# The depletion layer width at thermal equilibrium for one-sided abrupt p-n junction diode (where NB = ND­ or NA) is

71 views
in General
closed
The depletion layer width at thermal equilibrium for one-sided abrupt p-n junction diode (where NB = ND­ or NA) is
1. $\sqrt {\frac{{2\epsilon_s{V_{bi}}}}{{qN_B}}}$
2. $\sqrt {\frac{{q{N_B}}}{{2{\epsilon_s}{V_{bi}}}}}$
3. $\sqrt {\frac{{{\epsilon_s}{V_{bi}}}}{{2q{N_B}}}}$
4. ${\left( {\frac{{2{\epsilon_s}{V_{bi}}}}{{q{N_B}}}} \right)^2}$

by (30.0k points)
selected by

Correct Answer - Option 1 : $\sqrt {\frac{{2\epsilon_s{V_{bi}}}}{{qN_B}}}$

Depletion width for an unbiased abrupt pn junction diode is given by:

$W = \sqrt {\frac{{2ϵ}}{q}\left( {\frac{1}{{{N_D}}} + \frac{1}{{{N_A}}}} \right){V_{bi}}}$

This can be written as:

$W = \sqrt {\frac{{2ϵ}}{q} (\frac{N_A+N_D}{N_AN_D}){V_{bi}}}$

ND = Donor concentration on n side

NA = Acceptor concentration on p side

Vbi = Contact potential or the Built-in Potential

ϵ = Permittivity of the semiconductor

A one-sided pn junction is a junction

The one-sided p-n junction is defined as the junction in which one region is highly doped and another region is doped lower to form the p and n regions.

In this junction, the concentration of one side impurity is considered, as it dominates the other, i.e. for a one-sided junction with NA >> ND, the depletion width can be written as:

$W=\sqrt {\frac{{2\epsilon_s(N_A){V_{bi}}}}{{qN_B.(N_A.N_D)}}}$

$W=\sqrt {\frac{{2\epsilon_s{V_{bi}}}}{{qN_D}}}$

Similarly, if ND >> NA, the depletion layer width becomes:

$W=\sqrt {\frac{{2\epsilon_s{V_{bi}}}}{{qN_A}}}$

Generalizing this for any one-sided junction we can write:

$\sqrt {\frac{{2\epsilon_s{V_{bi}}}}{{qN_B}}}$

Where NB = NA or NB depending upon the doping profile.