Proceedings of the International Conference on Computer and Communication Engineering 2008
May 13-15, 2008 Kuala Lumpur, Malaysia
Digital Design Using Quantum-Dot Cellular automata (A Nanotechnology Method)
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Mehdi Askari1, Maryam Taghizadeh2, Khossro Fardad2 Department of computer and Electrical Engineering, Islamic Azad University, Omeidyeh, Iran 2 Department of computer, Islamic Azad University, Behbahan, Iran Email (
[email protected]) The rest of the paper is organized as follows. In Sec. 2, a brief review of QCA is presented. Sec. 3 introduces the concepts of QCA clocking. Circuit implementation and simulation follow in Sec. 4 and Sec. 5, respectively. Finally, section 6 concludes the paper and outlines directions for future work.
Abstract This paper presents the design, layout, and successful simulation of a QCA multiplexor. QuantumDot Cellular Automata (QCA) is one of several proposed computational nanotechnology paradigms that are being investigated as alternatives to CMOS at the nano-scale. QCA has been reported to offer relatively low power consumption and very high device density. Unlike conventional computers in which information is transferred from one place to another by means of electrical current, QCA transfers information by propagating a polarization state. In recent years, several researchers have started investigating relatively complex circuit architectures using QCA.
II. QCA BACKGROUND A quantum cell can be viewed as a set of four charge containers or dots, positioned at the corners of a square. Within this cell, two extra electrons are available, and by raising and lowering the potential barriers with the clock, an electron can localize on a dot. The electrons are forced to the corner positions by Coulomb repulsion. Thus, two different polarizations are available: P = 1 and P = -1 as shown in Fig.1. Respectively, these polarizations provide a logical one and a logical zero. If two cells are brought close together, Columbic interactions between the electrons cause the cells to take on the same polarization. If the polarization of one of the cells is gradually changed from one state to the other, the second cell exhibits a highly quick, bistable switching of its polarization [3].
I. INTRODUCTION As the CMOS technologies approach its fundamental physical limits, there has been extensive research in recent years in nanotechnology for future generation IC. It is anticipated that these technologies can achieve a density of 1012 devices/cm2 and operate at THZ frequencies. Among these new devices, quantum dot cellular automata (QCA) not only gives a solution at nano-scale, but also it offers a new method of computation and information transformation [1]. QCA is based upon the encoding of binary information in the charge configuration within quantum dot cells. Computational power is provided by the Columbic interaction between QCA cells. No current flows between cells and no power or information is delivered to individual internal cells. The local interconnections between cells are provided by the physics of cell-tocell interaction due to the rearrangement of electron positions [2-8]. In this paper, we design and simulate a QCA multiplexor. The proposed QCA multiplexor has been designed and stimulated using the QCADesigner tool for the “4-to-1” multiplexor case.
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A. Majority Gate The fundamental QCA logical circuit is the threeinput majority gate that appears in Fig. 2 [2]. The majority gate performs a three-input logic function. Assuming A, B, and C are inputs and the logic function of the majority gate F ( A , B , C ) = A . B + B . C + A . C . By fixing the is polarization of one input as logic “1” or “0”, we can obtain an OR gate and an AND gate respectively. So more complex logic circuits can be constructed from OR and AND gates.
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cells (referred to as a clocking zone) are raised or lowered or remain raised or lowered.
Figure1. Two polarized QCA Cells[11].
Figure. 5. The four phases of the QCA
Figure.3. QCA Wire
Figure 2. Majority Gate
B. QCA Logic Fig. 3 shows placing several of QCA cells placed side by side forms a wire. Logic values pass from cell to cell due to the Columbic interactions. The polarization of the input cell is propagated down the wire. As a result, the system attempting to settle to a ground state. Any cells along the wire that are antipolarized to the input would be at a higher energy level, and would soon settle to the correct ground state. When cells are placed diagonally to each other, they tend to have reverse polarizations due to the repulsion between electrons. This characteristic is used to implement an inverter, such as the one shown in Fig. 4. Unlike conventional CMOS in which it is the simplest block, it consumes considerable area in QCA.
Figure.4. QCA Inverter [11].
