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Abstract—We use three-dimensional self-consistent Kohn–. Sham's equations coupled with Poisson's equation to investigate the electrical behavior of laterally ...
IEEE TRANSACTIONS ON NANOTECHNOLOGY, VOL. 5, NO. 4, JULY 2006

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Engineering Quantum Confinement and Orbital Couplings in Laterally Coupled Vertical Quantum Dots for Spintronic Applications J. Kim, P. Matagne, Jean-Pierre Leburton, Fellow, IEEE, R. M. Martin, T. Hatano, and S. Tarucha

Abstract—We use three-dimensional self-consistent Kohn– Sham’s equations coupled with Poisson’s equation to investigate the electrical behavior of laterally coupled vertical quantum dots (LCVQD) for spin-qubit operation. The shape and the depth of the central gate are changed in different ways to correlate gate geometry with the coupling between the two quantum dots. Upon comparing LCVQD single-gate and the split-gate structures, we found that the two inherently different designs result in different energy barrier profiles leading to dissimilar wavefunction coupling between the two dots. Finally, we show that the doping concentrations in the layered structure could be optimized for practical two-qubit operation. Index Terms—Gallium compounds, quantum dots, quantum effect semiconductor devices, quantum theory, semiconductor device modeling, semiconductor heterojunctions.

I. INTRODUCTION

A

S THE SIZE OF electronic devices becomes smaller and approaches the dimensions of atoms, quantum effects emerge and interfere with proper device operation [1]. With these phenomena looming ahead in the near future, there is a growing interest in quantum computing, which is a new paradigm of information processing based on the manipulation of quantum units of information, or qubits. This is important because quantum algorithms have shown that quantum computers can expedite solutions of classes of problems previously deemed to be intractable with conventional computers [2], [3]. At the hardware level, it has been demonstrated that a controlled NOT (CNOT) gate and a single qubit gate are the universal building blocks to achieve all logic quantum functions [4]. The demonstration of single spin effects in quantum dot devices has provided new ground to the realization of a solidstate quantum computer [5]. Hence, coupled quantum dots are promising quantum systems for realizing CNOT gates where

Manuscript received December 14, 2005; revised January 31, 2006. This work was supported by in part by the DARPA-QUIST program under ARO Grant DAAD 19-01-1-0659 and in part by the Material Computational Center under NSF Grant DMR 0325939. The review of this paper was arranged by Associate Editor D. Frank. J. Kim, P. Matagne, and J.-P. Leburton are with the Beckman Institute for Advanced Science and Technology and Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA. R. M. Martin is with the Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA. T. Hatano is with the Tarucha Mesoscopic Correlation Project, Kanagawa 243-0198, Japan S. Tarucha is with the Department of Applied Physics, University of Tokyo, Tokyo 113-0033, Japan Digital Object Identifier 10.1109/TNANO.2006.877017

Fig. 1. (a) Cross-sectional view of the LCVQD system. The arrows indicate the direction of the current flow for charging the dots. (b) Top view of the split-gate LCVQD. The side gates surround the two dots providing confinement. The two central gates, which act as barriers between Dot1 and Dot2 are disconnected from one another. (c) Top view of the single-gate LCVQD. Unlike the split-gate, there is just a single, central gate cutting across the middle of the structure.

two electron spin qubits can be manipulated by external electric and magnetic fields [6]. From a system point of view, these nanostructures made of GaAs–AlGaAs materials offer several advantages with respect to other approaches to built a quantum computer, because their fabrication techniques are compatible with well-established solid-state-device technology. Moreover, quantum dot structures are scalable for system integration, while electron spins enjoy relatively long dephasing times in the same materials [7]. In this context, one of the most important technological issues is the design of coupled quantum dot devices for efficient CNOT operation. Among the most popular QDs, vertical GaAs–AlGaAs [8] structures achieved by mesa etching of a double barrier layered system are prime candidates because they have originally and successfully demonstrated spin effects controlled by external electric gates. In this paper, we consider laterally coupled vertical quantum dots (LCVQD) structures, shown schematically in Fig. 1. In these kind of structures, the two vertical dots are coupled laterally, which offers the advantage of modulating the interdot

