= Solution
<forward bias> opposes the built-in <electric field> and lowers the junction barrier from approximately $V_{\rm bi}$ to $V_{\rm bi}-V$. In the abrupt-junction <depletion approximation>,
$$
W=\sqrt{\frac{2\epsilon_s}{q}\left(\frac1{N_A}+\frac1{N_D}\right)(V_{\rm bi}-V)}.
$$
Thus \b[the <depletion region> narrows] and carriers cross the reduced barrier more readily. <electron> injection into the p side and hole injection into the n side increase strongly, allowing <radiative recombination> in an <LED>.
The injected minority-carrier <concentrations>, and therefore the ideal <diffusion> <electric current>, vary approximately as $\exp(qV/k_BT)$. This produces the steep forward branch of the <electric current>–<voltage> curve. One should not extrapolate the depletion-width formula to claim that the junction must lose its entire <depletion region> before conducting; appreciable <electric current> flows while a barrier remains, and high injection and series resistance eventually invalidate the simple formulas.
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