Molecular Quantum-dot Cellular Automata Research Articles

Ab initio studies of counterion effects in molecular quantum-dot cellular automata.

Molecular quantum-dot cellular automata (QCA) is a low-power computing paradigm that may offer ultra-high device densities and THz-speed switching at room temperature. A single mixed-valence (MV) molecule acts as an elementary QCA device known as a cell. Cells coupled locally via the electrostatic field form logic circuits. However, previously-synthesized ionic MV molecular cells are affected by randomly-located, nearby neutralizing counterions that can bias device states or change device characteristics, causing incorrect computational results. This ab initio study explores how non-biasing counterions affect individual molecular cells. Additionally, we model two novel neutral, zwitterionic MV QCA molecules designed to avoid biasing and other undesirable counterionic effects. The location of the neutralizing counterion is controlled by integrating one counterion into each cell at a well-defined, non-biasing location. Each zwitterionic QCA candidate molecule presented here has a fixed, integrated counterion, which neutralizes the mobile charges used to encode the device state.

Mixed-valence realizations of quantum dot cellular automata

This article reviews recent progress in the design and theoretical investigation of molecular implementations of quantum-dot cellular automata (QCA) for field-coupled nanocomputing applications. QCA is a classical computing paradigm based on Coulombic quantum interactions between nanoscale subunits consisting of two or more quantum dots. Shrinking these dots to the molecular scale maximizes device density and permits operation at ambient temperatures. The essential feature of molecular QCA systems is the presence of two or more coupled redox centers separated by spacers. In this work candidate systems ranging from simple organic molecules to self-assembled multi-center mixed-valence organometallic complexes are surveyed, and some of the challenges remaining to be faced both in theoretical understanding and practical implementation are discussed.

Designing boron-cluster-centered zwitterionic Y-shaped clocked QCA molecules

Quantum-dot cellular automata (QCA) is a nanoscale, transistor-less device technology. A single molecule may provide an elementary QCA device known as a cell. Molecular redox centers function as quantum dots, and the configuration of mobile charge on the dots encodes device states useful for classical computing. Molecular QCA may support ultra-high device densities and THz-scale switching speeds at room temperature. An applied electric field may be used to clock molecular QCA, providing power gain to boost weakened signals, as well as quasi-adiabatic device operation for minimal power dissipation in QCA devices and circuits. A zwitterionic, Y-shaped, three-dot molecule may function as a field-clocked QCA cell. We focus on the design of a counterion built into the center of the cell. Ab initio computations demonstrate that choice of counterion determines the number of mobile charges for encoding the device state on the three quantum dots. We use or as the central counterionic linker for two different Y-shaped, three-dot QCA molecules. While both molecules support the desired device states, the number of trapped charges in the counterion determines the number of mobile holes on the molecular quantum dots. This, in turn, determines whether the device state is encoded by a hole or an electron. This choice of encoding determines how the molecular QCA cell responds to a clocking field. The two counterions studied here lead to two QCA molecules with opposite responses to the clock, similar to the complementary responses of PMOS and NMOS transistors to gated voltage control.

Clocked molecular quantum-dot cellular automata circuits tolerate unwanted external electric fields

Quantum-dot cellular automata (QCA) may provide low-power, general-purpose computing in the post-CMOS era. A molecular implementation of QCA features nanometer-scale devices and may support ∼THz switching speeds at room-temperature. Here, we explore the ability of molecular QCA circuits to tolerate unwanted applied electric fields, which may come from a variety of sources. One likely source of strong unwanted electric fields may be electrodes recently proposed for the write-in of classical bits to molecular QCA input circuits. Previous models have shown that the input circuits are sensitive to the applied field, and a coupled QCA wire can successfully transfer the input bit to downstream circuits despite strong applied fields. However, the ability of other QCA circuits to tolerate an applied field has not yet been demonstrated. Here, we study the robustness of various QCA circuits by calculating their ground state responses in the presence of an applied field. To do this, a circuit is built from several QCA molecules, each described as a two-state system. A circuit Hamiltonian is formed and diagonalized. All pairwise interactions between cells are considered, along with all correlations. An examination of the ground state shows that these QCA circuits may indeed tolerate strong unwanted electric fields. We also show that circuit immunity to the dominant unwanted field component may be obtained by choosing the orientation of constituent molecules. This suggests that relatively large electrodes used for bit write-in to molecular QCA need not disrupt the operation of nearby QCA circuits. The circuits may tolerate significant electric fields from other sources as well.

