Question

A potential barrier V volts exists across a P-N junction. The thickness of the depletion region is 'd'. An electron with velocity 'v' approaches P-N junction from N-side. Find the velocity of the electron crossing the junction.

Answer 1

REF. Image.

Since, the electron is approaching the

barrier from n-side then

at some intermediates point

$F=eE$ where $E=$ electric field

$E=\frac{v}{d}$

$\Rightarrow F=\frac{ev}{d}$

$\Rightarrow$ deceleration $a=\frac{F}{m_e}=\frac{ev}{m_{e}d}$

$m_e\to$ mass of electron

if the electron crosses the barrier with

velocity ,$v_f$

then according Newton's III low of motion

$v_f^2=v^2-2\left(\frac{ev}{m_{e}d}\right)\times d$

$\Rightarrow v_f^2=v^2-\frac{2ev}{me}$