APPLIED PHYSICS LETTERS VOLUME 81, NUMBER 3 15 JULY 2002

Single-electron transistor as a radio-frequency mixer R. Knobel, C. S. Yung, and A. N. Clelanda) Department of Physics and iQUEST, University of California, Santa Barbara, Santa Barbara, California 93106 ͑Received 14 March 2002; accepted for publication 10 May 2002͒ We demonstrate the use of the single-electron transistor as a radio-frequency mixer, based on the nonlinear dependence of current on gate charge. This mixer can be used for high-frequency, ultrasensitive charge measurements over a broad and tunable range of frequencies. We demonstrate operation of the mixer, using a lithographically defined thin-film aluminum transistor, in both the superconducting and normal states of aluminum, over frequencies from 10 to 300 MHz. We have operated the device both as a homodyne detector and as a phase-sensitive heterodyne mixer. We demonstrate a charge sensitivity of Ͻ4ϫ10Ϫ3 e/ͱHz, limited by room-temperature electronics. An optimized mixer has a theoretical charge sensitivity of Շ1.5ϫ10Ϫ5 e/ͱHz. © 2002 American Institute of Physics. ͓DOI: 10.1063/1.1493221͔

Coulomb blockade can occur when current through a linear dependence of the current I on the coupled charge is device passes through high-resistance contacts to a small- employed to mix a rf signal to dc, while in the latter, the capacitance island. The condition for Coulomb blockade is signal is mixed with a local oscillator to generate a signal at ϵ 2 that the resistance of each contact must exceed RK h/e the difference frequency, close to dc, whose amplitude and Ϸ ⍀ 25.8 k , and the electrostatic charging energy EC of the phase may be measured. These techniques may be employed ϵ 2 ӷ island must satisfy EC e /2C⌺ kBT, where C⌺ is the ca- with any gated Coulomb blockade device, allowing measure- ␻ Ϸ pacitance of the island. The charging energy can be tuned ments at frequencies up to max I/e, above which nonadia- electrostatically using a gate capacitively coupled to the is- batic current transport and photon-assisted tunneling become land; the current is periodic in the gate charge, with a period significant. e, the charge of one electron. In this mode of operation, For this experiment, we used a lithographically patterned these devices are known as single-electron transistors SET, comprising two Al/AlOx /Al tunnel junctions and two ͑SETs͒.1,2 An important application of the SET is as an ul- interdigitated coupling capacitors, fabricated using electron trasensitive electrometer, with a theoretical charge beam lithography and shadow evaporation1 ͓see Fig. 1͑a͔͒. sensitivity3 of order 10Ϫ6e/ͱHz. The device was fabricated on a GaAs heterostructure to al- The high electrical resistance associated with Coulomb low in situ fabrication of nanomechanical structures:7 We blockade, coupled with the unavoidable stray cable capaci- plan to implement the mixer as a motion sensor for a nano- tance, has traditionally limited measurements with the SET mechanical resonator, capacitively coupled to the SET.8 to frequencies Շ104 Hz. This can be increased to about 1 The device was mounted on a dilution refrigerator and MHz by placing a first-stage amplifier in close proximity to cooled to Ӎ30 mK. All leads were filtered with metal pow- the SET.4,5 A significant innovation has recently been der filters9 and source and drain leads with RC filters at 1.5 demonstrated,6 where the SET is coupled through a tuned K and at room temperature. The SET was operated as a ␻ LC tank circuit, so that at the resonance frequency 0 mixer both in the superconducting state and in the normal ϭ1/ͱLC the output impedance of the SET is matched to a state, in a magnetic field of 1 T. Figure 1͑b͒ shows the 50 ⍀ cable. This technique, termed a radio-frequency SET ͑rf-SET͒, allows operation at resonance frequencies up to ϳ109Ϫ1010 Hz, with a demonstrated charge sensitivity near the theoretical limit. However, the measurement bandwidth about the resonant frequency is limited to a few percent of ␻ 0 , as the tank circuit quality factor must satisfy Q տͱ ⍀Ϸ 2RK/50 30 to achieve impedance matching. This limits applications of this device to measurements where the frequency of the signal to be measured is externally con- trolled, or is known beforehand to fairly high precision. In addition, the tuning circuit requires a well-characterized elec- trical environment, which is not always easily achieved ͑for ͒ FIG. 1. ͑a͒ Electron micrograph of a typical sample, showing the Ϸ50 example, with carbon nanotube-based transistors . ϫ50 nm2 overlap of the junctions and the two gate capacitors. The scale bar Here we demonstrate the use of the SET as a homodyne is 1 ␮m. ͑b͒ dc normal-state current–voltage characteristic of the SET at 30 detector and as a heterodyne mixer. In the former, the non- mK, where the modulation due to gate 1 is shown; the same behavior was seen when modulating gate 2. The device parameters extracted from this ϭ ϫ Ϫ16 ϭ ϫ Ϫ16 ϵ ϩ measurement are CG1 4.2 10 F, CG2 2.8 10 F, R R1 R2 a͒ Ϫ15 Electronic mail: [email protected] ϭ850 k⍀, and C⌺Ϸ2ϫ10 F.

