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.