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Gold Nanoparticles on Functionalized Silicon Substrate Under Coulomb Blockade Regime: An Experimental and Theoretical Investigation Olivier Pluchery, Louis Caillard, Philippe Dollfus, and Yves J. Chabal J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b06979 • Publication Date (Web): 25 Oct 2017 Downloaded from http://pubs.acs.org on October 29, 2017

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The Journal of Physical Chemistry

Gold Nanoparticles on Functionalized Silicon Substrate under Coulomb Blockade Regime: an Experimental and Theoretical Investigation. Olivier Pluchery* 1, Louis Caillard † 1,2, Philippe Dollfus 3, Yves J. Chabal 2

1

Sorbonne Université, UPMC Univ Paris 06, CNRS, Institut des Nanosciences de Paris, 4 place Jussieu, 75005 Paris, France.

2

Laboratory for Surface & Nanostructure Modifications, Department of Materials Science and Engineering, University of Texas at Dallas, 800 West Campbell Road, Dallas, Texas 75080, USA 3

Centre de Nanosciences et de Nanotechnologies, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 220 rue André Ampère, 91405 Orsay, France

ABSTRACT

Single charge electronics offers a way for disruptive technology in nanoelectronics. Coulomb blockade is a realistic way for controlling the electric current through a device with the accuracy of one electron. In such devices the current exhibits a step-like increase upon bias

ACS Paragon Plus Environment

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which reflects the discrete nature of the fundamental charge. We have assembled a double tunnel junction on an oxide-free silicon substrate that exhibits Coulomb staircase characteristics using gold nanoparticles (AuNPs) as Coulomb islands. The first tunnel junction is an insulating layer made of a Grafted Organic Monolayer (GOM) developed for this purpose. The GOM also serves for attaching AuNPs covalently. The second tunnel junction is made by the tip of an STM. We show that this device exhibits reproducible Coulomb blockade I-V curves at 40K in vacuum. We also show that depending on the doping of the silicon substrate, the whole Coulomb staircase can be adjusted. We have developed a simulation approach based on the orthodox theory that was completed by calculating the bias dependent tunnel barriers and by including an accurate calculation of the band bending. This model accounts for the experimental data and the doping dependence of Coulomb oscillations. This study opens new perspectives towards designing new kind of single electron transistors (SET) based on this dependence of the Coulomb staircase with the charge carrier concentration.


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1. Introduction The miniaturization of electronic devices has reached a limit in size where charge transport is strongly impacted by the atomic nature of interfaces and by quantum physics. The thinnest gate oxide is just a few atomic layers and any non-uniformity in the interface leads to breakdown and leakage currents when the SiO2 insulating layer is thinner than 3 nm1, 2. However these ultrathin layers when they are connected to nanoelectrodes produce ultrasmall capacitances.3 Such capacitances could be the primary building blocks of a Coulomb blockade nanodevice, such as a single electron transistor (SET) where the electric current itself reflects the discrete nature of the electric charge.4-6 Single charge devices are scrutinized as possible ways for new electronic devices7,

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or as new electron-counting

standards in metrology9. They however require a high morphological control in order to precisely adjust the tunnel barriers whereby single electron devices provide a way to investigate the transport mechanism through molecular barriers or chemically connected nanoparticles. They definitively constitute a path for enabling nano-electronics.10 Coulomb blockade occurs when a conducting or a semiconducting island is connected to two electrodes by two tunnel junctions, termed as double tunnel junction (DTJ). When an external bias is applied, the addition of a supplemental charge into the island is possible if an energy = ⁄2 is provided (e is the elemental charge and is the total capacitance of the island). As a result, the current as a function of the applied bias measured through such a DTJ, exhibits discrete steps called the Coulomb staircase. A simplistic approach considers the island as a metallic sphere (diameter dNP), for which the eigen capacitance is approximately given by = 2 . The electrostatic energy overcomes the thermal noise if > which is the case when dNP is smaller than 5 nm for room temperature operation. Most of the Coulomb blockade experimental demonstrations on single objects are conducted


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with metallic nanoparticles deposited on a metallic substrate.

