review changes

Author: deekshita04

experiment/posttest.json

@@ -4,10 +4,10 @@
     {
       "question": "1. Given T = 300 K, m<sub>n</sub> = 1.08 × 10<sup>-31</sup> kg, m<sub>p</sub> = 0.56 × 10<sup>-31</sup> kg, h = 6.626 × 10<sup>-34</sup> J·s, E<sub>F</sub> = 0.4 eV, E<sub>C</sub> = 0.2 eV, and E<sub>V</sub> = 0.1 eV, what are the electron concentration n0 and hole concentration p0?",
       "answers": {
-        "a": "n0 = 7.3 x 10<sup>26</sup> m, p0 = 1.1<sup>-3</sup> x 10<sup>18</sup> m<sup>-3</sup>",
-        "b": "n0 = 2.5 x 10<sup>26</sup> m, p0 = 3.0<sup>-3</sup> x 10<sup>18</sup> m<sup>-3</sup>",
-        "c": "n0 = 4.1 x 10<sup>26</sup> m, p0 = 1.8<sup>-3</sup> x 10<sup>18</sup> m<sup>-3</sup>",
-        "d": "n0 = 5.2 x 10<sup>26</sup> m, p0 = 2.7<sup>-3</sup> x 10<sup>18</sup> m<sup>-3</sup>"
+        "a": "n0 = 7.3 x 10<sup>25</sup> m<sup>-3</sup>, p0 = 1.1<sup>-3</sup> x 10<sup>17</sup> m<sup>-3</sup>",
+        "b": "n0 = 2.5 x 10<sup>25</sup> m<sup>-3</sup>, p0 = 3.0<sup>-3</sup> x 10<sup>17</sup> m<sup>-3</sup>",
+        "c": "n0 = 4.1 x 10<sup>25</sup> m<sup>-3</sup>, p0 = 1.8<sup>-3</sup> x 10<sup>17</sup> m<sup>-3</sup>",
+        "d": "n0 = 5.2 x 10<sup>25</sup> m<sup>-3</sup>, p0 = 2.7<sup>-3</sup> x 10<sup>17</sup> m<sup>-3</sup>"
       },
 
       "explanations": {
@@ -54,18 +54,18 @@
       "difficulty": "intermediate"
     },
     {
-      "question": "4. In an n-type semiconductor in the extrinsic region, given that ND = 5 × 10<sup>16</sup> , and ni = 9.65 × 10<sup>15</sup> m⁻³, what is the hole concentration p₀?",
+      "question": "4. In an n-type semiconductor in the extrinsic region, given that NN<sub>D</sub> = 5 × 10<sup>16</sup> , and n<sub>i</sub> = 9.65 × 10<sup>15</sup> m⁻³, what is the hole concentration p₀?",
       "answers": {
         "a": "1.72 × 10<sup>13</sup> m⁻³",
         "b": "1.86 × 10<sup>15</sup> m⁻³",
         "c": "2.09 × 10<sup>13</sup> m⁻³",
         "d": "1.95 × 10<sup>15</sup> m⁻³"
       },
       "explanations": {
-        "a": "Using the equations n₀ = N<sub>D</sub> and p₀ = n<sub>i</sub>² / n₀, we calculate p₀ as [calculated_value] m⁻³, which matches option [correct_option].",
-        "b": "Using the equations n₀ = ND - NA and p₀ = ni² / n₀, we calculate p₀ as [calculated_value] m⁻³, which matches option [correct_option].",
-        "c": "Using the equations n₀ = ND - NA and p₀ = ni² / n₀, we calculate p₀ as [calculated_value] m⁻³, which matches option [correct_option].",
-        "d": "Using the equations n₀ = ND - NA and p₀ = ni² / n₀, we calculate p₀ as [calculated_value] m⁻³, which matches option [correct_option]."
+        "a": "Using the equations n₀ = N<sub>D</sub> and p₀ = n<sub>i</sub>² / n₀, we calculate p₀ as 1.86 × 10<sup>15</sup> m⁻³, which matches option 'b'.",
+        "b": "Using the equations n₀ = N<sub>D</sub> and p₀ = n<sub>i</sub>² / n₀, we calculate p₀ as 1.86 × 10<sup>15</sup> m⁻³, which matches option 'b'.",
+        "c": "Using the equations n₀ = N<sub>D</sub> and p₀ = n<sub>i</sub>² / n₀, we calculate p₀ as 1.86 × 10<sup>15</sup> m⁻³, which matches option 'b'.",
+        "d": "Using the equations n₀ = N<sub>D</sub> and p₀ = n<sub>i</sub>² / n₀, we calculate p₀ as 1.86 × 10<sup>15</sup> m⁻³, which matches option 'b'."
       },
       "correctAnswer": "b",
       "difficulty": "beginner"