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Fig. 2. (a) Schematic of the split-gate LCVQD system showing all the layers. The depth of the central gate is denoted by z . The “dot” region is located in the InGaAs layer, between the two AlGaAs layers. (b) Schematic of the single-gate LCVQD system.

coupling potential by a center gate while controlling confinement and electron charging in individual dots by side gates. For this purpose, a particularly relevant technological issue is the shape of the central gate that could be fabricated in two separate pieces, in which case the LCVQD will be called “splitgate device” [Fig. 1(b)], or a subset of the split-gate device in which the central gate can be fabricated in a single transversal piece, in which case, the structure will be called “single-gate device”[Fig. 1(c)] [9]. The devices are designed such that the confinement and the coupling between the two dots are dependent on one another. In Section II, we describe the split-gate structure model in detail and depict the differences between the single and the split-gate structure. As with most previous analysis in double-dot structures [10]–[12], we focus on the ideal symmetric case in which the two dots are viewed as identical. In Section III, we briefly present the self-consistent computational approach based on the density functional theory [13], to simulate the LCVQD structure. In Section IV, we present our simulation results. Finally in Section V, we summarize the important issues covered in the paper and briefly mention some future works ahead pertaining to the LCVQD structures. II. QUANTUM DOT STRUCTURES The schematic layered structure of LCVQDs with orientation axes is shown in Fig. 1(a) [14]. The actual quantum dots are located below the two mesas within a double heterostructure barrier shown with two thick dark regions. The shape of the split-gate LCVQD structure is shown schematically in Fig. 1(b) and contains two separate central gates located in the middle of the device. The two side gates circumscribe the entire structure (except in the vicinity of the central gates) and provide electrostatic potential confinements such that the electrons are localized in the center of each quantum dots. A particular case of this LCVQD when the two central gates merge into a single gate running entirely across the whole structure in the -direction device is shown schematically in Fig. 1(c) [9]. The sizes of the individual dots are 0.4 m 0.4 m, and the depth of the simulated structure is measured along the direction to be 0.407 m from the top n GaAs layer to the bottom n GaAs for the split-gate structure (Fig. 2). In the simulations, the depth of the central gate (indicated by in Fig. 2) for the split-gate is varied from 50% to 100% of the overall depth of

the simulated structure. The width of the central gate is 0.05 m along the direction. The length of the split central gates was taken to be 0.08 m along the direction. The InGaAs layer, which contains the quantum dots, is 12 nm deep, and it is sandwiched between the two AlGaAs layers (6 and 50 nm deep), forming a double-heterostructure barrier. The n GaAs region located in the bottom of the structure (75 nm deep, cm ) is referred to as the back gate. The top part of the structure is composed of two n GaAs regions (each of them is 130 nm deep containing 3 10 cm and 2 10 cm donor dopant concentrations respectively) and an undoped GaAs (4 nm) spacer region. III. COMPUTATIONAL MODEL Our approach for simulating the electronic properties of the coupled QD structures is based on the density functional theory (DFT) in the effective mass approximation to describe the manybody effects on the conduction electrons in the QDs. We use a self-consistent scheme that discretizes the Kohn–Sham and Poisson equations according to the finite element method [15]. A nonuniform grid of dimensions 136 66 71 (numbers mapping to , , and ) is used for the whole structure. The three-dimensional (3-D) Kohn–Sham’s equations [16] coupled with the Poisson’s equation find the self-consistent electrostatic potential as well as the electron charge and spin density distributions in the QDs as a function of the applied voltages. The Kohn–Sham equations, one for spin up and the other for spin down, read

(1) where the respective Hamiltonians are expressed as

(2) is the position-dependent effective mass, and the electro: is the potential due static potential is the potential resulting from the to externally applied bias, ionized donors, and is the Hartree potential accounting for is the conducthe repulsive electron–electron interactions. tion band offset resulting from the boundaries of two different is the exchange-correlation potential for the spin materials. up and the spin down electrons, which we compute within the local spin density approximation (LSDA) [12], [17], [18]. The is computed by solving the Poisson’s electrostatic potential equation

