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Nanoelectronics single electron transistor

The shotgun marriage of chemistry and engineering called “Nanotechnology” is ushering in the era of self-replicating machinery and self-assembling consumer goods made from raw atoms. Utilizing the well understood chemical properties of atoms & molecules, nanotechnology proposes the construction of novel molecular devices possessing extraordinary properties. The single electron transistor or SET is a new type of switching device that uses controlled electron tunneling to amplify current.
By using the “Electron beam lithography” and “Electromigration”, the research leads to the designing of a single atom transistor with the help of the meticulously synthesized semiconductor crystals called “quantum dots”, which embodies the electrons confined in a channel and resembles same in its properties as an real atom.
This paper presents a scenario on existing and ongoing studies on NANO ELECTRONICS with the theoretical methods relevant to their understanding. Most of the preceding discussion is premised upon the implicit assumption. That future quantum effect Nano Electronic Devices will be fabricated in Nano Metre scale using molecules. Conductance quantization in ballistic regime has been described under various conditions. The behaviour of “Coulomb Island” through which the electrons can only enter by tunneling through one of the insulators is presented.
At last, the SET presents that it is the different construction is which is based on helical logic, atomic scale motion of electrons in an applied rotating electric field. INTRODUCTION

The discovery of the transistor has clearly had enormous impact, both intellectually and commercially, upon our lives and work. A major vein in the corpus of condensed matter physics, quite literally, owes its existence to this break through. It also led to the microminiaturization of electronics, which has permitted us to have powerful computers on our desktops that communicate easily with each other via the Internet. The resulting globalization of science, technology and culture is now transforming the ways we think and interact.
Over the past 30 years, silicon technology has been dominated by Moore’s law: the density of transistors on a silicon integrated circuit doubles about every 18 months. The same technology that allows us to shrink the sizes of devices. To continue the increasing levels of integration beyond the limits mentioned above, new approaches and architectures are required .In today’s digital integrated circuit architectures, transistors serve as circuit switches to charge and discharge capacitors to the required logic voltage levels. It is also possible to encode logic states by the positions of individual electrons (in quantum dot single-electron transistors, for example) rather than by voltages. Such structures are scaleable to molecular levels, and the performance of the device improves as the size decreases. Artificially structured single electron transistors studied to date operate only at low temperature, but molecular or atomic sized single electron transistors could function at room temperature.

Before we turn to the single atom transistors, the subject of this article, we need to learn about the Kondo effect.