Robust Electric-Field Input Circuits for Clocked Molecular Quantum-Dot Cellular Automata

Quantum-dot cellular automata (QCA) is a paradigm for low-power, general-purpose, classical computing designed to overcome the challenges facing CMOS in the extreme limits of scaling. A molecular implementation of QCA offers nanometer-scale devices with device densities and operating speeds which may surpass CMOS device densities and speeds by several orders of magnitude, all at room temperature. Here, a proposal for electric field bit write-in to molecular QCA circuits is extended to QCA circuits clocked using the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$z$</tex-math></inline-formula> component of an applied electric field. Input electrodes, which may be much larger than the cells themselves, apply an input <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$y$</tex-math></inline-formula> field component. The input field selects an input bit on a field-sensitive portion of the circuit, and a shift register transmits the input bit to downstream logic. The circuit is sensitive to the input field, since even a very weak input field selects a bit and drives the shift register as desired. The circuit also is robust: the coupling between the field-sensitive segment and the shift register fails at input field strengths much stronger than those needed to write a bit. A simple rotation of the the shift register cells eliminates this circuit failure, even under arbitrarily strong input fields. The modified circuit also tolerates a significant unwanted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x$</tex-math></inline-formula> field component, which is used neither for clocking nor for input. The write-in of classical bits to molecular QCA circuits is one road-block that must be cleared in order to realize energy-efficient molecular computation using QCA. Write-in may be achieved simply by using relatively large electrodes and clocked molecular circuits that respond to a weak input field and tolerate very strong applied fields without failing.

A Theoretical Procedure Based on Classical Electrostatics and Density Functional Theory for Screening Non-Square-Shaped Mixed-Valence Complexes for Logic Gates in Molecular Quantum-Dot Cellular Automata

Abstract Understanding the requisite geometry of molecules and peripheral components is an essential step in endowing molecules with logical functions in quantum-dot cellular automata. To respond to the real problem of structural distortion from the ideal square cell configuration, a practical procedure is presented that simplifies the molecular shapes for device design with features that combine aspects of classical electrostatics and density functional theory calculations. By applying this method to a library of biferrocenium dimers with a three-input junction, it was demonstrated in theory that a covalently bonded parallelogram dimer responds precisely to six different patterns of nanoscale electric fields and works correctly as a device cell in both AND and OR logic gates. The counterintuitive usefulness of the non-square-shape is rationalized by four ferrocene-based orbital orientations and a functional group arrangement, equalizing the disadvantageous energy asymmetry between the states 0 and 1. The present procedure was applied to quasi-square tetrametallic Ru complexes and it was found that these complexes do not work as logic gates. This procedure expands the range of existing candidate molecules from squares to parallelograms and facilitates screening for implementation.

Energy dissipation during two-state switching for quantum-dot cellular automata

We examine the energy dissipated by a two-state quantum system during a switching operation when interacting with a thermal environment. For an isolated system, the excess energy decreases exponentially with switching time. For classically damped systems, the energy dissipation decreases linearly with switching time. We model the quantum system coupled to a thermal environment using a Lindblad equation for the density matrix. For rapid switching, the exponential quantum adiabaticity holds. For slow enough switching, the damping from the bath yields linear dissipation, as in the classical limit. Between these two limits, when the switching time is comparable to the characteristic energy transfer time to the thermal bath, there is an inverted region when dissipation increases with longer switching times. Consequences for the design of molecular quantum-dot cellular automata are discussed.

Population congestion in 3-state quantum-dot cellular automata

The behavior of quantum-dot cellular automata (QCA) networks is typically understood through considering polarization-like interactions with energies arising from the agreement or disagreement of the defined polarization states of neighboring QCA devices. It is known that additional interactions are present in 3-state molecular QCA that alter the required clocking fields needed for a device operation. Recent efforts in implementing logic gates using patterned dangling bonds (SiDBs) on hydrogen passivated silicon reveal significant challenges arising from similar effects. The necessary applied electrical potential needed to increase the population of an SiDB is strongly dependent on the current population of its neighbors, an effect we term congestion. It is unclear whether the strength of these interactions may pose an obstacle for future applications of SiDBs as a nanoscale QCA architecture. In this work, we investigate 3-state QCA in the regime in which congestion is significant and determine the extent to which such effects can be mitigated for SiDB devices. We propose that while SiDB-based QCA wires may be achievable depending on limitations of inter-dot tunneling, higher density devices such as majority gates may need to be replaced by more architecture specific implementations unless net-neutral variants of SiDB QCA devices can be demonstrated.

