<Success style='float: center;margin-top:16rem;text-align:center'><B>Field and Potential in P-n Junction</B></Success> <div style='float: right; width:0%;'>  </div>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Field and Potential in P-n Junction</B></Success></p> <p><Primary style="float:center;text-align:center;font-size:24px;"><B>P-n Junction</B></Primary></p> <hr> <main> <div style='float: left; text-align: left; font-size: 22px; width:90%;'> <ol> <li>By properly doping impurities in a semiconductor material one can make p-type and n-type regions in the same sheet which meet at a planer layer. This system is called p-n junction.</li> </ol> </div> <img src='https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/6071114c-09f2-4633-ebc5-5a21eeccd600/public' width=28%> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style='font-size:18px'> <span style="color:blue">P-n Junction</span>$\to$Depletion Region$\to$Depletion Layer$\to$Energy in Semiconductor$\to$Forward Bias </footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Field and Potential in P-n Junction</B></Success></p> <p><Primary style="float:center;text-align:center;font-size:24px;"><B>Depletion Region</B></Primary></p> <hr> <main> <div style='float: left; text-align: left; font-size: 22px; width:100%;'> <ol start="2"> <li>Because of sharp concentration gradient at the junction, holes electrons diffuse across the junction and combine to make a region carrier free. This is known as Depletion region.</li> </ol> </div> <img src='https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/6071114c-09f2-4633-ebc5-5a21eeccd600/public' width = 28%> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style='font-size:18px'> P-n Junction$\to$<span style="color:blue">Depletion Region</span>$\to$Depletion Layer$\to$Energy in Semiconductor$\to$Forward Bias </footer> <p>======</p> <p><Success style="float:center;text-align:center;font-size:28px;" ><B>Field and Potential in P-n Junction</B></Success></p> <p><Primary style="float:center;text-align:center;font-size:24px;"><B>Depletion Layer</B></Primary></p> <hr> <main> <div style='float: left; text-align: left; font-size: 22px; width:100%;'> <ol start="3"> <li>On p-side of the Depletion Layer, holes are majority carriers and electrons are minority carriers. On n-side of Depletion Layer, Oppsite is true.</li> </ol> </div> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/6071114c-09f2-4633-ebc5-5a21eeccd600/public" width="28%"> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style='font-size:18px'> P-n Junction$\to$Depletion Region$\to$<span style="color:blue">Depletion Layer</span>$\to$Energy in Semiconductor$\to$Forward Bias </footer> <p>======</p> <p><Success style="float:center;text-align:center;font-size:28px;" ><B>Field and Potential in P-n Junction</B></Success></p> <p><Primary style="float:center;text-align:center;font-size:24px;"><B>Depletion Region</B></Primary></p> <hr> <main> <div style='float: left; text-align: left; font-size: 22px; width:100%;'> <ol start="4"> <li>Positive charge apears in the Depletion Region on n-side of the junction and negative charge appears on the p-side.</li> </ol> </div> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/6071114c-09f2-4633-ebc5-5a21eeccd600/public" width = "30%" /> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style='font-size:18px'> P-n Junction$\to$<span style="color:blue">Depletion Region</span>$\to$Depletion Layer$\to$Energy in Semiconductor$\to$Forward Bias </footer> <p>======</p> <p><Success style="float:center;text-align:center;font-size:28px;" ><B>Field and Potential in P-n Junction</B></Success></p> <p><Primary style="float:center;text-align:center;font-size:24px;"><B>Energy in Semiconductor</B></Primary></p> <hr> <main> <div style='float: right; width:100%;'> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/6071114c-09f2-4633-ebc5-5a21eeccd600/public" width="30%"> <!