Russian Microelectronics, Vol. 28, No. 2, 1999, pp. 67–88. Translated from Mikroelektronika, Vol. 28, No. 2, 1999, pp. 83–107. Original Russian Text Copyright © 1999 by Neizvestnyi, Sokolova, Shamiryan.

Single Electronics. Part 1 I. G. Neizvestnyi, O. V. Sokolova, and D. G. Shamiryan Institute of Semiconductor Physics, Siberian Division, Russian Academy of Sciences, pr. Akademika Lavrent’eva 13, Novosibirsk, 630090 Russia Received June 1, 1998

Abstract—The subject of this review is single electronics—the fast-developing domain of nanoelectronics, where charge is transferred by a minor number (down to one) of electrons. Theoretical principles of single electronics, which were put forward by K. Likharev and evolved by other authors, and practical implementation of single-electron devices are considered. The classification of their designs is suggested. In addition, possible ways of applying single-electron devices as gates and memory cells in digital circuitry are described. This review is by no means exhaustive but can give a good indication of advances in single electronics over recent years.

INTRODUCTION Since conventional microelectron devices are approaching the fundamental physical limit of miniaturization, interest in devices that can ensure further progress in electronics has quickened in the past few years. One of possible paths in this area is the fabrication of devices where the transfer of even several (down to one) electrons can be controlled. So-called singleelectron devices open up a new field of electronics— digital single electronics, in which a data bit can be represented by a single electron. In such devices, an electron is transferred by tunneling. Since tunnel times of an electron are rather small, the single-electron devices can theoretically offer an extremely high speed. Moreover, the work necessary for transferring an electron is also small; hence, the power consumption of the singleelectron circuits will be extremely low. For example, the theoretical limits of the speed and energy consumption of single-electron devices were estimated at several hundreds of terahertz and 3 × 10–8 W, respectively [1]. The phenomenon of single-electron tunneling was first predicted by Russian scientist Likharev in 1986 [2]; so, this discovery is radically new. Within a few years after the pioneering Likharev’s paper, a variety of works that gave experimental proof to all the effects predicted by Likharev appeared. Thus, the theory has found excellent experimental support. Due to certain reasons, which will be discussed in this review later, early experiments were performed at temperatures as low as several millikelvin, while at present, the single-electron effects are observed at room temperature. Room-temperature observation of these effects has been made possible by the use of a scanning tunnel microscope (STM). Devices operating at room temperature have been recently reported [3–11]. However, their dynamic parameters, in particular speed, and reproducibility are open to question. Reliable operation and reproducible parameters of these

devices have been observed only at 4.2 K. Nevertheless, unlike the situation with high-Tc superconductivity, where it is still unclear whether room-temperature superconductivity is possible or not, room-temperature single-electron effects have already been observed, and the problem is to develop devices suitable for commercial production by integrated technology. THEORETICAL GROUNDS OF SINGLE ELECTRONICS Basic Theory of Coulomb Blockade The theory of single-electron tunneling was first suggested by Likharev [12–14]. Theoretical issues were also covered by Tinkham [14], Geerligs [15], van Houten [16], and Kouwenhoven [17]. We shall consider Likharev’s theory in detail. The case of a single tunnel junction between two metal contacts was first described. Let the capacitance of such a system, which is essentially a capacitor, be C; hence, its energy is described by the well-known equation 2

Q E = ------- , 2C

(1)

where Q is the charge on the capacitor plates. Since the charge of an electron is a discrete quantity, the least change in energy ∆E will be 2

e ∆E = ------- , 2C

(2)

where e is the charge of an electron. For these effects to be observed, the condition ∆E @ kT,

(3)

should be met. Here, k is the Boltzmann constant and T is temperature. Physically, this condition requires that the least energy change exceed temperature fluctua-

1063-7397/99/2802-0067 $22.00 © 1999 åÄàä “ç‡Û͇ /Interperiodica”

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–e/2

+e/2

Q

Fig. 1. Charge energy of a junction vs. charge. The arrows indicate the addition (subtraction) of one electron [13].

tions. In addition, it is necessary that this change be larger than quantum fluctuations: hG ∆E@ ------- , C

(4)

where G = max(Gs, Gi), Gi is the conductivity of a tunnel junction, and Gs is the conductivity shunting the junction. From (4), we can write –1

G ! RQ ,

(5)

where RQ = ≈ 6.45 = kΩ is the quantum resistance. One of the most important assumptions in the theory of single-electron tunneling is that an initial charge Q0 on a tunnel junction may differ from 0 and, moreover, take values that are not multiples of the integral number of electrons. This can be explained by the fact that the initial charge may be produced by the polarization of nearby electrodes, by charged impurities, etc., and thus may take any value. Then the charge Q in equation (1) will have the form Q = Q0 – e. From the aforesaid, it follows that if Q lies between –e/2 and +e/2, the addition or subtraction of one electron would increase the energy in (1), i.e., is energetically unfavorable. This statement is illustrated in Fig. 1. It is seen that if the charge is even slightly less than e/2, the addition or subtraction of one electron causes the energy to grow (dash-and-dot arrows). If, on the other hand, the charge exceeds e/2, electron tunneling through the insulator becomes energetically favorable. Since the voltage across the capacitor V = Q / C, for voltages from –e/2 C to +e/2C, a tunnel current should be absent. In other words, to ensure tunneling through the junction, it is necessary to overcome Coulomb repulsive forces of electrons. The absence of the current with the voltage applied within the above limits was called the Coulomb blockade. Thus, the Coulomb blockade is the absence of current with a voltage applied to a tunnel junction h /4e2

because of Coulomb repulsion. To overcome the Coulomb Blockade, a voltage across the junction should be VCB = e/2C; (6) it is sometimes referred to as cutoff voltage. Hereafter, we shall use the term “Coulomb blockade voltage” and designation VCB. Consider current passage through an isolated tunnel junction. Since current has a continuous value, the charge on one side of the junction is accumulated gradually. When it becomes equal to e/2, one electron tunnels through the junction, and the process recurs. Here, it is appropriate to mention Likharev’s analogy [14] with drop fall from a leaky faucet: when a drop gains some critical weight, it falls, and the next drop begins to form. For a current I, the charge of a single electron is accumulated for a time t (i.e., e = It), and then the electron tunnels through the junction. It is easy to see that this process is periodic and has a frequency f = I/e, (7) where I is the current through the junction and e is the charge of a single electron. Such oscillations were called single-electron tunneling (SET) oscillations. It should be noted again that the Coulomb blockade is observed only if conditions (3) and (5) are met. They, especially temperature condition (3), impose severe restrictions on the design of single-electron devices. From equations (2) and (3), one can find the capacitance value necessary for the Coulomb blockade to occur at a given temperature T: 2

e C ! ---------. 2kT

(8)

Substituting the numerical values of e and k, we obtain that at T = 4.2, 77, and 300 K, this effect is observable for C ! 2 × 10–16, 10–17, and !3 × 10–18 F, respectively. Thus, for these devices to operate at high temperatures RUSSIAN MICROELECTRONICS

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C' V

R, C

Fig. 2. Equivalent circuit of a tunnel junction.

R1, C1 C' V R2, C2

Fig. 3. Equivalent circuit of a two-junction structure.

