Question #87054

A p-n junction diode is operating in the reverse breakdown region. To model the transition from Zener to Avalanche breakdown, its dynamic internal resistance is given by $r_d = \frac{dV_D}{dI} = \frac{\lambda}{E}$, where $V_D$ is the reverse voltage across the diode, $I$ is the reverse current, $E = \frac{V_D}{d}$ is the uniform electric field in the depletion region of width $d$, and $\lambda$ is a positive constant with units of $\Omega \cdot \text{V} \cdot \text{m}^{-1}$. The breakdown onset occurs at $V_D = V_Z$ where the macroscopic current $I \approx 0 \text{ A}$. The diode is connected in series with a resistor $R$ and a DC power supply of voltage $V_0$ ($V_0 > V_Z$). Which of the following expressions correctly gives the steady-state current $I$ in the circuit?