Charge Detection in an Array of CMOS Quantum Dots

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Charge Detection in an Array of CMOS Quantum Dots

Emmanuel Chanrion, David J. Niegemann, Benoit Bertrand, Cameron Spence, Baptiste Jadot, Jing Li, Pierre-André Mortemousque, Louis Hutin, Romain Maurand, Xavier Jehl, Marc Sanquer, Silvano De Franceschi, Christopher Bäuerle, Franck Balestro, Yann-Michel Niquet, Maud Vinet, Tristan Meunier, and Matias Urdampilleta

Phys. Rev. Applied 14, 024066 – Published 24 August 2020

Abstract

The recent development of arrays of quantum dots in semiconductor nanostructures highlights the progress of quantum devices toward a large scale. However, how to realize such arrays on a scalable platform such as silicon is still an open question. One of the main challenges lies in the detection of charges within the array. It is a prerequisite to initialize a desired charge state and read out spins through spin-to-charge conversion mechanisms. In this work, we use two methods based on either a single-lead charge detector or a reprogrammable single-electron transistor. By these methods, we study the charge dynamics and sensitivity by performing single-shot detection of the charge. Finally, we can probe the charge stability at any node of a linear array and assess the Coulomb disorder in the structure. We find an electrochemical potential fluctuation induced by charge noise comparable to that reported in other silicon quantum dots.

Received 26 January 2020
Revised 27 May 2020
Accepted 16 June 2020

DOI:https://doi.org/10.1103/PhysRevApplied.14.024066

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Capacitance Coulomb blockade Quantum information with solid state qubits Spin blockade

Double quantum dots Quantum dots

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Emmanuel Chanrion^1,*, David J. Niegemann ¹, Benoit Bertrand², Cameron Spence¹, Baptiste Jadot¹, Jing Li ³, Pierre-André Mortemousque², Louis Hutin², Romain Maurand³, Xavier Jehl³, Marc Sanquer ³, Silvano De Franceschi³, Christopher Bäuerle¹, Franck Balestro¹, Yann-Michel Niquet³, Maud Vinet², Tristan Meunier¹, and Matias Urdampilleta ^1,†

¹Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38402 Grenoble, France
²CEA, LETI, Minatec Campus, 38054 Grenoble, France
³Université Grenoble Alpes, CEA, IRIG, 38000 Grenoble, France

^*emmanuel.chanrion@neel.cnrs.fr
^†matias.urdampilleta@neel.cnrs.fr

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Vol. 14, Iss. 2 — August 2020

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Figure 1
(a) The $2 \times 4$ QD array. The silicon nanowire (blue) is covered with top gates (red), which are separated by spacers (green). The noncovered regions of the nanowire are highly doped to form electron reservoirs. (b) Cross section along the nanowire. (c) Cross section along one top gate. (d) SEM micrograph of a device similar to the ones used in the present study. (e) False-color SEM micrograph of the array using the same color code as in (a). The quantum dots (QD1–QD8) are localized below the top gates (1–8) in the corners of the nanowire. D, drain; S, source.
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Figure 2
(a) False-color SEM micrograph of the QD configuration in the SLQD detection mode. ”B” stands for “barrier gates,” where the voltage is set to $- 1$ V. (b) Equivalent electrical circuit of the device probed by dispersive readout. One quantum dot is used as an electrometer (SLQD) and is tunnel and capacitively coupled to the three neighboring QDs. Its gate is connected to an inductance to form an $L C$ resonant circuit that is probed by rf reflectometry. (c) Phase change of the resonant circuit as a function of $V_{SLQD}$ and $V_{1}$ . The signal lines correspond to a charge degeneracy of the electrometer dot, which experiences a shift in voltage for one electron added to QD1. The voltage shift corresponds to 2.4 linewidths of the detector. (d) Charge-stability diagram for QD1. (e) Simulation of the electron density inside the channel under the same polarization conditions as in the experiment and using the Thomas-Fermi approximation. A large density of electrons is present at the SLQD location, which overlaps with the QD6 potential. A large dot accumulates under the SLQD gate, and tends to spill over QD6, to which it is strongly coupled. D, drain; S, source.
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Figure 3
(a),(b) Stability diagrams for the (QD2, QD6) and (QD1, QD2) DQDs. The dispersive signal from the SLQD is plotted as a function of ( $V_{2}$ , $V_{6}$ ) and ( $V_{1}$ , $V_{2}$ ). (c) Stability diagram for the (QD2, QD6) DQD for extended charge configurations. We plot the shift in detector position (normalized by the peak linewidth) induced by a change in charge occupancy as a function of $V_{2}$ and $V_{6}$ . For each plot, the charge labeling is relative to the state at the bottom left of the diagram.
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Figure 4
(a) False-color SEM micrograph of the QD configuration in the SET detection mode. “B” stands for “barrier” ( $V = - 1$ V) and “R” stands for “reservoir” ( $V = 1.2$ V). (b) Charge-stability diagram for QD2. The derivative of the current through the device is plotted as a function of $V_{SET}$ and $V_{2}$ . In this case, the QD in front of QD2 is operated as a SET, while the other upper gates are set to high positive voltages (greater than $1.2 V$ ) to extend the reservoirs close to the SET. (c) False-color SEM micrograph of the QD configuration in the double-SET detection mode. The top linear array of quantum dots is operated as two SETs in series. The Coulomb blockade is probed by our measuring the current flowing through the structure. (d) Stability diagram for a (QD2, QD3) DQD in the few-electron regime. The detector is operated in the large-bias regime ( $3$ mV) to extend the region of sensitivity without the need for capacitive compensation. (e) Isodensity surfaces inside the channel computed in the Thomas-Fermi approximation at the following gate biases: $V = - 1 V$ on the barrier gates, $V = 1.2 V$ on the reservoir gates, $V = 0.8 V$ on the SET, and $V = 0.3 V$ on QD2 and QD3. As the bias is larger on the reservoir gates than on the SET, and because of the cross-capacitance between the upper and lower gates, the density in the SET reservoirs tends to spill toward QD3. This will further decrease the sensitivity of the SET to changes in the occupation of QD3. D, drain; S, source.
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Figure 5
Time-resolved measurement of a single charge tunneling out of QD2 probed by (a) dispersive and (b) current-based measurement for an integration time of 1 ms. The insets show the average of 150 time traces (solid lines). The QD2-lead tunnel rate $Γ_{t}$ is extracted with use of an exponential-decay model (dashed black line). (c),(d) Histograms of 8000 single-shot measurements with an integration of 1 ms. The signal-to-noise ratios are 7 and 15, respectively.
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Figure 6
(a) Coulomb peak of the SET located under $V_{2}$ . The inset shows derivative of the current against the gate voltage. (b) Power spectral density of the noise in the chemical potential on the two sides of the Coulomb peak at 350 mK. The blue curve is fit with use of a $1 / f^{β}$ model ( $β = 1.14$ ) and the red curve is fit with a function of the form $A / f^{β} + B / f^{2} / f_{c}^{2} + 1$ ( $β = 1.4$ and $f_{c} = 1$ Hz). (c) Stability diagram for the triple-dot system formed by QD2, QD6, and a defect in the channel.
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