Supplementary Information

Uniform charging energy of single-electron transistors

by using size-controlled Au nanoparticles

Norio Okabayashi1, Kosuke Maeda1, Taro Muraki1, Daisuke Tanaka2, Masanori Sakamoto2,

Toshiharu Teranishi3, and Yutaka Majima4,*

1Materials and Structures Laboratory, Tokyo Institute of Technlogy, 4259, Nagatsuta-cho, Yokohama

226-8503, Japan and CREST, Japan Science and Technology Agency, Yokohama 226-8503, Japan

2Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba,

Ibaraki 305-8571, Japan and CREST, Japan Science and Technology Agency, Kyoto 611-0011, Japan

3Institute for Chemical Research, Kyoto University, Gokasho, Uji-shi, Kyoto 611-0011, Japan and

CREST, Japan Science and Technology Agency, Kyoto 611-0011, Japan

4Materials and Structures Laboratory, Tokyo Institute of Technology, 4259, Nagatsuta-cho, Yokohama

226-8503, Japan; CREST, Japan Science and Technology Agency, Yokohama 226-8503, Japan; and

Department of Printed Electronics Engineering, Sunchon National University, Korea

*E-mail: majima@msl.titech.ac.jp

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Detail of SET fabrication and electron transport measurement.A schematic view of the overall fabrication process is shown in Figure S1. The initial

structure of the source, drain, and gate electrodes of Ti(2 nm)/Au(10 nm) is fabricated on a SiO2(300 nm)/Si substrate by electron beam lithography (ELS-7500EX, Elionix, Japan) and the lift-off process, where the average gap separation is approximately 25 nm (Fig. S1a). After the processes of cleaning the initial electrodes by ultraviolet ozone treatment and oxygen plasma ashing, the sample is immersed into the plating solution, where an Au foil is

dissolved into the iodine tincture to establish an equilibrium reaction such as [AuI4]-+2e-　⇆

[AuI2]-+2I- S1-S3. By adding ascorbic acid as a reducing agent into the solution, [AuI2]- becomes

dominant in the solution. The ascorbic acid further oxidizes the source/drain and gate

electrodes to yield many electrons, by which the plating reaction such as [AuI2]-+e- → Au+2I-

takes place especially around the electrodes. The plating rate is proportional to the amount of Au ions in the nanogapS2. Therefore, decreasing the separation of the nanogap leads to a decrease in the plating rate and finally terminates the plating process at a certain nanogap distance (self-termination, Fig. S1b). In our methods, the yield of nanogap electrodes with a gap separation of less than 5 nm is approximately 90%. After making the nanogap electrodes, the sample is immersed in an ethanol solution of octanethiol (CH3(CH2)7SH, 1 mM) for 24 h to form saturated SAMsS4, which protect the surface from contamination (Fig. S1c). The sample is then immersed in the ethanol solution of decanedithiol (HS-(CH2)10-SH, 500 mM) for 24 h, by which decanedithiol molecules are inserted into the defect siteS5,S6 or octanethiol molecules are substituted with decanedithiol moleculesS6 (Fig. 1d). Finally, the decanedithiol-inserted electrodes are immersed in a toluene solution of Au NP protected by decanethiol (CH3(CH2)9SH) for 12 h, by which NPs are adsorbed on the site with the decanedithiol molecules (Fig. S1e ).

Size-controlled Au NPs are chemically synthesized following the established schemeS7.

Synthesized Au NPs are observed by transmission electron microscopy (JEM 1011, JEOL,

Japan) and the sample image is shown in Fig. S2. The mean diameter of the Au NPs is 5.2 nm

and the standard deviation is 0.5 nm.

