1. 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.

2. 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.

3. 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.

4. Positive charge apears in the Depletion Region on n-side of the junction and negative charge appears on the p-side.

$p=P_1$

$x=0$

$p=P_2$

$\sigma = -P_1 dx$

$dE_1 = -\frac{P_1 dx}{2E}$

$E_1 = -\frac{P_1}{2E}x_1$

$E_1 = -\frac{P_1}{2E}x_1$

$dE_2 = \frac{P_2 dx}{2E},E_2=\frac{P_2 y}{2E}$

$dE_3 = -\frac{P_2 dx}{2E},E_3 = -\frac{P_2(x_2-y)}{2E}$

$(-\frac{P_1 x_1}{2 \epsilon})+(\frac{P_2 y}{2 \epsilon})+(-\frac{P_2}{2 \epsilon}(x_2-y))$

$=\frac{P_2}{2 \epsilon}[(-x_2)+y-(x_2-y)]$

$E=2 \frac{P_2}{2 \epsilon}[y-x_2]$,$x>0$

At, $x=x_2$

$E=0$

At $x=0$

$E=\frac{P_2}{\epsilon}(x-x_2)$

$d V=-E d x = -\frac{P_2}{\epsilon}(x-x_2) d x$

$V=-\frac{p_2}{\epsilon} \frac{(x-x_2)^2}{2}+C$

$0=-\frac{p_2}{2 \epsilon} x_2^2+C$

$V=-\frac{P_2}{2 \epsilon} [(x-x_2)^2 - x_2^2]$

$V=\frac{P_1 x_1^2 + P_2 x_2^2}{2 \epsilon} = \frac{P_2 x_2^2}{2 \epsilon}$ $\qquad\frac{P_1 x_1^2}{2 \epsilon}$

$x_2 = \frac{X P_1}{P_1 + P_2}$

$x_1 =\frac{X P_2}{P_1 + P_2}$

$V_0 =\frac{1}{2 \epsilon}[P_2 x_2 x_1+P_2 x_2^2]$ $=\frac{1}{2 \epsilon} P_2 x_2(x_1+x_2)=\frac{1}{2 \epsilon} P_2 x_2 X$

$V_0=\frac{1}{2 \epsilon} \frac{P_2 X^2 P_1}{P_1+P_2}$

$X^2= 2 \epsilon V_0 \frac{P_1+P_2}{P_1 P_2}$

$X=\sqrt{2 \epsilon_0 V_0 (\frac{1}{P_1}+\frac{1}{P_2})}\qquad$ $\qquad X=\sqrt{\frac{2 \epsilon V_0}{e} (\frac{1}{N_A}+\frac{1}{N_D})}$

• Barrior height is decreased width of Depletion region is also reduced

• Diffusion current will increase

• Drift current will remain the same

• Net current will increases