SCERPA: A Self-Consistent Algorithm for the Evaluation of the Information Propagation in Molecular Field-Coupled Nanocomputing

Among the emerging technologies that are intended to outperform the current CMOS technology, the field-coupled nanocomputing (FCN) paradigm is one of the most promising. The molecular quantum-dot cellular automata (MQCA) has been proposed as possible FCN implementation for the expected very high device density and possible room temperature operations. The digital computation is performed via electrostatic interactions among nearby molecular cells, without the need for charge transport, extremely reducing the power dissipation. Due to the lack of mature analysis and design methods, especially from an electronics standpoint, few attempts have been made to study the behavior of logic circuits based on real molecules, and this reduces the design capability. In this article, we propose a novel algorithm, named self-consistent electrostatic potential algorithm (SCERPA), dedicated to the analysis of molecular FCN circuits. The algorithm evaluates the interaction among all molecules in the system using an iterative procedure. It exploits two optimizations modes named Interaction Radius and Active Region which reduce the computational cost of the evaluation, enabling SCERPA to support the simulation of complex molecular FCN circuits and to characterize consequentially the technology potentials. The proposed algorithm fulfills the need for modeling the molecular structures as electronic devices and provides important quantitative results to analyze the information propagation, motivating and supporting further research regarding molecular FCN circuits and eventual prototype fabrication.

Molecular QCA embedding in microporous materials.

We propose an environment for information encoding and transmission via a nanoconfined molecular Quantum Dot Cellular Automata (QCA) wire, composed of a single row of head-to-tail interacting 2-dots molecular switches. While most of the research in the field refers to dots-bearing molecules bound on some type of surface, forming a bidimensional array of square cells capable of performing QCA typical functions, we propose here to embed the information bearing elements within the channels of a microporous matrix. In this way molecules would self-assemble in a row as a consequence of adsorption inside the pores of the material, forming an encased wire, with the crystalline environment giving stability and protection to the structure. DFT calculations on a diferrocenyl carborane, previously proposed and synthesized [J. A. Christie, R. P. Forrest, S. A. Corcelli, N. A. Wasio, R. C. Quardokus, R. Brown, S. A. Kandel, Y. Lu, C. S. Lent and K. W. Henderson, Angew. Chem., Int. Ed., 2015, 54, 15448], were performed both in vacuum and inside the channels of zeolite ITQ-51, indicating that information encoding and transmission is possible within the nanoconfined environment.

Characterisation of a bis‐ferrocene molecular QCA wire on a non‐ideal gold surface

Field-coupled nanocomputing represents one of the possible proposals for the post-Complementary Metal Oxide Semiconductor (CMOS) scenario. Contrarily to standard technology, the information is not propagated using electron transport, but via field interactions among single elements. The molecular quantum-dot cellular automata (QCA) is one of the most promising implementations; redox centres of oxidised molecules are used to concentrate charges. Coulomb interaction between redox centres enables the information propagation. The necessity for charge transport is overcome, entailing very low power consumption notwithstanding the nanometric size and the very high expected operating frequency. Nevertheless, as the Coulomb interaction strongly depends on the distance between charges, the position of each molecule plays a relevant role in the interaction. This work investigates the information propagation of a possible molecular wire thiolated on a non-ideal gold surface, where the intermolecular distance may vary due to the surface roughness and possible defects introduced in the formation of the molecular wire. The efficiency of the information transfer is analysed with the aim of providing significant constrains and suggestions for future fabrication steps.

Clock Topologies for Molecular Quantum-Dot Cellular Automata

Quantum-dot cellular automata (QCA) is a low-power, non-von-Neumann, general-purpose paradigm for classical computing using transistor-free logic. Here, classical bits are encoded on the charge configuration of individual computing primitives known as “cells.” A cell is a system of quantum dots with a few mobile charges. Device switching occurs through quantum mechanical inter-dot charge tunneling, and devices are interconnected via the electrostatic field. QCA devices are implemented using arrays of QCA cells. A molecular implementation of QCA may support THz-scale clocking or better at room temperature. Molecular QCA may be clocked using an applied electric field, known as a clocking field. A time-varying clocking field may be established using an array of conductors. The clocking field determines the flow of data and calculations. Various arrangements of clocking conductors are laid out, and the resulting electric field is simulated. It is shown that that control of molecular QCA can enable feedback loops, memories, planar circuit crossings, and versatile circuit grids that support feedback and memory, as well as data flow in any of the ordinal grid directions. Logic, interconnect and memory now become indistinguishable, and the von Neumann bottleneck is avoided.

