Greg Harm Sirinrath Sirivisoot

EN291 Nano-System Design October 23, 2005

Scribe Notes: Digital Logic using quantum-dot cellular automata (QCA)

Paper Summary The more transistors become smaller into nanometer, the more quantization of the charge in the channel and doping layer have to be realized carefully. Maybe it is not the best way to code information with the current MOS transistor. Thus, the quantum-dot cellular automata (QCA) are another alternative way to encode binary information, by using the arrangements of individual electrons, instead of using current and voltage likes FET. The fabrication of quantum dots is not yet practical. It is still in experimental stages, so not all difficulties have been overcome in creating a consistent, process that generates a high yield. However, the present research into how quantum dots are can be used for computing might help motivate the research of fabrication, which is most imperative. The advantages of QCA are the possibility for high packing densities and low power-delay products. Quantum dot computing is based on encoding information in binary by using quantum-dot cellular automata (QCA). There are 4 sites (dots), which are dots located at the vertices of a square and 2 mobile electrons. The electrons can change which site they occupy by tunneling. There are two possible ground-state polarizations for basic four-dot QCA, which can represent logic ‘0’ (’\’) and ‘1’ (‘/’), that is because of mutual electrostatic repulsion. The interconnection between two cells is Columbic. In the paper they mentioned about the fifth site dot in the center of the cell that it might be help to improve the behavior of the cell slightly. However, in the experiment we study, there were only four dots in one cell. In QCA, a polarization change consists of one electron switching positions to another site within the cell, as well as the other electron tunneling to its adjacent site. Thus, it looks like two electrons in the QCA cell change from occupying one diagonal to occupying the other. The fundamental QCA devices consist of the binary wires, inverters, splitters (fan out capability), and majority logic gates, which can act as AND or OR gates. There are five standard quantum dot cells used to make a majority logic gate: a central logic cell, an output cell, and three inputs. One of the inputs can be the program line for programming. If the program line is ‘0’, then the device will act like an AND gate and if the program line is ‘1’, then it will be an OR gate. The polarization of all three inputs will be voted for the polarization of the central cell, which passes the resulting logic to the output cell.

In the experiment, the fabrication process uses the standard Dolan bridge technique for creating the tunnel junction. The cell consists of four small Al island junctions (dots), which are connected by a ring, which is made from AlOx tunnel junction where the polarization of the cell can be switched by applied bias voltages. The Al islands are built by using electron beam lithography and subsequent shadow evaporation processes with an intermediate in situ oxidation step. They also noted that in the real QCA circuit, each cell in the majority gate responds to the polarization of neighboring cells; thus, we should ensure that the voltages applied to the central

cell’s gates produce the same effects as electrons switching in neighboring cells. The area of the tunnel junction is very important because it will control the Al island capacitance. This affects the charging energy of the island and hence the operating temperature of the device. Their design has an area of about 60 by 60 nm, which generates a junction capacitance of about 400 aF. QCA cells are scalable to molecular dimensions, which should be operated at room temperature. Although in this experiment they demonstrated operation using single electrons, it is also possible to use the magnetic domain to implement QCA.

Discussion 1. Quantum Dot What is the significance of the quantum dot?

Current experimental work has been done using Al islands and aluminum oxide tunnel junctions with (relatively) large excesses of electrons on each dot. The goal is to have each dot either have an excess (of some specific size) or have no excess at all. The difference can be measured as a difference in electric potential or as a difference in conductivity of the dot. Eventual goals include using molecules to act as the dots and (hopefully) using only a single electron difference in charge between being neutral and having an excess. 2. QCA (Quantum Dot Cellular Automata) What exactly is the quantum dot? What is the cell/array (looking at the figures)?

The circles (for example, in “Quantum-dot cellular automata: Review and recent experiments (invited)”, fig. 1) represent the islands. If the circle is filled in, it represents the fact that the island is in its excess state, which may be a single electron if working with molecules or could be hundreds or thousands when working with the aluminum islands.

The square (in the diagram) is the quantum dot cell or quantum dot cellular automata (QCA), which consists of four islands where you have either holes or dots. A cell is loaded with 2 groups of excess electrons. These electrons tend to occupy opposite corners (minimal energy configuration based on Coulomb forces). The number of excess electrons depends on both the capacitance of the island and the ambient temperature. In order to fabricate devices with smaller charges, they need to work with low-capacitance, low-temperature islands. 3. Tunneling and potential barriers Why can the QCA cells change configuration if there is no path or connection between the islands?