The Kondo effect

The effect arises from the interactions between a single-magnetic atom, such as cobalt, and the many electrons in an otherwise nonmagnetic metal such as copper. Such as an impurity typically has an intrinsic angular momentum or spin that interacts with all the surrounding electrons in the metal. As a result, the mathematical description of the system is a difficult many-body problem.
The electrical resistance of a pure metal usually drops as its temperature is lowered, because electrons can travel through a metallic crystal more easily when the vibrations of the atoms are small. However, the resistance saturates as the temperature is lowered below about 10k due to the presence of crystal lattice defects in the material, such as vacancies, interstitial, dislocations and grain boundaries. Electrical resistance is related to the amount of back scattering from defects, which hinders the motion of the electrons through the crystal. This text book resistive behavior of metal changes dramatically when magnetic atoms, such as cobalt, are added. The electrical resistance increases as the temperature is lowered further, in contrast to that of a pure metal. This effect was first observed in the 1930s.
This behaviour does not involve any phase transition, such as a metal-insulator transition. A parameter called the Kondo temperature (roughly speaking the temperature at which the resistance starts to increase again) completely determines the low-temperature electronic properties of the material. Considering the scattering from a magnetic ion that interacts with the spins of the conducting electrons. It was found that the second term in the calculation could be much larger than the first. The result is that the resistance of a metal increases logarithmically when the temperature is lowered. Hence the name ‘Kondo effect’. However, it also makes the unphysical prediction that the resistance will be infinite at even lower temperatures. It turns out that Kondo’s result is correct only above a certain temperature, which became known as the Kondo temperature, Tk. The impurity has only one electron with energy E. In this case, the electron can quantum-mechanically tunnel from the impurity and escape, if E is greater than Fermi level of the metal. Otherwise it remains trapped. The defect has a spin of ½ and its z-component is fixed as either ‘spin up’ or ‘spin down’. However, the so-called exchange process can take place that effectively flip the spin of the impurity from spin up to spin down or vice-versa, while simultaneously creating a spin excitation in the Fermi sea. When an electron is taken from the magnetic impurity in an unoccupied energy state at the surface of the Fermi Sea. The energy needed for this process is large, between 1 and 10eV, for the magnetic impurities. Classically, it is forbidden to take an electron from the defect without putting energy into the system. In quantum mechanics, however, the Heisenberg uncertainty principle allows such a configuration to exist for a very short time-around h/E, where h is the Planck constant. Within this time scale, another electron must tunnel from the Fermi Sea back to the impurity. However, since the uncertainty principle says nothing about the spin of this electron, its z-component may point in the opposite direction. In other words, the initial and final states of the impurity can have different spins. This spin exchange qualitatively changes the energy spectrum of the system. When many such processes are taken together, one finds that a new state-known as the Kondo resonance- is generated with exactly the same energy as the Fermi level.
Such a resonance is effective at scattering electrons with energies close to the Fermi level. Since the same electrons are responsible for the low-temperature conductivity of a metal, the strong scattering from this state increases the resistance. The Kondo resonance is unusual.
In contrast, the Kondo State is generated by exchange processes between a localized electron and free electron states. Since many electrons need to be involved, the Kondo effect is many body phenomenons. It is important to note that the Kondo State is always “on resonance” since it is fixed to the Fermi energy. Even though the system may start with energy E that is very far away from the Fermi energy, the Kondo effect alters the energy of the system so that it is always on resonance. The only requirement for the effect to occur is that the metal is cooled to sufficiently low temperatures below the Kondo temperature TK.
Enter nanotechnology

Nanotechnology aims to manipulate materials at the atomic scale. An important tool in the field is the scanning tunneling microscope (STM), which can image a surface with atomic resolution, move individual atoms across a surface and measure the energy spectrum at particular locations. Recently, the STM has been used to image and manipulate magnetic impurities on the surface of metals, opening a new avenue of research in to the Kondo effect. Quantum dots are small structures that behave like artificial atoms. Quantum dots are often called artificial atoms since their electronic properties resemble those of real atoms. A voltage applied to one of the gate electrodes of the device controls the number of electrons, N, that are confined in the dot. If an odd number of electrons is trapped within the dot is necessarily non zero and has a minimum value of S=1/2. This localized spin, embedded between large electron seas in the two leads, mimics the cobalt -in-copper system and many of the known Kondo phenomena can be expected to occur in these transistor-type devices.
One of main distinctions between a quantum dot and a real metal is related to their different geometries. In a metal, the electron states are plane waves, and scattering from impurities in the metal mixes electron waves with different momenta. This momentum transfer increases the resistance. In a quantum dot, however, all the electrons have to travel through the device, as there is no electrical path around it. In this case, the Kondo resonance makes it easier for states belonging to the two opposite electrodes to mix. This mixing increases the conductance (i.e. decreases the resistance). The advantage of quantum dots is the ease with which the parameters of these artificial atoms can be controlled. The conductance of a quantum dot depends only on T/Tk. The Kondo effect disappears when the number of electrons on the quantum dot is even. Moreover, at the lowest temperatures, the conductance approaches the quantum limit of conductance 2e2/h, where e is the charge of an electron. The Kondo cloud consists of electrons that have previously interacted with the same magnetic impurity. Since each of these electrons contains information about the same impurity, they effectively have information about each other. In other words, the electrons are mutually correlated.

Towards single-electron devices

Unlike field-effect transistors, single-electron devices are based on an intrinsically quantum phenomenon: the tunnel effect. This is observed when two metallic electrodes are separated by an insulating barrier about 1 nm thick - in other words, just 10 atoms in a row. Electrons at the Fermi energy can "tunnel" through the insulator, even though in classical terms their energy would be too low to overcome the potential barrier.
The electrical behaviour of the tunnel junction depends on how effectively the barrier transmits electron waves, which decreases exponentially with its thickness, and on the number of electron-wave modes that impinge on the barrier, which is given by the area of the tunnel junction divided by the square of the electron wavelength. A single-electron transistor exploits the fact that the transfer of charge through the barrier becomes quantized when the junction is made sufficiently resistive.