(above 77 K), the capacitance should lie in the interval of 10–18–10–19 F, or 0.1–1.0 aF. Figure 2 shows an equivalent circuit of the system. The tunnel junction is depicted by a rectangle, which is a conventional designation of a Coulomb tunnel junction. It is characterized by a resistance R and a capacitance C. Here, C' is the capacitance of feeding contacts. A voltage V is applied to the junction. From this circuit, it is seen that if the parasitic capacitance C' is larger than that of the junction, the capacitance of the entire system is defined by the shunting capacitance C', i.e., contact capacitance. In actual devices, the shunting capacitance cannot be made smaller than 10–15 F [13], which is at least two orders of magnitude greater than that required for SET observation even at liquid-helium temperatures. Thus, in a single-junction system, SET observation appears to be problematic with regard to the current level of technology. To solve this problem, a structure of two series-connected junctions has been suggested. An equivalent circuit of this structure is demonstrated in Fig. 3. It is seen that the capacitance of each junction is no longer shunted by the contact capacitance. The total electroRUSSIAN MICROELECTRONICS

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static energy of such a system can be expressed as 2

2

Q2 Q1 -, E = -------- + -------2C 1 2C 2

(9)

where subscripts 1 and 2 denote junction numbers. In physical terms, this structure is essentially a small conducting particle separated from the contacts by the tunnel junctions. Then Q1 = Q2 = Q, where Q is the charge on the particle, and (9) can be rewritten as 2

Q E = ---------. 2C Σ

(10)

Formula (10) is identical to formula (1) except that the capacitance C is replaced by CΣ = C1 + C2, which is the total capacitance of the two junctions, since the junctions are connected in parallel when viewed from the particle. Thus, when CΣ is substituted for C, formulas (2), (4), and (8) still stand. In (3) and (4), G must be replaced by max(G1, G2). A typical current–voltage characteristic (CVC) of the two-junction system with symmetric junctions is shown in Fig. 4. In [18], an exact solution for the potential profile of a single-electron trap is proposed. An analytical expression for the total free energy, including the electrostatic

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NEIZVESTNYI et al. I, pA 400

200

0

0.2

0.4 V, mV

Fig. 4. CVC of the double junction for gate voltages of 0 (solid line) and e/2C (dash line) at 20 mK. Analytical curves for a symmetric junction with the same capacitance and resistance are shown by dots [15].

energy, barrier height of an island with an electron, and a voltage necessary for unit charge transfer, was deduced. Coulomb Staircase Consider a two-junction system with asymmetric junctions. The rate of tunneling through junction 1 can be written as [15] δE 1 -, Γ 1 = ---------2 e R1

(11)

where δE1 = eV1 – e2/2C1 is the energy change at junction 1 when a voltage drop across it is V1 > VCB. Substituting δE1 into (11), we obtain V1 1 Γ 1 = -------- – ---------------. eR 1 2R 1 C 1

(12)

A similar expression can be written for Γ2. From (12), it follows that if R’s and C’s of the junctions differ, so do the tunnel rates. If R’s and C’s are the same, the current will smoothly rise with increasing voltage, since the number of electrons coming to the island is equal to the number of those leaving it. For asymmetric junctions, there will exist the charge of n electrons on the island. When the voltage is sufficient for an (n + 1) electron to be transferred to the island, a sudden jump of the

current will first be observed due to the junction with a high tunnel rate. Then the current will grow slowly, because of the low-rate junction coming into play, until an (n + 2) electron appears on the island. Thus, although the current through the system passes continuously, a particular voltage-dependent amount of electrons will exist on the island at each time instant. As a result, the CVC of the two-junction system will have a step form called the “Coulomb staircase.” The more asymmetric the junctions, the more pronounced the steps of the Coulomb staircase. If the junctions are symmetric, i.e., have the same RC time constants, the steps disappear. A family of Coulomb staircases evaluated by Likharev for different values of Q0 [13] is shown in Fig. 5. Figure 6 exhibits an experimental Coulomb staircase observed in the STM [8]. As noted above, the charge Q in equation (1) has the form Q = Q0 – ne,

(13)

where n is the integral number of electrons on the Coulomb island. Since Q0 is of a polarization nature, it could be controlled by placing alongside the third electrode, gate, and applying a voltage to the gate. Note that this charge can be varied in a continuous manner proportionally to the gate voltage. Thus, with Q0 varying continuously, the condition for a Coulomb blockade (see Fig. 1) will periodically be set. Consequently, RUSSIAN MICROELECTRONICS

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I, (e/2RCΣ)/div

Q0/e = 0 1/6

2/6

3/6

4/6 5/6 1

–2

–1

0

1

2 V/(e/CΣ)

Fig. 5. Analytical CVC of the circuit in Fig. 3 for various external charges (G1 ! G2, C1 = 2C2) [13].

when the gate voltage varies, a Coulomb blockade will periodically occur, and the current through a dot (or the dc voltage across it) will take an oscillatory character. Such oscillations (the dc voltage across the dot as a function of the gate voltage) are shown in Fig. 7. Cotunneling In systems with several junctions, along with consecutive (elementary) tunneling events, higher-order tunneling, so-called cotunneling is also possible [15]. In this case, the principle of energy conservation is valid only for the initial and final states of the whole chain of the junctions. In other words, the junction array is a specific “black box” at the input and output of which the energy of a tunneling electron is conserved, while its behavior at each individual junction, or within the box, is indeterminate. Moreover, inelastic tunneling, when the generation or recombination of electron– hole pairs takes place, is a possibility. RUSSIAN MICROELECTRONICS

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Quantum-Size Effects The theory outlined above is semiclassical, since Coulomb classical effects and quantum tunneling are considered simultaneously. However, single-electron systems may exhibit purely quantum effects related to the space confinement of objects. For systems with two or more junctions, small objects are present between the electrodes. Under certain (geometric and temperature) conditions, they can be regarded as quantum dots, i.e., zero-dimensional objects, where the energy spectrum is a set of discrete levels. Simple analysis showed [14] that in Al grains 4.3 nm across, quantum-size effects are observable at temperatures <1.5 K. For semiconducting dots, however, a necessary temperature will be higher because of a lower density of states. In the presence of discrete energy levels in a grain, an electron can tunnel only through them, and the energy-level structure will show up on the Coulomb staircase of a single-electron system, as exemplified in Fig. 8, where one step of the Coulomb staircase in the

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NEIZVESTNYI et al. I, pA

I, pA

10

50

dI/dU, pA/V 50

0

40

–50

30

5

–1 0

0 U (V)

1 20

10

–5

0 –10 –0.5

0 U, V

0.5

Fig. 6. CVC taken with the STM. The thick (upper) line is recorded at 300 K; the dash-and-dot line, numerically evaluated differential conductivity; fine lines (shifted vertically for clarity), theoretical evaluation. The insert shows a Coulomb staircase at 4.2 K [29].

presence of quantum-size effects is shown. Transport through discrete energy levels in a quantum dot is theoretically treated in [19]. Here, the effect of potential fluctuations on the transport properties of a quantum dot is studied in detail. These fluctuations were shown to make Coulomb oscillation peaks irregular. Effect of External Time-Dependent Fields on Coulomb Quantum Dots A number of works [20–22] were devoted to the effect of variable external fields on single-electron transport. Adachi et al. [20] and Hatano et al. [21] tried to elucidate how the modulation of the potential-barrier height in a quantum dot affects transport through it. It was found that the Coulomb blockade region is shifted because of interband excitation, the resonance structure of Coulomb peaks appears [20], and an electron tunnels through the barrier before its height becomes the least. The modulating-signal phase at which tunneling occurs depends on the signal amplitude as well as the height and width of the barrier. Zorin et al. [22] modulated the potential of a metal-island chain by a surface acoustic wave propagating over a piezoelectric substrate. Theoretically, a constant current I = ±ef, where f is the wave frequency, must pass through such a chain, with its sign

depending both on the constant bias of the islands and on the direction of wave propagation. To check the theoretical findings, the authors of [22] performed an experiment where a chain of eight islands with capacitances of 0.1 fF and resistances of 170 kΩ was modulated by a surface acoustic wave with a frequency f = 48 MHz. The passing constant current, however, was found to be much smaller than expected. This was explained by the presence of uncontrollable background charges. Effects Due to Coulomb Blockade Along with the Coulomb blockade itself, some works theoretically touched upon Coulomb-blockaderelated effects and their influence on the blockade. In [23], the situation where a Coulomb island can change its location relative to the electrodes was considered. This can take place when organic materials are used as tunnel insulators. It was shown that the Coulomb island will periodically change its location relative to the electrodes, acting as a shuttle for electron transfer. As a result, the Coulomb staircase will appear even for equal widths of the tunnel barriers. Hackenbroich et al. [24] analyzed the effect of changing the shape of a Coulomb island under the CouRUSSIAN MICROELECTRONICS

