Effect of Split Gate Size on the Electrostatic Potential and 0.7 Anomaly within Quantum Wires on a Modulation-Doped $\mathrm{GaAs}/\mathrm{AlGaAs}$ Heterostructure

Effect of Split Gate Size on the Electrostatic Potential and 0.7 Anomaly within Quantum Wires on a Modulation-Doped $GaAs / AlGaAs$ Heterostructure

L. W. Smith, H. Al-Taie, A. A. J. Lesage, K. J. Thomas, F. Sfigakis, P. See, J. P. Griffiths, I. Farrer, G. A. C. Jones, D. A. Ritchie, M. J. Kelly, and C. G. Smith

Phys. Rev. Applied 5, 044015 – Published 25 April 2016

Abstract

We study 95 split gates of different size on a single chip using a multiplexing technique. Each split gate defines a one-dimensional channel on a modulation-doped $GaAs / AlGaAs$ heterostructure, through which the conductance is quantized. The yield of devices showing good quantization decreases rapidly as the length of the split gates increases. However, for the subset of devices showing good quantization, there is no correlation between the electrostatic length of the one-dimensional channel (estimated using a saddle-point model) and the gate length. The variation in electrostatic length and the one-dimensional subband spacing for devices of the same gate length exceeds the variation in the average values between devices of different lengths. There is a clear correlation between the curvature of the potential barrier in the transport direction and the strength of the “0.7 anomaly”: the conductance value of the 0.7 anomaly reduces as the barrier curvature becomes shallower. These results highlight the key role of the electrostatic environment in one-dimensional systems. Even in devices with clean conductance plateaus, random fluctuations in the background potential are crucial in determining the potential landscape in the active device area such that nominally identical gate structures have different characteristics.

Received 12 August 2015

DOI:https://doi.org/10.1103/PhysRevApplied.5.044015

Physics Subject Headings (PhySH)

Mesoscopics Transport phenomena

Devices III-V semiconductors Quantum wires Two-dimensional electron gas

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

L. W. Smith^1,*, H. Al-Taie^1,2, A. A. J. Lesage¹, K. J. Thomas^3,†, F. Sfigakis¹, P. See⁴, J. P. Griffiths¹, I. Farrer^1,‡, G. A. C. Jones¹, D. A. Ritchie¹, M. J. Kelly^1,2, and C. G. Smith¹

¹Cavendish Laboratory, Department of Physics, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
²Centre for Advanced Photonics and Electronics, Electrical Engineering Division, Department of Engineering, 9 J. J. Thomson Avenue, University of Cambridge, Cambridge CB3 0FA, United Kingdom
³Department of Electronic and Electrical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom
⁴National Physical Laboratory, Hampton Road, Teddington, Middlesex TW11 0LW, United Kingdom

^*Corresponding author. luke.smith@wisc.edu Present address: Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA.
^†Present address: Department of Physics, Central University of Kerala, Riverside Transit Campus, Kasaragod 671 314, Kerala, India.
^‡Present address: Department of Electronic & Electrical Engineering, University of Sheffield, Sheffield S1 3JD, United Kingdom.

