Analytic 1-D $pn$ Junction Diode Photocurrent Solutions Following Ionizing Radiation and Including Time-Dependent Changes in the Carrier Lifetime From a Nonconcurrent Neutron Pulse

Circuit simulation codes, such as SPICE, are invaluable in the development and design of electronic circuits in radiation environments. These codes are often employed to study the effect of many thousands of devices under transient current conditions. Device-scale simulation codes are commonly used in the design of individual semiconductor components, but computational requirements limit their use to small-scale circuits. Analytic solutions to the ambipolar diffusion equation, an approximation to the carrier transport equations, may be used to characterize the transient currents at nodes within a circuit simulator. We present new analytic transient excess carrier density and photocurrent solutions to the ambipolar diffusion equation for 1-D abrupt-junction
$pn$
diodes. These solutions incorporate low-level radiation pulses and take into account a finite device geometry, ohmic fields outside the depleted region, and an arbitrary change in the carrier lifetime due to neutron irradiation or other effects. The solutions are specifically evaluated for the case of an abrupt change in the carrier lifetime during or after, a step, square, or piecewise linear radiation pulse. Noting slow convergence of the Fourier series solutions for some parameters sets, we evaluate portions of the solutions using closed-form formulas, which result in a two order of magnitude increase in computational efficiency.