To develop novel integrated circuits for standards and metrology based
on the unique properties of electronic devices that can manipulate
and detect individual electrons.
This project addresses three different needs: a fundamental representation of capacitance, a fundamental representation of electrical current, and general applications of single-electron tunneling (SET) devices, with a particular emphasis on future integrated nano-electronics.
For the first need: NIST is working on the development of intrinsic standards based on fundamental physical principles, such as the volt, based on the Josephson effect, and the ohm, based on the quantum Hall effect. The present representation of the SI farad is through silica-based artifact capacitors. Although these capacitors are of high quality, they are susceptible to drift in time and they may depend on other parameters such as temperature, pressure, and frequency. The metrology community, including both the national standards laboratories and domestic secondary calibration laboratories, needs a capacitance representation that is based on fundamental physical principles and not on properties of individual physical artifacts.
For the second need: At present, there is no fundamental representation of current; the representation of current is via the representations of voltage and resistance. Though these representations are based on fundamental physical principles and are of high quality, the representation of current is dependent upon them. An independent representation of current could provide significant additional confidence in the coherency of the representations of the SI electrical units through closure of the "metrology triangle" V = I R with all measurements based on fundamental constants.
For the third need: Various classes of future nanoelectronics beyond CMOS are projected to work with one or a few electrons. These include molecular electronics, semiconductor-based integrated circuits using single-electron memory or logic, and quantum computing (QC). For example, in QC, we are using our expertise to elucidate properties of transfer of superconducting "Cooper pairs," which are the basic mechanism for one realization of QC circuits. As another example, one endemic problem in single-electron logic is the "charge offset" phenomenon, which makes it difficult or impossible to integrate multiple SET-based devices together; again, we are using our expertise to attack this problem. In all three cases, our project has the capability to offer early guidance to these burgeoning fields, to assist companies in pursuing productive areas, and rejecting problematic ones. Because these fields are not yet mature, our relatively small efforts can yield large payoffs for the customers as they progress.
Our basic strategy for this project is to develop important applications in our areas of world-leading expertise. These areas, which are all intimately related to the single-electron tunneling transistor and other SET devices, include:
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Atomic force microscope image of an electron counter, the heart of a new capacitance standard based on counting electrons. The standard, shown in the schematic, consists of the electron counter, a capacitor, and a single-electron electrometer to monitor the process (not shown). The electron counter, based on seven nanometer-scale tunnel junctions in series, can "pump" electrons onto the capacitor with an error rate of less than 1 electron in 108. |
At present, the most mature application of SET devices within the project is using SET devices to develop an electron-counting capacitance standard (ECCS). By depositing a counted number, N, of electrons (of order 108) onto the plate of a capacitor (of value approximately 1 pF) and measuring the resulting voltage (approximately 1 V), one can calibrate the capacitance, C, through the definition of capacitance, C = Q / V, with the charge determined by the number of electrons, Q = N e.
A prototype of the ECCS has been demonstrated with repeatability on the order of 1 part in 107 and a relative standard uncertainty of 1 part in 106. The major tasks remaining are to continue to reduce the uncertainty and to develop a robust system for possible widespread use.
Using the expertise described earlier, we are pursuing three tracks towards a current standard based on counted electrons:
SET devices also can be
used as tools to measure the performance of other devices that operate
with individual electrons.
We are pursuing the study of electrostatic charge reconfiguration of
self-assembled monolayers (SAM) by fabricating and assembling a "nano-gap" capacitor.
This device, made using Si micromachining, allows us to make a capacitor
with a gap of only 50 nm, but an area of (80 mm)2; this area is large
enough to give us a measurable signal, while the gap is small enough
to measure charge motion over 1 nm or less.
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Demonstration of pumping electrons on and off a prototype capacitance standard. |
At present, the most advanced application for SET devices within the project is a new capacitance standard based on the fundamental definition of capacitance. A prototype of an Electron Counting Capacitance Standard (ECCS) has been demonstrated, with a repeatability of 1 part in 107 and a relative standard uncertainty of 1 part in106. This brings to fruition a decade of research aimed at creating this standard and shows the way toward even better performance in the future. The components of the standard are an electron counter, a capacitor, and an electrometer to monitor the process, as illustrated in the figure. The electron counter, shown in the Atomic Force Microscope image below, is based on seven nanometer-scale tunnel junctions in series. It can "pump" electrons onto the capacitor with an error rate of less than one electron in 108. The electron pumping is monitored with an SET-based electrometer fabricated on the same chip as the pump, with a charge sensitivity better than 10-2 electrons. The capacitor operates at cryogenic temperatures and uses vacuum as the dielectric, resulting in a frequency-independent capacitance. To operate the ECCS approximately 100 million electrons are placed, one at a time, on the capacitor. The voltage across the capacitor is then measured, resulting in a calibration of the cryogenic capacitor. This capacitance can then be transferred to room temperature using a standard ac bridge measurement technique. The figure below shows the result of pumping electrons on and off the capacitor, with a 20 second pause when fully charged to measure the voltage. The result is a value of capacitance in terms of the charge of the electron.
