RESEARCH: SHUTTLE
ELECTROMECHANICAL CHARGE SHUTTLE

The quest of counting electrons is one of the key challenges in metrology. It relates to the attempt of linking the electrical units directly with fundamental constants, as it it the case for voltage and resistance using the Josephson effect and the Quantum Hall effect, respectively. So far, a similar definition of current is yet to be achieved. To this end, Koenig and coworkers [1] report a novel device architecture that might be able to solve this task.

The present standard of the ampere dates back to 1948, when it was established by the International Standard of Units (SI) as “The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 newton per meter of length.”.

Alternatively, current can be defined as the amount of charge flowing past a certain point in a wire per unit time, linking the ampere with the elementary charge e through I = ef. This is when the precise counting of electrons comes in. The most accurate way to count electrons is to pass them through a device one-by-one. This can be achieved using single electron tunneling devices. In general, a single electron transistor (SET) consists of a small metallic island which is separated from a source and drain reservoir by tunneling barriers. At low enough temperatures, only one electrons can tunnel on and off the island at a time sequentially, since Coulomb repulsion prevents other electrons from entering the island.

At present, only two electrical units can be precisely measured making use of quantum effects: The volt is based on the Josephson effect U = (h/2e)f via the magnetic flux quantum Φ0 = h/2e, whereas the ohm is linked with the Quantum Hall effect U = (h/e2) I through the von Klitzing constant RK = h/e2. Tracing back the ampere to the elementary charge e using SET would allow to close the quantum metrology triangle, which links voltage, current and frequency via independent quantum effects based on the fundamental constants h and e.

A precise experimental verification of the quantum metrology triangle can be used to verify the underlying quantum effects and thus h and e with utmost precision.

In the past years, there have been several promising attempts to realize the missing quantum standard of the ampere. In an SET turnstile [2], a source drain voltage is applied across a series of tunneling barriers while a central gate is biased with an rf voltage to control the tunneling of individual electrons through the device. In SET pumps [3], a series of single electron transistors is gated subsequently shuffling electrons from source to drain without an applied bias voltage. Related devices employ surface acoustic waves [4] or time-dependent gate sequences [5] to pump single electrons. Besides these active approaches seeking to generate a well-defined current in a device, the rf SET [6] is an extremely sensitive electrometer capable of measuring individual electrons as they flow through a device and thus a candidate for a passive current standard.

Although accuracies up to 1.5 x 10-8 have been achieved [3], all of the above approaches suffer from a certain amount of leakage. Even though Coulomb blockade forbids additional electrons to tunnel, so-called cotunneling processes in which electrons coherently tunnel through the device via virtual states are still possible. This results in a parasitic current whith sets ultimate limits to the performance of the devices.

In 1998, the mechanical single electron transistor (mSET) was theoretically proposed [7]. In this device, the metallic island is placed on a vibrating beam which moves the island back and forth between two electrodes. Since the tunnel resistance increases exponentially with distance, charge transfer between the island and an electrode only occurs at the turning points of the shuttle motion. Therefore transport across the island is strictly sequential, making the mSET the only SET device in which cotunneling is not an issue.

Since the mSET has first been put forward, experimental groups have been seeking to realize such a single electron shuttle. So far, the mechanical motion of the island has been excited electrically. Common schemes are based on the capacitive coupling between a metallized part of the resonator (which may be the island or a separate gate) and fixed electrodes (using either the source and drain contacts or an extra set of electrodes) biased with a resonant rf voltage [8, 9]. In any case the measured current being on resonance with the driving voltage bears the risk of electrical crosstalk. And indeed, measured data has often been obscured by cross-coupling effects and hard to interpret. A related driving mechanism relies on self-oscillation of the island that sets in for large source drain bias. Self-oscillation has recently been observed above 4 volts [10].

Koenig et al. propose a novel device configuration in which an ultrasonic wave is used as mechanical drive [1]. In order to perfectly screen the shuttle from electric fields, the sample is placed inside a Faraday cage. This setup guarantees complete decoupling of the measured signal from the drive at arbitrary source drain voltages. The analysis begins with a careful comparison of the mechanical eigenmodes and the transport characteristics of large arrays of shuttles. A detailed investigation of the shuttling current as a function of the applied voltage bias under resonant actuation reveals a rich variety of electromechanical transport regimes.

In the limit of the device being completely determined by the island capacitance, the authors report a saturation of the shuttling current. In this regime the shuttle can be theoretically described using a single electron box model during contact time taking advantage of the above-described sequential nature of the mechanically generated tunnel current. Excellent agreement between the measured data and theoretical calculations is observed, which allows to anticipate the next step.

The only mechanical SET device that has been demonstrated to display Coulomb blockade consists of a fixed island across which electrons tunnel to a moving electrode, which makes it sensitive to cotunneling [11]. All shuttles with two time-dependent tunneling barriers reported so far have been operating far from the single electron tunneling regime. The present work for the first time enables to make quantitative predictions about the crossover to the Coulomb blockade regime which is a prerequesite of single electron counting purposes. The results clearly indicate that such experiments are well within reach of modern processing techniques.

Although the devices need to be scaled down significantly in order to display Coulomb blockade at helium temperatures, the work of Koenig opens up a whole new set of possible experiments towards a cotunneling-free current standard based on mechanical SET devices.

[1]     R. Koenig et al.,
        Ultrasonically driven nano-mechanical single electron shuttle,
        Nature Nanotechnology, 3, 482 (2008) [doi:10.1038/nnano.2008.178].

[2]     L. J. Geerligs et al.,
        Frequency-locked turnstile device for single electrons,
        Phys. Rev. Lett. 64, 2691 (1990).

[3]     M. W. Keller et al.,
        Accuracy of electron counting using a 7-junction electron pump,
        Appl. Phys. Lett. 69, 1804 (1996).

[4]     V. I. Talyanskii et al.,
        Single-electron transport in a one-dimensional channel by
        high-frequency surface acoustic waves,
        Phys Rev B 56, 15180 (1997).

[5]     M. D. Blumenthal et al.,
        Gigahertz quantized charge pumping,
        Nature Physics 3, 343 (2007).

[6]     R. J. Schoelkopf et al.,
        The Radio-Frequency Single-Electron Transistor (RF-SET):
        A Fast and Ultrasensitive Electrometer,
        Science 280, 1238 (1998).

[7]     L. Y. Gorelik et al.,
        Shuttle Mechanism for Charge Transfer in Coulomb Blockade
        Nanostructures,
        Phys. Rev. Lett. 80, 4526 (1998).

[8]     A. Erbe et al,
        Nanomechanical resonator shuttling single electrons at radio
        frequencies,
        Phys. Rev. Lett. 87, 096106 (2001).

[9]     D. V. Scheible et al.,
        Silicon nanopillars for mechanical single-electron transport,
        Appl. Phys. Lett.  84, 4632 (2004).

[10]   H. S. Kim et al.,
        Self Excitation of Nano-Mechanical Pillars,
        arXiv:0708.1646.

[11]   Y. Azuma et al.,
        One by one single-electron transport in nanomechanical Coulomb
        blockade shuttle,
        Appl. Phys. Lett. 91, 053120 (2007).

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