Algorithmic Self-Assembly of Circuits

The order we see in nature is self-assembled: atoms, crystals, cells, animals, solar systems, and galaxies are just a few examples. While we have been able to build phenomenal devices with controlled assembly techniques, we still cannot engineer machines at the scale of the ribosome. Can we understand the mechanism behind natural self-assembly and harness it to fabricate new devices? A systematic attack on this problem as been initiated [5, 1], and in this paper we use these techniques to explore how self-assembly could be used to fabricate nanoscale electrical circuits. We start with a simple model, where molecules are thought of as two dimensional square tiles [Wang] having different glue types on north, east, south and west sides. These glues have strengths associated with them which will be important later on. Now tiles that have matching glues stick to each other. The model that we have considered is an irreversible one, which means that once tiles stick together with a certain bond strength they do not come apart. In reality, molecular bonds are reversible. But some bonds are stronger than others, and if a molecule is attached in more than one place it is less likely to fall off. Analysis of the thermodynamics of these interactions shows that for some temperatures our model that “tiles with matching glues stick” is actually fairly accurate [7]. This is called the T = 1 model: the temperature T is such that only one matching bond is needed for two tiles to stick to each other. The behavior is different at other temperatures. As the temperature rises above T = 1, eventually it reaches a point where in equilibrium, a tile sticks to other tiles only if it can find two bonds (or one double strength bond). This gives us a new model of self assembly which seems more powerful than the first. Not surprisingly, it is called the T = 2 model.