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V, mV for I = 300 pA 0.06

0.04

0.02

0 –3

–2

–1

0

1

2

3 Vg, mV

Fig. 7. Voltage across the quantum dot as a function of the gate voltage for a constant current through the dot I = 30 pA [15].

lomb blockade conditions. Such a situation occurs if the Coulomb island is due to a limiting potential (depletion regions). It was shown that the capacitance of the island will change in this case, but qualitatively the situation will remain the same. In [25], the role of edge magnetoplasmons in the formation of Coulomb blockade was considered. Selfconsistent equations to evaluate Coulomb blockade under strong magnetic fields were derived. Richardson [26] theoretically studied the possibility of single-electron tunneling in tunnel diodes. It was shown that the properties of single-electron tunnel diodes will substantially deviate from those of conventional tunnel diodes. For example, a voltage-dependent step change in the saturation current with a period of e/2C may be observed. However, it remains unclear how to fabricate such diodes, since the contact capacitance will shunt that of the tunnel junction, suppressing the SET phenomenon. Works of Soldatov et al. [27, 28] showed that the “orthodox” theory of single electronics is inappropriate for explaining experimentally observed characteristics of molecular single-electron transistors; also, a computer program for modeling the characteristics in terms of a refined theory including the discrete nature of the energy spectrum of a base molecule was developed. IMPLEMENTATION OF SINGLE-ELECTRON DEVICES There are many designs of single-electron devices, but they all can be classified by the following signs. By the direction of current passing, the designs are subdivided into horizontal (lateral) and vertical. In the former, the current passes parallel to the surface of the RUSSIAN MICROELECTRONICS

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structure, while in vertical devices, the current flows perpendicularly to the surface. By the method of forming quantum dots, the devices are divided on those based on persisting and temporary (induced) quantum dots. Note that the term “quantum dot,” as applied to small-sized objects, is not always correct, since the energy spectrum may not be quantized. However, this term is common owing to the fact that spectrum quantization can be achieved by merely lowering the temperature. Hereafter, we shall adhere to this term. A persisting quantum dot always exists and most frequently is a metal or semiconducting cluster. An induced quantum dot is produced in a two-dimensional electron gas (2DEG) by applying depleting voltages; that is, it exists only during the operation of the device. Moreover, by the method of forming the 2DEG, the devices on induced quantum dots can be subclassified into inversion and heterostructural ones. In the inversion devices, the 2DEG is formed in inversion surface channels by applying an appropriate voltage. In the heterostructural devices, the 2DEG is present at the interface. By the number of quantum dots, the devices are subdivided into zero-dimensional (single-dot), one-dimensional (a chain of dots), and two-dimensional (an array of dots). By the controllability of quantum-dot parameters, uncontrollable (double-electrode) and controllable (multielectrode, with one or several gates) devices are distinguished. Let us consider the most commonly encountered single-electron designs.

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I, pA

80

(a)

60 40 20

dI/dV (1/GΩ)

0 80

320 mK (b)

60 40 20 0 4

6

8

10

V, mV

Fig. 8. (a) CVC corresponding to the beginning of the Coulomb staircase (320 mK) and (b) derivative dI/dV (see ref. 2 in [14]).

Devices Made with a Scanning Tunneling Microscope The example of vertical single-electron devices is an STM-based design. The idea is as follows. A small metal particle (metal cluster) is placed between a conductive substrate and the STM tip. It is separated from the substrate and the tip by tunnel junctions. Thus, this particle serves as a Coulomb island. According to the above classification, this is a zero-dimensional vertical uncontrollable device with a persisting quantum dot. It should be noted that STM-based single-electron devices were the first operating at room temperature. There are different methods of separating the particle from the substrate. Either the particle is deposited on a thin insulating layer [29–31] or the metal cluster is surrounded by nonconducting organic ligands [30, 31]. An approach used for all the designs is schematically illustrated in Fig. 8. Let us discuss substrate–particle–tip structures implemented in different works. As metal particles, gold was almost always used; however, the substrate and insulating materials differ. Shonenberg et al. [29, 30] applied Au (substrate) and ZrO2 (insulator). The same materials were used by van Kempen [31], but, along with Au, he also used In particles. Dorogi [12], like Shonenberg, also used Au as a substrate, but an insulating film was made from dithiole, a polymeric organic material. Uehara [32] employed oxidized Al both as a substrate and an insulator. In all the cases, the thickness of the insulator is about 1 nm. The methods of forming the Au particles are also similar: either a thin (0.2–1.0 nm) Au layer, which subsequently shrinks to clusters several nanometers in size, is applied on an insulating film [29–31] or preformed clusters are applied on an insulating film [32, 33].

In the case of the metal particles surrounded by organic molecules, Pt was employed as a core. Shonenberg [30] placed the particles into an aqueous solution of polyvinylpyrrolidone; as a result, a sheath of polymeric metallophilic molecules forms around the particle. Van Kempen [31] used Pt309Phen36O30 clusters, where Phen stands for a phenanthroline molecule, as a subject of investigation. CVCs obtained in the above works are similar and quantitatively differ insignificantly. All the authors observed Coulomb blockade and Coulomb staircase both at 4.2 K and at room temperature. In the latter case, these effects are naturally more pronounced. A typical CVC is represented in Fig. 6. To exclude the misinterpretation of the results obtained, most of the authors took the CVCs when the STM tip was located over the free surface rather than over the particle. As a result, linear ohmic CVCs were observed, which is an argument in favor of the suggestion that nonlinear CVCs are Coulomb effects. Together with taking the CVCs, many authors performed other experiments. For example, Shonenberg [29] studied the role of the initial charge Q0. Uehara [32] investigated visible emission arising when an electron is injected from the tip into the substrate. The maximum energy of an emitted photon is expressed as hνmax = eV, where V is the applied voltage. This statement is valid for macroscopic objects. For small particles, i.e., in the presence of a Coulomb blockade, the maximum energy must decrease by a quantity E = e2 / 2C, necessary to overcome the Coulomb blockade. Thus, the shift will be ∆E = hνmax – E. In the experiments, two particles were selected on the surface: “large” (of area 490 nm2) and “small” (32 nm2). RUSSIAN MICROELECTRONICS

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(b)

Tip

Tip

Phosphor

Cluster

Cluster

Oxide

Substrate

Substrate

Fig. 9. Implementation of a two-junction structure: (a) the STM tip is over a metal particle lying on an insulating layer and (b) a metal particle is surrounded by an insulating ligand layer, acting as a tunnel barrier [31].