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Vol. 5, Iss. 4 — April 2016

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Figure 1
(a) Typical trace of conductance $G$ as a function of the voltage applied to the split gate $V_{SG}$ . The vertical and horizontal dotted lines indicate the 1D definition voltage ( $V_{d}$ ) and conductance ( $G_{d}$ ), respectively. The left-hand arrow indicates pinch-off voltage $V_{p}$ . The inset shows a schematic split-gate device with dimensions $L$ and $W$ labeled. Source and drain Ohmic contacts are marked $S$ and $D$ , respectively. (b) Scatter plot of pinch-off voltage as a function of split-gate length $L$ . The triangles (circles) represent data from devices of width $W = 0.4$ $(0.6) μ m$ . The diamonds and error bars show the mean and standard deviation for each $L$ , respectively, offset horizontally by $0.1 μ m$ for clarity. Panels (c) and (d) show $V_{d}$ as a function of $L$ , for $W = 0.4$ and $0.6 μ m$ , respectively.
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Figure 2
Percentage of devices showing clean quantization as a function of split-gate length $L$ . Panels (a) and (b) show data for widths $W = 0.4$ and $0.6 μ m$ , respectively. The triangles (circles) indicate devices for which the first and second (first, second, and third) plateaus occur within $\pm 0.1 G_{0}$ , after correcting for series resistance.
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Figure 3
(a) Gray-scale diagram of the transconductance $d G / d V_{SG}$ as a function of $V_{SG}$ and source-drain bias $V_{SD}$ , from a typical device with dimensions $L$ $(W) = 0.4$ (0.4). Black (white) regions correspond to high (low) transconductance, i.e., transitions between plateaus (the plateaus themselves). The 1D subband spacings are estimated by the crossings of peaks in the transconductance [31] highlighted by dashed lines. Subband spacing $Δ E_{2, 3}$ is labeled for illustrative purposes. (b) Cumulative 1D subband spacings $Δ E_{n, m}$ as a function of pinch-off voltage $V_{p}$ . The blue, red, and green symbols correspond to $Δ E_{1, 2}$ , $Δ E_{1, 3}$ , and $Δ E_{1, 4}$ , respectively. Unique symbols represent devices of each size, as described in the legend. The error bounds show the cumulative error in the estimate. Data for $Δ E_{1, 3}$ and $Δ E_{1, 4}$ are offset vertically by 1 and 4 meV, respectively, for clarity. (c)–(e) Scatter plots of $Δ E_{n, n + 1}$ against $L$ for $n = 1$ , 2, and 3, respectively (to avoid confusion, the error bars on individual data points are not shown). The diamonds show the average for each $L$ (offset horizontally by $0.1 μ m$ for clarity), and error bounds indicate the average error.
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Figure 4
(a),(b) Lever arm $α_{1}$ as a function of lithographic length $L$ and 1D subband spacing $Δ E_{1, 2}$ , respectively. The diamonds in panel (a) represent the mean for each $L$ (offset by $0.1 μ m$ for clarity), and the error bars indicate the average error. (c) Experimentally measured conductance $G$ as a function of split-gate voltage $V_{SG}$ , for an example device (solid line). The dashed line shows a fit to the data using a modified saddle-point model. The transition between plateaus gives an estimate of barrier curvature $ℏ ω_{x, n}$ . (d) Characteristic length of the potential barrier $\sqrt{ℏ / m^{*} ω_{x, 1}}$ as a function of gate length $L$ . The diamonds and error bars represent the average value and the average error, respectively (offset by $0.1 μ m$ for clarity). (e) Curvature of the potential barrier $ℏ ω_{x, 1}$ as a function of $Δ E_{1, 2}$ . (f) Lever arm $α_{1}$ as a function of the characteristic length of the potential barrier. The different symbols in panels (b), (e), and (f) represent data for different length split gates as defined in the legend above panel (b).
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Figure 5
(a) Fitted conductance $G_{f} / G_{0}$ for the first 1D subband from 11 devices. Data are collapsed onto a universal curve by aligning $G_{f} / G_{0} = 0.5$ with $V_{SG} = 0$ , then scaling $V_{SG}$ by $α_{1} e / ℏ ω_{x, 1}$ . (b) Corresponding experimentally measured conductance $G_{e} / G_{0}$ , where the data are offset and scaled using the same parameters as (a). For $G_{e} / G_{0} < 0.5$ , the traces collapse onto a similar curve. Above $0.5 G_{0}$ , variations arise due to the differences in the 0.7 anomaly. (c) $G_{e} / G_{0}$ as a function of barrier curvature $ℏ ω_{x, 1}$ at fixed values of the scaled voltage axis $κ$ . From bottom to top, $κ$ increases from $- 0.5$ to 0.75 in steps of 0.25 [corresponding to vertical dashed lines, left to right, in panel (b)]. The dashed lines show a linear least-squares fit to $G_{e} / G_{0}$ for each value of $κ$ , as a guide to eye. (d) Conductance $G_{e} / G_{0}$ as a function of spacing between the first and second 1D subbands $Δ E_{1, 2}$ . In panels (c),(d), data points for each length split gate are indicated by the symbols defined in the legend.
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Physical Review Applied

Effect of Split Gate Size on the Electrostatic Potential and 0.7 Anomaly within Quantum Wires on a Modulation-Doped GaAs/AlGaAs Heterostructure

L. W. Smith, H. Al-Taie, A. A. J. Lesage, K. J. Thomas, F. Sfigakis, P. See, J. P. Griffiths, I. Farrer, G. A. C. Jones, D. A. Ritchie, M. J. Kelly, and C. G. Smith

Phys. Rev. Applied 5, 044015 – Published 25 April 2016

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Effect of Split Gate Size on the Electrostatic Potential and 0.7 Anomaly within Quantum Wires on a Modulation-Doped $GaAs / AlGaAs$ Heterostructure