Electron–Hole Confinement Symmetry in Silicon Quantum Dots

Letter pubs.acs.org/NanoLett

Electron−Hole Confinement Symmetry in Silicon Quantum Dots Filipp Mueller, Georgios Konstantaras, Paul C. Spruijtenburg, Wilfred G. van der Wiel, and Floris A. Zwanenburg* NanoElectronics Group, MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands ABSTRACT: We report electrical transport measurements on a gate-defined ambipolar quantum dot in intrinsic silicon. The ambipolarity allows its operation as either an electron or a hole quantum dot of which we change the dot occupancy by 20 charge carriers in each regime. Electron−hole confinement symmetry is evidenced by the extracted gate capacitances and charging energies. The results demonstrate that ambipolar quantum dots offer great potential for spin-based quantum information processing, since confined electrons and holes can be compared and manipulated in the same crystalline environment. KEYWORDS: quantum dots, spin qubits, quantum information processing, ambipolar transport, silicon, MOSFET

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Isolated electrons in intrinsic silicon have intensively been studied in MOSFET-based12,17,18 and dopant-based13,19−22 QDs as well as Si/SiGe heterostructure QDs.23 In contrast, confined holes24 in intrinsic silicon are relatively unexplored. Experiments on isolated holes in gate-defined MOSFET structures indicate that holes localize easier in potential fluctuations forming unintentional QDs.25,26 The connection between transport properties and the complex structure of the valence subbands27 is still unclear and makes the realization of intentional hole QDs both challenging and interesting. In this Letter, we present electrical transport measurements on ambipolar devices in intrinsic silicon, resulting in four key findings: (i) the realization of a gate-defined QD structure fully operational in the hole as well as the electron regime; (ii) the creation of an intentional hole QD defined between two barrier gates; (iii) comparison of confined electrons and holes in the same crystalline environment in intrinsic silicon; (iv) observation of electron−hole confinement symmetry. While usually different devices must be fabricated to investigate the two regimes, the ambipolar devices used here ensure the confinement of both charge carriers in the same crystalline environment including, among others, charge traps, impurities, and surface roughness, which are different for each device. This makes the presented ambipolar device a reliable and essential tool for the direct comparison of electron and hole properties. A schematic top-view and cross-section of our ambipolar double-barrier MOSFET device is shown in Figure 1. A nearintrinsic Si(100) wafer (ρ > 10 000 Ωcm) is used as a substrate. Phosphorus (n++) and boron (p++) implanted regions serve as

lectron spins in quantum dots (QDs) are promising candidates for quantum bits (qubits) in a quantum computer.1 Much progress has been made in GaAs/AlGaAs QDs.2−7 However, quantum information processing based on the spin degree of freedom requires long spin coherence times, which are limited in III−V systems because of the nonzero nuclear-spin-bath that causes dephasing via the hyperfine interaction.8,9 In contrast, longer electron-spin coherence times have been reported for silicon due to its weak spin− orbit and hyperfine coupling.10,11 For isotopically purified 28Si, which has zero nuclear magnetic moment, electron-spin coherence times in the order of milliseconds have been reported.12,13 So far, most experiments have focused on electron spins, but hole spins offer great potential for spin-based quantum information processing as well. A hole-spin qubit in silicon can benefit from its finite spin−orbit coupling, because it allows efficient electric-field-driven spin resonance applicable via local gate electrodes.14−16 Although it is still unclear whether the electron spin or the hole spin is most suitable as a qubit, analogous to classical complementary metal-oxide-semiconductor (CMOS), a “quantum CMOS” technology is conceivable. Ambipolar devices are beneficial since both few-electron and few-hole quantum dots can be made in a single device. This will open a series of experiments, investigating, for example, the electron−hole symmetry of orbital excited states, the spin filling of electrons into valleys and holes into valence subbands and the suitability of electron-spin and hole-spin qubits in the same crystalline environment. Ambipolar device operation has previously been reported for materials, such as black phosphorus,28,29 graphene,30 carbon nanotubes,31,32 siliconon-insulator (SOI),33 bottom-up grown Si nanowires34,35 and Ge QDs.36 © XXXX American Chemical Society

