Question #43752

A metallic photocathode with a vacuum work function $\phi_0$ (in $\text{J}$) is placed at the origin $x=0$. A semiconductor depletion region of absolute permittivity $\epsilon$ (in $\text{F}\cdot\text{m}^{-1}$) extends from $x=0$ to $x=w$ (in $\text{m}$). The depletion region contains a uniform positive space charge density $\rho = e N_D$, where $e$ is the elementary charge (in $\text{C}$) and $N_D$ is the donor number density (in $\text{m}^{-3}$). The electric field vanishes at $x=w$. Due to the Schottky effect, the internal electric field magnitude $E_0$ at the interface lowers the potential barrier for electron emission by $\Delta V = \sqrt{\frac{e E_0}{4\pi\epsilon}}$ (in $\text{V}$). What is the minimum incident photon frequency $\nu_{th}$ (in $\text{Hz}$) required to observe a non-zero photoelectric saturation current? (Here $h$ is Planck's constant in $\text{J}\cdot\text{s}$)