[en] Slow positrons in the energy range up to a few keV are useful for material sciences and surface studies. The Advanced Photon Source (APS) linear accelerator (linac) was designed to produce 8-mA of 450-MeV positrons. A 200-MeV, 1.7-Ampere electron beam impinges on a 7-mm-thick (2 radiation lengths) tungsten target, resulting in bremsstrahlung pair production of electrons and positrons. The existing target was optimized for high energy positron production, and most slow positrons produced by the electron-gamma shower remain trapped inside. The linac could also be used to produce slow positrons, and a modified target could increase the low energy positron yield. Use of a multilayer or segmented target reduces self-absorption by the target, and thus more fully utilizes the incident beam power for slow positron production. A slow positron yield of 10⁹/sec is expected from the existing incident electron beam. Multilayer targets could probably be used by other accelerator-based slow positron sources to improve slow positron yield without increasing the incident beam power. Two variations of a multilayer target concept are presented and discussed in this paper