Correct Answer - Option 4 : 0.86 V and 3.3 × 10
-5 cm
Concept:
The built-in potential barrier for a PN junction with given doping concentration Na, Nd, is given by:-
\( {{V}_{bi}}=\frac{kT}{q}\ln \left( \frac{{{N}_{a}}{{N}_{d}}}{n_{i}^{2}} \right)\)
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:
\(W = \sqrt {\frac{{2ϵ}}{q} (\frac{N_A+N_D}{N_AN_D}){V_{bi}}} \)
Calculation:
With Na = 5 × 1018 cm-3
Nd = 1 × 1016 cm-3
\(\frac{{KT}}{q} = 26\;mV\)
\({V_{bi}} = 26\;m\ln \left( {\frac{{{{10}^{16}} × 5 × {{10}^{18}}}}{{{{\left( {1.5 × {{10}^{10}}} \right)}^2}}}} \right)\)
= 26 m×ln (2.22 × 1014)
= 26 m × 33.03
Vbi ≃ 0.86 V
Now, the depletion width will be:
\(W = \sqrt {\frac{{2 × 1.04 × {{10}^{ - 12}} × 0.86}}{{1.6 × {{10}^{ - 19}}}} × \frac{{\left( {{{10}^{16}} + 5 × {{10}^{18}}} \right)}}{{{{10}^{16}} × 5 × {{10}^{18}}}}} \)
\( = \sqrt {\frac{{2 × 1.04 × {{10}^{ - 12}} × 0.86}}{{1.6 × {{10}^{ - 19}}}} × \frac{1}{{{{10}^{16}}}}} \)
Solving for the above, we get:
W = 3.3 × 10-5 cm