5, 11, 12

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However, replacing the

metallic substrate with a semiconductor, offers a wealth of new phenomena as well as adjustable parameters to control the electron flow through a single electron device. First, semiconductors readily oxidize at room atmosphere and if a tight control of oxidation is not secured, surface states will impact the electrical transport.13 Second, the fact that the substrate and the active island are of different materials leads to differences in the work functions and to a new charge equilibrium. Therefore the island is already charged at zero applied bias.14 Third, the use of a semiconductor opens specific functionalizing methods that can be adapted for adjusting the thickness of the organic insulator.15 But above all, depending on the doping level of the substrate, band bending will play a crucial role in the Coulomb blockade occurrence16 and, if accurately controlled, offers a unique handle to control the phenomenon.

The present article is a follow-up of previous studies of our group which were focused on the experimental results related to Coulomb blockade. Herein we elaborate the theoretical background for describing quantitatively this Coulomb blockade. We have fabricated a highly controlled grafted organic monolayer (GOM) on silicon as a robust, controllable insulator.8, 17 We have already described the morphological18 and electrical19 characterization of this GOM. Gold nanoparticles (AuNPs) were covalently bound to the GOM as shown in Figure 1 and we have shown earlier that they act as Coulomb islands and give rise to Coulomb staircase.16, 17, 20

Here, we describe an approach elaborated from the orthodox theory and we show that this

model precisely predicts the electrical behavior of the DTJ taking into account the band bending induced by the metallic nanoparticles, when brought in close vicinity of the silicon substrate. We have experimentally tested three doping levels for silicon and we show how both the position and the spacing of the Coulomb staircase depend on the carrier


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concentration. This opens the way for a new kind of single electron devices where the carrier concentration of the semiconducting substrate efficiently controls the tunnel barriers.

Figure 1. a) Scheme of the double tunnel junction (DTJ) considered in this work, made of a semiconductor substrate, a GOM as insulating layer, a gold nanoparticle as Coulomb island and an STM tip as second electrode. This is a SIMIM structure (Semiconductor Insulator-Metal-Insulator-Metal) b) The GOM layer is fabricated on oxide-free silicon and ensures an organic insulating layer. It is obtained by the reaction of ethyl 6heptenoate with a fully hydrogenated silicon followed by three chemical steps (details in Refs 16, 18 and 20). c) Corresponding band diagram, when a negative bias is applied

(corresponding to a positive STM gap voltage when conventional notations are used). is the band bending at the silicon-GOM-gold interface resulting from the applied

bias. In the condition depicted here, the gold island contains two supplementary electrons. ? is the molecular dipole.

2. Methods 2.1. Theoretical description of the double tunnel junction


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2.1.1. Band diagram The DTJ in our study is made of four materials: n-doped silicon, an organic layer, gold and tungsten. The molecule is covalently bound to silicon and is terminated by an amine group.16, 18, 20

The electrical parameters of this GOM have already been measured: the work function

of this surface is 3.4 eV, the HOMO and LUMO bands are at 7.5 and 1.0 eV below the vacuum level, respectively. This surface also exhibits a molecular dipole of −1.0 eV

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and

the effect of such dipoles was discussed elsewhere.21-23 The WF of gold and tungsten are taken at 5.1 and 4.5 eV, respectively. When the STM tungsten tip approaches the AuNP, an electrostatic equilibrium is established and drives silicon in depletion: > 0 (See SI). One specific aspect of this DTJ is that at zero bias, the island is already charged with electrons, whose number depends on the nanoparticle size.14 However this does not influence the Coulomb blockade, since the level spacing is equal to the energy independently on the number of electrons already stored in the island.

2.1.2. Band bending calculation Band bending is an important aspect of the DTJ in our system. At the interface siliconmolecule-gold, the electrostatic equilibrium establishes like in a Metal Oxide Semiconductor (MOS) structure and the conduction and valence bands of silicon may bend up or bend down which changes the type of carrier at the silicon/insulator interface from holes (inversion) to electrons (accumulation). Band bending appears like a supplemental energy barrier that the electron needs to overcome, and whose profile and extension depend on the applied bias and the semiconductor doping. It will affect the electric description of the first tunnel barrier. Band bending is measured by the potential => and the corresponding energy −=> shown in

Figure 1-c (See also Fig. S1 in the SI). The applied bias is noted BCDEF and corresponds to a potential applied to the metallic tip relative to the semiconducting substrate. The DTJ is made


