Investigation of possibility of high temperature quantum-dot cellular automata

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1 Journal of Physics: Conference Series Investigation of possibility of high temperature quantum-dot cellular automata To cite this article: G Varga 2007 J. Phys.: Conf. Ser View the article online for updates and enhancements. This content was downloaded from IP address on 12/10/2018 at 05:43

2 IOP Publishing Journal of Physics: Conference Series 61 (2007) doi: / /61/1/240 International Conference on Nanoscience and Technology (ICN&T 2006) Investigation of possibility of high temperature quantum-dot cellular automata G Varga Department of Physics, Budapest University of Technology and Economics vargag@phy.bme.hu Abstract. Quantum-dot cellular automaton at this moment works properly at very low temperature region. How to avoid or increase the low temperature limit is investigated. 1. Introduction Quantum-dot cellular automaton (QCA) is a promising paradigm of computational device in the scale of nano-meter [1]. Unfortunately at this moment QCA works properly only under very low temperature region, below 1K [2]. This fact is a very strict limitation of QCA. The low temperature limit stops the implementation of sophisticated computational processes. To resolve this problem we investigated the physical background of this limitation. The main point of this limitation that the ground energy of QCA electrons - in the case of polarization states and transition states - are very close to each other; in the range of 1K thermal energy. To increase the energy gaps of quantum-dot electrons the size of cells has to be decreased; the bond energy has to be increased or the shape of cells has to be changed [3]. Size decreasing increases quantum entanglement and confinement effect. Larger bond energy can be reached by using appropriate composite solid surfaces. Namely, stronger physical or chemical adsorption can occur on the surfaces. Technologically, suitable atomic level deposition method - on the surfaces - could realize the required quantum-dot formations. In general the QCA cells can be described by quantum mechanical theories. However, the interaction between the cells could be characterized by classical or semi-classical theory. Obviously, the magnetic interaction could be more resistant against the temperature washing out than the electrical interaction. But the larger size and slower switching time in the case of magnetic interaction could be the disadvantages. The different directions of research should look for not only the simple electrical and magnetic interaction between the QCA cells but the indirect quantum mechanical interactions too. First of all the method of present investigation is the qualitative description and parameter estimation of physical phenomena. On the other hand, quantum mechanical computer simulation of few-particle systems is applied. In that case the time dependent or independent Schrödinger equation system has to be solved numerically by efficient algorithm [4][5]. 2. Physics of QCA Traditional CMOS technology works based on the controlling of electron current. QCA works based on the propagation of electron state in space and time. The propagation of electron state strongly depends on thermal vibration, namely on the phonon and electron interaction. If the phonon interaction 2007 IOP Publishing Ltd 1216

3 1217 could be neglected the electron state propagation via the quantum-dot cells mainly depends on the weak interaction between the quantum-dot cells. In this case a possible physical model is the following: one cell is described as a few-electron problem by quantum mechanics and the interaction between the cells is considered by electrostatic field. If the phonon interaction is significant, electron states show statistical distribution in the cells. Unfortunately, the thermal fluctuation can wash out the clear quantum mechanical states. As a result of that the lowest energy states can not be distinguished and the signal will not be clear in the logic gates of QCA. The phonon interaction can be small if it causes small energy fluctuation to the energy gap. However, in the reality, the working temperature should be almost room temperature. The room temperature corresponds to approximately 25meV. This means the energy gaps should be larger than 25meV. QCA contains input cells and output cells in the case of logical gates. Controlling the input cells their electron distribution is changed and this new electron state generates a controlling electric field around its neighbours. As a consequence of it the electron distribution of their neighbours also will be changed and so on. As a result of this interaction the information of input cell state changing propagates via the logical gate influencing on the output cells. QCA operation demands changing the state of excessive electrons in the quantum-dot cells. This can be realized by the controlling process. Controlling process has to ensure the state transitions. State transitions are only possible if the excessive electrons of quantum-dot cells could be excited to higher energy states from the ground state. At least three phases of excessive electrons can be distinguished: ground state forcing to excited state going down to one of ground states. In general ground energy is degenerated. This ensures e.g. the two different polarization states that describe physically the logic 0 and 1. Obviously, it is important to ensure the clean phases. As it was mentioned, unfortunately the thermal vibration can cover up the phases and as a result of it the rate of noise-signal increases and demolishes operable logic gates. 3. Increasing of temperature limit To increase the temperature limit physical properties of quantum-dot cell have to be changed optionally: increasing of energy gaps: o decreasing cell size o changing of cell shape [3][6] o changing number of electrons [3] o larger bond energy effect using appropriate composite solid surfaces optimising the distance between cells [7] 3D quantum-dot cell arrangement implementation o using chemical molecules as quantum-dot cells [8] o quantum-dot (QD): natural (selfassembly, e.g. adsorbed particles on solid surfaces) [9] artificial [10] (e.g. Stranski-Kranstanov, litography) combination of natural and artificial QD (e.g. porous Al mask) [10] o magnetic QCA [6][11] optimum clocked driving [12][13]. The technological method of QCA implementation determines the typical energy gaps of the excessive electrons that are responsible for the temperature limit of QCA operation. The adsorbed atomic cell is a new concept in QCA realisation [9]. This is a version of preparing natural quantumdots (NQD). In this case, there is a solid surface substrate. This substrate is exposed by particle flux. As a result of the exposition, a part of the particles stick on the surface and 1st monolayer of

