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VLSI DESIGN2001, Vol. 13, Nos. 1-4, pp. 419-424Reprints available directly from the publisherPhotocopying permitted by license only

(C) 2001 OPA (Overseas Publishers Association) N.V.Published by license under

the Gordon and Breach Science Publishers imprint,member of the Taylor & Francis Group.

Detection of Quantum Cellular AutomatonAction in Silicon-on-insulator Cells

M. GATTOBIGIO, M. MACUCCI* and G. IANNACCONE

Dipartimento di Ingegneria dell’Informazione, Via Diotisalvi, 2 1-56126 Pisa, Italy

We present a proposal for an experiment to demonstrate QCA (Quantum CellularAutomaton) functionality for a cell fabricated with silicon-on-insulator technology. Thefundamental feature of a working QCA cell consists in the anticorrelated transition ofelectrons in the two pairs of dots forming the cell: we show how such a phenomenon canbe detected from the appearance of a "locking" effect between the Coulomb Blockadecurrent peaks relative to each pair. The proposed approach allows the detection ofQCAaction without the need for additional noninvasive charge detectors probing each dot.We have performed detailed numerical simulations on the basis of interdot capacitancevalues obtained from experimental data and determined the range of parameters withinwhich the effect should be detectable.

Keywords: Quantum Cellular Automata; Silicon; Monte Carlo

1. INTRODUCTION

The Quantum Cellular Automaton concept, firstproposed by Lent et al. [1], is an interestingapproach to nanoelectronics, based on two-dimen-sional arrays of bistable cells, which allow theimplementation of arbitrary combinatorial logiccircuits. The basic cell is made up of four quantumdots and contains two electrons: if confinement ineach dot is strong enough, the electrons will repeleach other, and will tend to align along one ofthe diagonals of the square cell. In the absenceof external electric fields or of other nearbycells, alignment along either diagonal is equallyprobable. If we place, next to the cell we are

considering, another cell with a well definedpolarization (indicated as "driver cell" in the fol-lowing), the electrons in the "driven cell" will tendto align parallel to those in the driver cell. If alogic value is associated with each polarizationconfiguration, it is apparent that such a value canbe propagated along a line of cells (binary wire) ina domino-like fashion and it has been shown thatcombinatorial logic functions can be easily ob-tained [2] by properly assembling two-dimensionalarrays of cells. This approach would have theadvantage of very limited power dissipation, sincecharges move only within a cell and there is no netcharge flow across the array, and significant per-spectives for extreme miniaturization, down to the

* Corresponding author, e-mail: massimo@mercurio.iet.unipi.it

419

420 M. GATTOBIGIO et al.

molecular level. However, many complex technicalproblems need to be solved before this technologycan be applied to practical purposes; in particularviable solutions must be found to the issues offabrication tolerances [3] and of detecting theoccupancy of each dot without perturbing the cellstate.The first experimental demonstration of a QCA

cell was obtained [4, 5] with metallic tunnel junc-tions with A1/A1Ox/A1 tunnel barriers, with a setupin which electrons are supplied to the cell viaexternal leads and polarization was measured bymeans of charge amplifiers based on single-elec-trons transistors capacitively coupled to the metalislands.A different approach is represented by the

fabrication of a 4-dot cell with GaAs/A1GaAs tech-nology, defining the dots by means of properlyshaped metal gates, deposited on top of a hetero-structure. In this case it is possible to fabricateminimally invasive charge detectors by means ofquantum point contacts, whose resistance is influ-enced by the charge stored in the quantum dots.The QCA cell implementation on which we are

currently focusing is based on silicon dots [6] de-fined by electron beam lithography and successivesize reduction by means of controlled oxidationon silicon-on-insulator material. This approachhas the advantage of allowing the fabrication ofextremely small dots (in the 10 nm range) and ofimproving the strength of the electrostatic inter-action in comparison to materials such as GaAs,due to the reduced dielectric permittivity of siliconoxide. It would be possible to add also chargedetectors, in the form, for example, of single-electron transistors, but this would translate intoadded complexity for a structure that alreadyrequires extremely challenging tuning proceduresto obtain simultaneous operation of the fourdots.We propose a measurement procedure that can

provide a clear demonstration of correlated elec-tron switching between the two pairs of quantumdots forming a cell from the observation of therelationship between the position of the Coulomb

Blockade current peaks through the dot pairs. AMonte Carlo code has been developed for the vali-dation of the proposed procedure and the deter-mination of the appropriate parameter values.