This quantization process is shown particularly clearly in a simple system known as a single-electron box (figure1). If a voltage source charges a capacitor, Cg, through an ordinary resistor, the charge on the capacitor is strictly proportional to the voltage and shows no sign of charge quantization. But if the resistance is replaced by a tunnel junction, the metallic area between the capacitor plate and one side of the junction forms a conducting "island" surrounded by insulating materials. In this case the transfer of charge onto the island becomes quantized as the voltage increases, leading to the so-called Coulomb staircase.
This Coulomb staircase is only seen under certain conditions. Firstly, the energy of the electrons due to thermal fluctuations must be significantly smaller than the Coulomb energy, which is the energy needed to transfer a single electron onto the island when the applied voltage is zero. This Coulomb energy is given by e2/2C, where e is the charge of an electron and C is the total capacitance of the gate capacitor, Cg, and the tunnel junctions. Secondly, the tunnel effect itself should be weak enough to prevent the charge of the tunneling electrons from becoming delocalized over the two electrodes of the junction, as happens in chemical bonds. This means that the conductance of the tunnel junction should be much less than the quantum of conductance, 2e2/h, where h is Planck's constant.
When both these conditions are met, the steps observed in the charge are somewhat analogous to the quantization of charge on oil droplets observed by Millikan in 1911. In a single-electron box, however, the charge on the island is not random but is controlled by the applied voltage. As the temperature or the conductance of the barrier is increased, the steps become rounded and eventually merge into the straight line typical of an ordinary resistor.

A single-electron transistor

The SET transistor can be viewed as an electron box that has two separate junctions for the entrance and exit of single electrons (figure 2). It can also be viewed as a field-effect transistor in which the channel is replaced by two tunnel junctions forming a metallic island. The voltage applied to the gate electrode affects the amount of energy needed to change the number of electrons on the island.
The SET transistor comes in two versions that have been nicknamed "metallic" and "semiconducting". These names are slightly misleading, however, since the principle of both devices is based on the use of insulating tunnel barriers to separate conducting electrodes.
In the original metallic version, a metallic material such as a thin aluminium film is used to make all of the electrodes. The metal is first evaporated through a shadow mask to form the source, drain and gate electrodes. The tunnel junctions are then formed by introducing oxygen into the chamber so that the metal becomes coated by a thin layer of its natural oxide. Finally, a second layer of the metal - shifted from the first by rotating the sample - is evaporated to form the island.
In the semiconducting versions, the source, drain and island are usually obtained by "cutting" regions in a two-dimensional electron gas formed at the interface between two layers of semiconductors such as gallium aluminium arsenide and gallium arsenide. In this case the conducting regions are defined by metallic electrodes patterned on the top semiconducting layer. Negative voltages applied to these electrodes deplete the electron gas just beneath them, and the depleted regions can be made sufficiently narrow to allow tunneling between the source, island and drain. Moreover, the electrode that shapes the island can be used as the gate electrode.

Operation of a SET transistor
So how does a SET transistor work? The key point is that charge passes through the island in quantized units. For an electron to hop onto the island, its energy must equal the Coulomb energy e2/2C. When both the gate and bias voltages are zero, electrons do not have enough energy to enter the island and current does not flow. As the bias voltage between the source and drain is increased, an electron can pass through the island when the energy in the system reaches the Coulomb energy. This effect is known as the Coulomb blockade, and the critical voltage needed to transfer an electron onto the island, equal to e/C, is called the Coulomb gap voltage.
Now imagine that the bias voltage is kept below the Coulomb gap voltage. If the gate voltage is increased, the energy of the initial system (with no electrons on the island) gradually increases, while the energy of the system with one excess electron on the island gradually decreases. At the gate voltage corresponding to the point of maximum slope on the Coulomb staircase, both of these configurations equally qualify as the lowest energy states of the system. This lifts the Coulomb blockade, allowing electrons to tunnel into and out of the island.
The Coulomb blockade is lifted when the gate capacitance is charged with exactly minus half an electron, which is not as surprising as it may seem. The island is surrounded by insulators, which means that the charge on it must be quantized in units of e, but the gate is a metallic electrode connected to a plentiful supply of electrons. The charge on the gate capacitor merely represents a displacement of electrons relative to a background of positive ions.