4 1218 the particles is growing. When the covering rate is one, in general a super lattice is formed on the top of the solid surface. This formation is basically two-dimensional and stable against the room temperature. If the covering rate is less than one a flexible arrangement of top layer adsorbed atom can be occurred, because other arrangement of adsorbed particles is also possible. Of course, this other arrangement could have different energy, but it could show stable state on room temperature, too. However, it is questionable whether how to control the arrangement of the adsorbed particles. Electromagnetic controlling supposes electromagnetic interaction. Electromagnetic interaction can cause movement of particles if they have extra electrostatic charge, large electric or magnetic moment. In the case of standard situation, there is no extra charge, but we can stimulate it by LASER light beam or gate voltages. During this stimulation outside electric field could control the set-up of adsorbed particles. The artificial quantum-dot (AQD) preparation applies e.g. Stranski-Kranstanov, lithography, evaporation or etching mask. The main problem is the size of AQD above 10nm. In that case, the quantum effects appear only at very low temperature. A promising method is published in [10] that is a combination of the preparation of NQDs and AQDs. AQDs are established by a porous Al mask etching process on Si, Si NQDs can be successfully obtained by applying a high hydrogen dilution and appropriate bias voltage. As a result of this fabricating, array of AQDs (45nm) is obtained containing small Si NDQs (3-6nm). The small NQDs cause the quantum behaviour on room temperature. A special arrangement of chemical molecules naturally can contain excessive electrons and behave as quantum-dot on room temperature [8]. However, QCA operation was not demonstrated until now. Idea of magnetic QCA [6][11] has been demonstrated in simple case, but its size much larger than nanometer [12][13]. The optimum clocked driving could increase low temperature limit, but until now the clocked driving was not able to increase the operation temperature close to the room temperature. Based on the investigations it seems the QCA room temperature operation demands small enough QDs that show quantum behaviour in room temperature, too. In next section, we estimate the needed size limit of QDs by computer simulation. 4. Computer simulation and temperature limitation Computer simulation is a fruitful method to understand physically and redesign the quantum-dot cell, logic gates and architecture. However, it is also very important the qualitative description and parameter estimation. The qualitative estimation provides the frame of physical quantities of QCA. Bottom up and top down approaching are also needed. The quantum-dot cell description demands a bottom up approaching, because quantum mechanical approach can describe the electron interaction and determine e.g. the so called switching time of a quantum cell and energy levels. To determine the energy gaps between the states of excessive electrons of quantum-dot cell the time independent Schrödinger equation was solved numerically. In this non-relativistic model, the Coulomb interaction was considered between the two electrons in 2D real space. Because of this model approximation, we had to solve a 4D eigenvalue problem of the partial differential equation. The numerical method is based on a very special finite difference scheme on 6 th order that was developed within the frame of this research. 2 ( ) + U ( r1 ) + U ( r2 ) + V ( r1 r2 ) ( r1, r2 ) Eψ ( r1, r2 ) 2m ψ = (1) where is Planck constant, m is electron mass, subscripts note electron 1 and 2, is Laplace operator, U is outside electric interaction energy, V is interaction energy between the electrons, r is position vector of electron, is eigenfunction and E is eigenenergy.

