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Physical Review B

Accuracy evaluation and mechanism crossover of single-electron transfer in Si tunable-barrier turnstiles

Gento Yamahata, Katsuhiko Nishiguchi, Akira Fujiwara

Published Apr 8, 2014• 32 citations
Publisher

Abstract

Using an error-counting scheme, we evaluated the accuracy of single-electron (SE) transfer in Si tunable-barrier turnstiles in a dilution refrigerator. The error counting was performed by shuttling SEs between a lead and a charge-accumulating node and detecting in real time the number of electrons in the node with an SE-resolution charge sensor. The best experimentally obtained error rate is about 100 parts per million (ppm), where the SE capture in the SE island occurs in thermal equilibrium due to the heating effect on SEs caused by pulse voltages applied to modulate the potential barrier. When we reduce the heating effect by suppressing the pulse voltages, there is a change in the SE transfer mechanism to nonequilibrium SE capture. We theoretically discuss the crossover point of the change. Moreover, at the minimum pulse voltage, the theoretical lower bound of the error rate estimated by fitting is on the order of 0.01 ppm. This suggests that Si SE-transfer devices are promising candidates for use as quantum current standards in metrology.

DOI
10.1103/physrevb.89.165302

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Using an error-counting scheme, we evaluated the accuracy of single-electron (SE) transfer in Si tunable-barrier turnstiles in a dilution refrigerator. The error counting was performed by shuttling SEs between a lead and a charge-accumulating node and detecting in real time the number of electrons in the node with an SE-resolution charge sensor. The best experimentally obtained error rate is about 100 parts per million (ppm), where the SE capture in the SE island occurs in thermal equilibrium due to the heating effect on SEs caused by pulse voltages applied to modulate the potential barrier. When we reduce the heating effect by suppressing the pulse voltages, there is a change in the SE transfer mechanism to nonequilibrium SE capture. We theoretically discuss the crossover point of the change. Moreover, at the minimum pulse voltage, the theoretical lower bound of the error rate estimated by fitting is on the order of 0.01 ppm. This suggests that Si SE-transfer devices are promising candidates for use as quantum current standards in metrology.
The dynamic capture of electrons in a semiconductor quantum dot (QD) by raising a potential barrier is a crucial stage in metrological quantized charge pumping. In this work, we use a quantum point contact (QPC) charge sensor to study errors in the electron capture process of a QD formed in a GaAs heterostructure. Using a two-step measurement protocol to compensate for 1/f noise in the QPC current, and repeating the protocol more than 106 times, we are able to resolve errors with probabilities of order 10−6. For the studied sample, one-electron capture is affected by errors in ∼30 out of every million cycles, while two-electron capture was performed more than 106 times with only one error. For errors in one-electron capture, we detect both failure to capture an electron and capture of two electrons. Electron counting measurements are a valuable tool for investigating non-equilibrium charge capture dynamics, and necessary for validating the metrological accuracy of semiconductor electron pumps.
We perform a theoretical study of nonequilibrium effects in charge transport through a hybrid single-electron transistor based on a small normal metal (N) island with the gate-controlled number of electrons, tunnel-coupled to voltage-biased superconducting (S) electrodes (SINIS). Focusing on the turnstile mode of the transistor operation with the gate voltage driven periodically, and electrons on the island being out of equilibrium, we find that the current quantization accuracy is a nonmonotonic function of the relaxation rate ${\mathrm{\ensuremath{\Gamma}}}_{\mathcal{F}}$ of the distribution function $\mathcal{F}(\ensuremath{\epsilon})$ on the island due to tunneling, as compared to the drive frequency fff, electron-electron $1/{\ensuremath{\tau}}_{ee}$, and electron-phonon $1/{\ensuremath{\tau}}_{eph}$ relaxation rates. Surprisingly, in the strongly nonequilibrium regime, $f\ensuremath{\gg}{\mathrm{\ensuremath{\Gamma}}}_{\mathcal{F}}\ensuremath{\gg}{\ensuremath{\tau}}_{ee}^{\ensuremath{-}1},{\ensuremath{\tau}}_{eph}^{\ensuremath{-}1}$, the turnstile current plateau is recovered, similarly to the ideal equilibrium regime, ${\ensuremath{\tau}}_{eph}^{\ensuremath{-}1}\ensuremath{\gg}{\mathrm{\ensuremath{\Gamma}}}_{\mathcal{F}}$. The plateau is destroyed in the quasiequilibrium regime when the electron-electron relaxation is faster than tunneling.
First I discuss various candidates of single-electron current pumps for quantum metrology. Then I focus on the hybrid normal-metal-superconductor turnstile in the form of a one-island single-electron transistor with one gate. The device demonstrates robust current plateaus at multiple levels of ef at frequency f. I discuss the various error mechanisms, based on our experiments and theoretical considerations. Ultimately the quantization accuracy is expected to be limited by either two-electron tunneling or by Cooper-pair-electron co-tunneling. We predict that it should be possible to achieve the metrological accuracy of 10-8, while maintaining the quantized current on the level of more than 10 pA, just by one turnstile with realistic parameters using aluminium as a superconductor. Recently we have managed to run ten turnstiles in parallel increasing the current level to above 100 pA. Work on suppressing the harmful sub-gap leakage current is in progress with encouraging experimental results.
Accuracy of single-electron currents produced in hybrid turnstiles at high operation frequencies is, among other errors, limited by electrons tunnelling in the wrong direction. Increasing the barrier transparency between the island and the leads, and the source-drain bias helps to suppress these events in a larger frequency range, although they lead to some additional errors. We experimentally demonstrate a driving scheme that suppresses tunnelling in the wrong direction hence extending the range of frequencies for generating accurate single-electron currents. The main feature of this approach is an additional AC signal applied to the bias with twice the frequency as the one applied to the gate electrode. This allows additional modulation of the island chemical potential. By using the new approach under certain parameters, we improve the single-electron current accuracy by one order of magnitude. Finally, we show through experimentally-contrasted calculations that our method can improve accuracy even in devices for which the usual gate driving gives errors ∼10−3\sim 10^{-3}∼10−3 at high frequencies and can bring them under 5×10−45\times 10^{-4}5×10−4.
The dynamic capture of electrons in a semiconductor quantum dot (QD) by raising a potential \nbarrier is a crucial stage in metrological quantized charge pumping. In this work, we use a quantum \npoint contact (QPC) charge sensor to study errors in the electron capture process of a QD formed in \na GaAs heterostructure. Using a two-step measurement protocol to compensate for 1/f noise in the \nQPC current, and repeating the protocol more than 106 times, we are able to resolve errors with \nprobabilities of order 106. For the studied sample, one-electron capture is affected by errors in \n30 out of every million cycles, while two-electron capture was performed more than 106 times \nwith only one error. For errors in one-electron capture, we detect both failure to capture an electron \nand capture of two electrons. Electron counting measurements are a valuable tool for investigating \nnon-equilibrium charge capture dynamics, and necessary for validating the metrological accuracy \nof semiconductor electron pumps.
We measure the average number of electrons loaded into an electrostatically-defined quantum dot (QD) operated as a tunable-barrier electron pump, using a point-contact (PC) charge sensor 1 micron away from the QD. The measurement of the electron number probes the QD loading dynamics even in the limit of slow gate voltage rise-times, when the pumped current is too small to measure. Using simulations we show that, with optimised QD-PC coupling, the experiment can make single-shot measurements of the number of electrons in the QD with sufficiently high fidelity to test the error rate of the electron pump with metrological precision.