(3) is the position-dependent permittivity and where total charge density given by the following:

is the

(4)

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and are the ionized donor and acceptor concenis the total hole concentration trations in the device layers, is the total electron concentration level given by level, and (5) in the QD region:

(5) is the number of electrons in the dot. where Since we are dealing with n-type semiconductor layers, we set and to be zero. We define two different regions both in the structure with no overlaps: a dot region in which quantum mechanical effects are predominant and a bulk region in which the free electron concentrations are described by semiclassical Thomas-Fermi distribution. We assumed the temperature to be 1.5 K in all our simulations. In order to solve the Poisson’s equations on the LCQVD structure, we assigned zero normal electric field boundary conditions on the top of the structure as well as on the sides of the structure below the side gates. The addition of Schottky barrier value and applied gate bias were imposed as boundary conditions on the surfaces bounded by the metal gates with V and as applied ( gate bias). Finally, we set the potential at zero on the bottom of the surface of the LCQVD. Solving the Kohn–Sham equation, we only looked at a subsection of the overall LCQVD structure realizing that the electron wavefunctions vanished rapidly outside of this region. The number of grid points used in solving the Kohn–Sham equation is 115 39 23 points along the , , and directions, respectively, which sustains a smaller volume, i.e., the QD region, than the whole device. The system of Kohn–Sham and Poisson’s equations is solved iteratively until obtaining self-consistent solution for Kohn–Sham orbitals and eigenvalues. The finite element method with trilinear polynomials is used to perform the self-consistent process. The discretized Poisson equation is solved using the damped Newton–Raphson method while generalized eigenvalue problem obtained as a result of Kohn–Sham equation discretization is approached by means of a subspace iteration method based on a simple Rayleigh–Ritz analysis. In order to determine the gate biases in which an electron is added to the system from the outside reservoir, we use Slater’s formula [19]

(6) corresponds to the total energy of the dot containing number of electrons, indicates the eigenenergy of the lowest unoccupied orbital (LUO) energy level, and represents the Fermi energy level. For our simulations we set the Fermi energy level to be equal to zero. The electron charging occurs when the dips below the Fermi level because, looking at Slater’s formula, one can see that when , , and the th configuration becomes more favorable in terms of energy.

Fig. 3. (a) Energy band profile along the x direction at y = 0 and z = 1300  A (side gate = 3:6 V, central gate = 0:7 V, z = 0:302 m). The arrow indicates the relative energy barrier height that separates the two dots. The inset shows the 2-D energy band profile along the x and the y directions. (b) Energy band profile along the z direction at x = 0 and y = 0 with the dotted line referring to the Fermi energy level. The inset shows the region in the double heterostructure layer.

0

0

IV. RESULTS The conduction band edge for zero electrons in the QDs of the split-gate device is illustrated in Fig. 3. In Fig. 3(a), we show the potential profile along the direction with two distinctive minima in each dot. The double arrow indicates the relative energy barrier level along the direction, which is about 7 meV. The Fermi energy is set at 0 meV in our simulations, which is well above the peak level of the barrier as seen from the figure. However, because the total energy of each eigenstate is a contribution of confinement along the three spatial directions (that is, ), the ground-state level eigenstates are located below the barrier maximum point, and thus the wavefunction is localized separately in the two dots. The inset in Fig. 3(a) shows the two-dimensional (2-D) energy band profile along the and directions. This contour plot focuses on the two QD regions in order to illustrate the 2-D energy confinement in the dots. Upon taking a slice of the energy band profile along the direction while keeping the and the coordinates constant near either of the dot regions, one observes a potential profile akin to a harmonic potential (not shown in the figures). Along the direction, the confinement is created by the energy barriers made possible by the AlGaAs–InGaAs–AlGaAs heterostructure [Fig. 3(b)]. In this figure, the origin of the horizontal axis is situated in the heavily doped substrate while the high values lie in the top mesa structure. The inset of Fig. 3(b) shows the quantum well slightly tilted to the right indicating the presence of a built-in field. For practical purposes, it is desirable that the two dots are more or less coupled (barrier height of around 5–15 meV) with

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Fig. 4. Variation of the energy barrier height versus central gate voltage is for three different split gate geometries: triangular, truncated triangular, and rectangular (in increasing order with respect to energy barrier). Solid lines: 100% of the total structure depth; dotted lines: 75% of the total structure depth. The side gate bias is kept constant at 3.6 V.

