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Microelectronic Engineering 84 (2007) 1614–1617

Microwave resonances in silicon-based single electron transistors

L.A. Creswell a,*, D.G. Hasko a, D.A. Williams b

a Microelectronics Research Centre, Cavendish Laboratory, University of Cambridge, J.J. Thompson Avenue, Cambridge CB3 0HE, UKb Hitachi Cambridge Laboratory, Hitachi Europe Ltd., J.J. Thompson Avenue, Cambridge CB3 0HE, UK

Available online 2 February 2007

Abstract

Phosphorus-doped silicon is one of the promising silicon-based materials for the potential realisation of a solid-state quantum com-puter. As a step towards the realisation of this goal, we have studied the response of phosphorus-doped silicon single electron transistors(SETs) to microwave frequency radiation, which might be used to control a quantum bit. The SET source-drain current showed gate-voltage dependent high Q-value resonances as the radiation frequency was swept and interactions between neighbouring resonances wereobserved as the gate voltage was varied. Pulses of microwave frequency radiation were also coupled to the SET and the amplitude of ahigh Q-value resonance showed the onset of oscillations as the pulse period increased.� 2007 Elsevier B.V. All rights reserved.

Keywords: Nanodevices; Quantum information; Microwave; Single electron transistors

1. Introduction

Quantum computers have attracted considerable inter-est due to their potential ability to solve currently intracta-ble problems [1]. Solid-state systems offer excellentprospects for the experimental realisation of a quantumcomputer due to their scalability and ease of integration.Two promising solid-state candidates are semiconductordouble quantum dots and isolated double quantum dotsin which charge or spin qubits are embodied in the statesof the dots [2,3]. In the isolated double quantum dot sys-tem, a single electron transistor (SET) is positioned closeto the isolated double quantum dot and used as a sensitiveelectrometer to determine the qubit state [4]. In this case,the SET source-drain current varies with the charge stateof the nearby quantum system(s).

In solid-state quantum computing schemes, manipula-tion of the quantum state is typically achieved by voltagepulses or by bursts of electromagnetic radiation [5,6]. Inthis paper, the effect of continuous wave and pulsed micro-wave radiation on an isolated SET is investigated. This

0167-9317/$ - see front matter � 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.mee.2007.01.094

* Corresponding author.E-mail address: lac49@cam.ac.uk (L.A. Creswell).

work aims to develop a fuller understanding of the effectof such manipulations on the electrometer. The SETsource-drain current was observed to be strongly depen-dent on the frequency and the pulse period of the micro-wave radiation.

The effect of electromagnetic radiation on single anddouble quantum dots has previously been studied, forexample [7,8], however there have been few high-resolutionstudies of the frequency response of a silicon SET.

2. Fabrication

SETs were fabricated using a highly phosphorus doped(3 · 1019 cm�3) silicon-on-insulator wafer. The wafer con-sists of an undoped silicon substrate, a buried silicon diox-ide layer, a doped silicon layer and a thermally growncapping silicon dioxide layer (Fig. 1a).

High-resolution electron beam lithography was used todefine the device geometry in a positive electron beam resist(high molecular weight poly(methylmethacrylate)). Thepattern was developed ultrasonically at room temperaturein a 3:1 mixture of propan-2-ol and methyl isobutyl ketone.This pattern was then converted into a sacrificial etch maskby evaporating, and then lifting-off 30 nm of aluminium. A

Fig. 1. Schematic showing the phosphorus-doped silicon SET fabrication process: (a) shows the wafer before processing and (b) shows the trench-isolateddevice.

Fig. 2. SEM image of a single-gate double dot silicon-on-insulator SETwith source, drain and gate terminals.

L.A. Creswell et al. / Microelectronic Engineering 84 (2007) 1614–1617 1615

subsequent reactive ion etch, using a gas mixture of SiCl4and CF4, removed the unmasked regions down to the bur-ied oxide layer, leaving a trench isolated device (Fig. 1b).The aluminium etch mask was then stripped by wet etchingprior to a furnace oxidation at 1000 �C. The oxidation stepminimises the number of surface trap states and hencereduces the occurrence of random telegraph noise. A scan-ning electron micrograph of a typical device is shown inFig. 2. The fabrication process is described in more detailin [9].