For these particles, the shift ∆E is 3.8 and 58 meV, respectively. Thus, the calculated difference between the shifts should be ≈54 meV. The experimental results are shown in Fig. 10. The difference was found to be ≈80 meV, which, in authors' opinion, agrees well with the rough estimates above. When the experiments were performed on the metal particles surrounded by the polymeric molecules [30, 31], it was found that the parameters vary with time and the permittivity and thickness of the sheath depend on the tip–particle distance. This was explained by the nature of organic polymeric molecules. In [34], organic molecules of liquid crystals and also fullerene molecules were used as Coulomb islands. The Coulomb effects here are considered in terms of both the classical theory and the solution of Schrödinger equation. Baksheev and Tkachenko (Institute of Semiconductor Physics, Siberian Division, Russian Academy of Sciences), the co-authors of [34], developed a mathematical model for determining parameters of single-electron devices from experimental characteristics. Organic molecules as Coulomb islands were also used in [27, 28], where, as in [34], a program for simulating characteristics of single-electron single-molecule devices was elaborated. Park et al. [7] used silver for the metal particles. A small amount of antimony was deposited on the silicon substrate for restructuring the silicon surface. Then this restructured surface was covered by silver, which shrank to 1–2-nm quantum dots. The room-temperature Coulomb staircase and the CVCs in different sites of the same quantum dot were studied. Quantum dots in the form of self-organizing Si nanocrystals deposited from pure silane were used in RUSSIAN MICROELECTRONICS

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[11]. The structures were studied with the STM. The effects were observed at room temperature. Matsumoto et al. [8] used the STM to fabricate a single-electron transistor. An oxidized silicon substrate (SiO2 thickness 100 nm) was covered by a thin (3 nm) titanium film. Upon applying a negative (relative to the titanium film) potential to the STM tip, the film was anodically oxidized, since the process was performed in wet air. Due to its small thickness, the titanium film was oxidized all the way through (to the underlying SiO2 layer). The width of the TiOx strip depended on the air humidity and was found to vary from 10 to 64 nm. In this way, the single-electron transistor operating up to room temperature was “drawn.” Unfortunately, this original idea is hardly appropriate for commercial production. Vertical Sandwich-Based Single-Electron Devices One of possible ways to implement the single-electron devices is the use of MBE-grown multilayer structures. Since MBE allows for the growth of layers with a one-monolayer accuracy, it only remains to confine the growth in the two other dimensions to produce the quantum dots. GaAs/AlGaAs heterostructures are largely used as a starting material. Austing et al. [35] studied an AlGaAs/GaAs-based double-barrier resonance tunnel structure shown in Fig. 11. Once the double-barrier structure had been grown, upper contacts with diameters of d = 0.3, 0.4, 0.5, and 0.7 µm were fabricated on its surface. Then, with the upper contacts used as masks, a 3000-Å-thick layer was etched off, and a gate contact was deposited. The distance from the gate to the double-barrier struc-

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NEIZVESTNYI et al. Intensity, arb. units

(a) 30 Large particle

Slit width

(b)

10

Small particle

1.946 eV

1.5

2.026 eV

2.0 Photon energy, eV

2.5

Fig. 10. Emission spectra for (a) small and (b) large particles. Two vertical bars indicate the absolute precision of the spectrograph– detector.

ture was 500 Å. A negative voltage applied to the gate produced depleted regions, which formed a quantum well between two barriers. Thus, the given structure represents a vertical controlled device with a single induced dot. The CVCs of this structure were taken, namely, the drain current vs. drain voltage dependence for various gate voltages and the drain current vs. gate voltage (or, in essence, vs. Q0) dependence for various drain voltages. When the gate voltage is absent, the structure behaves as a resonant-tunneling diode, while when the gate voltage is negative, i.e., the quantum dot is formed, Coulomb blockade is distinctly seen. All the characteristics were taken at T = 1.6 K.

These authors [36] also implemented a three-barrier structure, containing two quantum dots. The effect of the mutual arrangement of quantum levels in the dots on electron transport was studied. For a large mismatch between the quantum levels, the Coulomb blockade was found to be greatly suppressed. Another structure was studied in [37]. As a whole, it is similar to Austing’s structure, except that the gate and source electrodes coincide; i.e., the device is two-electrode. A negative bias and a small differential signal with a frequency of 210 kHz were applied to the gate. The measurements were made at liquid-helium temperatures in a vacuum. Haug et al. [38] employed a structure also similar to Austing’s structure, but here the column was etched to the substrate and the gate electrodes were absent. The RUSSIAN MICROELECTRONICS

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d Vd Source Gate

Gate Id

Two-barrier structure

Vg

9.2 nm Al0.28Ga0.72As 8.5 nm GaAs 7.8 nm Al0.28Ga0.72As Depletion region

Depletion region

Substrate (drain)

Fig. 11. Schematic representation of a submicron vertical single-electron transistor [35].

diameter of the column was 350 nm. The effect of a magnetic field on electron transport through such a dot at a temperature of 22 mK was investigated. A change in the Coulomb blockade voltage is due to that in the position of levels in the quantum dot subjected to the magnetic field. Also, transport through a two-dot system that involved the 2DEG in AlGaAs/GaAs heterostructures was studied. Such systems will be considered later. A similar structure was used in [39]; in this case, the diameter of the column was 500 nm, but once the structure had been fabricated, the column was etched in an oxygen plasma, and its diameter decreased. The operating temperature was 23 mK. Transport in relation to the asymmetry of the barriers confining the dot was investigated. The barrier asymmetry was shown to affect the position of the quantum levels in the well. The vertical single-electron devices, where selforganizing quantum dots are used, are of particular interest. These dots are formed as follows. During MBE growth of a crystalline material lattice-mismatched with the substrate, the film initially grows strained and pseudomorphic and then breaks down into individual nanometer islands, which serve as the quantum dots. In [40], transport through InAs self-organizing quantum dots on the GaAs substrate was studied by capacitive spectroscopy. The device operated at 4.2 K. RUSSIAN MICROELECTRONICS

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NbN granular film

Ion-beam etching 45°

NbN 50 nm

Fig. 12. Fabrication of a NbN strip. After the application of the granular film on a step and ion-beam etching, a narrow strip forms in the shadow of the step.

A theoretical model consistent with experimental data was worked out. In [41], Ge self-organizing dots on Si were examined. The Coulomb staircase was observed at 4.2 K.

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Schottky gate

L AlGaAs GaAs quantum wire GaAs quantum wire

Depletion layer (b)

Schottky gate

InGaAs quantum wire

InAlAs

L InGaAs Buffer layer

100 nm InP

Fig. 13. Two configurations of quantum wires [52].

This structure takes advantage of the maturity and cheapness of Si/Ge technology. Devices with Quantum-Dot Arrays Duruoz et al. [42] studied a two-dimensional 200 × 200-dot array fabricated as follows. On the surface of an AlGaAs/GaAs structure with the 2DEG at a depth of 77 nm, cross-shaped dots spaced at 0.8 µm intervals were produced by electron lithography. The gaps between the dots were etched to a depth of 80 nm, i.e., deeper than the 2DEG location. The array was entirely covered by a Cr/Au gate. Thus, the given structure is a controlled planar two-dimensional device with persisting quantum dots. The gate voltage led to an increase in the barrier height between the dots but was

less than the voltage completely depleting the 2DEG (630 mV). Rimberg et al. [43] studied one- and two-dimensional arrays of the quantum dots. The dots were Al islands separated by AlxOy tunnel gaps. The structure was formed by electron lithography. A total of 440 and 38 × 40 = 1520 islands were placed between the contacts in the one- and two-dimensional arrangements, respectively. The area of the tunnel contacts was 70 × 80 and 70 × 70 nm for the one- and twodimensional arrays, respectively. Miura et al. [44] produced a linear array by means of the STM. Quantum dots of amorphous carbon 30–40 nm in diameter were made of carbon molecules deposited with the electron beam of the instrument. The source of the carbon molecules in the vacuum chamber was diffusion-pump oil, since nitrogen in oil traps was absent. RUSSIAN MICROELECTRONICS

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VUG (< 0 V) VLG (> 0 V)

Upper gate Lower gate

Oxide

0.12 µm

10 nm

VD

50 nm 0.13 µm 0.1 µm

Channel Drain

Source

5 µm p–-Substrate

Fig. 14. Two-gate one-quantum-dot silicon single-electron transistor [53].

VUG VLG

Upper gate

VD

Oxide

Lower gate

n+

n+

Source

Drain

p–-Substrate

Fig. 15. Two-gate double-quantum-dot silicon single-electron transistor [54].

