Quantum Dot Molecules for Quantum Cellular Automata: Future Quantum Computer 31

Quantum Dot Molecules for Quantum CellularAutomata: Future Quantum Computer

N. Siripitakchai, S. Suraprapapich, S. Thainoi,S. Kanjanachuchai, and S. Panyakeow, Non-members

ABSTRACT

Ordered quantum dot molecules are grown by amodified MBE growth using thin-capping and re-growth processes. This technique yields QDs whichare uniform and aligned along [11̄0] directions. Thispaper presents an attempt to group 4-5 dots per eachquantum dot molecule, in order to form a physicalstructure that can function as quantum cellular au-tomata, giving rise to the possibility of developingquantum dot molecules for future computing appli-cations.

1. INTRODUCTION

Computers and electronic devices play a significantrole in our everyday life. Due to the need of higherefficiency, higher computing speed, smaller size andlonger life-time, numerous attempts have been madeto scale down the transistors size and to improve itscapabilities.

According to Moores law [1], the number of transis-tors per chip will double every 18 months. However,scaling technique encounters limits as the dimensionof a transistor approaches nanometer scale. The at-tempt to scale down a transistor is met with theproblems of short channel effects (SCE), power dissi-pation, quantum tunneling in depletion region, non-uniform doping and electron leakage in oxide layer[2]. In order to maintain the progress according tothe Moores law, a new computing architecture basedon quantum dots may be necessary.

Our research involves growing groups of quantumdots (QDs), or quantum dot molecules, that oper-ate according to the principle of quantum cellular au-tomata (QCA). Transistors with QCA structure havethe advantage of low power consumption, due to thefact that there is no current flow between adjacentQDs.

The QCA principle, based on Coulombs law, givesrise to devices that can operate as transistors withlow power consumption. It is possible to form thephysical architecture of QCA using top-down tech-nology such as shadow-mask patterning, lithographyand etching to form homogeneous QDs.

05PSJ03: Manuscript received on January 20, 2005 ; revisedon March 14, 2005.

The authors are with the Department of Electrical Engi-neering, Faculty of Engineering, Chulalongkorn University,Bangkok 10330, Thailand, E-mail: s panyakeow@yahoo.com.

Self-assembled QDs can be formed by molecularbeam epitaxy (MBE) using a template technique. Itrequires only the sequencing of thin-capping and re-growth processes. This bottom-up technique providesmany benefits and is more practical and suitable forindustrial fabrication. In particular, quantum dotmolecules consisting of 10-12 dots with a specific pat-tern aligned along the [11̄0] crystallographic directionhas been achieved.

In this paper, an attempt to reduce the numberof dots in each cell to 4-5 dots is presented. TheQCA principle is reviewed in section 2 followed byquantum dot molecule in section 3, and discussionand summary in section 4, respectively.

2. QUANTUM CELLULAR AUTOMATA(QCA)[1]

Fig.1: The basic QCA cell with two possible chargeconfigurations [3]

The principle of quantum cellular automata wasfirst proposed by Lent et al [3]. A basic QCA cellconsists of five dots, as shown in figure 1. Four dotsare positioned at each corner of the square and thefifth dot is located at the center.

Each cell contains two excess electrons which areable to tunnel between the dots. When the inter-dotbarriers are high, the electrons will be localized onindividual dots. The Coulomb repulsion between theelectrons tends to make them align at antipodal siteswith two possible configurations as shown in figure 1.These two stable states can be represented as a cellpolarization P = +1 and P = -1 which may be inter-preted as binary information: P = +1 corresponds toa bit ´1´ and P = -1 corresponds to a bit ´0´[4].

The Coulomb interaction between cells causes twoadjacent cells having the same polarization. Noticethat only binary information, not charge, is transmit-

32 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.3, NO.1 FEBRUARY 2005

ted. This means that there is no current flow betweenthe cells. This is the reason why QCA structures con-sume little power. Figure 2 shows examples of someQCA arrays. A QCA wire is shown in figure 2(a). AQCA inverter is shown in figure 2(b). And a QCAmajority gate is shown in figure 2(c). The logic gatein figure 2(c) can be used as an OR gate when inputA is kept fixed at ´1´, or as an AND gate when inputA is fixed at ´0´.

