Question #43714

A semiconductor photocathode has a threshold energy for photoemission equal to its temperature-dependent band gap $E_g(T)$. At low temperatures, the band gap follows the relation $E_g(T) = E_0 - \gamma T^2$, where $E_0$ and $\gamma$ are positive constants. The photocathode is illuminated by a light source whose spectral photon flux (number of photons per unit time per unit energy interval) is given by $\frac{d\Phi_p}{dE} = \frac{K}{E^4}$ for $E > 0$, where $K$ is a positive constant. Assuming a constant quantum efficiency for all incident photons with energy $E \ge E_g(T)$, what is the magnitude of the relative change in the saturation photocurrent, $\left| \frac{\Delta I_s}{I_s} \right|$, due to a small relative change in temperature $\frac{\Delta T}{T} = \delta$?