review-2

deekshita04 · deekshita04 · commit 877d91b685af · 2025-03-06T21:10:13.000+05:30
diff --git a/experiment/posttest.json b/experiment/posttest.json
@@ -37,29 +37,29 @@
       "difficulty": "beginner"
     },
     {
-      "question": "3. The intrinsic carrier concentration of silicon is 9.65*10^15 m^-3. When p0 is found by dividing this value by n0, it is different from the p0 we calculated.Which one is more accurate?",
+      "question": "3. At higher temperatures T>400K, in a doped n-type semiconductor, where would the Fermi level be?",
       "answers": {
-        "a": "p₀ calculated using the intrinsic carrier concentration formula",
-        "b": "p₀ calculated using the density of states and Fermi level formulas",
-        "c": "Both methods give the same accuracy",
-        "d": "Neither method is accurate"
+        "a": "Much closer to valance band",
+        "b": " Much closer on conduction band",
+        "c": "Fermi Level becomes 0 eV",
+        "d": "In the middle of conduction and valance band"
       },
       "explanations": {
-        "a": "For silicon, the intrinsic carrier concentration relation (n₀ ⋅ p₀ = nᵢ²) holds accurately due to well-defined intrinsic properties. Experimental data confirms that using nᵢ² / n₀ for p₀ is more reliable in silicon-based materials.",
-        "b": "For silicon, the intrinsic carrier concentration relation (n₀ ⋅ p₀ = nᵢ²) holds accurately due to well-defined intrinsic properties. Experimental data confirms that using nᵢ² / n₀ for p₀ is more reliable in silicon-based materials.",
-        "c": "For silicon, the intrinsic carrier concentration relation (n₀ ⋅ p₀ = nᵢ²) holds accurately due to well-defined intrinsic properties. Experimental data confirms that using nᵢ² / n₀ for p₀ is more reliable in silicon-based materials.",
-        "d": "For silicon, the intrinsic carrier concentration relation (n₀ ⋅ p₀ = nᵢ²) holds accurately due to well-defined intrinsic properties. Experimental data confirms that using nᵢ² / n₀ for p₀ is more reliable in silicon-based materials."
+        "a": "Recall what happend to carrier concentration at high temp.",
+        "b": "Fermi level is closer to conduction band for ptype semiconductor.",
+        "c": "No. That implies Ev is negative!!",
+        "d": "Yes, as its intrinsic."
       },
-      "correctAnswer": "a",
+      "correctAnswer": "d",
       "difficulty": "intermediate"
     },
     {
-      "question": "4. In an n-type semiconductor in the extrinsic region, given that ND = 5 × 10^16 m⁻³, Nλ = 1 × 10^15 m⁻³, and ni = 9.65 × 10^15 m⁻³, what is the hole concentration p₀?",
+      "question": "4. In an n-type semiconductor in the extrinsic region, given that ND = 5 × 10^16 m⁻³, and ni = 9.65 × 10^15 m⁻³, what is the hole concentration p₀?",
       "answers": {
         "a": "1.7 × 10^13 m⁻³",
-        "b": "1.8 × 10^13 m⁻³",
+        "b": "1.8 × 10^15 m⁻³",
         "c": "2.0 × 10^13 m⁻³",
-        "d": "1.9 × 10^13 m⁻³"
+        "d": "1.9 × 10^15 m⁻³"
       },
       "explanations": {
         "a": "Using the equations n₀ = ND - NA and p₀ = ni² / n₀, we calculate p₀ as [calculated_value] m⁻³, which matches option [correct_option].",
diff --git a/experiment/pretest.json b/experiment/pretest.json
@@ -36,33 +36,33 @@
       "difficulty": "beginner"
     },
     {
-    "question": "3. Given that f0(E)=0.8 and T=300 K, What is the Fermi level Ef relative to the energy level E=0.2 eV?",
+    "question": "3. Given that f0(E)=0.8 and T=300 K, What could be the possible value of f(E) at T=320K?",
       "answers": {
-        "a": "0.197 eV",
-        "b": "0.542 eV",
-        "c": "0.236 eV",
-        "d": "0.781 eV"
+        "a": "0.1 eV",
+        "b": "0.7 eV",
+        "c": "0.82 eV",
+        "d": "0.9 eV"
       },
       "explanations": {
         "a": "The Fermi-Dirac distribution function gives the probability that an energy states E is occupied by an electron: f(E) = 1 / (1 + exp((E - Ef) / (k * T)))",
         "b": "The Fermi-Dirac distribution function gives the probability that an energy states E is occupied by an electron: f(E) = 1 / (1 + exp((E - Ef) / (k * T)))",
         "c": "The Fermi-Dirac distribution function gives the probability that an energy states E is occupied by an electron: f(E) = 1 / (1 + exp((E - Ef) / (k * T)))",
         "d": "The Fermi-Dirac distribution function gives the probability that an energy states E is occupied by an electron: f(E) = 1 / (1 + exp((E - Ef) / (k * T)))"
       },
-      "correctAnswer": "c",
+      "correctAnswer": "b",
       "difficulty": "intermediate"
     },
     {
       "question": "4. Extrinsic Semiconductors conduct electricity because?",
       "answers": {
-        "a": "Atoms have very few valence electrons",
-        "b": "The valence band of the atoms is almost completely filled",
