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<h2 class="hd hd-2 unit-title">Problem 1.1</h2>
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<h2>Problem 1.1</h2>
<p>The operating characteristics of an ASE Americas Solar Panel are shown below. These data are laboratory-generated by the manufacturer, and show both Darkened and Fully-Illuminated behavior. </p>
<p><img width="600" src="/assets/courseware/v1/8d4fbc148622b1559a44dad63185f381/asset-v1:MITx+3.15.2x+2T2017+type@asset+block/315SolarCell.png" type="saveimage" target="[object Object]" /></p>
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<p>Now consider the following experiment: You would like to know how the solar cell's real-life performance compares to the laboratory measurements. You take the solar cell outside and you measure the following data. (These data were actually collected by a class of 3.15 students at MIT in October of 2010.) </p>
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<p>Were these data collected on a sunny day or an overcast day?</p>
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<p>What was the maximum generated power that we measured from the solar cell?</p>
<p>Power (in Watts):</p>
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<p>How long would the cell need to operate in Boston in October to obtain \(1kWh\) of energy?</p>
<p>Time (in hours):</p>
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<b> Part B </b>
<p>Consider the laboratory-generated curve again. What is the maximum power point shown on the laboratory-generated curve?</p>
<p>Power (in \(W\)):</p>
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<p>What is the ideal resistance of the load for the cell to generate maximum power under full illumination?</p>
<p>\(R_{load}\) (in \(\Omega\)):</p>
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<p>Compare this load to the load presented by an electric light bulb. Assume you have a \(60W\) light bulb connected to a \(120 V\) wall outlet.</p>
<p>\(R_{load}\) (in \(\Omega\)):</p>
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<h2>Problem 1.2</h2>
<p>For this week's final homework problem, we are going to consider the design of a silicon (\(E_g = 1.1 eV)\) pin photodiode. This photodiode should have an active area of \(1 mm^2\), with as fast a response time as possible when used in conjunction with a \(50\Omega\) load resistor. You should take \(\epsilon_r = 11.8\), and \(v_s\), the electron saturation drift velocity, as \(10^5 m/s\). Please note that there are many photodiode designs that would satisfy the contrants of this problem; we are going to work through one potential solution. </p>
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<p>First, let's consider the width of the intrinsic layer, \(W_i\). Smaller \(W_i\) means faster frequency response; however, if we continue to decrease \(W_i\) too much, the frequency response will become dominated by the RC time constant of the electrical circuit. </p>
<p>Given these two considerations, we determine that the optimal width of the intrinsic layer, \(W_i\) is \(23 \mu m\). </p>
<p>What frequency does this correspond to?</p>
<p>\(f_{max}\) (in GHz):</p>
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<p>Estimate the optimum detection wavelength.</p>
<p>\(\lambda_g\) (in \(\mu m\)):</p>
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<b>Part C </b>
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<p>Finally, let's estimate the minimum detectable light intensity, which will be limited by the noise of the system. This requires that the photogenerated current exceeds the minimum detectable current. You may assume that this minimum detectable current \(I_{min} = 10^{-7}A\).</p>
<p>At what rate must photons arrive at our photodiode to produce the minimum detectable current?</p>
<p>photons per second:</p>
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<p>What flux of photons on the active area is required to produce the minimum detectable current?</p>
<p>photon flux (in \(\frac{photons}{cm^2 s}\)):</p>
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<p>What light intensity does this correspond to?</p>
<p>\(I\) (in \(W/cm^2\)):</p>
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