"Pumping" Charges — Question 10

Question 10

Photon-driven charge separation has independent charge and energy limits

An idealized photo-source receives photons at rate Phi, each with energy $E_\gamma$. A fraction f produces one successfully collected electron-hole pair each. Each collected pair delivers charge magnitude e through the load at voltage V. Neglect other energy inputs.

1. Find output current and output power.

2. Use energy conservation to bound V if all electrical work must come from the successfully collected photons, and compare current and voltage constraints.

Question 10 - Solution

Photon-driven charge separation has independent charge and energy limits

(a) Method and calculation

$$I=ef\Phi.$$$$P_{\mathrm{out}}=VI=ef\Phi V,\quad P_{\mathrm{useful\ photons}}=f\Phi E_\gamma.$$

(b) Interpretation and further calculation

$$ef\Phi V\le f\Phi E_\gamma\Rightarrow V\le E_\gamma/e\quad(f\Phi>0).$$$$I\propto f\Phi,\quad V_{\mathrm{upper}}\text{ is independent of photon arrival rate in this bound}.$$

Physical check

This is an energy upper bound, not a prediction of a real solar cell voltage or efficiency.