Received: April 30, 2015 Revised: June 30, 2015

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DOI: 10.1021/acs.nanolett.5b01706 Nano Lett. XXXX, XXX, XXX−XXX

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Figure 2. Local charge carrier depletion in the Si channel. (a) Turn-on and pinch-off curves of a double barrier device. Arrows indicate the ramping directions of the different gates. For the black curve all gates are ramped simultaneously. For the barrier gate sweeps the lead gate and the other barrier gate are fixed at ±3.5 V. Both barriers can pinch off the source-drain current in the electron (green) as well as hole (red) regime. (b) Pinch-off curves for both barrier gates of 4 devices. Data taken at T = 4.2 K.

Figure 1. Ambipolar silicon quantum dot device. Schematic (a) top view and (b) cross section of the ambipolar QD device. Dark green and dark red areas are implanted regions that serve as electron and hole reservoirs, respectively. Gate electrodes are patterned on top of a thin SiO2 layer. A lead gate overlaps both implanted regions on the source and the drain side. Electrons (green) or holes (red) accumulate at the Si/SiO2 interface for positive (negative) applied lead gate voltages VL forming a two-dimensional electron (hole) gas, 2DEG (2DHG). Two barrier gates, B1 and B2, create tunnel barriers to the QD (middle panel a). (c) Atomic force micrograph of a measured device.

To illustrate moving back and forward between the electron and hole transport regimes, and local control of the electrochemical potential in both regimes, we measure the source-drain current ISD for different gate configurations of a double barrier device (Figure 2a, VSD = 1 mV and T = 4.2 K). First, we measure the current while simultaneously increasing the voltage of all gates up to 3.5 V (−3.5 V), a so-called turn-on curve. For gate voltages V > 1.9 V, the conduction band is pulled under the Fermi level. Electron transport occurs because energy states become available in the conduction band. Analogously, hole transport is measured for V < −2.6 V, where hole states are available in the valence band. Between −2.6 and 1.9 V the Fermi level lies in the band gap. Next, pinch-off curves are measured for each barrier gate: we sweep the voltage of one barrier gate, while keeping the lead gate and the other barrier gate at ±3.5 V. As the barrier gate voltage is decreased toward zero, the current is suppressed by the formation of a tunnel barrier underneath. If we compare the pinch-off curves of different devices (see Figure 2b, VSD = 15 mV), we observe that the coupling of the barrier gate to the 2DEG/2DHG varies between devices, and also between different barriers, most likely due to microscopic variations in the barrier gates and the dielectric properties. The results in Figure 2 show that barrier gates can locally control the charge carrier density in the 2DEG and 2DHG. Two double-barrier devices have been measured in a dilution refrigerator with a base temperature of 10 mK and an effective

electron and hole reservoirs. Gate-layers are patterned with electron-beam lithography (EBL) on top of a 10 nm thermally grown silicon dioxide. In a first EBL step two 30 nm wide barrier gates, B1 and B2, are patterned. After Al deposition and subsequent lift-off, the barrier gates are thermally oxidized on a hot plate at 150 °C for 5 min. This forms a 4−5 nm thick oxide preventing leakage between the barrier gates and the lead gate patterned in a second EBL step. The 85 nm wide lead gate (10 nm Al/60 nm Pd) overlaps both implanted regions so that a positive (negative) voltage on the gates accumulates electrons (holes) at the Si/SiO2 interface, forming a two-dimensional electron (hole) gas, 2DEG (2DHG). The two barrier gates, B1 and B2, are used to individually tune the tunnel coupling of the left and right reservoir to the QD formed between the gates. Confinement of the charge carriers results in discrete energy levels occupied by either electrons or holes, depending on the operating regime. The ambipolar device layout in Figure 1 allows the electron and hole QD to be electrostatically defined at the same location. B