During the switch phase, the interdot barrier is gradually raised, and the QCA cell settles down to one of the two ground polarization states as influenced by its neighbors. During the hold phase, the interdot barrier is held high, suppressing electron tunneling and maintaining the current ground polarization state of the QCA cell. During the release and relax phases, the interdot barriers are lowered, and the excess electrons gain mobility. In these two phases, a QCA cell remains unpolarized. Overall, the polarization of a QCA cell is determined when it is in its switch phase by the polarizations of its neighbors that are in switch and hold phases. The unpolarized neighbors in release and relax phases have no effect on determining the state of the QCA cell [9]. If QCA cells are lined up side by side and clocked appropriately, they act as a wire, propagating a signal down its length. In fact, a QCA circuit can be divided into zones, which allows the clock to be applied to groups of cells. In each zone, a single potential can modulate the barriers between the dots. The scheme of clock zones permits a cluster of QCA cells to make a certain calculation and then have its states frozen, and, finally, have its outputs used as inputs to the next clock zone [10]. As shown in Fig. 6, there is a 90 phase shift
III. QCA CLOCK QCA computation is performed by controlling the tunneling with a four phase “clock” signal as shown in Fig. 5. The clocking of QCA can be accomplished by controlling the potential barriers between adjacent quantum-dots [5-7]. The clock used in QCA consists of four phases: hold, release, relax, and switch. It is considered that the lag between adjacent phases is 90°. Rather, it can be said that the clock changes phase when the potential barriers that affect a group of QCA
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from one clock zone to the next. The different clocking zones are indicated in our layouts by the different shades of gray background of the cells as shown in Fig. 7.
and area. Simulation shows that occupied area for this design is 0.25μm2. For future work, the design can be optimized in terms of complexity and the number of clock zones. Also, computation time and power consumption can be computed for designing.
Figure. 6. QCA Clock Zone
Figure.7. Different Clocking Zone
IV. CIRCUIT IMPLEMENTATION The 4-to-1 QCA multiplexor design is shown in Fig. 8. There are three 2-to-1 multiplexors in a tree structure configuration to build a 4-to-1, two-stage multiplexor. Fig.9 shows a typical 2-to-1 multiplexor. The proposed QCA multiplexor has been designed and simulated using the QCADesigner [11] tool. This tool allows users to do a custom layout and then verify QCA circuit functionality by simulations. It includes two different simulations engines such as a bistable approximation and a coherence vector. The current QCA technology dose not specifically set the possible operating frequency and actual propagation delays. Thus, the maximum cell count can be set as a design parameter [12].
Figure. 8. 4 to 1 QCA Multiplexor
V. SIMULATION With QCADesigner ver.2.0.3, the circuit functionality is verified. The input and output waveforms are shown in Fig. 10. According to QCADesigner, this design has 124 cells (including input and output cells) and an area of approximately 0.25μm2 (each cell is 18nm × 18nm , with a 2 nm gap between cells). VI. CONCLUSION This paper presents design for 4-to-1 QCA multiplexor. The layout is done using QCADesigner and this design is analyzed according to the complexity
Figure 9. 2 to 1 QCA Multiplexor
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[4]
K. Hennessy and C. S. Lent, “Clocking of molecular quantumdot cellular automata,” J. Vac. Sci. Technol. B, 19(5): 1752– 1755 ,2001. [5] C. S. Lent and B. Isaksen, “Clocked molecular quantum-dot cellular automata,” IEEE Trans. on Electron Dev., 50(9): 1890– 1895, September 2003. [6] M. T. Niemier, M. J. Kontz and P. M. Kogge, “A design of and design tools for a novel quantum dot based microprocessor,” In 27th Ann. Design Automation Conference, pages 227–232, June 2000. [7] G. Toth and C. S. Lent, “Quasiadiabatic switching for metalisland quantumdot cellular automata,” J. Appl. Phys., 85(5): 2977–2984, March 1999. [8] A. Vetteth, K. Walus, V. Dimitrov and G. Jullien, “Quantumdot cellular automata carry-look-ahead adder and barrel shifter,” IEEE Emerging Telecommunications Technologies Conference, September 2002. [9] Kyosun Kim, Kaijie Wu, and Ramesh Karri, “The Robust QCA Adder Designs Using Composable QCA Building Blocks ,” IEEE Trans. On Computer-Aided Design of Integrated Circuits and System, Vol. 26, no. 1, pp. 176-183, January 2007. [10] O.Paranaiba V.Neto, M.A.C. Pacheco, C.R. Hall Barbosa, “Neural Network Simulation and Evolutionary Synthesis of QCA Circuits ,” IEEE Trans. On Computer, Vol. 56, no. 2, February 2007. [11] http://www.qcadesige.ca, 2006 [12] H. Cho, E.E. Swartzlander, “Adder Designs and Analyses for Quntum-Dot Celluar Automata,” IEEE Trans. On Nanotechnology, Vol. 6, no. 3, May 2007.
Figure 10. The Simulation Result
REFERENCES [1] [2] [3]
A.O. Orlov, I. Amlani, G.H. Bernstein, C.S. Lent, G.L. Snider, “Realization of a Functional Cell for Quantum-Dot Cellular Automata,” Science, Vol 277, pp 928-930, 1997. P.D. Tougaw and C.S. Lent, ”Logical devices implemented using quantum cellular automata,” Journal of Applied Physics, 75:1818, 1994.J. G. Snider, A. Orlov, C. Lent, G. Bernstein, M. Lieberman, T. Fehlner, “Implementation of Quantum-dot Cellular Automata,” ICONN 2006, pp 544-547.
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