The islands are separated by a small enough physical distance that quantum mechanical tunneling effects are applicable. The authors say that they use a model based on the time-independent Schrödinger equation under the approximation that intercellular interactions are electrostatically coupled and wavefunction overlap between cells is nonexistent. When two potential wells are close together (and separated by some potential barrier), the Schrödinger equation describes the probability of finding the particle at a given point, even if on the other side of the barrier.

In order to control the size of the potential barrier, the authors suggest a method where one inserts another small island between two corners of the cell. By applying a potential to this

separator island, one can control the height of the barrier and so control whether or not there’s a high probability that tunneling will occur. 4. Logic Gates Using QCA (Setup) How do you know which way the signal will travel or which cell will change?

We were confused at first as to why, for example, cell A would change the state of cell B and not vice versa. The cell used as the input must be fixed in its state. As in the previous section, we saw that it’s possible to hold a cell in its state (by raising the potential barrier), so that information can only flow out of it. Once you’ve determined which cell is input and have it fixed, the cells surrounding it will try to take on the input cell’s configuration (or whatever the lowest-energy configuration is). How close are the cells to each other? Might the distance between cells affect the result of gate’s output? Is this related to fabrication? How?

Signal integrity and quality is an issue but was not discussed in depth in the papers. Reasoning about the way QCA works, we thought that having a very regular spacing between cells, both in separation and lateral alignment, is important. The authors say that you can get away with some degree of lateral shifting of wires made from QCA cells. The regularity is important both to have a higher probability that all the cells will flip to the proper alignment (in the allotted time) and for determining what the minimum required period of the clock would be.

This quality control would be partly a design concern because you can plan on having wires that don’t run perfectly straight. It seemed that the larger question or problem would be the accuracy and precision with which you could manufacture identically sized cells and place them on the “circuit board”. 5. Logic Gates Using QCA (Operation) How are cells switched? How fast they are?

The fundamental use of QCA logic is for majority logic gates. A “device” cell will have 3 input cells on 3 different edges. The fourth edge will be the device output. The device assumes the configuration (state) of the majority of the 3 inputs because that is the lowest potential energy state of the system. These gates can be used as majority gates, as AND gates (fixing an input at ‘0’) and as OR gates (fixing an input at ‘1’). These cells can also be configured to be an inverter or to send both a signal and its complement. Cells must be clocked in order to control the direction and flow of information along the wire.

The papers didn’t talk much about the speed or potential speed of QCA cells. They mention that the experiments they run are performed at 0.1 Hz (10s period). Clearly this is not a useful clock speed, and these cells can either already operate faster or further research is required to obtain useful clock speeds. 6. Experimental Work How do we handle the misalignment defection? Clearly, a method is necessary to deal with manufacturing defects. It is not yet clear what degree of accuracy is required for performance to fall within predetermined tolerances. Again,

both the uniformity of cell size and cell spacing will be important in correctly functioning QCA logic. In “Experimental demonstration of a latch in clocked quantum-dot cellular automata”, figure 4(c), why is VD1 high on the interval of about 32 to about 50?

We discussed why the output (VD1) is high (even higher than before) once the control signal (Vc) goes low. The authors were not very clear on what was going on and we didn’t get much out of that figure. The point they claimed to be making was that they had a working latch, but the figure doesn’t show the situation with the clock being high and the input being low. Perhaps the rise in the output signal when the clock drops is caused by a similar effect that creates the multiple output levels in the majority gate operation. Or maybe the cell becomes more polarized once the clock drops and locks the electrons in place. We (the class) really didn’t come up with a reasonable answer to this. 7. Experimental Demonstration of a Latch in Clocked QCA What’s required to latch data?

A clocking scheme is required to create latches with QCA cells. In order to make the cell latch 1 bit, it must be held in a fixed state. As discussed earlier, this can be done by keeping the separator islands at high potential and preventing electrons from changing configuration. The clock signal is likely to be provided by a supporting technology, like CMOS. The signal can be delivered by a wire with a larger feature cell than that of the entire cell. The clock potential can be the same for many cells, and so it works out to have a relatively large wire delivering the signal.