DOI: 10.1021/acs.nanolett.5b01706 Nano Lett. XXXX, XXX, XXX−XXX

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Figure 3. Electron−hole symmetry in the linear transport regime. Source-drain current ISD versus VB1 and VB2 through the nanostructure for the hole (left panel) and the electron regime (right panel). Three regions can be distinguished, marked I−III. Regions I and II show Coulomb resonances parallel to one axis corresponding to single-charge tunneling through a Coulomb island formed underneath either barrier gate, as illustrated in the schematics (middle panels). In region III a QD is formed between B1 and B2, see Figure 4. Data taken at VSD = 1 mV and T = 10 mK. Region I in the electron regime is shifted because of a rearrangement of charges between measurements.

electron temperature of 22 mK.37 First, we study the linear transport regime, VSD = 1 mV, where we measure the sourcedrain current ISD through the nanostructure versus VB2 and VB1. The corresponding measurements for the hole regime (V < 0) and the electron regime (V > 0) are plotted in Figure 3 left and right panel, respectively. A constant lead gate voltage of VL = ∓6 V creates a conduction channel underneath the lead gate. To create tunnel barriers, we operate both barrier gates around the pinch-off voltage. The measured data show a very similar picture for the electron and the hole regime, where we distinguish three regions, marked I−III. Regions I and II exhibit similar Coulomb peaks38,39 parallel to the VB1 (VB2) axis in II (I). The resonances are independent of one barrier gate voltage indicating that charge carriers are confined underneath the other barrier gate, as illustrated in the schematics. These local Coulomb islands are discussed in detail elsewhere.40 The results in Figure 3 show symmetrical behavior in the linear transport regime for holes and electrons. In Figure 4 we have a closer look at region III, where both barriers are operated around the pinch-off voltage. In both the electron and hole regime, diagonal, equally spaced current peaks correspond to single-charge tunneling events. In between the peaks, the source-drain current is Coulomb blocked and the number of charges is constant. From the Coulomb peak spacing we extract capacitive couplings to the hole QD of CB1,h = 5.9 aF and CB2,h = 9.4 aF, for B1 and B2 respectively. For the electron QD we get values of CB1,e = 5.0 aF and CB2,e = 6.3 aF. The ratio CB1/CB2 of the two barrier gates is ∼0.62 for the hole QD and ∼0.78 for the electron QD. Because the two barriers B1 and B2 couple equally to the central island (CB1/CB2 ≈ 1), the dot must be created between the two barriers, as illustrated in Figure 4d. This was also measured for the other device. Here, the ratio CB1/CB2 < 1 means that the hole QD and the electron QD are slightly closer to B2. The QDs are operated in the manycharge-carrier regime. By varying VL we change the dot occupancy by 20 charge carriers in the hole (Figure 4c) and the electron regime (Figure 4e). To estimate the number of charge carriers we divide the difference between the applied gate voltage and the threshold voltage in the corresponding regime by the Coulomb peak spacing. This gives an estimated number of charge carriers between 50 and 100 for both regimes.

We study the Coulomb resonances in more detail using bias spectroscopy (Figures 4f and 4g). The current is plotted versus VSD and VL in color scale. We obtain sharp Coulomb diamonds for both the electron and the hole regime. Extracted charging energies EC = e2/CΣ of ∼4 meV correspond to a dot capacitance CΣ of ∼40 aF, consistent with a calculated capacitance of 37 aF using the lithographical dimensions of the dot (40 nm × 85 nm) in a parallel plate capacitor model. Inside the diamonds the device is in Coulomb blockade and the dot occupancy is constant (as indicated in Figures 4f and 4g). Varying the lead gate voltage changes the electrochemical potential of the QD. At the diamond edges, the electrochemical potential of the dot aligns with either the source or the drain electrochemical potential so that one dot level becomes available for transport and we measure single-electron (single-hole) tunneling through the QD. The uniformity of Coulomb diamonds in Figure 4 confirms transport through a single QD. The capacitance of the lead gate to the dot CL can be extracted from the period of Coulomb oscillations ΔVL, according to CL = e/ΔVL, where e is the elementary charge. Averaging over several charge transitions gives ΔVL,e = 35 mV for adding an electron, and ΔVL,h = 32 mV for adding a hole, corresponding to gate capacitances of CL,e = 4.5 aF and CL,h = 4.9 aF. This is consistent with the slightly higher EC for the electron QD (4.2 meV) compared to the hole QD (3.5 meV). Calculating the ratio of the lead gate capacitance to the total dot capacitance α = CL/CΣ gives nearly the same values αe = 0.12 (αh = 0.11) for the electron (hole) QD. The extracted electrostatic properties are summarized in Table 1. The results in Figure 4 and Table 1 show a symmetry of electrons and holes confined in a QD electrostatically defined between two barrier gates. The results reported in this Letter demonstrate the ability to occupy one and the same quantum dot with either electrons or holes. This encourages the realization of an ambipolar QD in the few charge carrier regime for several reasons. The first question is whether the observed symmetry holds for charging energies and orbital excited states in the few-charge-carrier regime. The same question applies to the spin filling of electrons into valleys and holes into heavy- and light-hole subbands. Second, ambipolar QDs with single-charge occuC