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Switching current histograms (z-axis) vs. gate polarization charge on a superconducting Cooper pair transistor. The double peaks for fixed gate polarization indicate that quasiparticles are poisoning the transistor island. |
In collaboration with Professor Michel Devoret (Yale), we have performed a number of experiments which verified a model for erratic quasiparticle tunneling in superconducting Cooper pair transistors (these are the superconducting versions of the SET). This phenomena, quasiparticle "poisoning," will limit the operation of the superconducting Cooper pair pump as well as charge-based qubits. Our work showed that the gap energies in the leads versus the island played a significant role in determining these poisoning rates.
In addition,
we have confirmed a "remote poisoning" phenomena,
whereby a voltage-biased junction device can cause poisoning in other
devices on the same chip, even if it is electrically isolated. This has important
implications for the electrometry that we will use in the Cooper pair
pump, as well as in charge-based qubits.
In collaboration with Konrad Lehnert at JILA, we have
assembled and demonstrated operation of a rf-SET at NIST, a version
of an SET electrometer read out by microwave reflectometry. This approach
greatly increases the bandwidth of the electrometer (to 3 MHz in our
present setup) and improves the charge resolution (to 50 µe/Hz1/2).
This is the basic technology we will use to perform the passive electron
counting experiments. Future work will focus on expanding the bandwidth
and narrowing the charge resolution to perform better than the quantum
limit.
Using techniques similar to the rf-SET measurement, we have measured
the modulation of the Josephson inductance of a Cooper pair transistor
while biased on the supercurrent branch. In this example, when a
quasiparticle enters the transistor island, the Josephson inductance
shifts causing a change in reflected power. In this plot, when a
quasiparticle has entered the island (the "odd state"), the reflected power increases. With this technique
we can observe these quasiparticle tunneling events in the time domain as
a telegraph signal.
Conventional operation of the rf-SET involves biasing the device on the quasiparticle branch of the current-voltage characteristic. This quasiparticle current creates quasiparticles in remote devices (which may be charge qubits or Cooper pair pumps), that may prevent successful operation. Recently, we have successfully demonstrated that it is possible to measure the Josephson inductance of a Cooper pair transistor while it is biased on the supercurrent branch. Using the same techniques as in the rf-SET, we have measured the quasiparticle poisoning in a single Cooper pair transistor in the time domain. Since this technique operates on the supercurrent branch we expect minimal generation of quasiparticles.
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a) Schematic cross-section of our SET electrometer integrated on a GaAs chip containing self-assembled quantum dots. b) SEM micrograph of an SET electrometer. We have identified single electron tunneling events into individual quantum dots located beneath the electrometer. |
The past two years have produced significant progress towards the development of a single-photon turnstile, a device designed to generate single photons on demand using semiconductor quantum dots (QD) and single-electron principles. A key step towards this goal is to measure the tunneling of single electrons onto individual quantum dots. We have succeeded in making these measurements by integrating an SET electrometer over a low density field of GaAs quantum dots (grown by Rich Mirin of the Optoelectronics Division). A schematic cross-section of the device is shown below, along with a scanning electron micrograph of the SET electrometer. Such nanoscale device integration is difficult and required extensive process development. Using these devices, we have clearly identified the addition of single electrons onto single quantum dots located below the SET. We have counted up to 3 electrons added to a single dot, and have measured the energy spectrum associated with adding electrons on this dot. This work has led to a recent publication showing how adding a gate electrode to the QD structure can improve its performance as a source of single photons for quantum cryptography.
