A tight-binding study of a 1-bit half-adder based on diode logic integrated inside a single molecule

The design of a 1-bit half-adder diode logic circuit inside a single molecule is investigated, with the chemical groups for diodes and wires bonded together to form the molecular circuit. With a circuit working in the ballistic transport regime, interference effects between the different electron paths in the circuit make the optimization of the circuit's logic function very delicate. In the tunnelling regime, these effects are partly suppressed. But the exponential decay of the current with the wire length imposes additional constraints for circuit design. A programmable gate logic array-like architecture would be expected be more useful for the design of a 1-bit adder in the ballistic regime due to the regularity of the circuit lattice, which might reduce interferences. On the other hand, a dedicated design which minimizes the amount of wiring might be the better choice for the tunnelling regime. However, we find that the logic output of classical diode logic circuits cannot be reproduced in either regime because Kirchhoff-like circuit rules do not apply. Furthermore, the geometry dependence of electron transmission in both regimes would make it impractical to build up logical functions like the SUM of an adder from simple OR- and AND-gates, even if the output pattern of these gates could be perfectly reproduced.