2. PRINCIPLE OF OPERATION

The proposed experiment will be described withreference to the layout represented in Figure 1,corresponding to the structure fabricated by Singleet al. [6] in silicon-on-insulator material. Thereare four lithographically defined islands, with fouradjustment gates. The barriers separating the dotsbelonging to the same pair and those separatingthe dots from the leads are obtained as geometricalconstrictions. Such a device can be represented, forthe sake of investigating its electrical behavior,with the equivalent circuit of Figure 2, where theTE’s and Tz’s are tunneling capacitors. In this cell,tunneling can occur only between dots belongingto the same pair, contrary to "classical" QCAcells, in which all dots are connected via tunnelingbarriers. This does not represent a significant

FIGURE Sketch of the Si-SiO2 QCA cell. Oxidized silicon isrepresented in grey. Tunnel capacitances correspond to the sixconstrictions.

QUANTUM CELLULAR AUTOMATON 421

FIGURE 2 Equivalent capacitance network of the QCA cell.

difference from the operational point of view, sincecharge configurations are the very same in bothcases. In Figure 2 we did not include the cap-acitances between the adjustment leads and thediagonally opposite dots, for the sake of simplicity.We have included them in our calculations andnoticed no relevant contribution. The same can besaid for the capacitances between the dots andthe backgate that is usually present under thestructure.

In order to understand the proposed procedure,it is convenient to focus first on the operation of asingle pair of dots, considering all voltage sourcesconnected to the other pair of dots as deactivatedand the corresponding electrodes as grounded. Inthe presence of a small voltage applied between theleft and right lead, a current will flow throughthe three tunneling junctions in a dot pair onlyif the chemical potentials of the three dots arealigned with those of the leads, which correspondsto having both dots on the edge between twostable occupancies.The chemical potentials in the dots can be varied

by means of the voltage applied to the adjustmentgates: if we apply a positive voltage ramp to thegate controlling the left dot and a negative ramp to

that connected to the right dot, and adjust therelative position of the ramps in such a way asto synchronize the transition from M+ to Melectrons in the right dot with that from N- to Nin the left dot, the Coulomb Blockade will be liftedand a current peak will be observed through thedots. The same will happen in correspondence withany other synchronous change of the occupancy inthe two dots. We assume that the rate of variationfor the applied voltages is very slow compared tothe tunneling rates and to the RC time constants,so that a quasi-static treatment is in order.The experiment can then be repeated for the

upper pair of dots (grounding the voltage sourceconnected to the lower pair), applying a ramp withpositive slope to the adjustment gate for the rightdot and a ramp with negative slope to the othergate, in order to obtain transitions in dot occu-pancy that are opposite to those achieved in thelower pair of dots. A shift is also included withrespect to the ramps for the lower pair, in order todisplace the peaks of I2 with respect to those of 11,as shown in Figure 3.

If both the upper and lower section are operat-ed simultaneously, the electrostatic interaction be-tween the dots will determine a synchronizationbetween opposite occupancy variation phenom-ena, thereby yielding a "locking" effect betweenthe peaks in the two currents (see Fig. 4), despitethe presence of the above mentioned shift.

6O

40

20

0

-0.6[ %" .......0 50

20

100

40 6’0Time (arbitrary units)

80 100

FIGURE 3 Time dependent current through the upper dots(solid line) and through the bottom dots (dashed line) when theother semicell is switched off.

