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Logic gates in graphene technology


2013-09-18 13:49:33

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This paper is related to an alternative method of generation and propagation of binary signal (Quantum Cellular Automata) that, in most of the literature, is implemented with quantum dots or quantum wells [1],[2]. By using some new different approaches based on graphene structures, the signal processing capabilities of QCA assemblies may be obtained at significantly reduced complexity compared to conventional quantum-based QCA assemblies, which typically operate at very low temperatures. A two-layer graphene structure is presented in order to overcome technological and operating limitations that affect traditional approaches.









graphene_1
Figure 1: Cell configuration conventionally defined as “0” and “1” logic. 

State-of-the-art QCA: Quantum dots

The quantum-dot [3] is an “artificial atom” obtained by including a small quantity of material in a substrate. The definition “artificial atom” for a quantum-dot is intended in an electrical sense, allowing the transition of a single electron (or a single hole) among a couple of them. In this field, the most common technology is based on an indium deposition on a GaAs substrate

This happens because the reticular structure of InAs is quite different from gallium and therefore indium tends to concentrate in very small islands. By using several layers of GaAs, pillow structures can be realized. Considering this vertical structure, location probabilities of electrons and holes can be considered as “distributed” on several dots.









graphene_2
Figure 2: Device cell is driven to “1” due to majority effect. 

Consider that four dots realized on the same layer constitute a QCA cell [2]. In each cell, two extra electrons can assume different locations by tunneling between the dots and providing the cell with a certain polarization. Coulombic repulsion causes the two electrons to occupy antipodal sites within the cell (see FIGURE 1). The dimension of the cells may be around 10 nm.

The array of interacting quantum cells can be considered a Quantum-dot Cellular Automata. However, it must be noted that no tunneling occurs between cells and the polarization of the cell is determined only by Coulombic interaction of its neighboring cells.

QCA operating principles

The status of each cell can therefore be, according to Fig. 1, only in “0” or “1” configuration, depending on the influence of its neighbor, producing a “majority” effect. In other words, the status which is more present at the border of the cell “wins” and it is copied on it due to polarization. An example is given in FIGURE 2.









graphene_3
Figure 3: Examples of QCA structure. 










graphene_4
Figure 4: QCA logic gates. 

Signal propagation happens as a “domino“ effect with a very low power consumption. Simple structures can be easily arranged, as in FIGURE 3.

By fixing the polarization in one of the cells in a “majority” crossing structure, AND and OR gates can be easily obtained (FIGURE 4).

Quantum dots: Current technology

One of the most promising technologies for implementing quantum dots, and therefore quantum cellular automata, is Bose-Einstein Condensates [4]. This approach overcomes the traditional one based on an Indium deposition on a GaAs substrate (small indium islands aggregation due to reticular diversity).

Bose-Einstein Condensates (BEC) are made by ultra-cold atom aggregation (typically rubidium or sodium isotopes) confined using laser manipulations and magnetic fields.

BEC’s properties are quite atypical and therefore are defined as the “fifth phase of matter,” after solids, liquids, gases and plasmas. Every atom in a BEC has the same quantum state, and therefore, a BEC can be considered a “macroscopical atom.” Tunnelling and quantum effects also occur at a macroscopical scale, with advantages on state definition and detection. A major drawback is the very low operating temperature (around 1°K) that may constitute a limit for physical implementation.









graphene_5
Figure 5: Structure of a graphene layer. Selected area is about 4 nm2. 

Proposed technology

In recent years, an increasing interest has been devoted to new materials, whose properties seem to be very promising for nanoscale circuit applications. Graphene [5] is a 0.3 nm thin layer of carbon atoms having a honeycomb structure, whose properties of conductivity, flexibility, transparency could have a deep impact on future integration technology (FIGURE 5).









graphene_6
Figure 6: An example of a graphene layer with four hemispherical “hills”.  

Graphene could also be doped as usual semiconductors are (despite the fact that, from its electrical properties, it can be considered a pure conductor), and therefore, it can be used to build nanometric transistors. However, the most interesting features that suggest graphene as a good material for QCA cells are the following:

      1. In contrast to metallic or semiconductor QCA, the dimensions of molecular automata allow for operation at ambient temperatures because they have greater electrostatic energy [6],[7].



      2. Low power requirements and low heat dissipation allow high density cell disposition [8],[9].



      3. Structure flexibility (see


FIGURE 6
    ) and physical bandgap arrangement allow cells to be built with the bistable behaviour of a two-charge system.