0003-6951/2002/81(3)/532/3/$19.00532 © 2002 American Institute of Physics Downloaded 05 Mar 2003 to 128.111.14.162. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/aplo/aplcr.jsp Appl. Phys. Lett., Vol. 81, No. 3, 15 July 2002 Knobel, Yung, and Cleland 533

FIG. 3. ͑a͒ Amplitude of the mixing signal as a function of the dc gate ͑ ϭ charge for a range of VSD offset for clarity, with VSD 4, 50, 100, and 150 ␮ ͒ ␻ ␲ϭ ␻ ␲ϭ ͑ ͒ V bottom to top , with LO/2 20 MHz and if/2 152.15 Hz. b ͑ ͒ FIG. 2. a Schematic diagram of mixing. The gate charge is set for maxi- Modeled mixing current as a function of the dc gate charge, VLOCG ͑ ͒ ͑ ͒ ϭ ϭ ͑ ͒ ͑ ͒ mum current dashed vertical line , and a signal and for heterodyne mixing 0.2e, VSCG 0.25e at 30 mK varying VSD as in a . c Measured if ͑ ͒ ␻ ␲ϭ local oscillator voltage are coupled to the gate. b Mixing circuit schematic current as a function of the rf charge on the gate for LO/2 20 MHz and ␻ ␲ϭ ϭ ␮ of both homodyne and heterodyne mixing. The SET is in the dashed box in if/2 152.15 Hz, with fixed source–drain bias VSD 90 V. The three ͑ ͒ ͑ ͒ ϭ ␮ the center. c Homodyne detector signal at dc, measured as a function of the traces are for varying VLOCG /e. d Modeled if current for VSD 100 Vat ͑ ͒ signal voltage. The signal at 20 MHz was applied to gate 2, while the SET 30 mK varying VLOCG as in c . was in the superconducting state. Points are experimental data, and the dashed line is the expected Bessel function response. ͑d͒ Heterodyne mixing ␻ ϭ ϭ ϭ spectral density about if 152.15 Hz, with CGVS 0.1e, CGVLO 0.3e, capacitance between the gate and source–drain leads can rf ␻ ␲ϭ ␻ ϭ␻ ϩ␻ LO/2 20 MHz, and S LO if , with the SET in the normal state. ͑ ͒ modulate VSD as well, causing deviations from Eq. 1 at The vertical axis is in units of input signal charge spectral density qS ϭ CGVS . larger rf amplitudes. For heterodyne mixing, the signal voltage is applied to one gate, and a local oscillator voltage V cos ␻ t to the normal-state current–voltage characteristic, as the dc bias on LO LO other gate. The source–drain current is modulated by both one gate was varied. The relatively large value of the SET signals, and a current is generated at the intermediate fre- resistance limits the noise performance and output band- quency ␻ ϭ͉␻ Ϫ␻ ͉. The if signal ͑magnitude and width, as discussed below. if S LO phase͒ was detected using a lock-in amplifier, whose refer- For near-optimal V , as shown in Fig. 2͑a͒, the SD ence signal was generated by a separate mixer, shown in Fig. source–drain current I is approximately sinusoidal in the SD 2͑b͒. High-pass filters ensured that this reference signal was gate voltage V , with peak-to-peak amplitude 2⌬I about G 0 not transmitted to the SET. The measured spectral response an average value I , and period e in the gate charge C V ; 0 G G is shown in Fig. 2͑d͒, showing the peak at ␻ as well as the at optimal source–drain bias ⌬I ϷI . For homodyne detec- if 0 0 sideband noise. tion, we bias the gate with a dc voltage V such that the G Figure 3͑a͒ shows the heterodyne mixer amplitude as the current is at a maximum, and apply a rf voltage V cos ␻ t. S S dc source–drain voltage V and dc gate voltage V are For frequencies smaller than the tunneling rate, the dc cur- SD G varied. The e periodicity in C V is observed, and the de- rent is then the time average of the instantaneous current G G pendence on V has the expected maximum near e/2C⌺ . ͗I ͓V ϩV cos(␻ t)͔͘. At frequencies of order I/e and SD SD G S S Figure 3͑c͒ shows the if current as a function of signal am- higher, electrons can be transferred through the SET nona- plitude V ; the same dependence is found when V is var- diabatically, reducing the Coulomb gap.10 At still higher fre- S LO ied. The gain of the device is tunable by varying the dc gate quencies, where the photon energy is comparable to the dif- bias, source–drain voltage, and oscillator power. The if re- ference in final energy states ប␻Ϸ⌬E, photon-assisted sponse was calculated using an analytic model for the SET,12 tunneling can occur. This effect is negligible in our and is shown in Figs. 3͑b͒ and 3͑d͒. The measured response measurements.11 For heterodyne mixing, we couple a local follows the predicted behavior, but is approximately a factor oscillator ͑LO͒ voltage V cos ␻ t to the other gate, as LO LO of 2 smaller than calculated. At present we do not understand shown in Fig. 2͑b͒. this discrepancy. The homodyne response is shown in Fig. 2͑c͒ for gate 2 Figure 4͑a͒ shows the frequency dependence of the at 20 MHz. For a model current dependence I ϷI SD 0 mixer signal, for fixed ␻ and constant LO and signal Ϫ⌬I cos(2␲C V /e), we expect if 0 G G power. Figure 4͑a͒ shows a measurable signal up to ␻ /2␲Ϸ300 MHz, limited by the ␻ /2␲ϳ300 MHz cut- 2␲C V LO max ͗ ͑ ͒͘ϭ ϩ⌬ ͯ ͩ G S ͪͯ ͑ ͒ off frequency for this device. Figure 4͑b͒ shows the ISD VS I0 I0 J0 , 1 e ϳ250 Hz output bandwidth for the SET. This can be in- creased by lowering the junction resistance, operating in the where J0 is the zeroth-order Bessel function. A fit to this superconducting state, and reducing the cable capacitance. dependence is shown in Fig. 2͑c͒; the zeroes in the response Use of a closely coupled preamplifier or tuned LC circuit allow us to calibrate the signal voltage VS . The nonzero could further increase the output bandwidth. Noise measure- Downloaded 05 Mar 2003 to 128.111.14.162. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/aplo/aplcr.jsp 534 Appl. Phys. Lett., Vol. 81, No. 3, 15 July 2002 Knobel, Yung, and Cleland

