(a) $\sqrt{ \frac{2\epsilon_{si}}{q} \left( \frac{N_A + N_D}{N_A N_D} \right) (\phi_o - V) }$
(b) $\sqrt{ \frac{2\epsilon_{si}}{q} \left( \frac{N_A N_D}{N_A + N_D} \right) (\phi_o - V) }$
(c) $\sqrt{ \frac{2\epsilon_{si}}{q} \left( \frac{N_A - N_D}{N_A + N_D} \right) (V - \phi_o) }$
(d) $\sqrt{ \frac{2\epsilon_{si}}{q} \left( \frac{N_A N_D}{N_A - N_D} \right) V }$
Out of these which is correct answer
Depletion Region Thickness in Reverse Bias
The thickness of the depletion region ($W$) in an abrupt p-n junction under reverse bias is determined by the material properties (permittivity $\epsilon_{si}$, elementary charge $q$), doping concentrations ($N_A$, $N_D$), built-in potential ($\phi_o$), and the applied reverse voltage ($V$).
Formula Structure Analysis
The standard derivation shows that the depletion width is proportional to the square root of the sum of the built-in potential and the applied reverse voltage, multiplied by a factor dependent on doping concentrations:
$W = \sqrt{ \frac{2\epsilon_{si}}{q} \left( \frac{1}{N_A} + \frac{1}{N_D} \right) (\phi_o + V) }$This simplifies to:
$W = \sqrt{ \frac{2\epsilon_{si}}{q} \left( \frac{N_A + N_D}{N_A N_D} \right) (\phi_o + V) }$Evaluating Option (a)
Option (a) is given by:
$ \sqrt{ \frac{2\epsilon_{si}}{q} \left( \frac{N_A + N_D}{N_A N_D} \right) (\phi_o - V) } $This formula correctly incorporates the doping term factor $\left( \frac{N_A + N_D}{N_A N_D} \right)$.
Evaluating Option (b)
Option (b) is given by:
$ \sqrt{ \frac{2\epsilon_{si}}{q} \left( \frac{N_A N_D}{N_A + N_D} \right) (\phi_o - V) } $This formula uses an incorrect doping term factor $\left( \frac{N_A N_D}{N_A + N_D} \right)$. The correct factor involves the sum of the reciprocals of the doping concentrations.
Conclusion
Based on the analysis of the doping term factor, formula (a) has the correct structure, while formula (b) does not. Therefore, option (a) is correct and option (b) is wrong.
Important Questions from PN Junction
In a semiconductor diode, the cut-in voltage is the voltage:
The leakage current in a pn junction is of the order of:
Diode junction breakdowns above 5 V are caused by:
The width of the depletion layer in a P-N junction diode
ln a p-n junction diode the forward current