-        "c": "The valence band of the atoms is partially filled",
-        "d": "Both A and C"
+        "a": "Ionisation energy required by carrier is higher",
+        "b": "Ionisation energies of silicon atoms change",
+        "c": "Carriers ionize easily at room temperature",
+        "d": "None"
       },
       "explanations": 
-      {"a": "Extrinsic semiconductors are doped with impurities to increase their conductivity.In n-type semiconductors, donor atoms provide extra electrons, making electrons the majority charge carriers.In p-type semiconductors, acceptor atoms create holes, making holes the majority charge carriers.These charge carriers (electrons or holes) move under the influence of an electric field, enabling electrical conduction.",
-        "b": "Extrinsic semiconductors are doped with impurities to increase their conductivity.In n-type semiconductors, donor atoms provide extra electrons, making electrons the majority charge carriers.In p-type semiconductors, acceptor atoms create holes, making holes the majority charge carriers.These charge carriers (electrons or holes) move under the influence of an electric field, enabling electrical conduction.",
+      {"a": "Ionisation energy for electron and holes decreases.",
+        "b": "Silicon ionisation energy for valence electron does not change",
         "c": "Extrinsic semiconductors are doped with impurities to increase their conductivity.In n-type semiconductors, donor atoms provide extra electrons, making electrons the majority charge carriers.In p-type semiconductors, acceptor atoms create holes, making holes the majority charge carriers.These charge carriers (electrons or holes) move under the influence of an electric field, enabling electrical conduction.",
         "d": "Extrinsic semiconductors are doped with impurities to increase their conductivity.In n-type semiconductors, donor atoms provide extra electrons, making electrons the majority charge carriers.In p-type semiconductors, acceptor atoms create holes, making holes the majority charge carriers.These charge carriers (electrons or holes) move under the influence of an electric field, enabling electrical conduction."},
       "correctAnswer": "c",
diff --git a/experiment/simulation/css/main.css b/experiment/simulation/css/main.css
@@ -366,4 +366,3 @@
         left: 70%;
     }
 }
-
diff --git a/experiment/simulation/doping.html b/experiment/simulation/doping.html
@@ -16,7 +16,7 @@
 				<div class="v-content instruction-list">
 					<ul style="list-style: disc;">
 						<li>The plot shown is an approximate plot of temperature vs the majority charge carriers.</li>
-						<li>"a" denotes freeze off region, "b" denotes extrinsic region and "c" denotes the intrinsic region </li>
+						<li>"a" denotes extrinsic region, "b" denotes freeze off region and "c" denotes the intrinsic region </li>
 						<li>Label the graph by typing"a", "b" or "c" (in lower case only) in the text boxes </li>
 						<li>Click "Submit" to check if the labeling is correct.</li>
 					</ul>
@@ -40,7 +40,7 @@
 				</div>
 				<div class="submit-quiz">
 					<button type="button" class="button is-primary" id="submit-btn">Submit</button>
-					<div id="resultMessage" style="display: none; text-align: center; font-size: 1.5em; margin-top: 20px; width: 100%;"></div> 
+					<div id="result-message" style="display: none; text-align: center; font-size: 1.5em; margin-top: 20px; width: 100%;"></div> 
 				</div>
 			</div>
         </div>
@@ -49,4 +49,4 @@
     <script src="https://cdn.jsdelivr.net/npm/chart.js"></script>
 	<script src="js/main.js"></script>
 </body>
-</html>
+</html>
diff --git a/experiment/simulation/index.html b/experiment/simulation/index.html
@@ -19,7 +19,9 @@
                     <ul style="list-style: disc;">
                         <li>The following three plots are those of carrier distribution vs Energy.</li>
                         <li>The fermi level of each of these plots is either near the midgap, below midgap or above midgap.</li>
-                        <li>Match the plots to what type of dopants are present in each semiconductor.</li>
+                        <li>Match the plots to what type of dopants are present in each semiconductor </li>
+                        <li>Match the plots by clicking on the images first anf then their label</li>
+                        <li>Once a line is drawn you cannot match either the diagram or label to another label or diagram. To undo your answers, please click on the refresh button. </li>
                     </ul>
                 </div>
             </div>
diff --git a/experiment/simulation/js/main.js b/experiment/simulation/js/main.js
@@ -1,4 +1,3 @@
-
 document.addEventListener("DOMContentLoaded", () => {
     const collapsibles = document.querySelectorAll(".v-collapsible");
 