----> </div> </main> <hr> <footer style='font-size:18px'> P-n Junction$\to$Depletion Region$\to$Depletion Layer$\to$<span style="color:blue">Energy in Semiconductor</span>$\to$Forward Bias </footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Field and Potential in P-n Junction</B></Success></p> <p><Primary style="float:center;text-align:center;font-size:24px;"><B>Energy in Semiconductor</B></Primary></p> <hr> <main> <div style='float: left; text-align: left; font-size: 22px; width:60%;'> <p>$p=P_1$</p> <p>$x=0$</p> <p>$p=P_2$</p> <p>$\sigma = -P_1 dx$</p> <p>$dE_1 = -\frac{P_1 dx}{2E}$</p> <p>$E_1 = -\frac{P_1}{2E}x_1$</p> </div> <div style='float: right; width:40%;'> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/6071114c-09f2-4633-ebc5-5a21eeccd600/public" width ="80%"> <!----> </div> </main> <hr> <footer style='font-size:18px'> P-n Junction$\to$Depletion Region$\to$Depletion Layer$\to$<span style="color:blue">Energy in Semiconductor</span>$\to$Forward Bias </footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Field and Potential in P-n Junction</B></Success></p> <p><Primary style="float:center;text-align:center;font-size:24px;"><B>Energy in Semiconductor</B></Primary></p> <hr> <main> <div style='float: left; text-align: left; font-size: 22px; width:60%;'> <p>$E_1 = -\frac{P_1}{2E}x_1$</p> <p>$dE_2 = \frac{P_2 dx}{2E},E_2=\frac{P_2 y}{2E}$</p> <p>$dE_3 = -\frac{P_2 dx}{2E},E_3 = -\frac{P_2(x_2-y)}{2E}$</p> </div> <div style='float: right; width:40%;'> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/6071114c-09f2-4633-ebc5-5a21eeccd600/public" width ="80%"> <!----> <!----> </div> </main> <hr> <footer style='font-size:18px'> P-n Junction$\to$Depletion Region$\to$Depletion Layer$\to$<span style="color:blue">Energy in Semiconductor</span>$\to$Forward Bias </footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Field and Potential in P-n Junction</B></Success></p> <p><Primary style="float:center;text-align:center;font-size:24px;"><B>Energy in Semiconductor</B></Primary></p> <hr> <main> <div style='float: left; text-align: left; font-size: 22px; width:50%;'> $E =E_1+E_2+E_3 $ <p>$(-\frac{P_1 x_1}{2 \epsilon})+(\frac{P_2 y}{2 \epsilon})+(-\frac{P_2}{2 \epsilon}(x_2-y))$</p> <p>$=\frac{P_2}{2 \epsilon}[(-x_2)+y-(x_2-y)]$</p> <p>$E=2 \frac{P_2}{2 \epsilon}[y-x_2]$,$x>0$</p> <p>At, $x=x_2$</p> <p>$E=0$</p> <p>At $x=0$</p> </div> <div style='float: right; width:50%;'> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/017120d1-0c96-4a6c-b010-2b8df2362100/public" width="70%"> <!----> </div> </main> <hr> <footer style='font-size:18px'> P-n Junction$\to$Depletion Region$\to$Depletion Layer$\to$<span style="color:blue">Energy in Semiconductor</span>$\to$Forward Bias </footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Field and Potential in P-n Junction</B></Success></p> <p><Primary style="float:center;text-align:center;font-size:24px;"><B>Energy in Semiconductor</B></Primary></p> <hr> <main> <div style='float: left; text-align: left; font-size: 22px; width:50%;'> <p>$E=\frac{P_2}{\epsilon}(x-x_2)$</p> <p>$d V=-E d x = -\frac{P_2}{\epsilon}(x-x_2) d x$</p> <p>$V=-\frac{p_2}{\epsilon} \frac{(x-x_2)^2}{2}+C$</p> <p>$0=-\frac{p_2}{2 \epsilon} x_2^2+C$</p> <p>$V=-\frac{P_2}{2 \epsilon} [(x-x_2)^2 - x_2^2]$</p> <p>$V=\frac{P_1 x_1^2 + P_2 x_2^2}{2 \epsilon} = \frac{P_2 x_2^2}{2 \epsilon}$ $\qquad\frac{P_1 x_1^2}{2 \epsilon}$</p> </div> <div style='float: right; width:50%;'> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/9b8ce167-2280-41ff-4add-2d7fa6870300/public" width="50%"> <!