  We propose a three terminal heat engine based on semiconductor superlattices
for energy harvesting. The periodicity of the superlattice structure creates an
energy miniband, giving an energy window for allowed electron transport. We
find that this device delivers a large power, nearly twice than the heat engine
based on quantum wells, with a small reduction of efficiency. This engine also
works as a refrigerator in a different regime of the system's parameters. The
thermoelectric performance of the refrigerator is analyzed, including the
cooling power and coefficient of performance in the optimized condition. We
also calculate phonon heat current through the system, and explore the
reduction of phonon heat current compared to the bulk material. The direct
phonon heat current is negligible at low temperatures, but dominates over the
electronic at room temperature and we discuss ways to reduce it.