422 M. GATTOBIGIO et al.

if" 30 -0 6v5" o 50 100

20

10

0 20 40 60 80 O0Time (arbitrary units)

FIGURE 4 Time dependent current through the upper dots(solid line) and through the bottom dots (dashed line) whenboth semicells are biased. The synchronization of current peaksimplies QCA operation.

This will demonstrate correlated switching and,therefore, cell operation.

3. SIMULATION CODE

Our initial checks on the feasibility of the proposedexperiment were performed with the public domainversion of the well-known SIMON [7] single elec-tron circuit simulator, but we then developed ourspecifically devised Monte Carlo simulator in orderto obtain a better numerical precision and a moredirect control of internal parameters. The compu-tational strategy is quite straightforward andanalogous to what has appeared in the literaturefor single electron circuits.The simulation is subdivided into a number of

steps, each corresponding to a given value of thegate voltages. Within each step a stationary MonteCarlo calculation is performed, letting the elec-trons cross the tunneling junctions according tothe following rules: the variation of free energy AEassociated with the crossing of each junction iscomputed, then the tunneling rates are evaluatedaccording to the "orthodox" Coulomb blockadetheory:

AEe2RT --e-/XE/(k.)

where Rv is the tunneling resistance, e is theelectron charge, kB the Boltzmann constant and Tthe temperature. A random number is generated,uniformly distributed in an interval which ispartitioned into sections with a width proportionalto the rate for each possible transition: the tran-sition corresponding to the section containing thegenerated random number is then chosen. Dotcharges are updated as a result of the transitionand a new iteration is performed, after generatingthe time elapsed during the current iteration asan exponentially distributed random number withaverage equal to the inverse of the total tunnelingrate (obtained as the sum of the rates for allpossible transitions). The procedure is repeated anumber of times sufficient to get reliable estimatorsof the quantities of interest: the charge in each dot,obtained by averaging the values at each iteration,and the current flowing through each junction,determined by taking the ratio of the total chargethat has traversed it to the sum of the times cor-responding to each iteration.The whole sequence is repeated for all the gate

voltage values into which the simulation has beensubdivided and results for the dot charges andjunction currents are collected. Our code has beentested on the structures of Ref. [6], and has yieldedresults that are in extremely good agreement withthe experimental data.

4. NUMERICAL RESULTSAND FEASIBILITY ASSESSMENT

The values of the geometrical capacitances be-tween dots have been evaluated by means of theFASTCAP [8] program, modeling the variouselectrodes as parallelepipeds approximating theactual geometries. We have assumed a dot sizeof 60 60 60nm, and a separation of 16nmbetween dots and of 100nm between each dotand the corresponding adjustment gate. Separa-tion between dots belonging to different pairs mustbe very small, otherwise coupling is too weak to

QUANTUM CELLULAR AUTOMATON 423

allow proper operation. As a rule of thumb, wehave found out that values of the couplingcapacitances between the upper and lower dotsmust be of the same order of magnitude as thatof the tunneling junctions. With this procedurethe following results have been obtained: CD=0.94 aF, Cv- 1.65 aF, CB-- 1.36 aF, Cc- 1.0 aF,Ca 0.94 aF. The capacitances of the tunneljunctions cannot be computed from simple geome-trical considerations, since, as it turns out fromthe experiments, localization in the dots and crea-tion of the barriers between them is substantiallythe consequence of the potential fluctuationsdue to the random distribution of dopants. Wehave therefore resorted to recent measurementresults [6] yielding the values: TE-9aF andTD-- 10aF.As a consequence of their relatively large value,

operation is possible only at very low tempera-tures, in order to avoid excessive thermal broad-ening that would prevent observation of the"locking" effect. We have performed calculationsfor a temperature of 0.2K, with external biasvoltages V1- V4 V5- V8- 1.7 mV.We start with V5, V6, V7, V8 turned off, i.e., with