If we further increase the gate voltage so that the gate capacitor becomes charged with -e, the island again has only one stable configuration separated from the next-lowest-energy states by the Coulomb energy. The Coulomb blockade is set up again, but the island now contains a single excess electron. The conductance of the SET transistor therefore oscillates between minima for gate charges that are integer multiples of e, and maxima for half-integer multiples of e (figure 3).
Accurate measures of charge
Such a rapid variation in conductance makes the single-electron transistor an ideal device for high-precision electrometry. In this type of application the SET has two gate electrodes, and the bias voltage is kept close to the Coulomb blockade voltage to enhance the sensitivity of the current to changes in the gate voltage.
The voltage of the first gate is initially tuned to a point where the variation in current reaches a maximum. By adjusting the gate voltage around this point, the device can measure the charge of a capacitor-like system connected to the second gate electrode. A fraction of this measured charge is shared by the second gate capacitor, and a variation in charge of ¼e is enough to change the current by about half the maximum current that can flow through the transistor at the Coulomb blockade voltage. The variation in current can be as large as 10 billion electrons per second, which means that these devices can achieve a charge sensitivity that outperforms other instruments by several orders of magnitude.
The precision with which electrons can be counted is ultimately limited by the quantum delocalization of charge that occurs when the tunnel-junction conductance becomes comparable with the conductance quantum, 2e2/h. However, the current through a SET transistor increases with the conductance of the junctions, so it is important to understand how the single-electron effects and Coulomb blockade disappear when the tunnel conductance is increased beyond 2e2/h.
Towards room temperature
Until recently single-electron transistors had to be kept at temperatures of a few hundred millikelvin to maintain the thermal energy of the electrons below the Coulomb energy of the device. Most early devices had Coulomb energies of a few hundred microelectronvolts because they were fabricated using conventional electron-beam lithography, and the size and capacitance of the island were relatively large. For a SET transistor to work at room temperature the capacitance of the island must be less than 10-17 F and therefore its size must be smaller than 10 nm.
.Perspectives on the future
Researchers have long considered whether SET transistors could be used for digital electronics. Although the current varies periodically with gate voltage - in contrast to the threshold behaviour of the field-effect transistor - a SET could still form a compact and efficient memory device. However, even the latest SET transistors suffer from "offset charges", which means that the gate voltage needed to achieve maximum current varies randomly from device to device. Such fluctuations make it impossible to build complex circuits.
One way to overcome this problem might be to combine the island, two tunnel junctions and the gate capacitor that comprise a single-electron transistor in a single molecule - after all, the intrinsically quantum behaviour of a SET transistor should not be affected at the molecular scale. In principle, the reproducibility of such futuristic transistors would be determined by chemistry, and not by the accuracy of the fabrication process. Only one thing is certain: if the pace of miniaturization continues unabated, the quantum properties of electrons will become crucial in determining the design of electronic devices before the end of the next decade.

A common thread between Stone Age, medieval, industrial and molecular nanotechnology is the exponential curve. This ever-accelerating curve representing human knowledge, science and technology will be driven a new way by what will probably become the first crude, pre-assembler nanotech products.
By treating atoms as discrete, bit like objects, molecular manufacturing will bring a digital revolution to the production of material objects. Working at the resolution limit of matter, it will enable the ultimate in miniaturization and performance. Research programs in chemistry, molecular biology and scanning probe microscopy are laying the foundations for a technology of molecular machine systems.
The motion of electrons in a transistor has been described as a complex dance. Switching action in one property of a transistor that has been demonstrated. Bardeen, Brattain and Shockley were concerned about the amplification properties of transistors they had invented. It remains to see whether amplification can be achieved to any experimentally observable extent in such a single atom transistor.

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