@@ -19,43 +18,43 @@ document.addEventListener("DOMContentLoaded", () => {
 });
 
 const plot1 = document.getElementById('plot1').getContext('2d');
-        new Chart(plot1, {
-            type: 'line',
-            data: {
-                labels: Array.from({ length: 601 }, (_, i) => i), // Temperature range from 0 to 600 K
-                datasets: [{
-                    label: 'n/N_D',
-                    data: Array.from({ length: 601 }, (_, T) => {
-                        if (T < 100) return T / 100 * 1.5; // Freeze-out region
-                        if (T < 400) return 1.0; // Extrinsic region
-                        return 1 + 0.002 * Math.pow(T - 400, 2); // Intrinsic region
-                    }),
-                    borderColor: 'black',
-                    borderWidth: 2,
-                    fill: false,
-                }]
+new Chart(plot1, {
+    type: 'line',
+    data: {
+        labels: Array.from({ length: 601 }, (_, i) => i), // Temperature range from 0 to 600 K
+        datasets: [{
+            label: 'n/N_D',
+            data: Array.from({ length: 601 }, (_, T) => {
+                if (T < 100) return T / 100 * 1.5; // Freeze-out region
+                if (T < 400) return 1.0; // Extrinsic region
+                return 1 + 0.002 * Math.pow(T - 400, 2); // Intrinsic region
+            }),
+            borderColor: 'black',
+            borderWidth: 2,
+            fill: false,
+        }]
+    },
+    options: {
+        responsive: false,
+        scales: {
+            y: {
+                min: 0, // Minimum y-value
+                max: 5, // Adjusted maximum y-value to fit the data
+                title: {
+                    display: true,
+                    text: 'n/N_D (Ratio)'
+                }
             },
-            options: {
-                responsive: false,
-                scales: {
-                    y: {
-                        min: 0, // Minimum y-value
-                        max: 5, // Adjusted maximum y-value to fit the data
-                        title: {
-                            display: true,
-                            text: 'n/N_D (Ratio)'
-                        }
-                    },
-                    x: {
-                        title: {
-                            display: true,
-                            text: 'Temperature (K)'
-                        }
-                    }
+            x: {
+                title: {
+                    display: true,
+                    text: 'Temperature (K)'
                 }
             }
-        });
-        
+        }
+    }
+});
+
 // Function to validate the inputs
 function validateInputs() {
     const input1 = document.getElementById('plot-input1').value.trim();
@@ -70,11 +69,10 @@ function validateInputs() {
         resultMessage.style.color = 'green';
     } else {
         resultMessage.style.display = 'block';
-        resultMessage.textContent = 'Incorrect';
-        resultMessage.style.color = 'red';
+        resultMessage.textContent = 'Incorrect. Please refer to theory.';
+        resultMessage.style.color = 'black';
     }
 }
 
