The authors give a precise analytic solution for the diffusion-reaction problem of a zero-height generating band situated on a reacting infinite plane. The problem is formulated from redox reactions on micro-electrodes; and thus, is connected with important applications in micro-electrode sensors and molecular electronic devices. The main idea is to use Riemann-Hilbert matching in the absence of time inversion symmetry. The singular integrals resulting from the solution of the Riemann-Hilbert problem are converted to non-singular forms that can be calculated numerically. The numerical results compare with time Fourier transforms of densities and currents that can be measured experimentally. The singularities of the exact solution are characterized and asymptotic expansions developed which are useful for analysis of experiments.