Question #43716

Consider an intrinsic semiconductor at room temperature with an intrinsic carrier concentration $n_i = 3.0 \times 10^{10} \text{ cm}^{-3}$. The recombination of electrons and holes is a bimolecular process, meaning the recombination rate per unit volume is given by $R = \beta n p$, where $n$ and $p$ are the electron and hole concentrations, respectively, and $\beta = 1.0 \times 10^{-10} \text{ cm}^3 \text{s}^{-1}$ is the recombination coefficient. In thermal equilibrium, the thermal generation rate $G_{th}$ balances the recombination rate. The semiconductor is now continuously illuminated, providing an additional, steady external generation rate of electron-hole pairs $G_{ext} = 1.6 \times 10^{11} \text{ cm}^{-3} \text{s}^{-1}$. Assuming uniform illumination and no spatial gradients, what is the steady-state excess electron concentration $\Delta n$ in the semiconductor?