Carbon nanotube RF-SETs

Multiwalled carbon nanotube RFSETs

Single electron transistors (SET) are the most sensitive electrometer ever made [1]. However, these devices are limited by very small bandwidth (few kHz) for charge detection. One way to circumvent such problem has been proposed by R.J. Schoelkopf et al. [2]: they used a reflected carrier wave from the impedance transformer circuit and the SET. The variation of the island charge changes the impedance of the SET. Consequently, the amplitude of the reflected wave is modulated according to the SET impedance changes. The optimal charge sensitivity is achieved when the SET and the wave impedance of the transmission line are perfectly matched. The SET bandwidth is limited by the loaded Q-factor of the impedance transformer. The theoretical maximum bandwidth can be found using the Bode-Fano criterion [3]. The best sensitivity have been obtained using superconducting SETs (also called Cooper pair box)made of Al-AlOx, approaching the shot noise limit of h/2π [4]. For normal state SET the theoretical value has been predicted to be around 1.4h/2π [5]. At liquid helium temperature, the best charge sensitivity so far has been measured of δq=1.9*10-6e/√Hz [6]. Because of their large charging energy and their small capacitance, carbon nanotubes are very promising for RF-SETs. Early measurements with multi walled carbon nanotubes have demonstrated great potential [7].

[1] M.H. Devoret and R.J. Schoelkopf, Nature 406, 1039 (2000).

[2] R.J. Schoelkopf, P. Wahlgren, A.A. Kozhevnikov, P. Delsing, and D.E. Prober, Science 280, 1238 (1998).

[3] D.M. Pozar, Microwave engineering, Addison-Wesley, New York, 1st edition (1990).

[4] A. Aasime, D. Gunnarsson, K. Bladh, P. Delsing, and R.J. Schoelkopf Appl. Phys. Lett. 79, 4039 (2001).

[5] A.N. Korotkov and M.A. Paalanen, Appl. Phys. Lett. 74, 4052 (1999).

[6] H. Brenning, S. Kafanov, T. Duty, S. Kubatkin and P. Delsing, J. Appl. Phys. 100, 114321 (2006).

[7] L. Roschier, M. Sillanpää, W. Taihong, M. Ahlskog, S. Iijima, and P. Hakonen, J. Low Temperature Phys. 136, 465 (2004).

Reflected amplitude on a logarithmic scale, log(Γ), as a function of the gate and bias. The lighter the color, the lower the reflection coefficient Γ.
Typical spectrums of the amplitude modulated signal of a multiwalled carbon nanotube sample. The upper curve corresponds to the optimum charge sensitivity point. It is seen that there is some contribution of the 1/f noise, but its effect starts to be dominated by the preamplifier noise at modulation frequency ωm ≥ 100 kHz. We found the charge noise to follow 1/f behaviour and a value 400 μe/√Hz at 20 Hz. The frequencies are ωm/2π = 588.3 MHz. The biggest peak at the center correspond to the reflected signal. The side peaks correspond to the gate charge excitation of 1/20e. The signal over noise ratio (SNR) is the ratio between the signal and the noise floor.

Singlewalled carbon nanotube RFSETs

Here we have measured an RF-SET based on a single walled nanotube in the strong tunneling regime at T=4.2 K: we showed the sensitivity obtained is comparable to the one measured by H. Brenning et al., J. Appl. Phys. 100, 114321 (2006), but with a much better gain*bandwidth (one order of magnitude larger). This study has been done in collaboration with Søren Andresen from the Niels Bohr Institute, Copenhagen, within the CARDEQ project.

(a) Schematic of the sample measured in these experiments. We use sapphire for lower loss and charge noise compared to conventional Si/SiO2. The single walled nanotubes are grown by chemical vapor deposition (CVD). From S.E.S. Andresen et al., J. Appl. Phys. 104, 0337145 (2008) [1].
Experimental set-up for RF-SET measurements, all immersed in liquid helium for cooling to 4.2 K. From S.E.S. Andresen et al., J. Appl. Phys. 104, 0337145 (2008) [2].
Coulomb diamonds measurements: (a) 2D-map of the differential conductance dI/dVbias in units of e2/h as a function of gate voltage VG and bias voltage Vbias. The lines mark the charge degeneracies. (b) Values of the addition energy Eadd deduced from (a) as the degeneracy crossings in Vbias. From S.E.S. Andresen et al., J. Appl. Phys. 104, 0337145 (2008) [3].
(a) Demodulated signal averaged over 5000 gate voltage sweeps of each 2 ms. Circles mark the points of perfect matching used in (b) and (c). (b) Power spectrum (0.3 MHz spectral resolution) under 754.2 MHz carrier excitation (−65 dBm) and 10 MHz gate modulation of 0.006e. (c) Charge sensitivity versus modulation frequency fmod, with/without a 100 MHz low-pass filter on the gate line (open/filled symbols). The lines indicate the roll-off limited by the bandwidth and 1/f noise at low frequency. From S.E.S. Andresen et al., J. Appl. Phys. 104, 0337145 (2008) [4].

Related publications

  • Highly sensitive and broadband carbon nanotube radio-frequency single-electron transistor

S.E.S. Andresen, F. Wu, R. Danneau, D. Gunnarsson, and P.J. Hakonen

J. Appl. Phys. 104, 0337145 (2008) [5], also in arXiv:0711.4936 [6]

  • Carbon nanotube radio-frequency single-electron transistor

L. Roschier, M.A. Sillanpää, T.H. Wang, M. Ahlskog, S. Iijima, and P.J. Hakonen

J. Low Temp. Phys. 136, 465 (2004)