Coulomb Blockade Oscillations as a Noninvasive ...

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Journal of the Korean Physical Society, Vol. 48, No. 6, June 2006, pp. 1312∼1315

Coulomb Blockade Oscillations as a Noninvasive Probe of Screening R. Nemutudi∗ Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, United Kingdom and iThemba LABS, Materials Research Group, Old Faure Road, FAURE, Cape, 7131, South Africa

C.-T. Liang Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, United Kingdom and Department of Physics, National Taiwan University, Taipei 106, Taiwan

M. J. Murphy, I. Farrer, C. G. Smith, D. A. Ritchie, M. Pepper and G. A. C. Jones Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, United Kingdom (Received 21 November 2005) Noninvasive measurement techniques utilize the fact that the local conditions in an electrical circuit can affect a nearby, but electrically isolated circuit. Such a technique can be used to measure the screening ability of an electron system. In this work, we study non-invasively the screening characteristics of a one-dimensional (1D) channel in close lateral proximity to a quantum dot that forms a separate and electrically isolated circuit. We use a one-dimensional (1D) channel to screen and in-plane electric field between the gate and the lateral quantum dot. The Coulomb blockade oscillations we observe through the quantum dot circuit and the corresponding variation in their periodicity at different gate voltage regions are a signature of the screening characteristics of a 1D channel both at zero magnetic field and in the quantum Hall region. The screening ability of the 1D channel is found to be approximately two orders of magnitude smaller than that of an ungated GaAs two-dimensional electron system. PACS numbers: 73.21.La, 73.23.Hk Keywords: Coulomb blockade, Noninvasive, Screening, Quantum dot

I. INTRODUCTION By using the electrostatic squeezing technique [1], it is possible to define a quantum dot that confines a finite number of electrons in an isolated region within a two-dimensional electron gas (2DEG). Consider a lateral quantum dot [2] weakly coupled to the source and the drain contacts where the tunneling conductance through the dot G is low, i.e., G  2e2 /h. If the energy required for adding an extra electron to the quantum dot is much higher than the chemical potentials in the source and the drain contacts, then transport through the quantum dot is prohibited. This is the Coulomb blockade (CB) of single electron tunnelling [3]. By changing the applied gate voltage to align the energy state required for adding an extra electron in the dot with the chemical potentials in the leads, transport through the dot can occur via single electron tunneling. At this stage, not only do electrons pass through the dot one at a time, but such a process takes place at no extra energy cost since the ∗ E-mail:

chemical potential of the dot is at resonance with those of the source and the drain. Sweeping the gate further, in either polarity, takes the device off resonance and reinforces the Coulomb blockade state. Thus, as the gate is continuously swept, conductance across the dot displays a series of Coulomb blockade oscillations, with the peaks representing the resonance states and the troughs the Coulomb blockaded states. Coulomb oscillations tend to be periodic in the gate voltage [3], except in cases where the dot size is so small that the single-particle energy spacing becomes significant. The periodicity of the oscillations can also be distorted as a result of the gradual depletion of the intervening 2DEG between the gate and the quantum dot. It is well known that an electric field emanating from an electrode is completely shielded by a grounded metal plate. In other words, a grounded metal has a perfect screening ability for an external electric field. However, the situation is somewhat different when considering a 2DEG in a GaAs/AlGaAs quantum well. It has been shown that a GaAs 2DEG only partially screens an external electric field from an electrode [4]. In the seminal

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Coulomb Blockade Oscillations as a Noninvasive Probe of Screening – R. Nemutudi et al.