For QCA application, the cell size and dot size arenot critical but they must trap single electron in eachdot. The distance among dots must allow electrontunneling within the cell. However, the cells are notneeded to be separated as in the QCA theory. Anoverlapping of quantum dot cells is possible also forthe QCA functioning.

The distance between dots and between cells is akey parameter giving Coulombic effect in QCA appli-cation [5]. In our preliminary study, we could controlthe dot size and dot density by variation of growthtemperature [6]. Therefore, low dot density couldprovide large distance between cells. An appropriatedot density is therefore a tool in controlling the dis-tance between dots and between cells of QDMs. Dotsize of QDMs is controlled by regrowth thickness asshown in the difference in regrown dot size at 0.9 MLand 1.2 ML. Further investigations of these dot pa-rameters for practical application of QDMs for QCAare needed.

In the next section, the growth of self-assembledInAs QDs on a lattice-mismatched GaAs substratewill be discussed.

Fig.2: QCA arrays working as (a) a wire, (b) aninverter or (c) a majority gate [7]

3. QUANTUM DOT MOLECULES

Fig.3: (a) Randomly distributed QDs (b) Nanoholesobtained by thin capping process (c) Nano-propellerquantum dots obtained by the regrowth of 0.6 ML ofInAs on the nanoholes. (d) Quantum dot moleculesobtained by the regrowth of 1.2 ML of InAs on thenanoholes. (e) Quantum dot molecules formed in asquare shape is an ideal basic QCA cell.

In this work, efforts were made to grow InAsQDs on GaAs substrate by Stranski-Krastranow (SK)growth mode using molecular beam epitaxy (MBE).In the beginning, the (001)-GaAs substrate under-goes in-situ oxide desorption stage. After oxide des-orption, a 400-nm thick GaAs buffer layer is grownat 580◦ C and then 1.8-ML of InAs at 500◦ C whichresults in randomly distributed QDs across the sub-strate surface, as shown in figure 3(a). Afterwards,6-ML of GaAs capping layer (∼1.66 nm) at 470◦ Cis grown. The lattice-mismatched capping layer in-creases the strain fields around the upper layer cover-ing the QDs. These strain fields transform the initialdots into nanoholes with bases aligned along the [11̄0]direction as shown in figure 3(b).

Then, 0.6 ML of InAs is grown on top of thenanoholes, giving rise to the nano-propellers shownin figure 3(c). The resulting QDs in figure 3(c) aremore uniform than the as-grown QDs in figure 3(a).

Quantum Dot Molecules for Quantum Cellular Automata: Future Quantum Computer 33

Increasing the thickness of InAs regrown layer to 1.2ML results in rather homogeneous QDs on the bladearound two sides of nano-propeller. These groups ofQDs are named ”quantum dot molecules”. The quan-tum dot molecules consist of 10-12 dots surroundingeach central dot. According to the QCAs principle,each cell should consist of only 4-5 dots, indicated bythe frame shown in figure 3(e).

When we grow GaAs capping layer on InAs QDs at450◦C, in stead of the original 470◦ C, nano-propellerwith shorter blades length is obtained. This is shownin figure 4. With these shorter nano-propeller tem-plate, we notice that the number of dots is reducedto 6-7 dots per molecule. The blades length of nano-propeller is an important key for reducing a numberof dots per molecules. Further investigations on cap-ping temperature, capping thickness and compositionof capping materials are in progress.

Fig.4: (a) Nano-propeller with blades length 275 nmobtained by thin capping process at 470◦C (b) Nano-propeller with shorter blades length 215 nm obtainedby thin capping process at 450◦C (c) Quantum dotmolecule with shapes length 156 nm.

4. DISCUSSION AND SUMMARY

Fig.5: PL spectra of regrowth QDs at different thick-nesses.