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of a succession of the following materials: semiconductor-molecule-metal-vacuum-metal. Given the values of the work functions of the materials, when no potential is applied, silicon is already in depletion. When a negative bias is applied to the tungsten electrode (semiconductor grounded), silicon is further driven in depletion until reaching inversion. The fact that silicon can be driven from depletion to inversion (very negative Vbias) or to accumulation (positive Vbias), changes the barrier profile experienced by the charge carriers. As a result this first barrier in the DTJ varies upon applied bias and this strongly influences Coulomb blockade. Notice that a negative bias Vbias corresponds to a positive energy −BCDEF

-30

Vbias = -1.5 V

-20

-10

0

tip

-2.0

Si GOM AuNP vac

-1.5

10

φs

b) n 40 K n+ 40 K n++ 40K

2 Interface potential (V)

interface potential

-1.0

Vbias - Vfb

-0.5

band bending

applied bias

a) 0.0

(VSTM = -Vbias)

in the band diagram of Figure 1-c.24

Potential (V)

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1

n+ n+

0

170 K 300 K

-1 V_STS_interf_2E15_40K V_STS_interf_1E18_40K V_STS_interf_7E19_40K V_STS_interf_1E18_300K V_STS_interf_1E18_170K

-2 -3 -2

Distance (nm)

-1

0

1

2

3

STM applied bias (V)

Figure 2. a) Actual potential profile calculated through the DTJ when a bias of −1.5 V is applied in the case of the n+ doping at 300K. Vfb is the flatband potential (Vfb = 0.373 V). The band bending is calculated at =F =−0.24 V and the depth of the depletion zone is 15 nm. b) Calculation of the potential drop through the DTJ in three cases as a function of the applied STM bias (at 300K and 40 K): n, n+ and n++. At zero bias the DTJ in depletion and when the STM bias is increased the system is driven into inversion.

Metal-Insulator-Semiconductor (MIS) structures are described in details in the textbook of Sze.24 Here our DTJ is a SIMIM structure (See Figure 1-a) whose electrostatics equilibium


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can be modeled in ideal cases with a software released by Knowlton.25 However the situation described in Figure 1-a departs from these ideal cases and we have setup a calculation strategy that can be summarized in the two following steps.26 (1) The electrostatic potential is calculated throughout the entire DTJ structure, under the assumptions that it is made of series of planar thin films: silicon substrate, GOM, gold layer, vacuum and tungsten. The derivation follows classical electrostatics where the Poisson equation is solved numerically.24 Briefly, the electrostatic potential =(Q) is calculated along a line going through the different layers. As shown in Figure 2-a the major potential drop occurs in the insulating layers (GOM and vacuum) and band bending is clearly visible in the semiconductor in the region between −15 nm and 0 nm. See SI for more calculations details. (2) Compared to the case treated by Southwick and Knowlton25, we have included the calculation of the Dirac integral for assessing the carrier density in the semiconductor, instead of the Boltzmann approximation. This allows considering cases of low temperatures (below 100 K). We have also included the electrostatic dipole for the insulating layer since in our case it is made of ordered molecules.19, 22 The results of these first two steps are illustrated in

Figure 2. Figure 2-a shows the potential profile across the DTJ where the various contributions to the overall potential drops are made clear: => , the band bending in the semiconductor, and the potential drops through the insulating layers (GOM and vacuum). Vfb is the flatband potential (Vfb = 0.373 V) which is the bias that needs to be applied at a metalsemiconductor interface to nullify the band bending. In practice, in the case of DTJs, it shows up as a supplemental contribution in the equilibrium of the potentials in stacked interfaces. It depends on the nature of the contacted materials. In what follows, it is crucial to distinguish between the bias applied to the whole junction (Vbias) and the potential across the junction itself (Vinterf) that controls Coulomb blockade. Vinterf is obtained by subtracting => (Figure 2a). If we were using a metallic electrode we would have Vinterf = Vbias. Also notice that the


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usual convention is that the bias in STM experiments (VSTM) is applied to the surface, relative to the tip. Therefore BCDEF = −B>RS . These calculations show that for a donor concentration ND = 2 × 1018 cm−3 (noted n+ in the following) and at RT, the width of the depletion layer is about 15 nm. Figure 2-b shows how Vinterf depends on the applied bias for different doping levels. Notice that for n++ doping, the behavior is metallic and Vinterf = Vbias. Figure 2-b also shows that at 40K, the semiconductor band bending strongly affects the interface potential when VSTM is in the range [−2.0; −0.4 V] which corresponds to the potential range where the silicon is in depletion. Out of this range, silicon is in inversion (VSTM > −0.4 V) or in accumulation (VSTM < −2.0 V), the slope is 1 and the effect will be limited to a potential offset.