0

the ground-state eigenenergy levels varying within a 1 meV around the Fermi energy level as general guidelines for the electron charging process. From a physical viewpoint, the barrier height in the split-gate device is induced by the two central gates. Increasing the bias of the central gates (making it more positive) decreases the height of the energy barrier between the dots. Each central gate extends to (where is the point from designated as the middle of the device) along the direction. in Fig. 2) in We use three different gate depths (indicated by our simulations (0.203 m, i.e., 50% of the total device depth, 0.302 m, i.e., 75% of the total device depth, and 0.407 m, i.e., 100% of the total device depth) while keeping the side gate bias constant at 3.6 V. (The discretization spacing of our simulated device led to values with three significant digits. For all intents and purposes, the difference in simulated results between, say a 0.203- m and a 0.2- m gate depth is insignificant). For this condition, the 0.203- m-deep central gate does not induce a positive energy barrier, resulting in the whole structure being more or less a single large quantum dot. For this reason, we use both 0.302- m and 0.407- m gate depths in the simulations, but the former appears more practical because it does not protrude all the way down to the bottom of the device. The geometry of the central gates is also varied in three different ways as defined in the - plane: 1) triangular; 2) truncated triangular; and 3) rectangular (see Fig. 4). As seen in the figure, there is a correlation between the shape of the gate and the energy barrier height. This point is important because in practice it is difficult to fabricate the device in precise manners, so the range of barrier heights provides insight into possible deviations from expected experimental data. From our simulation, one observes that the rectangular shape gates entail higher barrier heights compared to the other two shapes (truncated triangular and triangular) when all other parameters are kept equal. This effect is due to the increase in volume of the gates, which results in an increase of coulombic repulsions on the electrons in the QDs. Conversely, the triangular gate shape results in a lower barrier for the same reason. As expected, for all gate shapes, the barrier height decreases with increasing central gate bias in a fairly linear manner. We notice that simulations from central gate depth of 0.407 m lead to higher energy barrier heights compared to ones resulting from gate depth of 0.302 m, with everything else remaining constant. Upon further analysis, we conclude that the slope of the solid lines in Fig. 4, which represent the simulations for

Fig. 5. Conduction band edge along the x direction at y = 0 with central gate voltage as a parameter (side gate voltage = 3:6 V). The central gate voltage is varied from 0:8 V (top curve) to 0:5 V (bottom curve) by increments of 0.05 V. The arrow points to decrease in the central gate voltage.

0

0

0

0.407- m gate depth, are more negative than the slope of the dotted lines, which represents the simulations for 0.302- m gate depth, indicating a more sensitive variation in the barrier height for the 0.407- m gate depth structure. In Fig. 5, we focused on the impact of change of the central split gate voltage bias on the overall potential plot and on the barrier height. The diagram shows different conduction band profiles along the direction superimposed on top of one another with the central gate bias acting as the parameter (the central gate with truncated triangular shape is varied from 0.8 to 0.5 V with the increments set at 0.05 V). The side gate value is fixed at 3.6 V, the depth of the central gate is set at 75% (0.302 m) of the total structure depth, and the potential pro. The folfile is taken at the middle of the structure lowing phenomena are observed upon making the central gate bias more negative: 1) the relative barrier height increases as expected; 2) the “minimum” energy points of the two QDs move away from one another as the two dots become more decoupled due to the increase and the widening of the energy barrier; and 3) the entire potential well shifts upwards with respect to energy. When significant, this shift results in a depopulation of electrons when their eigenenergy levels rise above the Fermi level. As can be seen when the central gate bias is changed from 0.5 V to 0.8 V, the energy barrier between the two dots changed from 2.65 to 10.56 meV (i.e., a 26- eV/mV variation rate). Because the single-gate structure runs throughout the device, there exists a limit imposed on the depth of this central gate structure for proper device operation: this depth limit is at the edge of the plane separating the top layer from the AlGaAs–InGaAs–AlGaAs double heterostructure layer. If the depth of the gate protrudes lower than this well region, one can no longer observe the coupling between the two dots because the metal–semiconductor Schottky barrier. For the split-gate structure, however, this critical limit does not exist due to the absence of the central gate around the QD regions. Hence, even if the depth of the split gates protrudes throughout the entire structure, one can still expect a coupling between the two dots. This extra degree of freedom gives the split-gate device an advantage in terms of flexibility for the actual fabrication. Fig. 6 shows the variation of the energy barrier height with the position for both the split-gate and the single-gate structures . We set to (see Fig. 1 for the axis orientation) at be in the middle of the structure along the axis for both structures. The gate voltage biases are chosen as follows: 1) for the split-gate structure, the side gate and the central gate voltages

