Energy Dissipation in Molecular Quantum-Dot Cellular Automata (QCA) Switching

Quantum cellular automata (QCA) is a computing paradigm where binary information is encoded as charge configurations. Binary information is processed and transmitted through Coulomb interaction from neighboring cells. Power dissipation is low due to the absence of current flow. This paradigm is best suited for molecular implementation. High device densities and fast switching are possible with molecular QCA. This dissertation is a theoretical study of energy dissipation in molecular QCA cells during switching.

First, we calculate the excess energy left at the end of switching in isolated two-state and three-state QCA cells. This excess energy decreases exponentially with increasing switching adiabaticity. This presents a significant advantage over classical systems exhibiting linear dependence. For an open two-state system we use the Lindblad operators to model the impact of system-environment interaction. At rapid switching we observe exponential adiabaticity. At intermediate switching speeds we observe an inverted regime where the dissipated energy increases as the switching slows down. Subsequent slowing of switching results in a classical behavior. We then introduce molecular reorganization energy to an open two-state system. Here we model the energy lowering of a charge-occupied dot due to relaxation of surrounding atoms. The reorganization energy causes the Hamiltonian to be non-linear and allows multiple steady-state solutions at small biases. Charge localization is stabilized due to the self-trapping nature of the reorganization energy and the QCA cell can act as a memory element. But this bit stability comes at the expense of higher energy dissipation due to accelerated electron transfer. Finally, we extend the study to an open three-state system. Adiabatic switching during a write operation can cause the system to refrigerate the bath. For logically reversible operations like write or erase with copy, there is no fundamental lower limit to energy dissipation in accordance with Landauer principle. For erase without copy where no external bias is applied, the reorganization energy internally biases the system in the state it is in. This is a limitation of our model which makes this operation logically reversible. As future work, this model can be improved to include dissipation for nuclear degrees of motion.