2.1.3. Model for Coulomb blockade and current calculation A simulation program for describing the electron transport in Coulomb blockade regime, was developed using Matlab and another code written in C. The general approach is sequential tunneling through insulating barriers based on the transfer Hamiltonian theory.27, 28 This method consists in calculating the wave functions on both sides of the barrier and their penetration into the barrier. It has been developed for both semiconducting quantum dots28 and metallic islands.27 In the case of metallic conductors on both sides of the barrier, an analytic expression of wave functions has been derived within the WKB (Wentzel-KramersBrillouin) approximation that explicitly includes the electric field in the barrier, i.e. the voltage applied to the structure, beyond the orthodox theory of single charge tunneling. The wave functions are used to calculate the matrix element of the tunnel Hamiltonian and the tunneling rates within the first order perturbation theory. In the simple case of a single barrier, this approach has been shown to give the same current as an exact calculation based on the time-dependent Schrödinger equation. To calculate the current in a DTJ, these bias-


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dependent tunneling rates are introduced in the master equation.27,

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28

This approach

exclusively relies on the knowledge of the physical parameters of the device and the materials, without any fitting parameters. Here, the device parameters are mainly the distance dtip between the tip and the AuNP, the diameter dAuNP of the AuNP and the thickness dGOM of the organic layer, as sketched in Figure 3. Throughout this work, the medium between the tip and the AuNP is considered to be vacuum. The gold AuNP is considered to be perfectly spherical and homogeneous, without any surrounding ligand (See Figure 3-b). Its diameter is adjusted from 3 to 10 nm depending on the size of the AuNP in the experimental data. The organic layer is considered to be homogeneous and in direct contact with the AuNP. The electron effective mass was set to 0.26×me in Si and in the GOM, and me in the island and in the tip. The dielectric function of the GOM T was taken at 2.2, according to similar organic systems studied elsewhere.29 The capacitance of a sphere in the vicinity of a plane is taken from Ref.30 and calculated according to X

= ln U1 + VW Y [ + 2 Z

Equation 1

where dNP is the radius of the nanoparticle, D is the distance of the center of the nanoparticle to the silicon substrate and T is the relative dielectric function of the GOM.

Figure 3. Geometrical description of the model used for computing the current of our double tunnel junction. The central island is made of a spherical nanoparticle connected


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to the silicon substrate and the STM tip by two junctions represented by a resistor and a capacitor (a). Panels (b) and (c) depict the geometry used for calculating the tunnel barrier height (b) and the current density (c). The intensity of the current was computed by integrating the current density over effective surfaces that were approximated to two disks of surface SG and SD (See Figure 3-c) and taken ⁄10. As demonstrated earlier,27 this model clearly reproduces the ]^ = ]Z =

_`

Coulomb staircase. More details about the model are given in Tables S3 and S4 of the SI. We have also checked the validity of the model, and experimental results from another group11 were accurately reproduced. 2.2. Experimental methods A grafted organic monolayer made with a molecule of ethyl 6-heptenoate was prepared and further modified so that the surface was amine-terminated, following the procedure described elsewhere.16,

20

The GOM was measured to be 1.3 nm with elliposmetry.16,

18

Gold

nanoparticles were prepared in aqueous colloidal solution by reducing HAuCl4 with ascorbic acid and were measured to be spherical and with diameters between 4 and 12 nm (mean and standard deviation 8.5 ± 2.4 nm). AuNPs prepared with this chemical method were evaluated with high-resolution transmission electron microscope and they had shapes very close to spheres. In the present case, the degree of sphericity was quantified by calculating the elliptic ratio of the particles: ellipticity was found to be between 1 and 1.25 (1 being a perfect sphere) for 75% of the particles.20 They were attached onto the GOM by dipping the substrate for 10 min in the colloidal solution. The silicon substrate remained oxide-free.16, 18, 20 The sample was introduced in the UHV chamber of an Omicron VT-STM (base pressure 4x10−11 mbar) and shortly annealed at 150°C for 30 min for removing physisorbed molecules. Neither the size nor the crystallinity of the nanoparticles were modified during this this low-temperature


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annealing.14,

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STM and STS experiments were carried out at 40K, the sample being

connected to a cold finger cooled by a liquid helium flow.