the upper part of the cell disabled, and apply thepreviously described voltage ramps to the adjust-ment gates. The resulting current I1 flowingthrough the lower dots is reported in Figure 3with a dashed line. The time evolution of theadjustment voltages is reported in the inset. Thewhole procedure is then repeated for the uppersection, disabling the lower section. The voltagesources connected to V6 and V7 deliver voltageramps corresponding to those previously suppliedby V3 and V2, respectively, but with a 7 mV shift,which determines a displacement of the curve forI2 (reported with a solid line in Fig. 3) with respectto that for I.The final phase consists in operating both the

upper and lower section of the cell at the sametime: the peaks in 11 and I2 are now locked, asshown in Figure 4, which represents evidence ofthe correlated switching between the two halves of

the cell and therefore of QCA action. The lockingeffect is very sensitive to the choice ofparameters, inparticular to the already mentioned coupling cap-acitances between the upper and lower dots, and tothe temperature. If the coupling capacitances arereduced by a factor 10, no locking occurs, due tothe insufficient electrostatic interaction betweenthe upper and lower halves. Operation with the con-sidered layout is disrupted also if temperature isincreased above about K, due to thermal broad-ening of the current peaks, and the ensuing im-possibility to distinguish the actual separationbetween the peaks for 12 and I1, unless this is sowide that locking cannot take place even withrelatively large coupling capacitances.

5. CONCLUSIONS

We have proposed an experiment for the demon-stration of QCA action with silicon-on-insulatortechnology, based on the detection of the electro-static interaction between the two halves of a cellmade up of four silicon quantum dots embeddedin silicon oxide. A numerical Monte Carlosimulator has been devised, which has allowedthe determination of the range of circuit param-eters suitable for the experimental observation ofcorrelated switching between the two cell halves.The major difficulties, from the point of view ofthe actual experimental implementation, consistin obtaining large enough coupling capacitancesbetween the upper and lower dots and in per-forming measurements at temperatures belowK, with the associated decrease in current levels,

due to the reduced number of carriers. Overall,however, the experiment appears to be feasible,and its implementation is currently being pursued.

Acknowledgments

This work has been supported by the EuropeanCommission through the QUADRANT (n. 23362)and the ANSWERS (n. 28667) projects.

424 M. GATTOBIGIO et al.

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saturation in coupled quantum dots for quantum cellularautomata, Appl. Phys. Lett., 62, 714.

[2] Tougaw, P. D. and Lent, C. S. (1994). "Logical devicesimplemented using quantum cellular automata", J. Appl.Phys., 75, 1818.

[3] Governale, M., Macucci, M., Iannaccone, G., Ungarelli, C.and Martorell, J. (1999). "Modeling and manufacturabilityassessment of bistable quantum-dot cells", J. Appl. Phys.,85, 2962.

[4] Amlani, I., Orlov, A. O., Snider, G. L., Lent, C. S. andBernstein, G. H. (1997). "External charge state direction ofa double-dot system", Appl. Phys. Lett., 71, 1730.

[5] Orlov, A. O., Amlani, I., Bernstein, G. H., Lent, C. S. andSnider, G. L. (1997). "Realization of a functional cell forquantum-dot cellular automata", Science, 277, 928.

[6] Single, C., Augke, R., Prins, F. E., Wharam, D. A. andKern, D. P. (1999). "Single-electron charging in dopedsilicon double dots", Semic. Science and Technology, 14,1165.

[7] Wasshuber, C., Kosina, H. and Selberherr, S. (1997)."SIMON A Simulator for Single-Electron TunnelDevices and Circuits", IEEE Trans. Computer-AidedDesign, CAD-16(9), 937.

[8] Nabors, K., Kim, S. and White, J. (1992). "Fast capaci-tance extraction of general three-dimensional structures",IEEE Trans. on Microwave Theory and Techniques, 40(7),1496.