work of Luryi [5], it was suggested that partial penetration of an electric field through a highly conductive 2DEG allowed implementation of novel high-speed devices, such as three-terminal resonant tunneling transistors and gated-controlled thermionic emission transistors. Due to its large, but finite, Fermi energy, a 2DEG manifests itself as a “quantum capacitance” in a direction transverse to the quantum well. It has been experimentally demonstrated in the elegant work of Field et al that the local conditions in an electrical circuit can affect a nearby, but electrically isolated, circuit [6]. Experiments by Field et al have since led to the now well-established non-invasive measurement technique where two electrical circuits, drawing current from electrically isolated sources, are placed in so close lateral proximity that they electrostatically interact with each other. Under such conditions, one of the two circuits can be used as a passive part of the device which detects via electrostatic interaction the changing conditions in the other circuit. It is a non-invasive measurement technique since the passive part of the device, commonly known as the detector, non-invasively detects the state of the other circuit without invading it by firing electrons at the Fermi energy as is usually the case with conventional measurements. One such class of “noninvasive” measurements is the determination of the screening ability of an electron system. Field and co-workers have studied a quantum dot shaped in the upper 2DEG in which Coulomb oscillations in the quantum dot are observed as a function of the applied back-gate voltage [7]. The period of the observed Coulomb oscillations varies as the penetrating electric field through the lower 2DEG is changed. In this way, Coulomb oscillations serve as a noninvasive probe [8] of the local density of states in the lower 2DEG. In this Letter, we study a one-dimensional (1D) channel in close lateral proximity to a quantum dot in a separate and electrically isolated circuit [8]. We use a 1D channel to screen an in-plane electric field between a gate and a lateral quantum dot. In our case, Coulomb blockade oscillations observed through the quantum dot are a noninvasive probe of the screening characteristics of the 1D channel. We find that our disordered 1D channel has a finite screening ability (compressibility). The quantum capacitance of our 1D channel is approximately 10−4 F/m2 , i.e., two orders of magnitude smaller than that of a GaAs 2DEG.

II. EXPERIMENTAL DETAILS The device that we studied comprises a 1D channel in close proximity to a lateral quantum dot in an electrically isolated circuit fabricated by using local anodic oxidation induced by an atomic force microscope (AFM) [9–13]. Local anodic oxidation is a relatively new device fabrication technique that utilizes a conducting tip of

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Fig. 1. An AFM image of a quantum dot and a 1D channel fabricated using a local anodic oxidation process. (b) Equivalent circuit for the total capacitance seen by the in-plane gate (g1). C1 and C2 are the geometric capacitances per unit area. CQ is the the quantum capacitance due to the finite screening ability of the 1D channel.

an atomic force microscope to imprint oxide patterns on semiconducting or metallic surfaces. When the oxide is imprinted on the surface of an MBE-grown HEMT (high electron mobility transistor) whose two dimensional electron gas resides no deeper than 50 nm from the surface, the electrons underneath the oxide are depleted, and the 2DEG region under the oxide becomes an insulator. In this case, AFM-induced oxide lines are, therefore, used to define electron path and to confine electrons into preselected regions. An AFM image of the device fabricated as described is shown in Fig. 1(a), with the protruding oxide appearing as bright lines. The oxide lines measure an average of 18 nm on the vertical scale. The device is fabricated on a molecular-beam-epitaxially (MBE)grown GaAs/AlGas heterostructure with the 2DEG residing 34 nm beneath the surface. From quantum Hall-effect measurements, the ungated 2DEG has a carrier concentration of 3.7 × 1015 m−2 with a mobility of 44.4 m2 /Vs in the dark. Experiments were performed in a dilution refrigerator at a base temperature of T ≈ 50 mK. The two-terminal conductances of both the 1D channel and quantum dot were measured simultaneously using standard phase-sensitive ac lock-in techniques. Although the magnitude of the applied excitation voltage (10 µV) was the same on both circuits, the excitation frequency on the quantum dot circuit was 77 Hz while that of the 1D channel was 33 Hz.

III. RESULTS AND DISCUSSION The conductance through the lateral quantum dot shows CB oscillations as a function of gate 1 (g1). Thus, the capacitance between the dot and g1 can be determined. However, in this case, such a capacitance will include the screening effects of the intervening 1D channel. By applying a large enough negative bias on g1, the electrons within the 1D channel can be depleted, and only then, in the absence of screening by the 1D-channel, can the direct capacitance between g1 and the quantum

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Fig. 2. Conductance measurements of both the 1D channel and the lateral quantum dot as functions of Vg1 at Vg2 = −0.495 V and B = 0 T.