3. Results 3.1. Experimental evidence of Coulomb blockade for n++ doped substrate

Figure 4. Scanning Tunnel Spectra (STS) on the n++ silicon substrates at 40K on a 6.6 nm (STM height 5.5 nm) gold nanoparticles attached on GOM. Simulated STS curve, where no doping was included since a degenerately doped silicon sample behaves like a metallic electrode. Panel a) is the current, panel b) is the conductance obtained by numerical derivation and panel c) is the STM image (30x30 nm, −2V, 30 pA). The applied bias corresponds to the bias of the surface relative to the STM tip.

In the case of a degenerately doped silicon substrate, with ND = 7 × 1019 cm−3 (noted n++ in the following) Figure 4-a) shows the I-V curve obtained on the AuNP shown in Figure 4-c),


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whose height was measured to be 5.5 nm according to the STM (height profile, not shown). Conductance is obtained by numerical differentiation and isplotted in Figure 4-b). This clearly shows the Coulomb peaks, measured at 350, 660, 960 and 1180 mV at positive bias. They are equally spaced with a Coulomb spacing of 272 ± 9 mV. For the negative peaks, spacing is 290 mV. The width of the zero current domain is measured at 550 mV (as shown in Figure 4-a). In usual Coulomb blockade on metallic substrates, this zero-current region would be equal to the step spacing (290 mV). This overgap is due to the peculiar electronic characteristics of the GOM that gives rise to an ambipolar conduction regime: conduction is due to electrons for positive bias and to holes in the negative bias region.32 The switching from hole to electrons has to overcome a barrier of 260 mV (550 – 290 mV). This can be seen in the band diagram in Figure 1-c and is explained further in the SI.

This case (Si n++) is similar to the ‘usual’ case when the substrate is metallic which is largely reported in the literature. See for example Refs.5, 11, 12, 33 In this case, the orthodox model correctly describes the I-V curves as shown in Figure 4. There is no need to take into account any band bending phenomenon. The diameter of the nanoparticle in the simulation is 6.6 nm (the other parameters are given in the SI). The fact that AuNPs appears roughly 1 nm smaller in STM than they actually are, was already noted when comparing their size with the values obtained in AFM20 and is due to the high electric resistance of the DTJ that forces the STM tip approaching the nanoparticle. The capacitance of the two junctions are CGOM = 1.3 aF and Cvac = 0.58 aF. The good match between experimental results and simulation confirms that the various elements of our description are correct: electronic parameters for describing the GOM and the transport model.


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3.2. Doping dependence of Coulomb Blockade STS curves were recorded for different values of the doping of Si substrates: Nd = 2×1015, 1×1018 and 7×1019 cm−3 (denoted n, n+ and n++ respectively). In all three cases Coulomb blockade was observed for various nanoparticles and on several set of substrates. STS curves shown in Figure 5 are taken on AuNPs of approximately the same size (diameters between 5 and 6.5 nm measured from the height profile in the STM images). It shows clearly the role of dopant concentration, as expected from a semiconductor. The Coulomb staircase is visible as shallow oscillations and the width of the zero current region (current below 1 pA) is 475 mV, 690 mV and 1110 mV for doping n++, n+ and n respectively. For moderate STM voltage, the substrate is in depletion as shown in Figure 1-c and is slowly driven into inversion when the voltage is increased. The onset of the positive current does not strongly depends on the carrier concentration. However, for negative STM bias, the silicon is in accumulation and the current onset is clearly dependent on the doping.

Figure 5. Experimental STS at 40K for three different dopings and for similar AuNPs of diameters 5.5, 6.5 and 5.0 nm. The arrows point to the first step of the Coulomb staircase for each doping.


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4. Discussion 4.1 Coulomb blockade as a function of nanoparticle diameter We restrict to the n+ substrate. Thirty three AuNPs were analyzed with STS and two typical I-V curves recorded on a 7.3 and 5.4 nm AuNPs are plotted in Figure 6-a). The STM image in Figure 6-c) shows AuNP#1 along with three other nanoparticles. These particles are spherical although their shapes look elongated on the figure. These apparent shapes and sizes result from the convolution with the STM tip whose radius of curvature is estimated at 810 nm. The corresponding conductance curves are plotted in Figure 6-b). The conductance curves were calculated numerically. The simulated STS curves were calculated with the model described above and the bias voltage was corrected after calculating the band bending induced by the presence of the gold nanoparticle. This correction tends to positively shift the positions of the steps and to increase the zero current region in the gap (see Figure S8 in the SI for a direct visualization of the effect of this bias correction). The first step is measured at +0.35 V and would have shown up +0.13V if there were no band bending. The experimental dependence of the step width as a function of nanoparticle diameter is plotted in Fig. 6-d. It shows a roughly linear evolution as could be anticipated with the simplistic model that predicts a step width given ∆B = ⁄2 . The smallest AuNP investigated is 4 nm and the corresponding step width is 370 mV. It is roughly linear with diameter until 8 nm where it reaches 250 mV.


