NTT Basic Research Laboratories (NTT-BRL) and the National Physical Laboratory (NPL) in UK have performed high-accuracy measurements of a single-electron transfer device comprising silicon transistors^*1 and demonstrated single-electron transfer at 1 GHz (10⁹ Hz) with a world-record accuracy in the gigahertz regime: an error rate^*2 of less than 9.2 × 10^-7.

Since high-accuracy single-electron transfer leads to a current with high accuracy, our result is an important step toward the realization of a current standard^*3, which corresponds to a ruler to measure electric current. A current standard based on the single-electron transfer would be one that could most directly realize the ampere (the base unit of electric current), which, according to a recent proposal, should be redefined. Furthermore, it could be used for the quantum metrology triangle^*4 experiments, which check the consistency of fundamental physical constants. This would significantly contribute to the field of the fundamental physics.

This work will be published in the online version of "Applied Physics Letters" on the 5th of July, 2016 (EST).

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Background

It was proposed in 2011 that the International System of Units (SI)^*5 be redefined using invariants of nature such as the Planck constant h and the elementary charge e (Fig. 1). In the redefinition, the definition of the ampere (the base unit of electric current) will be changed. The new ampere will be set by generating a current ef (f: frequency) using a current standard, with the numerical value of e fixed (e is now a measured value). Since a single-electron transfer device, which can convey electrons one by one using clock control, connects e to the ampere (Fig. 1), it is attracting much attention as a device that could be used for the most direct current standard. Furthermore, if a high-accuracy current standard based on single-electron transfer is realized, it could be used for the quantum metrology triangle experiments (Fig. 1). Since such experiments will enable us to check the consistency of fundamental physical constants, they will contribute to the field of fundamental physics.

A practical current standard must operate at high speed, corresponding to a high current level, with high accuracy. Toward this goal, NTT-BRL have been studying single-electron transfer devices using silicon transistors. Silicon nanofabrication techniques accumulated over time have succeeded in greatly reducing the size of silicon devices. This is important for achieving high-accuracy operation suitable for the current standard. To show the expected high-accuracy operation, we needed a detailed evaluation of the transfer accuracy, but the measurement condition had not been optimized. In addition, gallium arsenide-based single-electron transfer devices, in which high accuracy was previously reported, have not been able to operate at more than 1 GHz without a significant loss of accuracy.

Achievements

We performed high-accuracy measurements of a current generate using a silicon single-electron transfer device (Fig. 2) comprising silicon transistors at 1 GHz and achieved a world-record accuracy in the gigahertz regime: a transfer error rate of less than 9.2 × 10^-7 (Fig. 3). The silicon single-electron transfer device was fabricated by NTT, and the measurements were performed by using high-accuracy current measurement system (Fig. 4 and Fig. 5) at NPL in UK. The value is about two orders magnitude better than that obtained from conventional measurements of silicon single-electron transfer devices. In addition, we performed a similar experiment at 2 GHz, which shows an error rate of about 3 × 10^-6. This indicates that our device breaks the 1-GHz barrier and is suitable for high-speed operation.

Details of measurements and observation

1. Device structure: We fabricated silicon transistors with a double-layer gate structure (Fig. 2). The lower layer comprises two fine gate electrodes (entrance gate G1 and exit gate G2) formed on a silicon nanowire. The upper layer is a large gate electrode, which covers the entire region of the silicon nanowire.
2. Operating principle: By applying negative voltages to the entrance and exit gates, two electron potential barriers are formed in the silicon nanowire, leading to a fine region (single-electron island^*6) between the two barriers (Fig. 2). In addition, by applying a high frequency signal with frequency f to the entrance gate, a single electron is captured by the island from the left source lead and eventually ejected to the right drain lead. When one electron is transferred in each cycle, the output current is ef. Since the height and width of the entrance barrier are largely modulated to transfer electrons, this type of device is referred to as a tunable-barrier single-electron transfer device.
3. High-speed characteristics: Figure 6 shows transfer current measured with a conventional measurement system (Fig. 4). The horizontal axis is voltage applied to the exit gate (V_Exit), which is here used to tune the potential of the single-electron island. We observe a current plateau^*7 at up to 6.5 GHz. The 6.5-GHz operation is the fastest operation to date, although the accuracy is worse than that at 1 and 2 GHz.
4. Accuracy evaluation: Figure 3 shows results of the high-accuracy current measurement at 1 GHz, performed using the high-accuracy measurement system (see Fig. 4 and Technical Features 3-2) at NPL. The current plateau in Fig. 3 corresponds to an expansion of the flattest region of the characteristics at 1 GHz in Fig. 6. The current measurements at the current plateau proves that the transfer current with an uncertainty^*8 of 9.2 × 10^-7 matches ef. This indicates that the operation has high accuracy; that is, the transfer error rate is less than 9.2 × 10^-7. In addition, since this value is determined by the uncertainty of the measurement system, we expect that the actual transfer error rate is much lower (theoretically, it is less than 10^-8).

