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Iranian International Conference on Microelectronics (IICM)

Analysis of electrostatic interaction between a charge trap and a quantum dot based single electron transistor

Fatemeh Hamedvasighi, Majid Shalchian

Published Oct 25, 2023• 2 citations
Publisher

Abstract

In this article, we studied the effect of a single charge trap on the charge stability diagram of a quantum dot-based single electron transistor. The anomalies in the Coulomb characteristic diagram of the quantum dot, system energy, occupation probabilities, and conductivity of the quantum dot have been investigated. These anomalies are caused by the electrostatic interaction of the quantum dot with the charge trap. The trap is capacitively connected to the quantum dot and can be empty or occupied by an electron; considering a few quantum states of the system, we solved the master equation using Fermi's golden rule to obtain the tunneling rates and the matrix of tunneling coefficients. Then, calculating the inverse of the matrix of coefficients, the probability of each quantum state has been obtained. Validation of the analysis is performed by comparing the simulation results with the experimental data. Finally, we have demonstrated that our study provides a tool to detect the charge presence in a trap near a quantum dot, which can potentially be used for the readout of quantum gates.

DOI
10.1109/iicm60532.2023.10443127

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In this article, we studied the effect of a single charge trap on the charge stability diagram of a quantum dot-based single electron transistor. The anomalies in the Coulomb characteristic diagram of the quantum dot, system energy, occupation probabilities, and conductivity of the quantum dot have been investigated. These anomalies are caused by the electrostatic interaction of the quantum dot with the charge trap. The trap is capacitively connected to the quantum dot and can be empty or occupied by an electron; considering a few quantum states of the system, we solved the master equation using Fermi's golden rule to obtain the tunneling rates and the matrix of tunneling coefficients. Then, calculating the inverse of the matrix of coefficients, the probability of each quantum state has been obtained. Validation of the analysis is performed by comparing the simulation results with the experimental data. Finally, we have demonstrated that our study provides a tool to detect the charge presence in a trap near a quantum dot, which can potentially be used for the readout of quantum gates.
We predict large regions of the charge stability diagram using a multiband and multielectron configuration interaction model of a double quantum dot system. We account for many-body interactions within each quantum dot using full configuration interaction and solve for single-particle density operators. This allows charge states to be predicted more accurately than the extensively used classical capacitance model or the single-band Hubbard model. The resulting single-particle mixed states then serve as inputs into an atomic orbital picture that allows for the explicit calculation of the underlying Hubbard model parameters by performing the appropriate integrals. This numerical approach allows for arbitrary choices of electrostatic potential and gate geometry. A common assumption when calculating charge stability diagrams from the Hubbard model is that the charge stability diagrams are periodic, but we find that the tunnel couplings for valence electrons in dots with N=3N=3N=3 electrons are significantly enhanced when compared to single-electron dots. This difference is apparent in the charge stability diagram for higher occupancy Coulomb diamonds. We also quantitatively explore how the barrier gate strength and dot pitch impact this behavior. Our work should help improve the future realistic modeling of semiconductor-dot-based quantum circuits.
There has been considerable progress in electro-statically emptying, and re-filling, quantum dots with individual electrons. Typically the quantum dot is defined by electrostatic gates on a GaAs/AlGaAs modulation doped heterostructure. We report the filling of such a quantum dot by a single photo-electron, originating from an individual photon. The electrostatic dot can be emptied and reset in a controlled fashion before the arrival of each photon. The trapped photo-electron is detected by a point contact transistor integrated adjacent to the electrostatic potential trap. Each stored photo-electron causes a persistent negative step in the transistor channel current. Such a controllable, benign, single photo-electron detector could allow for information transfer between flying photon qubits and stored electron qubits.
There has been considerable progress in electrostatically emptying, and refilling, quantum dots with individual electrons. Typically the quantum dot is defined by electrostatic gates on a GaAs∕AlyGa1−yAs modulation-doped heterostructure. We report the filling of such a quantum dot by a single photoelectron, originating from an individual photon. The electrostatic dot can be emptied and reset in a controlled fashion before the arrival of each photon. The trapped photoelectron is detected by a point contact transistor integrated adjacent to the electrostatic potential trap. Each stored photoelectron causes a persistent negative step in the transistor channel current. Such a controllable, benign, single photoelectron detector could allow for information transfer between flying photon qubits and stored electron qubits.
We investigate the characteristics of purely electrostatic interactions with external gates in constructing full single-qubit manipulations. The quantum bit is naturally encoded in the spatial wave function of the electron system. Single-electron transistor arrays based on quantum dots or insulating interfaces typically allow for electrostatic controls where the interisland tunneling is considered constant, e.g., determined by the thickness of an insulating layer. A representative array of $3\ifmmode\times\else\texttimes\fi{}3$ quantum dots with two mobile electrons is analyzed using a Hubbard Hamiltonian and a capacitance matrix formalism. Our study shows that it is easy to realize the first quantum gate for single-qubit operations, but that a second quantum gate comes only at the cost of compromising the low-energy two-level system that encodes the qubit. We use perturbative arguments and the Feshbach formalism to show that this compromising of the two-level system is a rather general feature for electrostatically interacting qubits and is not just related to the specific details of the system chosen. We show further that full implementation requires tunable tunneling or external magnetic fields.
A system is described in which an Al-based superconducting single-electron transistor (S–SET) is fabricated directly above an electrostatically defined quantum dot formed in a two-dimensional electron gas. This arrangement allows the coupling capacitance between the S–SET central island and the dot to be comparable to the tunneling capacitances of the dot. As a result, the measured sensitivity of the S–SET referred to charge on the dot is 1.2×10−4 e/Hz, about an order of magnitude better than previously reported results. The increased sensitivity makes this system ideally suited for broadband measurements such as study of individual tunneling events.
We present time-domain electron counting studies on charge fluctuations in a mesoscopic system. In this measurement, a radio-frequency single-electron transistor (RF-SET) acting as a fast electrometer is capacitively coupled to a quantum dot (QD) electrostatically defined in a GaAs/AlGaAs heterostructure. Random telegraph signals (RTSs) were observed on the RF-SET and were interpreted as resulting from individual electrons tunneling into/out of the QD hence switching the QD charge state between N and N+1 electrons near the charge degeneracy point. Periodic behavior of the switching events is observed as the number of average electrons in the electron box is decreased one by one. The occupation time of the excess electron is directly measured and changes from a few microseconds to a few milliseconds as the tunneling resistance of the QD is increased. Histogram of the occupation time obtained from the time-domain electron counting measurements agrees well with the frequency-domain power spectrum analysis, both suggesting a Poissonian process at the charge degenerate point, in agreement with a model consisting of two charge states. Real time electron counting techniques can play a powerful role in studies on temporal electronic correlations, as well as quantum information processing schemes. Techniques that will improve the charge sensitivity of the RF-SET will also be discussed.