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Figure 6. STS at 40K for n+ doped Si for various nanoparticle sizes. Experimental STS are shown on two nanoparticles a) along with the conductance curves in graph b). The STM image is shown in c) with a scan size of 60 x 100 nm (scanning parameters: −2V and 30 pA). d) The evolution of the step width is shown as a function of the nanoparticle diameter for 33 different particles.

4.2 Coulomb blockade as a function of doping concentration These results show that the position of the steps for a given size of nanoparticles depends on the carrier concentration of the substrate. If the doping could be adjusted this would be a way to shift the step position. From the model discussed above, it is possible to predict how the Coulomb steps depend on the carrier concentration of the silicon substrate. We have used our model to predict the evolution of the Coulomb oscillation in the case of an 8 nm nanoparticle at 40K on a substrate assuming it is possible to modulate the carrier concentration from 1015 to 1020 cm−3. The result is the conductance map shown in Figure 7-a


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where the dependence on the carrier concentration and on the applied STM bias is visible. The Coulomb peaks correspond to the brighter areas of this map. When these brighter lines are vertical, it means there is no dependence with the carrier concentration. The violet central line is the zero current region where no electron is allowed to flow through the DTJ. It is not at 0 V as would have been the case in symmetric metallic DTJ11 but at −0.33 V as long as the carrier concentration is not greater than 6×1017 cm−3. Figure 7-b shows three conductance curves extracted from the conductance map. This is striking how the modulation of the carrier concentration shifts the overall curves, similarly as would do the change of a gate voltage in a single electron transistor. For example the first Coulomb step is predicted at −0.22 V for ND = 1017 cm−3, −0.36 V for ND = 1018 cm−3 and −0.90 V for ND = 1019 cm−3.

Figure 7. a) Simulation of the conductance map showing the dependence of the Coulomb oscillations as a function of carrier concentration in the silicon substrate. Conductance


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is plotted for a nanoparticle of 8 nm at 40 K when doping ND is varied from 1015 to 1020 cm−3. b) Cross sections of the map showing the conductance curves for three values of ND: (i) 1×1017, (ii) 1×1018, (iii) 1×1019 cm−3. It clearly shows how the Coulomb staircase is affected by the carrier concentration. The violet arrows indicate the zero current regions where the current is blocked. For ND = 1×1018, the shape of conductance (ii) can be understood with the help by Fig 2b where the interfacial bias is plotted when the STM bias is swept from +1.5 to −1.5 V. As long as VSTM > −0.5 V, the slope of Vinterface vs. VSTM is 1 and the Coulomb steps are equally spaced. However when VSTM decreases below −0.5 V, the substrate starts entering in depletion and the applied STM bias partially drops in the depletion zone. As a consequence the Coulomb oscillations turn more spaced and less visible (See curve (ii) in Figure 7-b). This effect is also clearly visible in the conductance (i) of Figure 7-b) when VSTM is below −1.0 V. Therefore, changing the carrier concentration of the silicon substrate allows shifting the Coulomb oscillations, without changing the Coulomb spacing. This can give rise to similar effects as those observe with to the conventional Single Electron Transistor (SET). They are characterized by the so-called Coulomb diamonds when conductance is mapped as a function of VGS and VDS.4,

6, 34

In our approach the role of gate voltage is played by the carrier

concentration. A prototype of SET based on this principle is currently under testing and will be described in a later publication.