The interelectrode distance was 2 µm. The device reliably operated at temperatures to 9.4 K. In recent years, a trend to employ random twodimensional arrays of quantum dots has arisen. It was shown [45] that devices built around Coulomb island chains have the best characteristics for digital applications. However, with regard to the current level of nanotechnology, the fabrication of a straight chain of relaRUSSIAN MICROELECTRONICS

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tively small dots is unfeasible. The way out is to create a random two-dimensional array of self-organizing quantum dots where tunneling will follow the energetically most favorable path, i.e., along some chain of the dots. The disadvantage of this approach lies in the possibility of existing several such chains. A device with InAs self-organizing quantum dots on GaAs is an example [46]. The GaAs surface was cov-

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PolySi

Source

Si Drain Quantum wire Buried oxide Si Fig. 16. Quantum single-electron transistor [19].

40 nm

811938

7KY

. . .. . X150K

... . .. 280 ns

Fig. 17. SEM micrograph of a single-dot electron transistor [56]. RUSSIAN MICROELECTRONICS

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ID, pA 1.5 T = 100 K 77 K 46 K 1.0

20 K

5.4 K

0.5

0

0.5

1.0

1.5

2.0 VG, V

Fig. 18. Drain current vs. gate voltage dependence for the electron transistor at various temperatures [56].

SiO2 SiO 2

e–

e–

e–

poly-Si

y-Si

pol

e–

poly-Si

Tunnel barrier

Fig. 19. Single-electron transistor from [59].

ered by 2.5 InAs monolayers, which then shrank to islands with a mean diameter of 26 nm and a standard deviation of 11%. The island density and height were 8.7 × 1010 cm–2 and 5 nm, respectively. Their center distance was 26 nm; i.e., for the positive deviation, the islands merged. The tunneling probability was high because of the small interisland distance. The photoluminescent properties of this array were investigated. In [3], silicon nanocrystals between two electrodes were deposited. The electrodes were made as follows. RUSSIAN MICROELECTRONICS

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After the electron lithography stage, a Si / SiO2 / polySi sandwich structure was subjected to reactive ion etching (RIE), which was completed as soon as an etch pit reached SiO2. As a result, a gap of 26–70 nm between the electrodes was formed. The Si nanocrystals with a mean size of 8 nm were deposited from a microwave SiH4 + H2 plasma. For an interelectrode distance of 70 nm, the Coulomb blockade and Coulomb staircase were observed up to 200 K. When the interelectrode distance was 26 nm, the staircase was observed even at

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Q2

C2

C1

F1 Q1 400 nm Drain

0.5

1.0

1.5

2.0

µm

Fig. 20. Single-electron transistor micrograph obtained with the atomic force microscope [62].

room temperature, but the blockade was absent presumably due to large leakage currents. Yoshikawa et al. [47] used a NbN film consisting of granules about 5 nm across. Using the shadow evaporation technique (Fig. 12), they made a 10-nm-high 50-nm-wide 200-nm-long NbN strip. The Coulomb blockade was observed at temperatures below 3 K.

In [48], polycrystalline bismuth nanobridges were made. The structures were fabricated by using a gallium ion beam, laser cutting, and electron-beamassisted bismuth nitride deposition. As a result, two 300-nm-wide bismuth films connected by a bismuth bridge 50–100 nm across were formed. The CVCs were taken at 4.2 K. Quantum-Wire Devices

1 µm

(2 DEG)

Fig. 21. Device from [63].

Devices based on quantum wires, i.e., one-dimensional electron arrangements, can be separated out into a specific class. These one-dimensional quantum wires in a number of ways break down into individual quantum dots, making possible the observation of the Coulomb effects. Ohata et al. [49] produced a quantum wire on the side wall of an ultrathin (15 nm) silicon layer on the insulating substrate, using SOI technology. How this wire broke down to form individual islands remains unclear (possibly because of charged traps present at the interface); however, the authors saw distinct Coulomb blockade and staircase at 4.2 K. Moreover, they succeeded in integrating a single-electron transistor and a conventional MIS transistor on the same wafer. The possibility of Coulomb blockade in Schottkygate-controlled InAlAs/InGaAs and GaAs/AlGaAs heterostructural quantum wires was studied in [50–52]. MBE and selective etching produced the complex-facRUSSIAN MICROELECTRONICS

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SINGLE ELECTRONICS. PART 1 Vl

83

Vr

2 DEG

2 DEG

Quantum dot

Vr

Vl

Fig. 22. Transistor model to simulate device characteristics [65].

(d)

(a) (e)

PMMA Ge PMMA SiOx Si (b)

1

(c)

(f)

2

(g)

Fig. 23. Shadow evaporation technique described in the text [15].

eted surfaces on which the quantum wires were fabricated (see Fig. 13). The Coulomb effects were observed up to 50 K. The breakdown of the wires is explained by potential fluctuations. Silicon Single-Electron Devices The authors of [53–55] suggested a structure operating like an induced-channel MOS transistor. It had one [53, 55] or two [54] quantum dots (Figs. 14, 15). The gate is comprised of two electrically disconnected RUSSIAN MICROELECTRONICS

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parts. With a positive voltage applied to the lower part (lower gate), an inversion n-channel forms in the p-substrate, and when the upper gate is negatively biased, depletion regions occur, which disintegrate the channel, producing quantum dots. These devices are one- or double-induced-dot planar controlled devices. Leobandung et al. created both electron [56] and hole [57] devices exploiting the Coulomb blockade effect (Fig. 16). An insulating layer was produced by implanting oxygen into the silicon substrate. Then, the necessary pattern was formed on the surface by elec-

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Cg J1

Cm J2

(a)

1 µm

Fig. 24. SEM micrograph of two capacitively coupled single-electron transistors made by the shadow evaporation technique [67].

tron etching and RIE, followed by thermal gate oxidation to decrease the dot size and rise the barrier height between the dot and electrodes. A polysilicon gate was applied on the surface. The electron and hole devices were made on the n- and p-substrates, respectively. These transistors are controlled planar devices with one persisting dot. The micrograph taken in a scanning electron microscope (SEM) is shown in Fig. 17, and Fig. 18 depicts the dependence of the drain current on the gate voltage for the electron transistor at different temperatures. Similar curves were obtained for the hole device. It is worth mentioning that the two above transistors are the first single-electron devices (except STMfabricated) to operate at temperatures above 77 K. Later, the same authors improved the design of these transistors [9, 10]. A silicon dot above the channel was fabricated by a self-aligned technique. Initially, the object, made by electron lithography, was no more than 25 nm across but was then oxidized to a size of 7 × 7 nm2. A so-called “floating dot” was obtained, which, being charged by one or several electrons, changed the pinchoff voltage of the transistor. The dot was charged by applying 10-ms pulses to the gate. With the pulse amplitude smoothly increasing, the pinch-off voltage changed stepwise with a step of 55 mV. This testifies that the dot was charged by individual electrons. The charge on the dot was retained for 5 s. All the measurements were taken at room temperature. This argues for creating a single-electron memory cell operating at room temperature, although its speed calls for further

