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<h2 class="hd hd-2 unit-title">Photodetectors</h2>
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<h2>Photodetectors</h2>
<ul>
<li>Photodetectors are pn junction diodes operating in reverse bias.</li>
<li>When we shine light on a pn junction and a photon is absorbed within the minority carrier diffusion length (\(L_n\) or \(L_p\)) of the junction, a reverse bias current is produced:</li>
</ul>
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<ul>
<li>Photons with \(E<E_g\) are not absorbed by the photodetector. Photons with \(E_g \geq E\) generate an electron-hole pair.</li>
<li>However, pn photodiodes are slow, since their response time is limited by the time it takes the minority carriers to diffuse into the depletion region.</li>
<li>pin photodiodes use an intrinsic layer (actually, a lightly doped layer) to extend the depletion region. Device response time becomes much faster since most carriers are now generated within the depletion region and move by drift. </li>
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Example 1.1A
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<p>Consider a Ge pin photodiode with a \(5 \; mm^2\) active area. (\(E_g = 0.67 \; eV\) for Ge) Assume that \(1.85 \mu m\) light is arriving at the surface of our photodetector at a rate of \(9 \times 10^{11}\) photons/s.</p>
<p>Calculate the photon flux arriving at the surface of our photodetector:</p>
<p>Flux (in photons/cm<sup>2</sup>s):</p>
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<p>What light intensity does this correspond to? </p>
<p>(You can calculate light intensity \(I\) as flux x q x energy)</p>
<p>\(I\) (in \(W/cm^2\)):</p>
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Exercise 1.1C
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<p>Estimate the current produced by the light.</p>
<p>Current (in \(A\)):</p>
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<p>Instead assume that \(1.65 \mu m\) light is incident on the detector. All of the other parameters remain the same. What happens to the intensity of light and the current generated?</p>
<p>Intensity:</p>
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<input type="radio" name="input_01a7676d7b1c4bac8b0be38a5297000f_2_1" id="input_01a7676d7b1c4bac8b0be38a5297000f_2_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="01a7676d7b1c4bac8b0be38a5297000f_2_1-choice_0-label" for="input_01a7676d7b1c4bac8b0be38a5297000f_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_01a7676d7b1c4bac8b0be38a5297000f_2_1"> The light intensity increases
</label>
</div>
<div class="field">
<input type="radio" name="input_01a7676d7b1c4bac8b0be38a5297000f_2_1" id="input_01a7676d7b1c4bac8b0be38a5297000f_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="01a7676d7b1c4bac8b0be38a5297000f_2_1-choice_1-label" for="input_01a7676d7b1c4bac8b0be38a5297000f_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_01a7676d7b1c4bac8b0be38a5297000f_2_1"> The light intensity decreases
</label>
</div>
<div class="field">
<input type="radio" name="input_01a7676d7b1c4bac8b0be38a5297000f_2_1" id="input_01a7676d7b1c4bac8b0be38a5297000f_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="01a7676d7b1c4bac8b0be38a5297000f_2_1-choice_2-label" for="input_01a7676d7b1c4bac8b0be38a5297000f_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_01a7676d7b1c4bac8b0be38a5297000f_2_1"> The light intensity remains the same
</label>
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<span id="answer_01a7676d7b1c4bac8b0be38a5297000f_2_1"/>
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<span class="status unanswered" id="status_01a7676d7b1c4bac8b0be38a5297000f_2_1" data-tooltip="Not yet answered.">
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<p>Current:</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div class="choicegroup capa_inputtype" id="inputtype_01a7676d7b1c4bac8b0be38a5297000f_3_1">
<fieldset aria-describedby="status_01a7676d7b1c4bac8b0be38a5297000f_3_1">
<div class="field">
<input type="radio" name="input_01a7676d7b1c4bac8b0be38a5297000f_3_1" id="input_01a7676d7b1c4bac8b0be38a5297000f_3_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="01a7676d7b1c4bac8b0be38a5297000f_3_1-choice_0-label" for="input_01a7676d7b1c4bac8b0be38a5297000f_3_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_01a7676d7b1c4bac8b0be38a5297000f_3_1"> The current generated by the light increases
</label>
</div>
<div class="field">
<input type="radio" name="input_01a7676d7b1c4bac8b0be38a5297000f_3_1" id="input_01a7676d7b1c4bac8b0be38a5297000f_3_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="01a7676d7b1c4bac8b0be38a5297000f_3_1-choice_1-label" for="input_01a7676d7b1c4bac8b0be38a5297000f_3_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_01a7676d7b1c4bac8b0be38a5297000f_3_1"> The current generated by the light decreases
