= Solution
Joining p-type and n-type regions initially allows majority carriers to diffuse across and recombine. Exposed negative acceptor charge on the p side and positive donor charge on the n side form a <depletion region>. Its <electric field> points from n to p and balances <diffusion> at equilibrium. The <Fermi level> is then spatially constant, while the conduction and <valence band> edges bend across the <built-in potential>; this equilibrium barrier cannot supply continuous <power> to a load.
<forward bias> makes p positive relative to n, reducing the barrier from $qV_{bi}$ to $q(V_{bi}-V)$. <electrons> enter p material and holes enter n material, becoming <minority carriers> whose <diffusion> and <recombination> sustain the current. <reverse bias> enlarges the barrier and leaves a much smaller minority-carrier current until breakdown. The ideal <diffusion> model gives \b[$I=I_0[e^{qV/k_BT}-1]$], the <Shockley diode equation>; depletion-region <recombination>, series resistance and breakdown limit this approximation. Minority-carrier injection on both sides is essential to the junction theory.<The Theory of p-n Junctions in Semiconductors and p-n Junction Transistors by William Shockley>[1949, pp.435–436: rectification, electron and hole currents, and injection]{ref}
\Image[/past-exam-of-the-physics-a-course-of-the-university-of-cambridge/2011/paper-1-junction-bands.png]
{title=Junction band bending and three device functions}
{description=Original schematic electron-energy diagrams, not quantitative band solutions. Equilibrium has one flat Fermi level; biased and illuminated panels indicate separate carrier quasi-Fermi levels. The photon arrows distinguish LED emission from solar-cell absorption.}
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