investigation. The problem of reproducibility in obtaining the 10-nm structures by electron lithography was not concerned, however. A similar design was reported in [4, 5]. The floating dot was made as above, but its initial size was 70 × 70 nm2 and after oxidation decreased to 30 × 30 nm2. The room-temperature drain current vs. gate voltage characteristics exhibit hysteresis, which was attributed to the effects of single-electron tunneling. In the structures without the floating dots, the hysteresis effect was not observed. Another design of this type (but without a floating dot) with like characteristics was fabricated by Fujiwara et al. [58]. However, this transistor had large dimensions and was operable only to 28 K. One more similar structure with the only difference in the geometry was described in [6]. The channel width was decreased by anisotropically etching to 30 nm. This made it possible to observe the traces of the Coulomb staircase at room temperature. The structure suggested in [59] is shown in Fig. 19. This device was made as follows. A Si/SiO2 island was fabricated by electron lithography and RIE. Then a thin (2 nm) oxide layer was grown on the side surface of the island by thermal oxidation. Feed electrodes were made from the top polysilicon layer by means of electron lithography and RIE, as shown in Fig. 19. The island served as a quantum dot, and tunneling proceeded through the thin side oxide of the island. The overlap capacitance between the island and electrodes was relatively small due to the thick SiO2 layer above the island. The substrate acted as the gate electrode. This device is classified as above. As follows from Fig. 19, the area of the tunnel contact is defined by the island height and feed electrode width, which were 30 and 100 nm, respectively. Thus, the electrode capacitance was found to be 50 aF for a side oxide thickness of 2 nm. The temperatures were made at 4.2 K. Of interest is the design of a single-hole transistor suggested in [60]. The device includes quantum wires with quantum dots that are spontaneously produced in ultrashallow p–n junctions formed by non-steady-state diffusion. Varying the temperature and parameters of the oxidized layer on the single-crystal silicon surface, one can control interstitial and substitutional impurity diffusion into the substrate. The width of the p+-layer (10–20 nm) is of the order of the Fermi hole wavelength, which allows holes to be quantized in it, i.e., quantum wells with the 2D hole gas to appear. The presence of the fundamental conductivity steps at T = 77 K points to the formation of the p+-layer of quantum wires. This phenomenon is explained by strong Coulomb correlation. The application of a voltage to the gate results in the spontaneous formation of an electrostatic relief along the quantum wires, causing holes to be localized, i.e., dynamic quantum dots to arise. The Coulomb staircase was distinct at 77 K. RUSSIAN MICROELECTRONICS

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(a)

(b)

(c)

(d)

(e)

(f)

Fig. 25. Self-aligned process stages used in fabricating the single-electron transistor [68].

AlGaAs/GaAs Heterostructural Devices with 2DEG The basis for these devices is the formation of quantum dots in the 2DEG by applying depleting voltages to the electrodes on the sample surface [38, 61–64]. Such structures are planar controlled devices with one or several quantum dots. These devices differ in the configuration of the control electrodes and the number of quantum dots. For example, in [61], the electrode thickness was about 300 nm. The device operated at temperatures < 1 K. A similar structure but with two quantum dots was studied by the same authors in [64]. Here, the transformation of a two-dot device into a single-dot one upon changing the gate potentials was investigated. Figure 20 is the micrograph of the single-dot device taken with an atomic force microscope [62]. The operating temperature of this device is T = 25 mK. The design developed in [63] (similar to that in [38]) is schematically depicted in Fig. 21. It operates at temperatures below 35 mK. For the device shown in Fig. 22, Furusaki and Matveev [65] derived the analytical dependences of the linear conductivity on the gate voltage and temperature. RUSSIAN MICROELECTRONICS

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A promising approach was suggested by Baumgartner et al. [66]. An n-type 2DEG-containing GaAs/AlGaAs heterostructure was covered by a Zn-doped SiO2 layer. This layer was then locally heated by a laser beam 330 nm in diameter, which scanned the surface with a rate of 7 nm/s. The beam power was 4.5 mW. Zinc diffused into the heterostructure, where, being a p-dopant, produced depletion regions. Thus, a quantum dot was fabricated by confining the 2DEG with the depletion regions, as in the works cited above; here, however, these regions persisted rather than were induced by the gate voltages. Otherwise, this structure is no different from conventional 2DEG devices. The operating temperature lies below 4.2 K. Al/AlxOy /Al Devices In these devices, the possibility of obtaining a thin alumina film is employed. The shadow evaporation technique, described in the review of Geerligs [15], is common in this case. The process stages are shown in Fig. 23. At stage (a), a three-layer PMMA/Ge/PMMA resist film is patterned by electron lithography. Stages (b)–(d) are successive etchings of the resist. Stage (e) is isotropic selective

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etching of the lower PMMA layer to form suspension Ge bridges. Stage (f) is Al evaporation at different angles. After the first evaporation, Al oxidizes, and another Al layer is evaporated at a different angle so that the shadow from the Ge bridge is shifted. A tunnel contact forms where these two Al layers overlap. The remaining resist is stripped at stage (g). The devices fabricated in such a way are discussed in [67], and the micrograph of one of them is represented in Fig. 24. Tunnel junctions J1 and J2 are formed by overlapping the feed electrodes and the square metal islands. The device operates at T = 60 mK. A similar process was described by Zimmerman [69]; in this case, however, Al evaporation is used to make a mask: the metal is deposited on a trench, etched in the resist, at two different angles, and the trench narrows. With this technique, its width can be made as narrow as 100 nm. The advantage of this approach is its simplicity, since conventional optical lithography and wet etching are sufficient to fabricate the structure. Figure 25 shows the cross-sectional view of a device fabricated by the self-aligned technology described in [68]. This process also includes many stages. Stage (a) is the formation of a narrow Al strip; stage (b), the application of a resist across the strip; stage (c), etching of exposed parts of the strip; and stage (d), the oxidation of the edge sides of the Al strip. At stage (e), the structure is entirely covered by Al, and at stage (f), the resist with the Al overlayer is stripped off. In the resulting arrangement, the edge-oxidized remainder of the strip is adjacent to two electrodes and serves as a Coulomb island. The width and thickness of the strip were 80–150 and 50 nm, respectively, and the resist film across the strip was 150 nm thick. The device operates to T = 2 K. There are other ways of implementing the singleelectron devices; for example, Kubatkin et al. [71] described a device where a Coulomb island was made of YBaCuO high-temperature superconducting ceramic. The island measures 200 × 150 × 1000 nm3, and the operating temperature of the devices is T = 0.5 K. In the next part of this review, we shall consider possible applications of single-electron devices. REFERENCES 1. Likharev, K.K., On the Possibility of Creating Analog and Digital IC Based on Discrete Single-Electron Tunneling, Mikroelektronika, 1987, vol. 16, no. 3, pp. 195– 209. 2. Averin, D.V. and Likharev, K.K., Coherent Oscillations in Small-Sized Tunnel Junctions, Zh. Eksp. Teor. Fiz., 1986, vol. 90, no. 2, pp. 733–743. 3. Dutta, A., Kimura, M., Honda, Y., Otobe, M., Itoh, A., and Oda, S., Fabrication and Electrical Characteristics of Single Electron Tunneling Devices Based on Si Quantum Dots Prepared by Plasma Processing, Jpn. J. Appl. Phys., 1997, vol. 36, pp. 4038–4041.