</label>
</div>
<div class="field">
<input type="radio" name="input_01a7676d7b1c4bac8b0be38a5297000f_3_1" id="input_01a7676d7b1c4bac8b0be38a5297000f_3_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="01a7676d7b1c4bac8b0be38a5297000f_3_1-choice_2-label" for="input_01a7676d7b1c4bac8b0be38a5297000f_3_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_01a7676d7b1c4bac8b0be38a5297000f_3_1"> The current generated by the light stays the same
</label>
</div>
<div class="field">
<input type="radio" name="input_01a7676d7b1c4bac8b0be38a5297000f_3_1" id="input_01a7676d7b1c4bac8b0be38a5297000f_3_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="01a7676d7b1c4bac8b0be38a5297000f_3_1-choice_3-label" for="input_01a7676d7b1c4bac8b0be38a5297000f_3_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_01a7676d7b1c4bac8b0be38a5297000f_3_1"> The current generated by the light goes to zero
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<span id="answer_01a7676d7b1c4bac8b0be38a5297000f_3_1"/>
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<h3 class="hd hd-3 problem-header" id="dcb639b2d7d14b32a7e95147ef560144-problem-title" aria-describedby="block-v1:MITx+3.15.2x+2T2017+type@problem+block@dcb639b2d7d14b32a7e95147ef560144-problem-progress" tabindex="-1">
Problem 1.1E
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<p>Instead assume that \(2.0 \mu m\) light is incident on the detector. All of the other parameters remain the same. What happens to the intensity of light and the current generated?</p>
<p>Intensity:</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_dcb639b2d7d14b32a7e95147ef560144_2_1">
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<div class="field">
<input type="radio" name="input_dcb639b2d7d14b32a7e95147ef560144_2_1" id="input_dcb639b2d7d14b32a7e95147ef560144_2_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="dcb639b2d7d14b32a7e95147ef560144_2_1-choice_0-label" for="input_dcb639b2d7d14b32a7e95147ef560144_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_dcb639b2d7d14b32a7e95147ef560144_2_1"> The light intensity increases
</label>
</div>
<div class="field">
<input type="radio" name="input_dcb639b2d7d14b32a7e95147ef560144_2_1" id="input_dcb639b2d7d14b32a7e95147ef560144_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="dcb639b2d7d14b32a7e95147ef560144_2_1-choice_1-label" for="input_dcb639b2d7d14b32a7e95147ef560144_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_dcb639b2d7d14b32a7e95147ef560144_2_1"> The light intensity decreases
</label>
</div>
<div class="field">
<input type="radio" name="input_dcb639b2d7d14b32a7e95147ef560144_2_1" id="input_dcb639b2d7d14b32a7e95147ef560144_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="dcb639b2d7d14b32a7e95147ef560144_2_1-choice_2-label" for="input_dcb639b2d7d14b32a7e95147ef560144_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_dcb639b2d7d14b32a7e95147ef560144_2_1"> The light intensity remains the same
</label>
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<span id="answer_dcb639b2d7d14b32a7e95147ef560144_2_1"/>
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<p>Current:</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div class="choicegroup capa_inputtype" id="inputtype_dcb639b2d7d14b32a7e95147ef560144_3_1">
<fieldset aria-describedby="status_dcb639b2d7d14b32a7e95147ef560144_3_1">
<div class="field">
<input type="radio" name="input_dcb639b2d7d14b32a7e95147ef560144_3_1" id="input_dcb639b2d7d14b32a7e95147ef560144_3_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="dcb639b2d7d14b32a7e95147ef560144_3_1-choice_0-label" for="input_dcb639b2d7d14b32a7e95147ef560144_3_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_dcb639b2d7d14b32a7e95147ef560144_3_1"> The current generated by the light increases
</label>
</div>
<div class="field">
<input type="radio" name="input_dcb639b2d7d14b32a7e95147ef560144_3_1" id="input_dcb639b2d7d14b32a7e95147ef560144_3_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="dcb639b2d7d14b32a7e95147ef560144_3_1-choice_1-label" for="input_dcb639b2d7d14b32a7e95147ef560144_3_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_dcb639b2d7d14b32a7e95147ef560144_3_1"> The current generated by the light decreases
</label>
</div>
<div class="field">
<input type="radio" name="input_dcb639b2d7d14b32a7e95147ef560144_3_1" id="input_dcb639b2d7d14b32a7e95147ef560144_3_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="dcb639b2d7d14b32a7e95147ef560144_3_1-choice_2-label" for="input_dcb639b2d7d14b32a7e95147ef560144_3_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_dcb639b2d7d14b32a7e95147ef560144_3_1"> The current generated by the light stays the same
</label>
</div>
<div class="field">