----> <!----> </div> </main> <hr> <footer style='font-size:18px'> P-n Junction$\to$Depletion Region$\to$Depletion Layer$\to$<span style="color:blue">Energy in Semiconductor</span>$\to$Forward Bias </footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Field and Potential in P-n Junction</B></Success></p> <p><Primary style="float:center;text-align:center;font-size:24px;"><B>Energy in Semiconductor</B></Primary></p> <hr> <main> <div style='float: left; text-align: left; font-size: 22px; width:100%;'> <p>$x_2 = \frac{X P_1}{P_1 + P_2}$</p> <p>$x_1 =\frac{X P_2}{P_1 + P_2}$</p> <p>$V_0 =\frac{1}{2 \epsilon}[P_2 x_2 x_1+P_2 x_2^2]$ $=\frac{1}{2 \epsilon} P_2 x_2(x_1+x_2)=\frac{1}{2 \epsilon} P_2 x_2 X$</p> <p>$V_0=\frac{1}{2 \epsilon} \frac{P_2 X^2 P_1}{P_1+P_2} $</p> <p>$ X^2= 2 \epsilon V_0 \frac{P_1+P_2}{P_1 P_2}$</p> <p>$X=\sqrt{2 \epsilon_0 V_0 (\frac{1}{P_1}+\frac{1}{P_2})}\qquad$ $\qquad X=\sqrt{\frac{2 \epsilon V_0}{e} (\frac{1}{N_A}+\frac{1}{N_D})}$</p> </div> <!--<div style='float: right; width:50%;'>--> <!--<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/9fa58ca2-8c4e-49ad-428b-ddd9c6c3a500/public" width="70%">--> <!----> <!----> </div> </main> <hr> <footer style='font-size:18px'> P-n Junction$\to$Depletion Region$\to$Depletion Layer$\to$<span style="color:blue">Energy in Semiconductor</span>$\to$Forward Bias </footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Field and Potential in P-n Junction</B></Success></p> <p><Primary style="float:center;text-align:center;font-size:24px;"><B>Energy in Semiconductor</B></Primary></p> <hr> <main> <div style='float: center; text-align: center; font-size: 22px; width:100%;'> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/9fa58ca2-8c4e-49ad-428b-ddd9c6c3a500/public" width="50%"> </div> <div style='float: right; width:0%;'> <p><img alt="image" src="/subject-images/iitpal/image/physics-class-12-unit-14-chapter-04-field-and-potentialin-p-n-junction-l-4_8-_sibpjz5a2g-10.jpg"></p> </div> </main> <hr> <footer style='font-size:18px'> P-n Junction$\to$Depletion Region$\to$Depletion Layer$\to$<span style="color:blue">Energy in Semiconductor</span>$\to$Forward Bias </footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Field and Potential in P-n Junction</B></Success></p> <p><Primary style="float:center;text-align:center;font-size:24px;"><B>Forward Bias</B></Primary></p> <hr> <main> <div style='float: right; width:100%;'> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/47b1481b-b9d8-47a4-70a8-d86c44367b00/public" width="35%"> <!----> </div> </main> <hr> <footer style='font-size:18px'> P-n Junction$\to$Depletion Region$\to$Depletion Layer$\to$Energy in Semiconductor$\to$<span style="color:blue">Forward Bias</span> </footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Field and Potential in P-n Junction</B></Success></p> <p><Primary style="float:center;text-align:center;font-size:24px;"><B>Forward Bias</B></Primary></p> <hr> <main> <div style='float: left; text-align: left; font-size: 22px; width:50%;'> <ul> <li> <p>Barrior height is decreased width of Depletion region is also reduced</p> </li> <li> <p>Diffusion current will increase</p> </li> <li> <p>Drift current will remain the same</p> </li> <li> <p>Net current will increases</p> </li> </ul> </div> <div style='float: right; width:50%;'> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/e475995c-0057-48ae-ebb2-0cbee3085d00/public" width="70%"> <!----> </div> </main> <hr> <footer style='font-size:18px'> P-n Junction$\to$Depletion Region$\to$Depletion Layer$\to$Energy in Semiconductor$\to$<span style="color:blue">Forward Bias</span> </footer>

<p><Success style='float: center;margin-top:16rem;text-align:center'><B>Thank you</B></Success></p>