4. Nakajima, A., Futatsugi, T., Kosemura, K., Fukano, T., and Yokoyama, N., Si Single Electron Tunneling Transistor with Nanoscale Floating Dot Stacked on a Coulomb Island by Self-Aligned Process, Appl. Phys. Lett., 1997, vol. 71, pp. 353–355. 5. Nakajima, A., Futatsugi, T., Kosemura, K., Fukano, T., and Yokoyama, N., Room Temperature Operation of Si Single Electron Memory with Self-Aligned Floating Dot Gate, Appl. Phys. Lett., 1997, vol. 70, pp. 1742–1744. 6. Ishikiro, H. and Hiramoto, T., Quantum Mechanical Effects in the Silicon Quantum Dot in a Single Transistor, Appl. Phys. Lett., 1997, vol. 71, pp. 3691–3693. 7. Park, K.-H., Ha, J.S., Yun, W.S., Shin, M., Park, K.-W., and Lee, E.-H., Room Temperature Observation of Single Electron Tunneling Effect in Self-Assembled Metal Quantum Dots on a Semiconductor Substrate, Appl. Phys. Lett., 1977, vol. 71, pp. 1469–1471. 8. Matsumoto, K., Ishii, M., and Segawa, K., Application of Scanning Tunneling Microscopy Nanofabrication Process to Single Electron Transistor, J. Vac. Sci. Technol., B, 1996, vol. 14, pp. 1331–1335. 9. Guo, L., Leobandung, E., and Chou, S.Y., A Room Temperature Silicon Single-Electron Metal-OxideSemiconductor Memory with Nanoscale Floating Gate and Ultranarrow Chanel, Appl. Phys. Lett., 1997, vol. 70, pp. 850–852. 10. Guo, L., Leobandung, E., and Chou, S.Y., Silicon Single-Electron Transistor Memory Operating at Room Temperature, Science (Washignton, D.C., 1883), 1997, vol. 275, pp. 649–651. 11. Fukuda, M., Nakagawa, K., Miyazaki, S., and Hirose, M., Resonant Tunneling Through a Self-Assembled Si Quantum Dot, Appl. Phys. Lett., 1997, vol. 70, pp. 2291–2293. 12. Averin, D.V. and Likharev, K.K., Coulomb Blockade of Single-Electron Tunneling and Coherent Oscillations in Small Tunnel Junctions, J. Low Temp. Phys., 1986, vol. 62, no. 3/4, pp. 345–373. 13. Likharev, K.K., Correlated Discrete Transfer of Single Electrons in Ultrasmall Tunnel Junctions, IBM J. Res. Develop., 1988, no. 1, pp. 144–158. 14. Likharev, K.K. and Claeson, T., Single Electonics, Sci. Am., 1992, vol. 6, pp. 80–85. 15. Tinkham, M., Coulomb Blockade and an Electron in a Mesoscopic Box, Am. J. Phys., 1996, no. 64, pp. 343– 347. 16. Geerligs, L.J., Charge Quantization Effects in Small Tunnel Junctions, Physics of Nanostructures, Cambridge: Cambridge Univ. Press, 1992, pp. 171–204. 17. Van Houten, H., Coulomb Blockade Oscillation in Semiconductor Nanostructures, Surf. Sci., 1992, no. 263, pp. 442–445. 18. Kouwenhowen, L.P., Marcus, C.M., McEuen, P.L., Tarucha, S., Westervelt, R.M., and Wingreen, N.S., Electron Transport in Quantum Dots, Proc. Advanced Institute on Mesosocopic Electron Transport, 1997. 19. Hu, G.Y. and O’Connel, R.E., Exact Solution of the Electrostatics for a Single Electron Multijunction Trap, Phys. Rev. Lett., 1995, no. 74, pp. 1839–1842. 20. Isawa, Y. and Suwa, F., Transport through Discrete Energy Levels in Quantum Dots, Jpn. J. Appl. Phys., 1995, no. 34, pp. 4492–4495. RUSSIAN MICROELECTRONICS

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SINGLE ELECTRONICS. PART 1 21. Adachi, S., Fujimoto, K., Hatano, T., and Isawa, Y., Current Response of Quantum Dot Modulated by TimeDependent External Fields, Jpn. J. Appl. Phys., 1995, no. 34, pp. 4298–4301. 22. Hatano, T., Fujimoto, K., and Isawa, Y., Role of Displacement Current in Quantum-Dot Turnstile Devices, Jpn. J. Appl. Phys., 1995, no. 34, pp. 4488–4491. 23. Zorin, A.B., Pekola, J.P., Hirvi, K.P., and Paalen, M.A., Pumping of a Single Electron with a Travelling Wave, Physica B (Amsterdam), 1995, no. 210, pp. 461–467. 24. Gorelik, L.Y., Isacsson, A., Voinova, M.V., Kasemo, B., Shekhter, R.I., and Jonson, M., Shuttle Mechanism for Charge Transfer in Coulomb Blockade Nanostructures, E-Print Archive (http:@xxx.lanl.gov) CondMat/9711196, 1997. 25. Hackenbroich, G., Heiss, W.D., and Weidenmuller, H.A., Deformation of Quantum Dots in the Coulomb Blockade Regime, E-Print Archive (http:@xxx.lanl.gov) CondMat/9702184, 1997. 26. Shikin, V., Coulomb Blockade in Double Junction Systems and Edge Magnetoplasmons, Phys. Low-Dim. Struct., 1996, no. 7/8, pp. 55–58. 27. Richardson, W.H., Possibility of a Single Electron Tunneling Diode and a Controllable Saturated Tunneling Current, Appl. Phys. Lett., 1997, no. 71, pp. 1113–1115. 28. Soldatov, E.S., Trifonov, A.S., and Khanin, V.V., STM Investigation of Correlated Electron Tunneling through a Single Molecule, Trudy Vserossiiskogo soveshchaniya “Zondovaya mikroskopiya-97” (Proc. All-Russia Conf. “Probe Miscroscopy,”) Nizhnii Novgorod, 1997. 29. Soldatov, E.S., Trifonov, A.S., Khanin, V.V., Korotkov, A.N., Gubin, S.P., Kolesov, V.V., Yakovenko, S.A., and Khomutov, G.B., High Temperature Single-Electron Tunneling in the Molecular Cluster Based Structures, Proc. Int. Conf. “Mesoscopic and Strongly Correlated Electron Systems”, Chernogolovka, 1997. 30. Schonenberg, C., van Houten, H., and Donkersloot, H.C., Single-Electron Tunneling Observed at Room Temperature by Scanning-Tunneling Microscopy, Europhys. Lett., 1992, vol. 20, no. 3, pp. 249–254. 31. Schonenberg, C., van Houten, H., Donkersloot, H.C., van der Putten, A.M.T., and Fokkink, L.G.J., SingleElectron Tunneling Up to Room Temperature, Phys. Scr., 1992, no. 45, pp. 289–291. 32. Van Kempen, H., Dubois, J.G.A., Gerritsen, J.W., and Schmid, G., Small Metallic Particles Studied by Tunneling Microscopy, Physica B (Amsterdam), 1995, no. 204, pp. 51–56. 33. Uehara, Y., Ohayama, S., Ito, K., and Ushioda, S., Optical Observation of Single Electron Charging at Room Temperature, Jpn. J. Appl. Phys., 1996, no. 35, pp. 167– 170. 34. Dorogi, M., Gomez, J., Osifchin, R., Andres, R.P., and Reifenberger, R., Room-Temperature Coulomb Blockade From a Self-Assembled Molecular Nanostructure, Phys. Rev. B, 1995, vol. 52, pp. 9071–9077. 35. Nejo, H., Aono, M., Baksheyev, D.S., and Tkachenko, V.A., Single-Electron Charging of a Molecule Observed in Scanning Tunneling Scattering Experiments, J. Vac. Sci. Technol., 1996, vol. 14, pp. 2399– 2402. RUSSIAN MICROELECTRONICS

