under what condition?</p>
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<p>Consider the "forward" bias condition shown in Figure 1. Which statements are true about the device under this bias condition?</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_6bcc1728ef054bbf8e5d759be2279f82_2_1">
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<input type="checkbox" name="input_6bcc1728ef054bbf8e5d759be2279f82_2_1[]" id="input_6bcc1728ef054bbf8e5d759be2279f82_2_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="6bcc1728ef054bbf8e5d759be2279f82_2_1-choice_0-label" for="input_6bcc1728ef054bbf8e5d759be2279f82_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_6bcc1728ef054bbf8e5d759be2279f82_2_1"> Both sides of the semiconductor have more depletion than in the unbiased case.
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<input type="checkbox" name="input_6bcc1728ef054bbf8e5d759be2279f82_2_1[]" id="input_6bcc1728ef054bbf8e5d759be2279f82_2_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="6bcc1728ef054bbf8e5d759be2279f82_2_1-choice_1-label" for="input_6bcc1728ef054bbf8e5d759be2279f82_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_6bcc1728ef054bbf8e5d759be2279f82_2_1"> Both sides of the semiconductor have less depletion than in the unbiased case.
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<input type="checkbox" name="input_6bcc1728ef054bbf8e5d759be2279f82_2_1[]" id="input_6bcc1728ef054bbf8e5d759be2279f82_2_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="6bcc1728ef054bbf8e5d759be2279f82_2_1-choice_2-label" for="input_6bcc1728ef054bbf8e5d759be2279f82_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_6bcc1728ef054bbf8e5d759be2279f82_2_1"> This bias condition could lead to accumulation in the semiconductors. (Assume a sufficiently large bias is applied.)
</label>
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<div class="field">
<input type="checkbox" name="input_6bcc1728ef054bbf8e5d759be2279f82_2_1[]" id="input_6bcc1728ef054bbf8e5d759be2279f82_2_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="6bcc1728ef054bbf8e5d759be2279f82_2_1-choice_3-label" for="input_6bcc1728ef054bbf8e5d759be2279f82_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_6bcc1728ef054bbf8e5d759be2279f82_2_1"> This bias condition could lead to inversion in the semicondutors. (Assume a sufficiently large bias is applied.)
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<input type="checkbox" name="input_6bcc1728ef054bbf8e5d759be2279f82_2_1[]" id="input_6bcc1728ef054bbf8e5d759be2279f82_2_1_choice_4" class="field-input input-checkbox" value="choice_4"/><label id="6bcc1728ef054bbf8e5d759be2279f82_2_1-choice_4-label" for="input_6bcc1728ef054bbf8e5d759be2279f82_2_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_6bcc1728ef054bbf8e5d759be2279f82_2_1"> No current flows when the device is forward biased.
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<p>Consider the "reverse" bias condition shown in Figure 3. Which statements are true about the device under this bias condition?</p>
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<input type="checkbox" name="input_6bcc1728ef054bbf8e5d759be2279f82_3_1[]" id="input_6bcc1728ef054bbf8e5d759be2279f82_3_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="6bcc1728ef054bbf8e5d759be2279f82_3_1-choice_0-label" for="input_6bcc1728ef054bbf8e5d759be2279f82_3_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_6bcc1728ef054bbf8e5d759be2279f82_3_1"> Both sides of the semiconductor have more depletion than in the unbiased case.
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<input type="checkbox" name="input_6bcc1728ef054bbf8e5d759be2279f82_3_1[]" id="input_6bcc1728ef054bbf8e5d759be2279f82_3_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="6bcc1728ef054bbf8e5d759be2279f82_3_1-choice_1-label" for="input_6bcc1728ef054bbf8e5d759be2279f82_3_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_6bcc1728ef054bbf8e5d759be2279f82_3_1"> Both sides of the semiconductor have less depletion than in the unbiased case.
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<input type="checkbox" name="input_6bcc1728ef054bbf8e5d759be2279f82_3_1[]" id="input_6bcc1728ef054bbf8e5d759be2279f82_3_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="6bcc1728ef054bbf8e5d759be2279f82_3_1-choice_2-label" for="input_6bcc1728ef054bbf8e5d759be2279f82_3_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_6bcc1728ef054bbf8e5d759be2279f82_3_1"> This bias condition could lead to accumulation in the semiconductors. (Assume a sufficiently large bias is applied.)
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<div class="field">
<input type="checkbox" name="input_6bcc1728ef054bbf8e5d759be2279f82_3_1[]" id="input_6bcc1728ef054bbf8e5d759be2279f82_3_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="6bcc1728ef054bbf8e5d759be2279f82_3_1-choice_3-label" for="input_6bcc1728ef054bbf8e5d759be2279f82_3_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_6bcc1728ef054bbf8e5d759be2279f82_3_1"> This bias condition could lead to inversion in the semiconductors. (Assume a sufficiently large bias is applied.)
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<div class="field">
<input type="checkbox" name="input_6bcc1728ef054bbf8e5d759be2279f82_3_1[]" id="input_6bcc1728ef054bbf8e5d759be2279f82_3_1_choice_4" class="field-input input-checkbox" value="choice_4"/><label id="6bcc1728ef054bbf8e5d759be2279f82_3_1-choice_4-label" for="input_6bcc1728ef054bbf8e5d759be2279f82_3_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_6bcc1728ef054bbf8e5d759be2279f82_3_1"> No current flows when the device is reverse biased.
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Question 4.4
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<p>A MOSFET is made from an n-type semiconductor (meaning that the source and the drain are p-type regions, and the body is n-type). Band diagrams of the MOS gate under different applied V<sub>g</sub> are shown below: </p>
<p>
<b>Figure 1 </b>
</p>
<img alt="" src="/assets/courseware/v1/461ff7e5a58b843cbd8fc5cb9eebd237/asset-v1:MITX+3.15.1x+2T2017+type@asset+block/315PS4Ex4_1.jpg" width="400"/>
<p>Describe the gate voltage applied in Figure 1:</p>
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<option value="\(V_g \lt 0\) "> \(V_g \lt 0\) </option>
<option value="\(V_g = 0\)"> \(V_g = 0\)</option>
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<p>What is the condition of the semicondutor shown in Figure 1?</p>
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<option value="accumulation"> accumulation</option>
<option value="depletion"> depletion</option>
<option value="inversion"> inversion</option>
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<p>
<b>Figure 2 </b>
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<p>Describe the gate voltage applied in Figure 2:</p>
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<p>What is the condition of the semiconductor shown in Figure 2?</p>
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