 // Add event listener to the submit button
-document.getElementById('submit-btn').addEventListener('click', validateInputs);
-
+document.getElementById('submit-btn').addEventListener('click', validateInputs);
diff --git a/experiment/theory.md b/experiment/theory.md
@@ -24,6 +24,68 @@ In other words, states below the fermi level have a low probability of being emp
 
 At 0K, the particles(electrons) are at the lowest energy stae. Hence, all states with energy below Fermi Level (E < E<sub>f</sub>) are completely occupied(Probability = f(E) = 1). All states with E > E<sub>f</sub> are unoccupied (f(E)=0). With increase in temperature, thermal energy is gained by the particles. Hence, particles move from states below the fermi level to the states above the fermi level. As a result th eFermi level function plot 'spreads' out more and more as the temperature increases.
 
+## Electron Density and Hole Density
+Number of electrons per c.c. in the conduction band at energy <br>
+E(i.e. between E & E+dE) = g<sub>c</sub>(E)f(E)dE
+where 
+$$
+E \geq E_{c}
+$$
+
+$$
+n = \int_{E_{c}}^{\inf} g_{c}(E)f(E)dE
+$$
+This can be approximated for
+$$
+E_{C} - E_{F} \geq 3kT
+$$
+by,
+$$
+n = N_{C}e^{E_{f}-E_{C}/k_{B}T}
+$$
+
+Number of holes per c.c. in the valence band at energy <br>
+E(i.e. between E & E+dE) = g<sub>v</sub>(E)[1-f(E)]dE
+where 
+$$
+E \leq E_{v}
+$$
+
+$$
+p = \int_{0}^{E_{v}} g_{v}(E)[1-f(E)]dE
+$$
+This can be approximated for
+$$
+E_{F} - E_{V} \geq 3kT
+$$
+by,
+$$
+p = N_{V}e^{E_{V}-E_{f}/k_{B}T}
+$$
+
+where, N<sub>v</sub> is the effective density of stes in the valence band
+$$
+N_{V} = 2(\frac{m_{v}^{2}k_{B}T}{2\pi \hbar^{2}})^{3/2}
+$$
+
+For an intrinsic material(not doped), the electron concentration is,
+$$
+n_{i} = N_{C}e^{E_{i}-E_{C}/k_{B}T}
+$$
+and the hole concentration is
+$$
+n_{i} = N_{V}e^{E_{V}-E_{i}/k_{B}T}
+$$
+
+Therefore,
+$$
+n = n_{i}e^{E_{f}-E_{i}/k_{B}T}
+$$
+and
+$$
+p = n_{i}e^{E_{i}-E_{f}/k_{B}T}
+$$
+
 
 ## Equilibrium Carrier Densities
 Equilibrium carrier densities refer to the number of carriers in the conduction and valence band with no externally applied bias. The electron densities are calulated by counting and adding up all the filled states. Hence, product of fermi function and DOS(Density of States) (refer to the  <a href="https://virtual-labs.github.io/exp-dos-fermi-iiith/"> previous experiment</a> for details), is taken and integrated for the required energy range. Similarly for holes, Integrating product of probability of state being empty (1-f(E)) and 

Original file line number	Diff line number	Diff line change
`@@ -366,4 +366,3 @@`
`366`	`366`	`left: 70%;`
`367`	`367`	`}`
`368`	`368`	`}`
`369`		`-`