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36. Austing, D.G., Honda, T., Takura, Y., and Tarucha, S., Sub-Micron Vertical AlGaAs/GaAs Resonant Tunneling Single Electron Transistor, Jpn. J. Appl. Phys., 1995, no. 34, pp. 1320–1325. 37. Austing, D.G., Honda, T., and Tarucha, S., GaAs/AlGaAs/In GaAs Vertical Triple Barrier Single Electron Transistors, Jpn. J. Appl. Phys., 1997, no. 36, pp. 1667–1671. 38. Ashoori, R.C., Stormer, H.L., Weiner, J.S., Pfeiffer, L.N., Pearton, S.J., Baldwin, K.W., and West, K.W., SingleElectron Capacitance Spectroscopy of Discrete Quantum Levels, Phys. Rev. Lett., 1992, no. 68, pp. 3088– 3091. 39. Haug, R.J., Blick, R.H., and Schmidt, T., Transport Spectroscopy of Single and Coupled Quantum Dot Systems, Physica B (Amsterdam), 1995, no. 212, pp. 207– 212. 40. Shmidt, T., Haug, R.J., van Klitzing, K., Forster, A., and Luth, H., Single-Electron Transport in Small ResonantTunneling Diodes with Various Barrier-Thickness Asymmetries, Phys. Rev. B, 1997, vol. 55, pp. 2230– 2235. 41. Medeiros-Ribeiro, G., Pikus, F.G., Petroff, P.M., and Efros, A.L., Single-Electron Charging and Coulomb Interaction in InAs Self-Assembled Quantum Dots Analysis, Phys. Rev. B, 1997, vol. 55, pp. 1568–1573. 42. Duruoz, C.I., Clarke, R.M., Marcus, C.M., and Harris, J.S., Jr., Conduction Threshold, Switching, and Hysteresis in Quantum Dot Arrays, Phys. Rev. Lett., 1995, vol. 74, pp. 3237–3240. 43. Rimberg, A.J., Ho, T.R., and Clarke, J., Scaling Behavior in the Current–Voltage Characteristic of One- and TwoDimensional Arrays of Small Metallic Islands, Phys. Rev. Lett., 1995, vol. 74, pp. 4714–4717. 44. Miura, N., Numaguchi, T., Yamada, A., Konagai, M., and Shirakashi, J., Single-Electron Tunneling Through Amorphous Carbon Dots Array, Jpn. J. Appl. Phys., 1997, vol. 36, pp. L1619–L1621. 45. Vyshenskii, S.V., High-Temperature Single Electronics, Mikroelektronika, 1995, vol. 24, no. 4, pp. 243–253. 46. Tackeuchi, A., Nakata, Y., Muto, S., Sugiyama, Y., Usuki, T., Nishikawa, Y., Yokoyama, N., and Wada, O., Time-Resolved Study of Carrier Transfer Among InAs/GaAs Multi-Coupled Quantum Dots, Jpn. J. Appl. Phys., 1995, vol. 34, pp. L1439–L1441. 47. Yoshikawa, N.Y., Kimijima, H., Miura, N., and Sugahara, M., Single-Electron Tunneling Effect in Nanoscale Granular Microbridges, Jpn. J. Appl. Phys., 1997, vol. 36, pp. 4161–4165. 48. PERST, 1996, vol. 3, no. 4, pp. 1–2. 49. Ohata, A., Toriumi, A., and Uchida, K., Coulomb Blockade Effects in Edge Quantum Wire SOI MOSFETs, Jpn. J. Appl. Phys., 1997, vol. 36, pp. 1686–1689. 50. Okada, H., Fujikura, H., Hashizume, T., and Hasegawa, H., Observation of Coulomb Blockade Type Conductance Oscillations Up to 50 K in Gated InGaAs Ridge Quantum Wires Grown by Molecular Beam Epitaxy on InP Substrates, Jpn. J. Appl. Phys., 1997, vol. 36, pp. 1672–1677. 51. Okada, H., Kasai, S., Fujikura, H., Hashizume, T., and Hasegawa, H., Basic Control Characteristics of Novel Schottky In-Plane and Wrap Gate Structures Studied by

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55. 56.

57. 58.

59.

60. 61.

NEIZVESTNYI et al. Simulation and Transport Measurements in GaAs and InGaAs Quantum Wires, Jpn. J. Appl. Phys., 1997, vol. 36, pp. 4156–4160. Kasai, S., Jinushi, K., Tomozawa, H., and Hasegawa, H., Fabrication and Characterization of GaAs Single Electron Devices Having Single and Multiple Dots Based on Schottky In-Plane-Gate and Wrap-Gate Control of TwoDimensional Electron Gas, Jpn. J. Appl. Phys., 1997, vol. 36, pp. 1678–1685. Matsuoka, H. and Kimura, S., Transport Properties of a Silicon Single-Electron Transistor at 4.2 K, Appl. Phys. Lett., 1995, vol. 66, pp. 613–615. Matsuoka, H. and Ahmed, H., Transport Properties of Two Quantum Dots Connected in Series Formed in Silicon Inversion Layer, Jpn. J. Appl. Phys., 1996, vol. 35, pp. L418–L420. Matsuoka, H. and Kimura, S., Thermally Enhanced CoTunneling of Single Electrons in a Si Quantum Dots at 4.2 K, Jpn. J. Appl. Phys., 1995, vol. 34, pp. 1326–1328. Leobandung, E., Guo, L., Wang, Y., and Chou, S.Y., Observation of Quantum Effects and Coulomb Blockade in Silicon Quantum Dot Transistors at Temperatures Over 100 K, Appl. Phys. Lett., 1995, vol. 67, pp. 938– 940. Leobandung, E., Guo, L., and Chou, S.Y., Single Hole Quantum Dot Transistors in Silicon, Appl. Phys. Lett., 1995, vol. 67, pp. 2338–2340. Fujiwara, A., Takahashi, Y., Murase, K., and Tabe, M., Time-Resolved Measurement of Single-Electron Tunneling in a Si Single-Electron Transistor With Satellite Si Islands, Appl. Phys. Lett., 1995, vol. 67, pp. 2957–2959. Ohata, A., Niyama, H., Shibata, T., Nakajima, K., and Toriumi, A., Silicon-Based Single-Electron Tunneling Transistor Operated at 4.2 K, Jpn. J. Appl. Phys., 1995, vol. 34, pp. 4485–4487. PERST, 1996, vol. 3, no. 23/24, pp. 3–4 (Abstracts of Papers, Int. Symp. “Nanostructures-96: Physics and Technology,” St. Petersburg, 1996, pp. 404–407). Waugh, F.R., Berry, M.J., Mar, D.J., and Westervelt, R.M., Single-Electron Charging in Double and Tri-

62. 63.

64.

65. 66.

67.

68.

69. 70. 71.

ple Quantum Dots with Tunable Coupling, Phys. Rev. Lett., 1995, vol. 75, pp. 705–708. Hofmann, F., Heinzel, T., Wharam, D.A., and Kotthaus, J.P., Single Electron Swiching in a Parallel Quantum Dot, Phys. Rev. B, 1995, vol. 51, pp. 13872–13875. Pasquier, C., Glattli, D.C., Meirav, U., Williams, F.I.B., Jin, Y., and Etienne, B., Coulomb Blockade of Tunneling in 2D Electron Gas, Surf. Sci., 1992, vol. 263, pp. 419– 423. Crouch, C.H., Livermore, C., Westervelt, R.M., Campman, K.L., and Gossard, A.C., Evolution of the Coulomb Gap in Tunnel-Coupled Quantum Dots, 1997, vol. 71, pp. 817–819. Furusaki, A. and Matveev, K.A., Coulomb Blockade Oscillation of Conductance in the Regime of Strong Tunneling, Phys. Rev. Lett., 1995, vol. 75, pp. 709–712. Baumgartner, P., Wegscheider, W., Bichler, M., Schedelbeck, G., Neumann, R., and Abstreiter, G., Single-Electron Transistor Fabricated by Focused Laser Beam– Induced Doping of a GaAs/AlGaAs Heterostructure, Appl. Phys. Lett., 1997, vol. 70, pp. 2135–2137. Visscher, E.H., Verbrugh, S.M., Lindeman, J., Hadley, P., and Mooij, J.E., Fabrication of Multilayer Single-Electron Tunneling Devices, Appl. Phys. Lett., 1995, vol. 66, pp. 305–307. Gotz, M., Bluthner, K., Krech, W., Nowack, A., Fuchs, H.-L., Kley, E.-B., Thieme, P., Wagner, Th., Eska, G., Hecker, K., and Hegger, H., Preparation of Self-Aligned In-Line Tunnel Junctions for Application in Single-Charge Electronics, J. Appl. Phys., 1995, vol. 78, pp. 5499–5502. Zimmerman, N.M., A Simple Fabrication Method for Nanometer-Scale Thin-Metal Stencils, J. Vac. Sci. Technol., B, 1997, vol. 15, no. 2, pp. 369–372. Wang, X. and Grabert, H., Coulomb Charging at Large Conduction, Preprint, 1997. Kubatkin, S.E., Tzalenchuk, A.Ya., Ivanov, Z.G., Delsing, P., Shekhter, R.I., and Claeson, T., Coulomb Blockade Electrometer with a High-Tc Island, Pis’ma Zh. Eksp. Teor. Fiz., 1996, no. 63, pp. 112–117.

RUSSIAN MICROELECTRONICS

Vol. 28

No. 2

1999