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<h2 class="hd hd-2 unit-title">Question 3.1</h2>
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<h2>Question 3.1</h2>
<p>A pn junction is made of two different materials, one with a larger bandgap than the other. Assume <br /> m<sub>n</sub><sup>*</sup> = m<sub>p</sub><sup>*</sup> for each material. The band diagram of each material looks like this:</p>
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Part A
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<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><p>Which band diagram which represents the equillibrium band structure of a junction made from these two materials?</p>
<img src="/assets/courseware/v1/c89b7d153160500d21af0fe8c0e0634d/asset-v1:MITX+3.15.1x+2T2017+type@asset+block/315Ex3_1_B.png" alt="Band Diagram A: E_v is flat, E_f is flat. E_c decreases as we move from Material A to Material B. Band Diagram B: E_v is flat, E_f is always mid-gap. E_c decreases as we move from Material A to Material B. Diagram C: E_c decreases, and E_v increases as we move from Material A to Material B. E_f is mid-gap in Material A and close to E_c in Material B. Band Diagram D: E_c decreases, and E_v increases as we move from Material A to Material B. E_f is flat. " width="800"/>
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<p>Describe the drift and diffusion that take place at equillibrium in the region where the bands are tilted.</p>
<p>Electron Diffusion:</p>
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<p>Hole Diffusion:</p>
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<p>Electron Drift:</p>
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<p>Hole Drift: </p>
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Part B
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<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><p>Now assume that a positive voltage of \(0.2V\) is applied to Material A. Select the band diagram that shows the resulting band structure in this case:</p>
<img src="/assets/courseware/v1/c89b7d153160500d21af0fe8c0e0634d/asset-v1:MITX+3.15.1x+2T2017+type@asset+block/315Ex3_1_B.png" alt="Band Diagram A: E_v is flat, E_f is flat. E_c decreases as we move from Material A to Material B. Band Diagram B: E_v is flat, E_f is always mid-gap. E_c decreases as we move from Material A to Material B. Diagram C: E_c decreases, and E_v increases as we move from Material A to Material B. E_f is mid-gap in Material A and close to E_c in Material B. Band Diagram D: E_c decreases, and E_v increases as we move from Material A to Material B. E_f is flat. " width="800"/>
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<p>When a positive voltage of \(0.2V\) is applied to material, a net electron current and a net hole current begin to flow. </p>
<p>Indicate which statement is correct regarding the electron current:</p>
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<p>Indicate which statement is correct regarding the hole current:</p>
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<b>Part D</b>
<p>
Again assume that a positive voltage of \(0.2V\) is applied to Material A. Click on the curve that represents the electron concentration in Material A when the junction is forward biased:
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Again assume that a positive voltage of \(0.2V\) is applied to Material A. Click on the curve that represents the electron concentration in Material B when the junction is forward biased:
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<h2 class="hd hd-2 unit-title">Question 3.2</h2>
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<h2>question 3.2</h2>
<p>A Schottky diode consists of a junction between a metal and a semiconductor. You can imagine creating a Schottky diode from a pn junction by replacing the p-type material with a metal. The energy diagram is shown below:</p>
<p> </p>
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<p>The quantity eΦ<sub>b</sub> represents the height of the Schottky barrier. In the exercises below, you will need to use the drag-drop tool to create graphs of the charge density, electric field, and the built-in voltage at equillibrium. (Hint: In the metal, any charge present resides only at the interface with the semiconductor, so you can think of the charge density like a delta function.) You may find it helpful to sketch out these graphs for yourself before creating them with the drag-drop tool. </p>
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<b>Part A: Charge Density</b>
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<b>Part B: Electric Field</b>
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<b>Part C: Built-in Voltage</b>
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<h2 class="hd hd-2 unit-title">Question 3.3</h2>
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Question 3.3
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<p>You have a Si pn junction at room temperature with \(N_A = 10^{19} cm^{-3}\) and \(N_D = 10^{18} cm^{-3}\). (You may assume the following carrier mobilities for Silicon: \(\mu_h = 70 cm^2 /V \cdot s\) and \(\mu_e = 250 cm^2/ V \cdot s\). You may also assume a minority carrier lifetime of \(\tau = 10^{-8} s\) for both electrons and holes, and \(n_i = 10^{10}cm^{-3}\).)</p>
<b>Part A</b>
<p>What is the diffusivity of the holes in the Silicon?</p>
<p>\(D_p\) (in \(cm^2/s\)):</p>
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<p>What is the diffusivity of the electrons in the Silicon?</p>
<p>\(D_n\) (in \(cm^2/s\)):</p>
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<p>What is the minority carrier diffusion length for holes?</p>
<p>\(L_p\) (in \(cm\)):</p>
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<p>What is the minority carrier diffusion length for electrons?</p>
<p>\(L_n\) (in \(cm\));</p>
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<b>Part B</b>