5 1219 Figure 1. One can see the probability density function (PDF) of ground state of one of the two excessive electrons. The quantum-dot cell contains four quantum-dots. In the graphs the Control parameter relates to the amplitude of homogeneous control electric field. Control 0 corresponds to no control electric field in the potential box with inner potential barrier. PDF has same symmetry as the quantum-dots in the cells. If the electric field is high enough the electron is forced to one of the four quantum-dots. Table1. The table shows the energy levels of a two-electron system solving the equation (1) numerically in the case of a potential box. a is the size of the potential box. Most right column shows the energy difference between the first excited and the ground state. E level [mev] (2)-(1) a=1nm a=1.5nm a=2nm a=2.5nm a=5nm a=10nm Figure 1 shows how to control excessive electrons of quantum-dot cells. Probability density function (PDF) of ground state of one of the two excessive electrons could be seen. The quantum-dot cell contains four quantum-dots. In the graphs the Control parameter relates to the amplitude of homogeneous control electric field. Control 0 corresponds to no control electric field in the potential box with inner quantum-dot barrier. PDF has same symmetry as the quantum-dots in the cells. If the control electric field is high enough the electron is forced to one of the four quantum-dots. This is a clear verification that the position of excessive electrons in the quantum-dot cells can be positioned by appropriate bias voltage, namely the probability function could be localized. Table 1 lists the energy levels of a two-electron system solving the equation (1) numerically in the case of a potential box without inner potential barrier. a is the size of the potential box. Most right column shows the energy difference between the first excited and the ground state. Figure 2 depicts the energy difference between the first excited and ground state as a function of potential box size. It is very important to note that the energy difference axis in logarithmic scale. This fact supports the

6 1220 experience that size of the quantum-dot and quantum-dot cell has extremely important role in the existence of the low temperature limit of QCA. Figure 2. One can see the energy difference between the first excited and ground state as a function of potential box size. 5. Conclusion Significantly new idea of the QCA design has to be required to avoid the low temperature limit. If the low temperature limit is not eliminated the QCA paradigm will not be realized as a new efficient architecture of computational. To eliminate the low temperature limit form size of one QCA cell should be smaller than 5nm to reach the room temperature working. Realization possibility is the usage of chemical molecules or adsorbed atomic cells on solid surfaces or special combination of AQDs and NQDs. Furthermore the optimum clocked driving to decrease thermal fluctuation is also very important. 6. Acknowledgement We wish to thank András Ványolos for his contribution to develop the numerical solution of equation (1). The research was supported by Hungarian Scientific Research Fund (T038158). References [1] Cole T, Lush J C 2001 Progress in Quantum Electronics [2] Sturzu I, Kanuchok J L, Khatun M, Tougaw P D, 2005 Physica E [3] Bajec I L, Zimic N, Mraz M, 2006 Microelectronic engineering 83 (2006) [4] Varga G, 2002 Journal of Physics: Condensed Matter Varga G, Vanyolos A, Solution of 4D time independent Schrödinger equation by 6 th order finite difference scheme, to be published [5] Varga G, Scattering Animations, [6] Imre A, Csaba Gy, Bernstein G H, Porod W, Metlushko V, 2003 Superlattices and Microstructures [7] Ravichandrana R, Limb S K,Niemiera M, 2005 INTEGRATION, the VLSI journal [8] Lent C S, Isaksen B, 2003 IEEE TRANSACTIONS ON ELECTRON DEVICES 50 NO Aviram A, 1998 J. Amer. Chem. Soc. 112 no [9] Wang K L, Liu J L, Jin G, 2002 Journal of Crystal Growth [10] Ding G Q, Shen W Z, Zheng M J, Xu W L, He Y L, Guo Q X, 2005 Journal of Crystal Growth [11] Imre A, G Csaba, Metlasunko V, Bernstein G H, Porod W, 2003 Physica E [12] Kummamuru R K, Liu M, Orlov A O, Lent C S, Bernstein G H, Snider G L, 2005 Microelectronics Journal [13] Orlov A O, Kummamuru R, Ramasubramaniam R, Lent C S, Bernstein G H, Snider G L, 2003 Surface Science