Question #43848

A spherical p-n junction has a depletion region extending from an inner radius $r = a$ to an outer radius $r = b$. The metallurgical junction is located at $r = R = \frac{a+b}{2}$. The effective volume charge density $\rho(r)$ within the depletion region is modeled as $\rho(r) = \frac{A \epsilon}{r^2}$ for $a \le r < R$, and $\rho(r) = -\frac{A \epsilon}{r^2}$ for $R < r \le b$, where $A$ is a positive constant with units of Volts, and $\epsilon$ is the permittivity of the semiconductor. Assuming the electric field is zero for $r < a$ and $r > b$, what is the magnitude of the built-in potential difference $\Delta V$ across the depletion region?