Whilst the different forms of conventional (charge-based) memories are well suited to their individual roles in computers and other electronic devices, flaws in their properties mean that intensive research into alternative, or emerging, memories continues. In particular, the goal of simultaneously achieving the contradictory requirements of non-volatility and fast, low-voltage (low-energy) switching has proved challenging. Here, we report an oxide-free, floating-gate memory cell based on III-V semiconductor heterostructures with a junctionless channel and non-destructive read of the stored data. Non-volatile data retention of at least 10⁴ s in combination with switching at ≤2.6 V is achieved by use of the extraordinary 2.1 eV conduction band offsets of InAs/AlSb and a triple-barrier resonant tunnelling structure. The combination of low-voltage operation and small capacitance implies intrinsic switching energy per unit area that is 100 and 1000 times smaller than dynamic random access memory and Flash respectively. The device may thus be considered as a new emerging memory with considerable potential.