Effectiveness of Molecules for Quantum Cellular Automata as Computing Devices

Notwithstanding the increasing interest in Molecular Quantum-Dot Cellular Automata (MQCA) as emerging devices for computation, a characterization of their behavior from an electronic standpoint is not well-stated. Devices are typically analyzed with quantum physics-based approaches which are far from the electronic engineering world and make it difficult to design, simulate and fabricate molecular devices. In this work, we define new figures of merits to characterize the molecules, which are based on the post-processing of results obtained from ab initio simulations. We define the Aggregated Charge (AC), the electric-field generated at the receiver molecule (EFGR), the Vin–Vout and Vin–AC transcharacteristics (VVT and VACT), the Vout maps (VOM) and the MQCA cell working zones (CWZ). These quantities are compatible with an electronic engineering point of view and can be used to analyze the capability of molecules to propagate information. We apply and verify the methodology to three molecules already proposed in the literature for MQCA and we state to which extent these molecules can be effective for computation. The adopted methodology provides the quantitative characterization of the molecules necessary for digital designers, to design digital circuits, and for technologists, to the future fabrication of MQCA devices.

Electric-Field Inputs for Molecular Quantum-Dot Cellular Automata Circuits

Quantum-dot cellular automata (QCA) is a low-power, non-von-Neumann, general-purpose paradigm for classical computing using transistor-free logic. An elementary QCA device called a "cell" is made from a system of coupled quantum dots with a few mobile charges. The cell's charge configuration encodes a bit, and quantum charge tunneling within a cell enables device switching. Arrays of cells networked locally via the electrostatic field form QCA circuits, which mix logic, memory and interconnect. A molecular QCA implementation promises ultra-high device densities, high switching speeds, and room-temperature operation. We propose a novel approach to the technical challenge of transducing bits from larger conventional devices to nanoscale QCA molecules. This signal transduction begins with lithographically-formed electrodes placed on the device plane. A voltage applied across these electrodes establishes an in-plane electric field, which selects a bit packet on a large QCA input circuit. A typical QCA binary wire may be used to transmit a smaller bit packet of a size more suitable for processing from this input to other QCA circuitry. In contrast to previous concepts for bit inputs to molecular QCA, this approach requires neither special QCA cells with fixed states nor nanoelectrodes which establish fields with single-electron specificity. A brief overview of the QCA paradigm is given. Proof-of-principle simulation results are shown, demonstrating the input concept in circuits made from two-dot QCA cells. Importantly, this concept for bit inputs to molecular QCA may enable solutions to or provide insights into other challenges to the realization of molecular QCA, such as the demonstration of molecular device switching, the read-out of molecular QCA states, and the layout of molecular QCA circuits.

Molecular Quantum Dot Cellular Automata Based on Diboryl Monoradical Anions

Field-effect transistor (FET)-based microelectronics is approaching its size limit due to unacceptable power dissipation and short-channel effects. Molecular quantum dot cellular automata (MQCA) is a promising transistorless paradigm that encodes binary information with bistable charge configurations instead of currents and voltages. However, it still remains a challenge to find appropriate candidate molecules for MQCA operation. Inspired by recent progress in boron radical chemistry, we theoretically predicted a series of new MQCA candidates built from diboryl monoradical anions. The unpaired electron resides mainly on one boron center and can be shifted to the other by an electrostatic stimulus, forming bistable charge configurations required by MQCA. By investigating various bridge units with different substitutions (ortho-, meta-, and para-), we suggested several candidate molecules that have potential MQCA applications.

Jahn-Teller effect in molecular electronics: quantum cellular automata

The article summarizes the main results of application of the theory of the Jahn-Teller (JT) and pseudo JT effects to the description of molecular quantum dot cellular automata (QCA), a new paradigm of quantum computing. The following issues are discussed: 1) QCA as a new paradigm of quantum computing, principles and advantages; 2) molecular implementation of QCA; 3) role of the JT effect in charge trapping, encoding of binary information in the quantum cell and non-linear cell-cell response; 4) spin-switching in molecular QCA based on mixed-valence cell; 5) intervalence optical absorption in tetrameric molecular mixed-valence cell through the symmetry assisted approach to the multimode/multilevel JT and pseudo JT problems.

Electric-field-driven electron-transfer in mixed-valence molecules.

