Space Charge Limited Discharge from Microscopic Electrical Defects in Xerographic Photoreceptors

Microscopic electrical defects in the photoreceptor termed Charge Deficient Spots (CDS) can give rise to objectionable print defects in xerographic systems such as laser printers. Experimental measurements of the current voltage characteristics of individual defects [1] exhibit a space charge limited behavior (current proportional to the square of the voltage) consistent with the defects representing injection spots (emitters) from the ground plane of the photoreceptor. Previous theoretical and numerical studies have explored the relationship between the emitter size and the current in various geometries, where the emitter is on the ground electrode while the other electrode is biased at a constant potential. In this paper, we explore the problem of practical interest in xerography, i.e. how a photoreceptor is discharged by these microscopic defects. A photoreceptor with uniform surface charge is discharged by space charge limited injection from a finite sized defect at the ground plane. We explore the surface charge distribution as function of time. The time scale of interest is the duration between the charging subsystem (where the photoreceptor is precharged in the dark) and development subsystem (where the photoreceptor is developed with charged toner). If the discharged area grows sufficiently in this time duration then the toner will develop in this area leading to a print defect in machines that use Discharged Area Development. The severity of the defect will depend on the modulation transfer function (MTF) of the development subsystem. In this paper we consider the growth of the discharge area as a function of time, and its dependence on the size of the defect. The problem is formulated mathematically using well known equations for charge transport in dielectric media, with space charge limited injection at the emitter. Axisymmetric geometry is assumed. We describe a computational methodology based on hybrid boundary integral equation method and finite volume method. Finally we discuss the implication of our numerical simulation results to xerographic printers.