KIM et al.: ENGINEERING QUANTUM CONFINEMENT AND ORBITAL COUPLINGS IN LATERALLY COUPLED VERTICAL QUANTUM DOTS

Fig. 6. (a) Variation of the barrier height as a function of the distance along the y direction for both the single and the split-gate structure (single-gate: side gate = 3:6 V, central = 0:561 V; split-gate: side gate = 3:6 V, central gate = 0:6 V). The two solid lines represent curves for the split-gate structure: the upper one derived from using “absolute” energy barrier heights whereas the lower one from using “relative” energy barrier heights. The two dotted lines represent curves for the single-gate structure: again, the upper one derived from using absolute energy barrier height whereas the lower one from using relative energy barrier height. (b) Contour plots of the first four eigenfunctions for both structures.

0 0

0

are set to 3.6 and V, respectively; 2) for the single-gate structure, side-gate voltage and the central gate voltage are set to 3.6 and 0.561 V, respectively. The biases are chosen in such a for both devices is 4.7 meV way that the energy barrier at (by the method described in the previous section). However, toward the QD edges (that is, moving moving away from away from the middle of dot region along the axis), the rate of change in energy barrier height for the split-gate structure is higher than that of the single-gate. Here, we compute the energy barrier height in two different ways. In the first case, we indicate the energy difference at each point along the barrier with respect to the absolute minimum point of the potential in the QD A at . In the second case, we compute the energy difference between the barrier height and the relative potential minimum along the direction at each point along the barrier. For both methods, the energy barrier of the split-gate increased at a faster rate than barrier of the single-gate. Moreover, one can see from Fig. 6 that the “relative” energy barrier height of the single-gate device decreases upon moving of the structure. In this particular away from middle configuration (that is with side gate voltage V and cenV), the relative minimum energy value tral gate voltage in the QD region increases more rapidly than the relative maximum barrier height value for the single-gate device along the direction from the barrier center . We attribute this effect to the large difference between the side and the central gate voltage values. However, this behavior of the relative energy barrier height along the direction may vary depending on the side and the central gate voltage value. In focusing on the tunnel coupling between the two QDs, we conclude that the split-gate device offers advantages over the single-gate in

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Fig. 7. (a) The first 6 electron charging diagram for spin up levels at center gate = 0:56 V for the truncated triangular gate geometry split-gate structure with simulated gate depth of 0.302 m. Electron charging occurs at biases corresponding to vertical upward transitions in the eiegenenergy levels. (b) Spin down levels.