Fig. 3. Microwaves are coupled to the device from a co-axial waveguide: (a) sha leadless chip carrier and (b) shows the modified measurement socket.

3. Measurements

A leadless chip carrier measurement socket [10] wasmodified to include a co-axial microwave waveguide, per-pendicular to the device under test. The polished end ofthe open circuit waveguide was terminated approximately0.5 mm from the device enabling microwaves to be coupledto the SET (Fig. 3). A 3 dB attenuator was used to ther-mally anchor the central conductor to the shield and min-imise reflections from the termination. The SET wasmounted in a leadless chip carrier, and the source-draincurrent measured with low pass filtering. All measurementswere conducted at 4.2 K by the direct immersion of thedevice in liquid helium.

4. Results and discussion

The source-drain current of an SET was measured dur-ing the application of microwave frequency radiation (2–15 GHz). Repeatable changes in the source-drain currentwere observed as the frequency was swept. Low Q reso-nances (Q-values � 100) were observed over the entire fre-quency range investigated. These resonances are believed toresult from cavity resonances. Repeatable high Q reso-nances (Q-values up to 105) were observed at frequenciesgreater than approximately 3 GHz (photon energy10 leV) (Fig. 4). Below this threshold frequency, high Q-value resonances were not observed in any of the devicestested. Similar frequency dependencies were observed in

ows a cross-section schematic of the waveguide and the device bonded into

Fig. 4. A typical frequency extract showing approximately 20 positive andnegative high Q-value resonances in the SET source-drain current.

Fig. 5. Differentiated data showing the gate-voltage dependence of aselection of high Q-value resonances in a double quantum dot SET. Theinsert contains raw data, offset for clarity, showing interaction betweentwo neighbouring resonances.

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nanowire, single quantum dot and double quantum dotSETs. The high Q resonances changed in amplitude andposition as the gate voltage was varied and interactionsbetween neighbouring resonances were seen (Fig. 5).

Fig. 6. Effect of pulsed radiation on the source-drain current of an SET. An eqthe pulse period increased: (a) shows the variation of the resonance amplitude athe amplitude variation of the four resonances in (a) as the pulse period incre

The effect of pulsed radiation on the source-drain cur-rent of an SET was also investigated. Fig. 6a shows thechange in amplitude and position of four resonances asthe pulse period is varied. The amplitude of the highest Q

resonance (A, Q-value �105) shows the onset of oscilla-tions as the pulse period increases (Fig. 6b). An estimateof the lifetime of an excitation can be obtained from theQ-value of the resonance e.g. resonance A at 4.782 GHzhas a lifetime of approximately 3 ls. The lower Q reso-nances (B, C and D, Q-values �104) have estimated life-times of approximately 0.3 ls. Their amplitudes do notoscillate as the pulse period increases.

The mechanism responsible for the SET microwave res-onances is currently under investigation. A proposed mech-anism must account for the large number of resonances,their high Q-values and their variation with gate voltage.

The resonances show different dependences on the SETgate voltage (Fig. 5). This indicates different degrees ofcapacitive coupling to the gate and hence that they origi-nate in different regions of the device.

The main energy levels within the SET are the Coulombblockade charging levels, however the difference betweenthese levels is three orders of magnitude larger than theenergy of the applied microwave radiation. Hence, theseexcitations must arise from sublevels within the devicestructure. The confinement energies of a mesoscopic semi-conductor device are known to have a rich interactingstructure, as observed here. In order to index these levelsunambiguously, a quantitative model of the detailed elec-tronic structure is required. The development of this model,as well as further studies into the hyperfine effect of thephosphorus donors, is currently underway.

5. Conclusions

The source-drain current of an isolated SET is stronglydependent on the frequency of the coupled microwave radi-ation. When the frequency is swept, high Q-value reso-nances are observed at frequencies greater than 3 GHz. Ifan SET is to be used as a sensitive electrometer in environ-ments with electromagnetic radiation, such complicateddependencies must be fully understood.

ual on-off time was used to ensure that heating effects remained constant asnd position with pulse period. The data are offset for clarity and (b) showsases. The lines in (b) are included to guide the eye.

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Acknowledgements

The authors thank Rob McNeil for constructing themodified Ney socket sample holder. LAC thanks EPSRCand Hitachi Europe Ltd. for their financial support.

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