Different techniques are currently available to reshape a graphene layer. Despite the fact that industrial processes are not yet implemented, it is arguable that a serial production of a QCA graphene cell could be possible, and simple, well-defined process steps for the single cell are identified.









graphene_7
Figure 7: Graphene based QCA cell structure. The four hemispherical cavities allow the two negative charges to be hosted in both configurations of logic states.  

Idea for structure and process steps

The basic idea is to realize a square structure with four cavities in which two negative charges (suitable ions or molecules) could be placed and moved depending on neighborhood polarization. Graphene manipulation may allow dimensions of the cells that are quite comparable to the traditional semiconductor Q-dots approach (for a solid state single electron transition cell, the distance among dots is typically 20nm, and the average distance among interacting cells is 60nm). However, in order to cope with the chosen ion charge (Coulombic interaction can be stronger if compared with single electrons) and with process requirements, a slight increase of distances is also possible. The structure is based on a two layer graphene arrangement (see FIGURE 7).

The top layer (Layer 1) needs some more process steps in order to realize the four hemispherical cavities. The different energy levels among the layers (obtained by establishing different potentials for the two conductors) forces negative charges, in absence of external polarization, to stay on the bottom of the holes. Supposing a dimension of 15-20nm for each cavity in order to host suitable electronegative molecules or ions (e.g. Cl-, F-, SO4--), the process steps could be the following:

Layer 2 definition (bottom layer process steps):
    1. Graphene chemical vapor deposition (CVD) on copper.

    2. Graphene (layer 2) transfer on the target substrate (through copper wet etching and standard transfer techniques).

Layer 1 definition (top layer process steps):
    1. Graphene chemical vapor deposition (CVD) on copper.

    2. Resist spin-coating (ex: PolyMethylMethAcrylate, PMMA) on graphene CVD (on copper).

    3. E-Beam lithography for hemispherical cavities definition.

    4. Resist selective removal (ex: TetraMethyl Ammonium Hydroxide chemistry).

    5. Graphene etching (plasma O2).

    6. Resist removal (ex: acetone).

    7. Graphene (layer 1) transfer on layer 2 (through copper wet etching and standard transfer techniques).

In addition to the “physical” bandgap realized with this structure, an electronic bandgap could be created on Layer 1 during the third process step. Defects induced in hemispherical cavities may allow a bandgap of 1.2eV to be reached.

Signal transduction of the resulting logic level

After the signal processing performed by the QCA network, the resulting logic state is stored in the last QCA cell. In order to be used by other electronic devices, this information has to be converted into a suitable voltage level. From an operative point of view, it is sufficient to detect a negative charge in the right up position of the last cell; if it is present, according to Fig. 1, the logic state is “1”, otherwise it is “0”. This operation is not so trivial, due to the quantity of the charge to be detected and to the small dimension of its location. To this end, among several different strategies, two approaches could be suitable: the ion approach and the optical approach.

Ion approach.This approach can be performed by using channel electron multipliers (or channeltrons), which are ion detectors with high amplification (108). Every ion can generate a cascade of electrons inside the detector, and therefore, consistent charge pulses that can be counted. In our case, there is no ion flux across a surface, and therefore, counting is not needed (information is only ion presence or absence). However, the detection area is very small (quarter cell). This problem could be solved by attaching carbon nanotubes (e.g. ,10nm diameter each) to charge pulse amplifier terminals, in order to increase their resolution, acting as nano-guides.

Optical approach. The basic principle of this approach is in theory quite simple: in order to detect an object of nanometric dimensions like molecules or ions, a suitable wavelength waveform should be used. For the described application, X-ray radiation seems to be the most appropriate, ranging its wavelength among 1 pm and 10 nm. However, the complexity of the detection set (high precision is needed in order to minimize bit error) and the huge number of the transducers that require large numbers of bit conversions, may in some cases indicate this solution as too expensive with respect to the ion approach. •

References

1.W. Porod, World Scientific Series on Nonlinear Science, 26, 495 (1999).

2.I. Amlani et al., Science, 284, 289 (1999).

3.G. Tóth et al., J. Appl. Phys., 85, 2977 (1999).


4.J.R. Ensher et al., Phys. Rev. Lett. 77, 1996 (1996).

5.K. Novoselov et al., Science, 306, 666 (2004)

6.X. Du et al., Nature, 462, 192 (2009)

7.K. I. Bolotin et al., Phys. Rev. Lett., 101, 096802 (2008)

8.F. Schwierz, Nat. Nanotechnol., 5, 487 (2010)

9.D. Frank, et al., IEEE Electron Dev. Lett., 19, 385. (1998)




DOMENICO MASSIMO PORTO is a systems analysis specialist staff engineer, audio and body division technical marketing, automotive product group, STMicroelectronics, Milan, Italy.