Wide-Band Capacitance Measurement on a Semiconductor Double Quantum Dot for Studying Tunneling Dynamics
Takeshi Ota, Toshiaki Hayashi, Koji Muraki, and Toshimasa Fujisawa*
Physical Science Laboratory, *Tokyo Institute of Technology
The electronic properties of a semiconductor quantum dot, that forms a basic for solid-state qubits, can be often well described by a capacitance that characterizes the static and dynamic response of a quantum dot to externally applied voltages. We propose and demonstrate a new experimental technique to measure impedance (both resistance and capacitance) of semiconductor quantum dots in order to study tunneling dynamics . Figure 1(a) schematically shows the experimental setup. A DQD and a nearby quantum point contact (QPC) are formed in a two-dimensional electron gas at the interface of a GaAs/AlGaAs heterojunction by applying negative voltages to surface Schottky metal gates. A square wave VDQD(t) applied to the DQD induces a single-electron tunneling both on and off and between the dots and the resultant change in the charge state of the DQD QDQD(t) modulates the conductance of the QPC. By applying another square wave VQPC(t) with a relative phase θ to the QPC, we measure the averaged dc current <IQPC> through the QPC by a Lock-in detection. <IQPC> is proportional to the capacitance (conductance) when θ = 0 (π/2). The capacitance signal appears as a peak or a dip depending on the location of the DQD and the QPC. Figure 1(b) shows the capacitance signal measured at 1 kHz as a function of the gate voltages VUR and VUL. The data reveal a charge stability diagram which forms a honeycomb-shaped structure characteristic of a weakly coupled DQD. In a strongly coupled DQD, the capacitance undergoes a quantum mechanical correction due to the interdot tunnel coupling, and quantum capacitance CQ is observed. Figure 1(c) shows the variation of CQ due to interdot tunneling with VUC. As the interdot coupling is weakened by making VUC more negative, the dip becomes sharper. These results suggest that the size and the width of the dip reflect the strength of the quantum mechanical coupling. This CQ, given by the second derivative, or the curvature, of the energy band E with respect to the gate voltage VG, i.e., CQ ≡ d 2 E/dVG2 , is therefore expected to be capable of distinguishing the bonding and antibonding states of single-electron systems or the singlet and triplet states of two-electron systems.
This work was partly supported by SCOPE from the Ministry of Internal Affairs and Communications of Japan.
 T. Ota et al., Appl. Phys. Lett. 96 (2010) 032104.
Fig. 1. Schematic illustration of the experimental setup (a), <IQPC> as a function of VUL and VUR (b),
<IQPC> as a function of the bias offset ε at several VUC (c).
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