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Author: Rachpon Kalra

Supervisors: Dr. A. Morello, Dr. C. C. Escott, Prof. A. S. Dzurak

Design and Modeling of Silicon Spin Qubits for

Quantum Computing

Research Theme: Fundamental and Enabling Research

Motivation

Quantum computation offers the potential for an exponential improvement in the computation time of certain important algorithms. This project investigates a proposed modification to a recently developed architecture for a qubit (quantum bit) device, where quantum information is stored as the spin state of the

Performing TCAD simulations of the device [Figure 3 (b)], we extracted V(r), the tunnel barrier potential-profile [Figure 3 (c)], for different voltages applied to the gates.

quantum information is stored as the spin state of the unshared valence electron of a phosphorous atom.

Principle of Operation

Phosphorous atoms are implanted in a window in a silicon substrate, next to a single electron transistor (SET).

Figure 3:

(a) The model with the rate

Figure 1: Diagram of the existing qubit device (in blue), with one donor atom shown. The modification is the rate gate, shown in red.

(a) The model with the rate gate used in FastCap.

(b) The model used in TCAD; gates shown in grey.

(c) An example of the tunnel barrier between the electron and the SET, extracted from TCAD simulations.

Results

The device is set up such that only a spin-up electron can tunnel through to the SET, shifting its current peak by ∆q/e. The measurement of the resulting ∆ISET

constitutes a measurement of the spin of the electron.

Figure 2: The SET’s initial current peaks are shown in blue. In red, shifts of ∆q/e = (a) 0.03 and (b) 0.2, are shown, along with their ∆ISET.

Figure 4: ∆q/e values extracted from FastCap as color intensity plots with limits 0 and 1, for the device (a) without and (b) with the rate gate. Black shapes enclose the region on the map containing ideal ∆q/e values.

The rate gate reduces the ∆q/e values by, on average, 20%. However, as illustrated [Figure 4 (b)], there is still a fairly large region of donor positions with usable ∆q/e values.

Aim

This project investigates the insertion of a ‘rate gate’ between the top gate and the donor gate [Figure 1].

A present limitation of the device is that it has no control over the tunneling rate of the donor electron (signal speed).

∑−=∆

donor

SETdonor

C

Ceq

Figure 5: Tunnel rates for a donor with ∆q/e ≈ 0.3, 33 nm from the SET.

Conclusion

∑Clearly, adding another metallic gate decreases the ratio of the donor’s mutual capacitance to the SET, to its total capacitance. We set out to determine:

• the resulting drop of ∆q/e values due to the rate gate• and its effectiveness in controlling tunnel rates.

Methodology

We comprehensively modeled the device with and without

These results show that the rate gate may be able to change the tunnel rate of a donor by 3 orders of magnitude, with a voltage range ~0.2 V: an extremely encouraging result.

ENGINEERING @ UNSW

UNSW

Conclusion

The rate gate may have remarkable control over the tunnel rates of donor electrons, and the small drop in the ∆q/e does not compromise the functionality of the device. The device is to be fabricated soon.

We comprehensively modeled the device with and without the rate gate in the capacitance extraction code, FastCap [Figure 3 (a)], to determine the distribution of ∆q/e values.

We approximated the tunnel rate of a donor electron, Γ, proportional to the tunneling probability, T2, calculated by:

( )( )

−−≈ ∫

d

dEVmT0

22r)r(/*22exp h