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This paper reports on a programmable reconfigurable self-assembly (PRS) process to enable heterogeneous integration of components on nonplanar substrates. The proposed process makes use of solder-based receptors that can be activated electrically. Metal contacts on segmented semiconductor devices bind to liquid-solder-based-receptors on a substrate during the fluidic self-assembly. Programmability is implemented using solder-based receptors that can be switched "ON" and "OFF" using integrated heaters. We have evaluated the feasibility of the proposed PRS concept through computer simulations using ANSYS to estimate: i) the necessary power to heat selected receptors to above the melting point of the solder and ii) the minimal spacing between receptors for preventing thermal crosstalk. A prototype platform has been fabricated to experimentally test the PRS process. The programmable sequential assembly of multiple types of components onto target positions has been demonstrated, including 300-μm-sized light-emitting diodes (LEDs) and silicon dies. Three types of defects were identified and eliminated using improved component designs, transient heating, and adequate heat sinks. A prototype color LED display segment that contains a total of 36 red, green, and yellow LED segments and 72 interconnects has been used to test the concept. The outlined process provides a new concept to the parallel integration of microdevices and systems that require electrical interconnects between components.