0

terms of control. The overall area underneath the split-gate central gates is less than the area underneath the single-gate due to their respective intrinsic designs. Thus, for a same amount of change in the central tuning gate biases for both structures, the change in the electric field and consequently the change in energy directly underneath the gates is larger in the single-gate device. With everything else being equal, the interdot coupling in the split-gate device appears therefore smoother and consequently more controllable compared to the single-gate device. From Fig. 6(b), one sees that the different profiles of the energy barrier influence also the electron wavefunction coupling. Despite the fact that the two structures have the same barrier height , in the split-gate structure electron waveof 4.7 meV at functions are relatively more decoupled than in the single-gate structure, as seen from the contour plots by comparing the distances between the centroids of the wavefunctions situated in the two QDs. Fig. 7 shows the electron charging diagram for both electron spins with the central gate set at 0.56 V. The energy barrier separating the two dots for this bias is around 4 meV. The vertical axis measures the first six single particles’ energy levels in the two QDs as a function of the side gate bias. The six eigenenergies are the degenerate state, the degenerate state, the two states, and the two nondegenerate states, nondegenerate listed here in order of increasing energy levels. Because of the weaker confinement of the coupled QD system along the dilevels are located rection compared to the direction, the levels in terms of energy; so are the and below the levels. The overall decrease of these levels with increase gate bias is due to the lowering of the potential energy in the QDs. The dotted line indicates the electron Fermi energy level, which again is set at 0 meV. The solid lines indicate the eigenenergy

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levels for the spin electrons, and the dashed lines indicate the eigenenergy levels for the spin electrons. When these energy levels fall below the Fermi energy level, electrons are added to the system one or two at a time depending upon the configuration of the quantum system, and determined by Slater’s formula (see Section III). When an electron is added to the quantum dot, the overall eigenenergy for all levels jumps up due to the sudden increase of the electrostatic energy in the QDs. On the charging diagram, one can readily pinpoint biases at which electron charging occurs by noting the abrupt vertical transitions. In our particular configuration, we obtain double charging on the degenerate state for the first and second electrons at 3.64 V and for the third and the fourth elecside gate bias 3.52 V, since the wavefunctions are trons at side gate bias symmetrically localized in their respective dots [see Fig. 6(b)]. Due to the initial decoupling between the two dots for the first four electrons, electron spins are uncorrelated. In the simulations we impose that a single spin electron and a single spin electron enter the system followed by another pair of spin and spin electrons. Up to V, the total spin of the electrons remains at zero throughout the process, and thus the spin degeneracy remains intact. However, at this point, the coulomb energy of the first four electrons lifts the degeneracy state, which becomes successively occupied by the of the fifth and sixth electrons that enter the coupled QD system at V and V, respectively. The dashed lines, which represent the spin down levels on the charging diV because of the lifting of agram, emerge above the spin degeneracy after the charging of the fourth electron. Similar charging diagrams are also obtained with a single-gate LCVQD [9]. For practical purposes, it is important to avoid operating the QD device in voltage ranges that might possibly lead to unwanted gate current leaks, which would be the case V. However, our simulations show that upon for increasing the side gate bias to a value around 2.0 , the ground-state eigenenergy level in the QD falls around 30–40 meV below the Fermi level. This is problematic for two-qubit CNOT gate operation, since many electrons would be present in the dots. Even if the device design is modified such that electron eigenenergy rises above the Fermi energy level, then the energy barrier height becomes too high, changing the structure essentially into two decoupled single dots. Therefore, it is imperative to optimize the split-gate structure in order to operate in appropriate voltage value ranges, suitable eigenenergy levels, and practical coupling interaction. In order to prevent drastic changes to the current split-gate structure, one can proceed by either reducing the n GaAs dopant concentration (see Fig. 2) in the layer just above the undoped spacer region, or alternatively by reducing the n GaAs dopant concentration in the layer located in the bottom of the structure. Fig. 8 shows the correlation between the changes in the doping concentrations in both cases with the side gate and the central gate fixed at 1.9 and 0.4 , respectively. In both cases, reducing the dopant concentrations ultimately solved the problem by shifting the eigenenergy levels upward, while keeping the barrier height relatively constant. However, while a reduction of the n GaAs doping by 50% of its original value

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Fig. 8. (a) Variation of the barrier height and the ground state eigenenergy level with respect to the n GaAs concentration in the split-gate structure. The eigenenergy level moves above the Fermi energy level when the dopant concentration is reduced to 10 cm . (b) Variation of the barrier height and the ground state eigenenergy level with respect to changes in n GaAs concentration in the split-gate structure. The eigenenergy level moves above the Fermi energy level when the dopant concentration is reduced to 2 10 cm .

