The potential barrier existing across an unbiased p - n junction is...

The potential barrier of an unbiased $p$-$n$ junction is $V_0 = 0.2 \text{ V}$.

When the junction is forward-biased, the applied voltage $V_f$ opposes the potential barrier. The effective potential barrier becomes:

$V_{eff} = V_0 - V_f$

$V_{eff} = 0.2 - 0.1 = 0.1 \text{ V}$

For a hole (charge $e$) to diffuse from the $p$-side to the $n$-side, its minimum kinetic energy must be equal to the energy required to overcome this effective potential barrier.

K_\min = e V_{eff}

K_\min = e(0.1 \text{ V}) = 0.1 \text{ eV}