Consider a small silicon photodiode with a \(100 \mathrm{~cm}^{2}=10 \mathrm{~cm} \times 10 \mathrm{~cm}\) area. When \(2 \mathrm{~V}\) of reversed bias is applied, the reverse saturation current is \(30 \mathrm{nA}\). When the photodiode is short-circuited and exposed to blackbody radiation with a power density of \(1000 \mathrm{~W} / \mathrm{m}^{2}\), a short-circuit current circulates. Assume 100\% quantum efficiency where each photon creates one electron-hole pair and all pairs are separated by the \(\mathrm{p}-\mathrm{n}\) junction of the diode.

(a) What is the value of this current?

(b) What is the open-circuit voltage of the photodiode at \(300 \mathrm{~K}\) under the above illumination?

The sun can be modeled as essentially a \(6000 \mathrm{~K}\) black body. When the power density of such radiation is \(1000 \mathrm{~W} / \mathrm{m}^{2}\), the total photon flux is \(4.46 \times 10^{21}\) photons \(/ \mathrm{m}^{2}\)-s. It can be shown that essentially half of these photons have energy equal or larger than \(1.1 \mathrm{eV}\), the bandgap energy, \(W_{g}\), of silicon.