ϭ ϭ ␦ Ϸ timized SET with R 2RK ,C 1 fF, we find qS( f ) 1.5 ϫ10Ϫ5e/ͱHz. This optimized SET would have a current Ϸ gain of gI 30 at 100 MHz and 3 at 1 GHz. An important question remains regarding the impact of 1/f charge noise: If this noise modulates the mixer gain, it will contribute at ␻, while if not the mixer can operate outside the 1/f noise- ␻ dominated band even for low if . In conclusion, we have demonstrated the use of a litho- ͑ ͒ ␻ ␻ graphically defined single-electron transistor as a radio- FIG. 4. a Mixing signal amplitude as a function of LO at constant if ϭ152.15 Hz; the signal and LO powers were Ϫ68 and Ϫ61 dBm, respec- frequency mixer that allows the detection of signals over a tively. The low-frequency rolloff is due to high-pass filtering, and the high- fully tunable 300 MHz band. The use of this technique is frequency rolloff is due to the ISD /e limitation. The dashed line is a guide to ͑ ͒ ␻ ␻ ϭ complementary with SET bandwidth-enhancing techniques the eye. b Mixing signal as a function of if for LO 50 MHz. The dashed line is a fit that gives a Ϫ3 dB single-side bandwidth of 250 Hz. such as the rf-SET. The generic nature of the mixer response, and the ease with which the mixer operation can be config- ␻ ured, should allow its application in devices using carbon ments near the intermediate frequency if at optimum gain nanotubes, single molecules, and quantum dots in addition to ␦ Ͻ ϫ Ϫ3 ͱ yield a signal charge sensitivity qS 4 10 e/ Hz, lim- metal tunnel junction circuits. ited by noise in the room-temperature electronics ͓Fig. 2͑d͔͒. The heterodyne response can be understood by using the The authors acknowledge the financial support provided sinusoidal approximation for the current–charge response. by the National Science Foundation XYZ-On-A-Chip Pro- ⌬ ␻ The heterodyne current Iif at if is then related to the gram, Contract No. ECS-9980734, and by the Research Cor- signal and LO voltages VS and VLO by poration through a Research Innovation Award. They thank ␲ ␲ Bob Hill for processing support. 2 CGVS 2 CGVLO ⌬I ϭ2⌬I J ͩ ͪ J ͩ ͪ , ͑2͒ if 0 1 e 1 e