experiment/pretest.json

@@ -36,7 +36,7 @@
       "difficulty": "beginner"
     },
     {
-    "question": "3. Given that f0(E)=0.8 and T=300 K, What could be the possible value of f(E) at T=320K?",
+    "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": "0.1 eV",
         "b": "0.7 eV",

experiment/theory.md

@@ -18,19 +18,22 @@ $$
 f_{o}(E) = \frac{1}{2}\tag{3.2}
 $$
 
-In other words, states below the fermi level have a low probability of being empty and the states above the fermi level have a low probability of being filled and states above the fermi level have a high probability of being filled
+In other words, states above the fermi level have a low probability of being empty and the states below the fermi level have a low probability of being filled.
 
 <p><img src="images/Fig_3.2.png" ></p> 
 
-At 0 K, 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.
+At 0 K, the particles (electrons) are at the lowest energy state. 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 the Fermi 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
+$$
+E \quad(i.e. \quad between \quad E \quad & \quad E+dE) \quad = g_{c}(E)f(E)dE
+$$
 where 
 $$
 E \geq E_{c}\tag{3.3}
 $$
+and g<sub>c</sub>(E)f(E)dE corresponds to the density of states in the conduction band.
 
 $$
 n = \int_{E_{c}}^{\inf} g_{c}(E)f(E)dE \tag{3.4}
@@ -57,7 +60,7 @@ E \leq E_{v} \tag{3.8}
 $$
 
 $$
-p = \int_{0}^{E_{v}} g_{v}(E)[1-f(E)]dE \tag{3.9}
+p = \int_{-inf}^{E_{v}} g_{v}(E)[1-f(E)]dE \tag{3.9}
 $$
 This can be approximated for
 $$
@@ -123,7 +126,7 @@ $$
 This equation describes the law of mass action and relates the carrier concentration in doped semiconductor to intrinsic semiconductor.
 
 ## Intrinsic Fermi level 
-For an n-type semiconductor, the fermi level is Between the intrinsic level(E<sub>i</sub>) conduction band (E<sub>C</sub>). The number of electrons in the conduction band is much larger and donor band energy(E<sub>D</sub>) is closer to the conduction band. Similarly, the fermi level of a p-type semiconductor is between (E<sub>i</sub>) valence band (E<sub>V</sub>) . The number of holes in the valence band is much larger and acceptor band energy ((E<sub>A</sub>)) is closer to conduction band.
+For an n-type semiconductor, the fermi level is Between the intrinsic level(E<sub>i</sub>) conduction band (E<sub>C</sub>). The number of electrons in the conduction band is much larger and donor band energy(E<sub>D</sub>) is closer to the conduction band. Similarly, the fermi level of a p-type semiconductor is between (E<sub>i</sub>) valence band (E<sub>V</sub>) . The number of holes in the valence band is much larger and acceptor band energy ((E<sub>A</sub>)) is closer to valence band.
 
 We found that the electron density can be written as-
 $$
@@ -170,7 +173,7 @@ The total carrier concentration is always represented by 𝑛 for free electrons
 
 ## Ionisation of Dopant and Temperature Dependence
 
-Ionisation of dopant with increase in temperature is shown below. At 0K, there is noionization of the dopant impurities nor of any Silicon atom, as a result the semiconductor has almost zero carriers (called Freeze Out). As temperature increases slowly 0-100 K, only the dopant impurities start ionizing and result in an increase in number of carriers until all dopants are ionized (n=N_D) (100K < T < 400K). Contribution by silicon atoms is not much at these temperatures. However, at much higher temperatures (T >400 K), silicon also starts to generate large number of electron hole pair and total carrier concentration increases drastically. This is shown by region marked as ‘intrinsic 
+Ionisation of dopant with increase in temperature is shown below. At 0K, there is no ionization of the dopant impurities nor of any Silicon atom, as a result the semiconductor has almost zero carriers (called Freeze Out). As temperature increases slowly 0-100 K, only the dopant impurities start ionizing and result in an increase in number of carriers until all dopants are ionized (n=N_D) (100K < T < 400K). Contribution by silicon atoms is not much at these temperatures. However, at much higher temperatures (T >400 K), silicon also starts to generate large number of electron hole pair and total carrier concentration increases drastically. This is shown by region marked as ‘intrinsic 
 region.
 
 <div align="center"><img src="images/Fig_3.3.png" width="400ps" height="auto"></div>