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is sufficient, a more drastic reduction of the n GaAs concentration to 10% of its original value would move the ground state closer to the Fermi level for few electrons operation. V. CONCLUSION We have provided a computer analysis of quantum confinement and orbital coupling in LCVQDs for applications in quantum information processing. In comparing split-gate and single-gate devices, quantum mechanical coupling between the dots are substantially different. In particular, we showed that for equal voltage and gate depth, split-gate structures induce higher potential barriers between the two dots, which results in stronger localization of the electron wave functions in their respective dots than in the single-gate structures. Moreover, although the split-gate structure offers the advantage of flexibility in terms of gate control, quantum mechanical coupling is substantially dependent on the shape and depth of the gate electrodes. In this context, we emphasized the choice of appropriate biasing between central gate (coupling control) and side gates (confinement and charge control) to reduce the significant and undesired influence of the former on the charge stability in the coupled dot system. Finally, we showed the doping level in the GaAs leads should be chosen adequately to limit the variation of the side gate voltage within a suitable range to guarantee proper quantum operations while preventing gate current leakage. REFERENCES [1] K. Ismail, S. Bandyopadhyay, and J. P. Leburton, Quantum Devices and Circuits. London, U.K.: Imperial College Press, 1997. [2] L. Grover, “Quantum mechanics helps in searching for a needle in a haystack,” Phys. Rev. Lett., vol. 79, pp. 325–328, 1997.

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in electrical engineering in the Department of Electrical and Computer Engineering at the University of Illinois in Urbana-Champaign. His research focuses on quantum dot device simulations.

P. Matagne, photograph and biography not available at the time of publication.

Jean-Pierre Leburton (M’83–SM’88–F’96) received the License (B.S.) and Doctorat (Ph.D.) degrees in physics with the highest honors from the University of Liege, Belgium, in 1971 and 1978, respectively. He was a Research Scientist with the Siemens A.G. Research Laboratory, Munich, Germany. He joined the University of Illinois in 1981, where he is currently Professor in the Department of Electrical and Computer Engineering at the University of Illinois, Urbana-Champaign. He is also Research Professor in the Coordinated Science Laboratory and a full-time Research Faculty Member in the Beckman Institute. In 1992, as a Visiting Professor, he held the Hitachi LTD Chair on Quantum Materials at the University of Tokyo, and was a Visiting Professor in the Federal Polytechnic Institute in Lausanne, Switzerland in 2000. He is author and coauthor of about 250 technical papers in international journals and books. He is currently involved with research in semiconductor nanostructures and quantum device simulation. At the frontiers of solid-state electronics, his current research focuses on quantum wires and quantum dots for which he predicted and interpreted a wide range of physical phenomena. Recently, he was involved in the theoretical investigation of single-electron charging effects and spintronics in GaAs quantum dots and in silicon devices for quantum information processing. His current research interest also encompasses molecular and ionic transport through semiconductor nanopores for applications in DNA sensing and sequencing. Prof. Leburton has an impressive list of invitations to international conference and research institutions, and has served on numerous conferences committees. In 1993 he was awarded the title of Chevalier dans l’Ordre des Palmes Academiques by the French Government. He is a Fellow of the American Physical Society (APS), the Optical Society of America (OSA), the American Association for the Advancement of Science (AAAS), and the Electrochemical Society (ECS). He is also a member of the New York Academy of Science. He is the ISCS-2004 recipient of the Quantum Device Award, and of the Gold Medal for scientific achievement awarded for the 75th anniversary of the Alumnus association of his Alma mater, the University of Liege, Belgium, in 2004

R. M. Martin, photograph and biography not available at the time of publication.

T. Hatano, photograph and biography not available at the time of publication. J. Kim was born in Seoul, Korea, in 1978. He received the B.S. degree in electrical engineering from the University of California, Berkeley, in 2001 and the M.S. degree in electrical engineering from the University of Illinois, Urbana-Champaign, in 2004. He is currently working toward the Ph.D. degree

S. Tarucha, photograph and biography not available at the time of publication.