Solution (source code)

= Solution

Absorption of <photons> with $h\nu\gtrsim E_g$ creates electron-hole pairs, the upward band-diagram arrow. In the <depletion region> the built-in field drives <electrons> towards n material and holes towards p material; <diffusion> also delivers carriers generated within a <diffusion length> outside that region. Selective contacts collect the two signs. Illumination maintains a nonequilibrium <quasi-Fermi-level splitting>, allowing a voltage and useful current through an external load; it is the light, rather than the equilibrium barrier, that supplies the <energy>.

Taking forward diode current as positive, an ideal illuminated junction has
$$
\boxed{I=I_0(e^{qV/k_BT}-1)-I_{ph}},\qquad
\boxed{I_{sc}=-I_{ph},\quad V_{oc}=\frac{k_BT}{q}\ln(1+I_{ph}/I_0).}
$$
<power> is delivered where $VI<0$ in this convention. Reflection, below-gap transmission, carrier thermalization, <recombination> and resistive losses limit real conversion; even an ideal single junction has radiative detailed-balance limits.<Detailed Balance Limit of Efficiency of p-n Junction Solar Cells by William Shockley and Hans-Joachim Queisser>[1961, Journal of Applied Physics 32, pp.510–519: radiative detailed-balance limit]{ref}