Our work in collaboration with a group in NTT (Nippon Telephone and Telegraph), Japan, has made a great deal of progress in investigating Si-based devices that can control the motion of single electrons. In the past two years, we have demonstrated such control in three different types of devices, pumps, turnstiles, and CCDs. The most promising device for the future is the CCD, both because we have recently demonstrated in subsequent work that such devices can be made with improved reliability and homogeneity, and because we demonstrated that this device has the potential to run at higher speed. In one of our publications, we showed that the CCD can pump single electrons at rates as fast as 100 MHz, corresponding to 15 pA; this is an improvement by about a factor of five over previous results in metal-based pumps. However, we have to note that we were not able to do detailed error rate measurements in the CCDs; this work is now occurring.
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The pumping current in a CCD versus control voltage. The plateaus correspond to pumping 1e, 2e, ..., per cycle; note that the plateaus are at the same level for frequencies between 5 and 100 MHz. |
We have also recently finished our first theoretical analysis of error mechanisms and error rates in Si-based turnstiles and CCDs. From a fundamental point of view, the most interesting result was the elucidation of a new mechanism, the "dynamical error." This error can result from the inability of the quantum dot to form the Coulomb blockade quickly enough; research into this mechanism should advance fundamental understanding of Coulomb blockade. By considering in addition thermal, frequency, and heating errors, we predicted that with devices accessible at present we should be able to achieve 0.01 ppm error rates at frequencies up to 200 MHz. Of course, we need to perform the experimental work to verify or refute these predictions.
More recently, we have done a detailed study of the SET transistor behavior of several different devices made using the CCD architecture. In addition to an interesting array of fundamental properties, we found that in three different devices the parameters (specifically, a variety of cross capacitances) vary by no more than 15 percent between the devices. In previous fabrications using the pattern-dependent oxidation process, the homogeneity was no better than 50 percent, and sometimes much worse. This substantial improvement in homogeneity makes it much more likely that we should be able to integrate devices for general applications, and specifically to parallelize a number of CCDs to get a higher value of current.
O. Naaman and J. Aumentado, "Time-domain measurements of quasiparticle tunneling rates in a single-Cooper-pair transistor," Phys. Rev. B 73, 172504 (2006).
O. Naaman and J. Aumentado, "Poisson Transition Rates from Time-Domain Measurements with a Finite Bandwidth," Phys. Rev. Lett. 96, 100201 (2006)
K. D. Osborn and M. W. Keller, "Single-photon pump," to appear in Appl. Phys. Lett. (2006).
Akira Fujiwara, Neil M. Zimmerman, Yukinori Ono, Yasuo Takahashi, "Current quantization due to single-electron transfer in Si-wire charge-coupled devices," Appl. Phys. Lett. 84, 1323 (2004) .
Neil M. Zimmerman, Emmanouel Hourdakis, Yukinori Ono, Akira Fujiwara, Yasuo Takahashi, "Error Mechanisms and Rates in Tunable-Barrier Single-Electron Turnstiles and CCD's," J. Appl. Phys. 96, 5254 (2004).
K. D. Osborn, M. W. Keller, and R. P. Mirin, "Single-electron transistor spectroscopy of InGaAs self-assembled quantum dots," Physica E 21, 501-505 (2004).
J. Aumentado, M. W. Keller, J. M. Martinis, and M. H. Devoret, "Nonequilibrium Quasiparticles and 2e Periodicity in Single-Cooper-Pair Transistors," Phys. Rev. Lett. 92, 066802 (2004).
Yukinori Ono, Neil M. Zimmerman, Kenji Yamazaki and Yasuo Takahashi, "Turnstile Operation Using a Silicon Dual-Gate Single-Electron Transistor," Jpn. J. Appl. Phys. 42, L1109 - 11 (2003).
X. Jehl, M. W. Keller, R. L. Kautz, J. Aumentado, and J. M. Martinis, "Counting Errors in a Voltage-Biased Electron Pump," Phys. Rev. B 67, 165331 (2003).
Neil M. Zimmerman, Mahmoud A. El Sabbagh, and Yicheng Wang, "Larger Value and SI Measurement of the Improved Cryogenic Capacitor for the Electron-Counting Capacitance Standard." IEEE Transactions on Instrumentation and Measurement 52, 608 - 11 (2003)
M. W. Keller, "Standards of current and capacitance based on single-electron tunneling devices," Recent Advances in Metrology and Fundamental Constants - FERMI School CXLVI, Varenna, Italy, ed. T.J. Quinn, S. Leschiutta, and P. Tavella, IOS Press, Amsterdam, pp. 291-316, (2001).
M. W. Keller, A. L. Eichenberger, J. M. Martinis, N. M. Zimmerman, "A capacitance standard based on counting electrons," Science 285, 1706 (1999).