dot be obtained. Our experimental results can be modelled following the work of Luryi [5]. Fig. 1(b) shows the equivalent circuit for the total capacitance seen by g1. C1 and C2 are the geometric capacitances per unit area. The quantum capacitance CQ in parallel with C2 is a result of the extra energy required for placing electrons in the quantum well. For a 2D electron∗ system, m the quantum capacitance is given by CQ = e2 π~ 2 , where ∗ m is the electron effective mass and e is the charge of an electron. Within the model of Luryi [5], the CB period [7] has been shown to be is given by e ∆V = − (C1 + C2 + CQ ), (1) AC1 C2 where A is the area of the quantum dot. For Vg2 = 0 and Vg1 = 1 V, we observe Aharonov-Bohm-type oscillations as a function of the applied perpendicular magnetic field [14,15] with a period, ∆B, of 33.4 mT, giving a dot area A of 1.24 × 10−13 m2 . The capacitances C1 and C2 can be measured directly. C2 can be determined from the CB period (≈ 13.5 mV) observed upon applying a voltage directly to the 1D-channel, which yields C2 = 9.56 × 10−5 F/m2 . By applying a large enough negative bias on g1, the channel can be depleted; thus, there is now no screening effect from the channel (CQ = 0). In this case, the CB period is simply given by e (C1 + C2 ). (2) ∆V = − AC1 C2 Using Eq. (2), we find the capacitance C1 to be 4.24 × 10−5 F/m2 . Figure 2 shows conductance measurements of both the 1D channel [16,17] and the lateral quantum dot as functions of Vg1 at Vg2 = −0.495 V. Instead of clean ballistic conductance steps, we observe resonant features [18–21] due to the presence of disorder within our 1D channel [22–24]. The conductance resonances observed in the dot circuit are ascribed to Coulomb blockade oscillations

Journal of the Korean Physical Society, Vol. 48, No. 6, June 2006

Fig. 3. (a) Conductance measurements of both the 1D channel and the lateral quantum dot as functions of Vg1 at Vg2 = −0.4 V and B = 7 T. (b) Conductance measurements of both the 1D channel and the lateral quantum dot as functions of Vg1 at Vg2 = −0.7 V and B = 7 T.

[18–20]. It is clear that the average CB period in region 1 (≈ 74 mV) is larger than that in region 3 (≈ 44 mV) where the channel is pinched off. As there is no screening from the 1D channel in region 3, Eq. (2) is applicable. In regions 1 and 2, we use Eq. (1) to measure the average quantum capacitances, which turn out to be 9.42 × 10−5 F/m2 and 6.26 × 10−5 F/m2 , respectively. These values are two orders of magnitude smaller than that (≈ 4.47 × 10−2 F/m2 ) of a GaAs 2DEG. The measured CB periods in both regions 1 and 2 are larger than that in region 3, demonstrating that our disordered 1D channel has a finite compressibility. It is interesting to compare our noninvasive measurements at zero magnetic field (B = 0) with those in the integer quantum Hall region. Figs. 3(a) and (b) show conductance measurements of both the 1D channel and the lateral quantum dot as functions of Vg1 at B = 7 T. The conductance step shown in Fig. 3 (b) corresponds to a Landau-level filling-factor ν = 1 state. As Fig. 3 (a) shown, we can see that the averaged CB period (≈ 69 mV) for Vg1 > 0.5 V is larger than that (≈ 47 mV) close to pinch-off (Vg1 < −0.1 V), consistent with our results at B = 0. This demonstrates that our disordered 1D channel has a finite screening ability in the integer quantum Hall region. The measured CB period in Fig. 3 (a) is very close to that measured in region 3, as shown in Fig. 2. This is expected as there is no screening from the 1D-channel. The measured CB period, therefore, reflects the direct capacitance between g1 and the lateral quantum dot. For the conventional Coulomb blockade region, the CB period is approximately B independent, consistent with our experimental results. We also find the average CQ at B = 7 T to be 7.83 × 10−5 F/m2 , a value comparable in order of magnitude with those obtained at B = 0.

Coulomb Blockade Oscillations as a Noninvasive Probe of Screening – R. Nemutudi et al.

IV. CONCLUSIONS In conclusion, we have performed noninvasive measurements on the screening ability for a disordered 1D channel. The quantum capacitance of such a system is found to be ≈ 10−4 F/m2 , two orders of magnitude smaller than that of a GaAs 2DEG. Our results provide direct experimental evidence of a finite compressibility of a disordered 1D channel both at zero magnetic field and in the integer quantum Hall region.

ACKNOWLEDGMENTS This work was funded by the Engineering and Physical Sciences Research Council, United Kingdom, the National Science Council, Taiwan (42006F) and the National Research Foundation, South Africa.

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