The electron transport properties of SETs are measured by using a mechanical

refrigerator-type prober (GRAIL10-LOGOS01S, Nagase, Japan) and a semiconductor device

analyzer (B1500, Agilent, USA). The measurement temperature is controllable between 9 and

300 K. The pressure in the measurement chamber evacuated by a 50 L/s turbo molecular

pump is approximately 10-6 Pa at 9 K. The typical measurement time is 2 h for acquiring one

dI/dV_VgVd plot; this measurement is usually repeated around 3 to 4 times to increase the

signal_to_noise ratios. The dI/dV_Vd plot is acquired by differentiating the I_Vd curve

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numerically, where the data are averaged for several points of drain bias (smoothing) to

increase the signal-to-noise ratio. After measuring the electron transport properties, the

structure of fabricated SETs is checked by SEM (SU8000, Hitachi high-tech, Japan). In order

to observe the Au NPs on the electrodes, an acceleration voltage of -2.5 kV and a sample bias

of -1.5 kV are typically employed.

Quantized effects of Au NPs.

The quantized energy (E) of NP with radius r is written like dE=22ħ2/mkFVol, where ħ is

the plank constant, m is the electron mass, kF is the Fermi wave vector (12.1 nm-1 for Au) and

Vol is the volume of NP (4r3/3)S8. In the case of Au NP with a diameter 5.2 nm, E is

estimated to be 1.7 meV and this quantum effect can be observed as satellite lines at the

temperature less than E/(3.5kB)(=6 K)S8.

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Figure S1. Schematic viewing of the fabrication process based on combination of top-down

and bottom-up processes. (a) First, initial electrodes with the gap separation of 25 nm are

fabricated by electron beam lithography. (b) Second, the nanogap electrodes with the

separation less than 5 nm are made by immersing the initial electrodes in the electroless

plating solution. (c) Third, octanethiol SAM is formed on the nanogap electrodes by

immersing the nanogap electrodes in the ethanol solution containing octanethiol (1mM) for

24h. (d) Fourth, decanedithiol molecules are inserted into the SAM by immersing the sample

in the ethanol solution containing decanedithiol (500 mM) for 24h. (e) Finally, by immersing

the sample in the toluene solution containing Au nanoparticles (NPs) for 12h, Au NPs are

adsorbed on the electrodes where the decanedithiol molecules are inserted. By employing this

processes, we can make many SETs in parallel.

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Figure S2. A transmission electron microscopy image of chemically-synthesized Au NPs. The

Au NPs are protected by the decanethiol molecules, which prevent the aggregation of NPs.

Some connections between two NPs are due to the irradiation of the electron beam. The

average diameter and the standard deviation are estimated to be 5.2 and 0.5 nm, respectively.

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Figure S3. Various Coulomb diamonds measured at 9 K, which is used to analyze the

tunneling parameters of SETs (see Table. S1). All devices show the idealized Coulomb

diamond constituted by the lines with two slopes or the marginally deformed pattern.

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Figure S4. Temperature dependent (a-f) Coulomb diamonds, (g) Coulomb oscillations and (h)

on/off current ratio estimated from the Coulomb oscillations.

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Table SI. Statistical analysis of the tunneling parameters for single NP SETs (see Fig. S3).

Ec C1 C2 Cg R1 R2 Q0

(meV) (aF) (aF) (zF) (G) (G) (e-)

#1 43 0.90 0.92 32.0 6.3 1.2 -0.19

#2 55 0.72 0.72 14.0 110 32 -0.13

#3 50 0.78 0.82 3.1 12 0.8 0.00

#4 47 0.85 0.85 7.5 1.3 0.35 -0.26

#5 46 0.80 0.95 5.0 0.35 0.32 -0.02

#6 50 0.86 0.72 12.0 42 30 -0.45

#7 49 0.72 0.90 10.0 0.40 0.30 0.00

#8 44 0.85 0.95 5.0 0.14 0.46 0.40

#9 50 0.82 0.78 6.0 2.00 5.0 -0.45

avg. 48 0.81 0.85 10.5 2.9* 1.6* -0.12

4 0.06 0.09 8.8 0.3–2.9** 0.2–10** 0.26

*geometrical average

**range of resistance estimated from the geometrical standard deviation

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