The growth of quantum dot molecules using thin-capping and regrowth processes is simple and thequantum dot molecules obtained are uniform. Thisis confirmed by photoluminescence (PL) measure-

ments and the associated full-width at half maximum(FWHM). The FWHM of 0.6-ML InAs regrowth is24 meV as shown in figure 5, which is lower thanthose obtained from other conventional quantum dots(∼40-60 meV). The narrower FWHM implies betterdot uniformity.

As the regrown InAs thickness is increased to 0.9and 1.2 ML, the FWHM increases to 31 and 46 meV,respectively. This implies the degraded uniformity.

In summary, our modified MBE process using thin-capping and regrowth yields QDs which are more uni-form than the conventional QDs. Further work isneeded in order to reduce the number of dots in eachcell to 4-5 dots to suit the structure of the basic QCAcell.

ACKNOWLEDGEMENT

The authors acknowledge financial supports fromthe Asian Office for Aerospace Research and Devel-opment (AOARD), and the Thailand Research Fund(TRF) through the Royal Golden Jubilee Ph.D. pro-gram and senior researcher award.

References

[1] Gordon E. Moore, “Cramming More Compo-nents Onto Integrated Circuits”, Electronics,April 19, 1965

[2] James D. Plummer, Fellow, IEEE, and Peter B.Griffin, “Material and Process Limits in SiliconVLSI Technology (Invited Paper)”, Proceedingsof the IEEE, Vol.89, No.3, March 2001

[3] C.S. Lent, P.D. Tougaw, and W. Porod,“Bistable saturation in coupled quantum dots forquantum cellular automata”, Applied PhysicsLetter., vol.62, pp.714-716,1993.

[4] J. Timler and C. S. Lent, “Power gain and dissi-pation in quantum-dot cellular automata”, Jour-nal of Applied Physics., vol. 91, pp. 823-831,2002.

[5] C.S. Lent and P.D. Tougaw, “Lines of interactingquantum-dot cells: A bianry wire”, Journal ofApplied Physics., vol. 74, pp. 6227-6233, 1993.

[6] R. Songmuang, S. Kiravittaya, M. Sawadsar-ingkarn, S. Panyakeow, and O.G. Schmidt,“Photoluminescence investigation of low temper-ature capped self-assembled InAs/GaAs quan-tum dots”, Journal of crystal Growth., vol. 251,pp. 166-171, 2003.

[7] Tougaw, P. Douglas, Lent, Craig S, “Logi-cal devices implemented using quantum cellu-lar automata”, Journal of Applied Physics 75(3):1818-25, 1994.

34 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.3, NO.1 FEBRUARY 2005

Suwaree Suraprapapich was born inKhonkaen, on March 24, 1981. Shereceived the B. Eng. Degree withfirst class honors in Electrical Engineer-ing from Kasetsart University, Bangkok,Thailand in 2002. She is Ph.D. stu-dent in Electrical Engineering at Chu-lalongkorn University.

Supachok Thainoi was born inBangkok, Thailand, on October 12,1956. He received the M.S. Degree inNuclear Technology from ChulalongkornUniversity, Bangkok, Thailand in 1999.He is a Research Assistant in the Semi-conductor Device Research Laboratory,Electrical Engineering Department, Fac-ulty of Engineering, Chulalongkorn Uni-versity. His current interests owe in thefield of III-V Compound semiconductor

and radiation detectors.

Songphol Kanjanachuchai receivedthe M.Eng. Degree with first class hon-ours in Electrical and Electronic Engi-neering from Imperial College of Sci-ence, Technology and Medicine, Univer-sity of London, in 1995. He later went tothe Cavendish Laboratory, CambridgeUniversity, where in 1999 he receivedPh.D. degree in Physics for his workin Si/SiGe-based single-electron- andsingle-hole quantum dot transistors. His

interests include nanofabrication techniques, quantum-sized ef-fects in silicon and compound semiconductor transistors, highfrequency devices and novel materials for (opto-) electronic ap-plications such as self-assembled quantum dots, carbon nan-otubes and molecular wires.

Somsak Panyakeow is a professorrank 11, Faculty of Engineering, Chu-lalongkorn University. His research in-terest covers wide range of semiconduc-tor devices and materials including theirapplications in optoelectronics and na-noelectronics.