Analytic light—or radiation—induced $pn$ junction photocurrent solutions to the multidimensional ambipolar diffusion equation

We transform the $n$-dimensional ambipolar transport equation to the $n$-dimensional nonhomogeneous heat equation, which has been solved for most common initial and boundary conditions. Thus, general solutions to the nonhomogeneous heat equation, obtained in a robust form through finite Fourier transforms, provide an easy approach to solving the ambipolar transport equation, which previously had been solved with more difficulty through Laplace transform techniques. We then obtain a general analytic one-dimensional time-dependent solution to the excess carrier and current densities in a $pn$ junction diode in response to a transient radiation or light pulse under low-injection conditions. We derive most of the known analytic solutions to this problem and we examine the limiting behavior of these solutions to show that they are consistent. The model includes the effects of a constant electric field in the quasineutral region, a finite diode length, and an arbitrary generation function in terms of space and time. In the area of light communication, we use the model to examine the impact of doping parameters on the buildup of diffusive photocurrent that limits the signal bandwidth. Solutions to the ambipolar diffusion equation assuming more general initial and boundary conditions are easily obtained via the given transformation. The model may be applied to problems involving photodiodes, light-emitting diode or laser communication, transient radiation effects in microelectronics, dosimetry, or the response of solar cells to light.