<input type="radio" name="input_dcb639b2d7d14b32a7e95147ef560144_3_1" id="input_dcb639b2d7d14b32a7e95147ef560144_3_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="dcb639b2d7d14b32a7e95147ef560144_3_1-choice_3-label" for="input_dcb639b2d7d14b32a7e95147ef560144_3_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_dcb639b2d7d14b32a7e95147ef560144_3_1"> The current generated by the light goes to zero
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<span id="answer_dcb639b2d7d14b32a7e95147ef560144_3_1"/>
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<h2 class="hd hd-2 unit-title">Photovoltaics</h2>
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<h2>Photovoltaics</h2>
<ul>
<li>Photovoltaics operate in the 4th quadrant, where \(V > 0\) and \(I < 0\).</li>
<li>When connected to a load (such as a battery charger or a lightbulb) with a load resistance \(R_L\)</li>
<ul>
<ul>
<li>\(V = IR\), where \(V\) is voltage, \(I\) is current and \(R\) is the resistance of the load.</li>
</ul>
</ul>
<li>The power output from the solar cell is \(P = IV\).</li>
<li>We select \(R_L\) to maximize \(IV\).</li>
<li>The diagram below shows two potential load resistors \(R_{L,1}\) and \(R_{L,2}\). \(R_{L,2}\) generates more power than \(R_{L,1}\) since the \(IV\) product is larger.</li>
</ul>
<p><img src="/assets/courseware/v1/7b27d7f92f61c6250eca9604de30d397/asset-v1:MITx+3.15.2x+2T2017+type@asset+block/315PV.jpg" alt="The diagram shows two potential load resistors R_L,1 and R_L,2. The IV product for R_2 is larger than the IV product for R_1" width="450" type="saveimage" target="[object Object]" /></p>
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<h3 class="hd hd-3 problem-header" id="2d806413ff1d414c96c0b9156bc4c085-problem-title" aria-describedby="block-v1:MITx+3.15.2x+2T2017+type@problem+block@2d806413ff1d414c96c0b9156bc4c085-problem-progress" tabindex="-1">
Exercise 1.1A
</h3>
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<p>A solar cell has the following performance characteristics:</p>
<table style="width:50%">
<tr>
<td>\(R\) </td>
<td>\(V\) (\(V\))</td>
<td>\(I\) (\(A\))</td>
</tr>
<tr>
<td>\(R_{L,1}\)</td>
<td>\(2.0\)</td>
<td>\(1.2\)</td>
</tr>
<tr>
<td>\(R_{L,2}\)</td>
<td>\(2.5\)</td>
<td>\(1.1\)</td>
</tr>
<tr>
<td>\(R_{L,3}\)</td>
<td>\(3.0\)</td>
<td>\(0.6\)</td>
</tr>
</table>
<br/>
<br/>
<p>What is the power generaged by the solar cell using each of the three load resistors?</p>
<p>Power, \(R_{L,1}\) (in \(W\)):</p>
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<p>Power, \(R_{L,2}\) (in \(W\)):</p>
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<p>Power, \(R_{L,3}\) (in \(W\)):</p>
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Exercise 1.2B
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<p>Which load resistor gives the best solar cell performance?</p>
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Exercise 1.2C
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<p>What resistance does this correspond to?</p>
<p>\(R\) (in \(\Omega\)):</p>
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<h2 class="hd hd-2 unit-title">Absorption</h2>
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<h2>Absorption</h2>
<ul>
<li>When making a solar cell, we want to absorb as much of the incident light as possible.</li>
<li>\(I(x) = I_0exp(-\alpha x)\)</li>
</ul>
<p style="padding-left: 30px;">where \(\alpha\) is the absorption coefficient (usually in \(cm^{-1}\) or \(m^{-1})\)</p>
<p style="padding-left: 30px;">\(I_0\) is the initial intensity of the light</p>
<p style="padding-left: 30px;">\(I(x)\) is the intensity of light a distance \(x\) into the material</p>
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<li>A graph of \(\alpha\) vs. wavelength is shown below for a number of semiconductors:</li>
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<ul>
<li>A large \(\alpha\) means that the material is a good absorber and the light is absorbed efficiently.</li>
<li>\(\alpha\) is highly dependent on both the band gap energy and on the direct or indirect nature of the band gap.</li>
<li>The required thickness of a solar cell depends on \(\alpha\), and is typically a few times \(\alpha\).</li>
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Example 1.3A
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<p>\(600 \; nm\) light is incident on a crystalline silicon solar cell.</p>
<p>How thick does the solar cell need to be to ensure that \(99\%\) of the light is absorbed?</p>
<p>\(x\) (in \(\mu m\)):</p>
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\(\)
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Exercise 1.3B
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<p>Assume instead that we make our solar cell out of amorphous Si. What happens to the required solar cell thickness?</p>
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