Technical Features

1. Fabrication techniques of silicon nanodevices
   NTT-BRL have been accumulating techniques for fabricating nanometer-scale silicon transistors at a wafer level for a long time. We can fabricate devices that have the double-layer gate structure and small single-electron island with high yield. With decreasing size of the single-electron island, the electron charging energy determining the single-electron transfer accuracy becomes large, leading to high accuracy operation. The high-accuracy operation in this study was achieved by making confinement region by applying gate voltages to a silicon wire with a diameter on the order of 10 nm.
2. High-accuracy current measurement system [techniques at National Physical Laboratory (NPL)]
   Commercial current meters have a measurement uncertainty of about 10^-4 at best. To achieve higher accuracy measurements, we compared the single-electron transfer current with a reference current generated using a high-accuracy 1-GΩ standard resistor (Fig. 4 and Fig. 5). Since the standard resistor is precisely calibrated, we can perform high-accuracy measurements with an uncertainty of about 10^-6. By using this method, we demonstrated high-accuracy operation, which was difficult to achieve with the conventional measurement systems we had used. In addition, measurements of devices fabricated using different materials at different research institutes have also been performed. Taken together, these results and ours indicate that a tunable-barrier single-electron transfer device has universality^*9 with a level of 10^-6.

Future Plans

We aim to demonstrate operation at higher accuracy toward the realization of a practical current standard. One approach is to improve the high-accuracy measurement system. The next target is a high-accuracy measurement with an uncertainty of 1 × 10^-7 (in collaboration with the quantum current standard project in Europe). Another approach is to count the number of transferred electrons using a charge detector with single-electron resolution. This could prove an error rate of less than 1 × 10^-8, which is the target value of the current standard (Fig. 7). In addition, we will investigate why the error rate increases at the 6.5-GHz operation. When this work is successfully completed, we aim to perform the quantum metrology triangle experiments with high precision and to develop devices that directly realize the new ampere.

Publication information

G. Yamahata, S. P. Giblin, M. Kataoka, T. Karasawa, A. Fujiwara
"Gigahertz single-electron pumping in silicon with an accuracy better than 9.2 parts in 10⁷" Applied Physics Letters (2016).

Related information

NPL also issues a press release about this work.
http://www.npl.co.uk/news/record-speed-and-accuracy-achieved-with-single-electron-pumps

Glossary

*1 ... Silicon transistor
These are devices fabricated using semiconducting silicon, which can switch or amplify electrical signals. In this work, we used field-effect transistors, in which electric current flowing in silicon is turned on or off by applying a voltage to a gate electrode. The gate electrode is formed on silicon via an insulator consisting of silicon dioxide.

*2 ... Error rate
To be precise, this is the relative error rate, which is the transfer-error probability when a single electron is transferred. For example, an error rate of 1 × 10-6 means that an average of one error occurs during a million transfers.

*3 ... Current standards
These are standards for the base unit of electric current (the ampere). The ampere is now defined by a force produced by the same current flowing through two infinite-length conductors in a vacuum. However, since it is difficult to exactly achieve the conditions described in the definition in actual experiments, it has been suggested in the redefinition of the SI base units that the ampere be set by fixing the elementary charge e. In a practical current standard based on single-electron transfer, an error rate of less than 10^-8 and a current level of higher than 1 nA (a frequency higher than 6.3 GHz) are desirable values. By using a device with such values, it is possible to perform quantum metrology triangle experiments with high precision.

*4 ... Quantum metrology triangle
This is an experiment in which a current generated from a single-electron transfer device is compared with that generated from a combination of the quantum Hall resistance standard and Josephson voltage standard. The single-electron transfer and Josephson effect respectively lead to a transfer current and Josephson voltage from a frequency f. The current is proportional to the voltage through a quantum Hall resistor (Ohm’s law). As a result, the relation between the three can be described using a triangle (Fig. 1). From this experiment, one can check the consistency of the fundamental physical constants R_K, K_J, e, and h.

*5 ... International System of Units (SI)
These are internationally adopted units, in which seven base units — time [the second (s)], length [the meter (m)], mass [the kilogram (kg)], electric current [the ampere (A)], thermodynamic temperature [the kelvin (K)], amount of substance [the mole (mol)], and luminous intensity [the candela (cd)] — are defined. Other units are derived from these base units. In the proposed redefinition of the SI units, instead of defining the base unit, fundamental physical constants are fixed and the base units are set from the constants (Fig. 1).

*6 ... Single-electron island
This is a fine island, in which the electron charging energy is sufficiently larger than the energy fluctuation originating from heat. Therefore, the constant number of electrons can be accumulated in it. The number of accumulated electrons can be controlled by externally applying voltage. In this study, we used a voltage applied to the exit gate G2 (V_Exit) to control the number of electrons.

*7 ... Current plateau
This is a region where current levels are almost constant when a voltage is changed. Since the region is expected to be used as a standard of an electric current, it must be sufficiently flat and wide. When the flat region is wide, the device has a high transfer accuracy and is strong against voltage noises.

*8 ... Uncertainty
In this press release, we use this word in the sense of relative standard uncertainty. Uncertainty is a parameter that represents the reliability of measurement results. With a certain probability, a true value exists within a range of uncertainty. Uncertainty with the size of a standard deviation is referred to as standard uncertainty. Standard uncertainty divided by a measured value is referred to as relative standard uncertainty.

*9 ... Universality
This is one of important points for application to standards. The universality of a single-electron transfer device means that, when we use a sample with a certain quality, a current level of ef is achieved independently from the place of fabrication and measurement, material, and device structure.