Surface acoustic waves (SAWs) have been used to transport single electrons across long distances of several hundreds of microns. They can potentially be instrumental in the implementation of scalable quantum processors and quantum repeaters, by facilitating interaction between distant qubits. While most of the work thus far has focused on SAW devices in doped GaAs/AlGaAs heterostructures, we have developed a method of creating lateral p-n junctions in an undoped heterostructure containing a quantum well, with the expected advantages of having reduced charge noise and increased spin-coherence lifetimes due to the lack of dopant scattering centers. We present experimental observations of SAW-driven single-electron quantized current in an undoped GaAs/AlGaAs heterostructure, where single electrons were transported between regions of induced electrons. We also demonstrate pumping of electrons by a SAW across the submicron depleted channel between regions of electrons and holes, and observe light emission at such a lateral p-n junction. Improving the lateral confinement in the junction should make it possible to produce a quantized electron-to-hole current and hence SAW-driven emission of single photons.