in terms of the first-order Bessel function J1 . The small sig- ϭ⌬ ⌬ 1 ͑ ͒ nal if current gain gI Iif / IS is optimized for VLO at the T. A. Fulton and G. J. Dolan, Phys. Rev. Lett. 59,109 1987 . Ϸ 2 Single Charge Tunneling, edited by H. Grabert and M. H. Devoret, NATO first maximum of J1 , CGVLO 0.293e. For a current source ͑ ͒ ⌬ ϭ␻ Ӷ␻ ⌬ ASI Series, No. 294 Plenum, New York, 1992 . IS SCGVS Se, the current at optimal bias is Iif 3 A. N. Korotkov, Phys. Rev. B 49, 10381 ͑1994͒. ϭ Ϸ ⌬ ϭ ␻ ␻ ⌬ 4 gIIS 3.66 I0CGVS /e 1.83( max / S) IS . Current gain J. Pettersson, P. Wahlgren, P. Delsing, D. B. Haviland, T. Claeson, N. is therefore expected at frequencies below ␻ ϳ300 MHz Rorsman, and H. Zirath, Phys. Rev. B 53, R13272 ͑1996͒. max 5 for this device. E. H. Visscher, J. Lindeman, S. M. Verbrugh, P. Hadley, J. E. Mooij, and W. van der Vleuten, Appl. Phys. Lett. 68, 2014 ͑1996͒. We estimate the expected charge noise for the mixer us- 6 R. J. Schoelkopf, P. Wahlgren, A. A. Kozhevnikov, P. Delsing, and D. E. ␻ Ϸ ͑ ͒ ing the current shot noise SI( ) 2eISD . The output noise at Prober, Science 280, 1238 1998 . ␻, referenced to the input charge noise power S (␻), is ap- 7 A. N. Cleland and M. L. Roukes, Nature ͑London͒ 392, 160 ͑1998͒. q 8 ͑ ͒ proximately M. P. Blencowe and M. N. Wybourne, Appl. Phys. Lett. 77,3845 2000 . 9 J. M. Martinis, M. H. Devoret, and J. Clarke, Phys. Rev. B 35, 4682 2eI 2eI ͑1987͒. ͑␻͒ϭ SD Ϸ SD ͑ ͒ 10 R. J. Fitzgerald, J. M. Hergenrother, S. L. Pohlen, and M. Tinkham, Phys. 3 , 2͒ ⌬ 2͒ ץ ⌬ץ Sq ͑ Iif / qs ͑3.66 I0 /e Rev. B 57, 9893 ͑1998͒. 11 ͑ ͒ ␦ Ϸ ͱ P. K. Tien and J. P. Gordon, Phys. Rev. 129, 647 1963 . yielding input charge noise qS( f ) 0.97 e/I0. For our de- 12 K. Uchida, K. Matsuzawa, J. Koga, R. Ohba, S. Takagi, and A. Toriumi, ␦ Ϸ ϫ Ϫ4 ͱ ͑ ͒ vice this yields qS( f ) 1.3 10 e/ Hz, while for an op- Jpn. J. Appl. Phys., Part 1 39, 2321 2000 .

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