Molecular quantum-dot cellular automata is a computing paradigm in which digital information is encoded by the charge configuration of a mixed-valence molecule. General-purpose computing can be achieved by arranging these compounds on a substrate and exploiting intermolecular Coulombic coupling. The operation of such a device relies on nonequilibrium electron transfer (ET), whereby the time-varying electric field of one molecule induces an ET event in a neighboring molecule. The magnitude of the electric fields can be quite large because of close spatial proximity, and the induced ET rate is a measure of the nonequilibrium response of the molecule. We calculate the electric-field-driven ET rate for a model mixed-valence compound. The mixed-valence molecule is regarded as a two-state electronic system coupled to a molecular vibrational mode, which is, in turn, coupled to a thermal environment. Both the electronic and vibrational degrees-of-freedom are treated quantum mechanically, and the dissipative vibrational-bath interaction is modeled with the Lindblad equation. This approach captures both tunneling and nonadiabatic dynamics. Relationships between microscopic molecular properties and the driven ET rate are explored for two time-dependent applied fields: an abruptly switched field and a linearly ramped field. In both cases, the driven ET rate is only weakly temperature dependent. When the model is applied using parameters appropriate to a specific mixed-valence molecule, diferrocenylacetylene, terahertz-range ET transfer rates are predicted.

Effect of a Clock System on Bis-Ferrocene Molecular QCA

Molecular quantum-dot cellular automata (mQCA) is found to be the most promising among all emerging technologies. It is expected to show remarkable operating frequencies (THz), high device densities, noncryogenic working temperature, and reduced power consumption. The computation relies on a new paradigm based on the interaction between nearby molecular QCA cells. This computation requires the aid of an external signal normally referred to as clock that enables/inhibits the molecular activity. The influence of clock on realistic molecules has never been deeply studied. In this paper, we performed a thorough analysis of the clock signal added to the molecular QCA cell based on an ad hoc synthesized bisferrocene molecule. Ab-initio simulations and further postprocessing of data have been used for characterizing the performance of bisferrocene molecule under the influence of a clock signal. Quantitative results on the molecule in terms of newly defined figures of merits, i.e., aggregated charge , equivalent voltage, and Vin-Vout trans-characteristic have been shown. Meanwhile, we demonstrate when and how much the presence of clock signal enhances or hinders the interactions between QCA molecules. These unprecedented data give a fundamental improvement to the knowledge on how information can be propagated through QCA devices. The results suggest directions to chemists, technologists, and engineers on how to proceed in the next steps for this promising technology.

Process Variability and Electrostatic Analysis of Molecular QCA

Molecular quantum-dot cellular automata (mQCA) is an emerging paradigm for nanoscale computation. Its revolutionary features are the expected operating frequencies (THz), the high device densities, the noncryogenic working temperature, and, above all, the limited power densities. The main drawback of this technology is a consequence of one of its very main advantages, that is, the extremely small size of a single molecule. Device prototyping and the fabrication of a simple circuit are limited by lack of control in the technological process [Pulimeno et al. 2013a]. Moreover, high defectivity might strongly impact the correct behavior of mQCA devices. Another challenging point is the lack of a solid method for analyzing and simulating mQCA behavior and performance, either in ideal or defective conditions. Our contribution in this article is threefold: (i) We identify a methodology based on both ab-initio simulations and post-processing of data for analyzing an mQCA system adopting an electronic point of view (we baptized this method as “MoSQuiTo”); (ii) we assess the performance of an mQCA device (in this case, a bis- ferrocene molecule) working in nonideal conditions, using as a reference the information on fabrication-critical issues and on the possible defects that we are obtaining while conducting our own ongoing experiments on mQCA: (iii) we determine and assess the electrostatic energy stored in a bis-ferrocene molecule both in an oxidized and reduced form. Results presented here consist of quantitative information for an mQCA device working in manifold driving conditions and subjected to defects. This information is given in terms of: (a) output voltage; (b) safe operating area (SOA); (c) electrostatic energy; and (d) relation between SOA and energy, that is, possible energy reduction subject to reliability and functionality constraints. The whole analysis is a first fundamental step toward the study of a complex mQCA circuit. It gives important suggestions on possible improvements of the technological processes. Moreover, it starts an interesting assessment on the energy of an mQCA, one of the most promising features of this technology.

Field-induced electron localization: Molecular quantum-dot cellular automata and the relevance of Robin–Day classification

Mixed-valence complexes are potential candidates for the molecular quantum-dot cellular automata (QCA) approach, which encodes binary information using the configuration of localized and mobile charges. In the Robin–Day classification of mixed-valence complexes, charge localization/delocalization is determined by the ratio of the nuclear reorganization energy and the electron transfer (ET) matrix element. We point out that the driving force for charge localization in molecular QCA is the Coulomb interaction between neighboring molecules rather than nuclear relaxation. This suggests a different criterion for the relevant charge localization, one based on the ET matrix element and the driving bias of a neighboring molecule.