<p>Calcuate \(J_0\) for the diode described above.</p>
<p>\(J_0\) (in \(A/cm^2\)):</p>
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<p>Use the ideal diode equation to predict the current density when a forward bias of \(0.02 V\) is applied to the diode.</p>
<p>\(J\) (in \(A/cm^2\)):</p>
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<p>Use the ideal diode equation to predict the current density when a reverse bias of \(-0.04 V\) is applied to the diode.</p>
<p>\(J\) (in \(A/cm^2\)):</p>
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<h2 class="hd hd-2 unit-title">Question 3.4</h2>
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<p>Now we are going to examine Band Diagrams and Concentration Profiles of the diode described in Question 3.3. Remember, you have a Si pn junction with \(N_A = 10^{19} cm^{-3}\) and \(N_D = 10^{18} cm^{-3}\). Again, assume that the diode is operating at room temperature (\(300 K\)). Please use \(n_i = 1 \times 10^{10} cm^{-3}\) in your calculations. </p>
<b>Part A </b>
<p> </p>
<p>The band structure and concentration profile are given below for the diode at equilibrium.</p>
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<p> </p>
<p>Determine the following values for the diode at equilibrium:</p>
<p> </p>
<p> </p>
<p>\(V_0\) (in \(V\)): (Please calculate \(V_0\) to three decimal places.) </p>
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<p>\(E_i - E_F\) on the p<sup>++</sup> side (in \(eV\)):</p>
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<p>\(E_F - E_i\) on the n<sup>+</sup> side (in \(eV\)):</p>
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<p>\(p_p\) (in \(cm^{-3}\)):</p>
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<p>\(n_p\) (in \(cm^{-3}\)):</p>
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<div class="script_placeholder" data-src="/static/js/capa/src/formula_equation_preview.b1967ab28c31.js"/>
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<p>\(n_n\) (in \(cm^{-3}\)):</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 6" role="group"><div id="formulaequationinput_28270b4bf98347a69c5d75cd8042f21e_7_1" class="inputtype formulaequationinput">
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<p>\(p_n\) (in \(cm^{-3}\)):</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 7" role="group"><div id="formulaequationinput_28270b4bf98347a69c5d75cd8042f21e_8_1" class="inputtype formulaequationinput">
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<p>\(W\) (in \(cm\)):</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 8" role="group"><div id="formulaequationinput_28270b4bf98347a69c5d75cd8042f21e_9_1" class="inputtype formulaequationinput">
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<b>Part B </b>
<p> </p>
<p>The band structure and concentration profile are given below for the same diode when a forward bias voltage of \(1V\) is applied. </p>
<img width="700" src="/assets/courseware/v1/496b4d4198cf00ba501be41023c99186/asset-v1:MITX+3.15.1x+2T2017+type@asset+block/315Ex3_4_new2.png"/>
<p> </p>
<p>Determine the following values for the diode under the forward bias conditions described above:</p>
<p> </p>
<p> </p>
<p>\(V_0 - V_A\) (in \(V\)):</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="formulaequationinput_195b6d464f224d77b92b6077daeb4ae3_2_1" class="inputtype formulaequationinput">
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<span class="trailing_text" id="trailing_text_195b6d464f224d77b92b6077daeb4ae3_2_1"/>
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<p>\(E_i - E_{f,p}\) (in \(eV\)):</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div id="formulaequationinput_195b6d464f224d77b92b6077daeb4ae3_3_1" class="inputtype formulaequationinput">
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<p>\(E_{f,n} - E_{i}\) (in \(eV\)):</p>
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<p>\(n_p\) (in \(cm^{-3}\)):</p>
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<input type="text" name="input_195b6d464f224d77b92b6077daeb4ae3_5_1" id="input_195b6d464f224d77b92b6077daeb4ae3_5_1" data-input-id="195b6d464f224d77b92b6077daeb4ae3_5_1" value="" aria-describedby="status_195b6d464f224d77b92b6077daeb4ae3_5_1" size="20"/>
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<img src="/static/images/spinner.bc34f953403f.gif" class="loading" alt="Loading"/>
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<p>\(p_n\) (in \(cm^{-3}\)):</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 5" role="group"><div id="formulaequationinput_195b6d464f224d77b92b6077daeb4ae3_6_1" class="inputtype formulaequationinput">
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\(\)
<img src="/static/images/spinner.bc34f953403f.gif" class="loading" alt="Loading"/>
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<div class="script_placeholder" data-src="/static/js/capa/src/formula_equation_preview.b1967ab28c31.js"/>
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<p>\(W\) (in \(cm\)):</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 6" role="group"><div id="formulaequationinput_195b6d464f224d77b92b6077daeb4ae3_7_1" class="inputtype formulaequationinput">
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<b>Part C</b>
<p> </p>
<p>The band structure and concentration profile are given below for the diode when a reverse bias voltage of \(1V\) is applied. </p>
<img width="700" src="/assets/courseware/v1/280dbff1618195180606f19fd43c80c4/asset-v1:MITX+3.15.1x+2T2017+type@asset+block/315Ex3_4_new3.png"/>
<p> </p>
<p>Determine the following values for the diode under the reverse bias conditions described above:</p>
<p> </p>
<p> </p>
<p>\(V_0 - V_A\) (in \(V\)):</p>
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<p>\(E_i - E_{f,p}\) (in \(eV\)):</p>
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<p>\(E_{f,n} - E_i\) (in \(eV\)):</p>
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<p>\(W\) (in \(cm\)):</p>
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