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Figure 4. Electron−hole symmetry in Si QDs. (a) Zoom in to region III of Figure 3a (VL = −6 V) and (b) zoom in to region III of Figure 3b (VL = 6 V). In both cases VSD = 1 mV. Regular Coulomb peaks, which are diagonal in the VB2−VB1 plot, correspond to single-charge tunneling through a QD formed between the barrier gates. (c and e) Coulomb peaks of 20 charge transitions in each regime for fixed barrier gate voltages (VB1 = −1.85 V, VB2 = −1.5 V, VSD = 0.5 mV, and VB1 = 1.72 V, VB2 = 1.34 V, VSD = 1 mV, respectively). (d) Schematic cross section of the device showing the location of the formed QD. Insets of panels c and e illustrate the corresponding potential profiles of the hole and electron QD, respectively. (f and g) Nonlinear transport through the hole QD (VB1 = −1.85 V, VB2 = −1.5 V) and the electron QD (VB1 = 1.72 V, VB2 = 1.34 V), respectively.

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Table 1. Electrostatic Properties of the Electron and the Hole QD

electron QD hole QD

CB2 (aF)

CB1 (aF)

CB1/ CB2

EC (meV)

ΔVL (mV)

CL (aF)

α=CL/CΣ (eV/V)

6.3

5.0

0.78

4.2

35

4.5

0.12

9.4

5.9

0.62

3.5

32

4.9

0.11

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

After completion of these measurements, we became aware of experiments on similar device structures elsewhere.41 The authors declare no competing financial interest.

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ACKNOWLEDGMENTS FAZ acknowledges support from the Foundation for Fundamental Research on Matter (FOM), which is part of the Netherlands Organization for Scientific Research (NWO), and support from the European Commission under the Marie Curie Intra-European Fellowship Programme. WGvdW acknowledges financial support from the European Research

pancy can break new ground in spin-based quantum information processing, since the suitability of electron-spin and hole-spin qubits can be compared in the same crystalline environment. Taking the advantages of either qubit one could think of a future “quantum CMOS” technology based on ambipolar QDs. D

DOI: 10.1021/acs.nanolett.5b01706 Nano Lett. XXXX, XXX, XXX−XXX

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Council (Grant No. 240433). The authors would like to thank A. S. Dzurak and M. Veldhorst for helpful discussions.

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DOI: 10.1021/acs.nanolett.5b01706 Nano Lett. XXXX, XXX, XXX−XXX

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Nano Letters (40) Mueller, F.; Konstantaras, G.; van der Wiel, W. G.; Zwanenburg, F. A. Single-Charge Transport in Ambipolar Silicon Nanoscale FieldEffect Transistors. Appl. Phys. Lett. 2015, 106, 172101. (41) Betz, A. C.; Gonzalez-Zalba, M. F.; Podd, G.; Ferguson, A. J. Ambipolar Quantum Dots in Intrinsic Silicon. Appl. Phys. Lett. 2014, 105, 153113.

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DOI: 10.1021/acs.nanolett.5b01706 Nano Lett. XXXX, XXX, XXX−XXX