5. Conclusion In this work we have presented a set of experimental STS data where Coulomb blockade is clearly detected at 40K, for various sizes of the gold nano-island (diameter between 4 and 10 nm) and with silicon substrates of various doping levels. We have developed a model that combine an improved orthodox theory model with an accurate band bending calculation. The


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model is able to account quantitatively for the STS experimental data. This double tunnel junction works in accumulation, depletion and inversion respectively when the STM bias increases from −1.5 to +1.5 V. The overall Coulomb staircase is shown to depend on the doping level of the substrate because the energy profile of the first tunnel barrier is modified by the band bending induced in the silicon substrate. At 40K, a 8 nm nanoparticle covalently bounded to a n+ silicon substrate, via a GOM, will give rise to Coulomb oscillations with a width of 270 mV. And if the doping is changed, the overall characteristics is shifted. This is a remarkable property that can be used to design the concept of a single electron transistor (SET) where the gate voltage would be replaced by the modulation of the density of the carriers. This is the case in fully depleted transistors. This study establishes the foundations of a now kind of SET based on the modulation of the carrier concentration of the substrate. ASSOCIATED CONTENT Supporting Information. Electric characteristics of the organic layer; details on the derivation of the band bending; parameters used for running the simulations; simulated STS curves for various tip-nanoparticle distances; experimental STS data of Coulomb blockade; conductance map at 170K AUTHOR INFORMATION Corresponding Author * Corresponding author, [email protected] Present Addresses † present address for Louis Caillard: Aveni Company, 15 rue du Buisson aux Fraises, 91300 Massy, France Author Contributions


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The manuscript was written through contributions of all authors. ACKNOWLEDGMENT Funding Sources OP is grateful for a sabbatical stay granted by La Pampa Foundation. LC acknowledges support from Nanotwinning FP7 grant, NN294952 and from a Chateaubriand fellowship. Part of this work was supported by the NSF Grant CHE-1300180, University of Texas at Dallas. REFERENCES 1. Wang, L. L.; Peng, W.; Jiang, Y. L., A Modified 1/ f Noise Model for MOSFETs With Ultra-Thin Gate Oxide. IEEE Electron Device Letters 2016, 37, (5), 537-540. 2. Peng, H.; Feng, Q., Reliability Modeling for Ultrathin Gate Oxides Subject to Logistic Degradation Processes with Random Onset Time. Qual. Reliab. Engng. Int. 2013, 29, (5), 709-718. 3. Mullen, K.; Benjacob, E.; Jaklevic, R. C.; Schuss, Z., I-V Characteristics of Coupled Ultrasmall-Capacitance Normal Tunnel-Junctions. Phys. Rev. B 1988, 37, (1), 98-105. 4. Ray, V.; Subramanian, R.; Bhadrachalam, P.; Liang-Chieh Ma; Kim, C.-U.; Koh, S. J., CMOS-Compatible Fabrication of Room Temperature Single-Electron Devices. Nature Nanotechnology 2008, 3, 603-608. 5. Lehmann, H.; Willing, S.; Moller, S.; Volkmann, M.; Klinke, C., Coulomb Blockade Based Field-Effect Transistors Exploiting Stripe-Shaped Channel Geometries of SelfAssembled Metal Nanoparticles. Nanoscale 2016, 8, (30), 14384-14392. 6. Azuma, Y.; Onuma, Y.; Sakamoto, M.; Teranishi, T.; Majima, Y., Rhombic Coulomb Diamonds in a Single-Electron Transistor Based on an Au Nanoparticle chemically anchored at both ends. Nanoscale 2016, 8, (8), 4720-4726. 7. Bhadrachalam, P.; Subramanian, R.; Ray, V.; Ma, L.-C.; Wang, W.; Kim, J.; Cho, K.; Koh, S. J., Energy-Filtered Cold Electron Transport at Toom Temperature. Nat Commun 2014, 5, 4745. 8. Pluchery, O., Gold Nanoparticles to Drive Single-Electron Currents. SPIE Newsroom 2015. 9. Stewart, M.; Zimmerman, N., Stability of Single Electron Devices: Charge Offset Drift. Applied Sciences 2016, 6, (7), 187. 10. Vilan, A.; Yaffe, O.; Biller, A.; Salomon, A.; Kahn, A.; Cahen, D., Molecules on Si: Electronics with Chemistry. Advanced Materials 2010, 22, (2), 140-159. 11. Schouteden, K.; Vandamme, N.; Janssens, E.; Lievens, P.; Van Haesendonck, C., Single-Electron Tunneling Phenomena on Preformed Gold Clusters Deposited on Dithiol Self-Assembled Monolayers. Surf. Sci. 2008, 602, (2), 552-558. 12. Zhao, J.; Sun, S.; Swartz, L.; Riechers, S.; Hu, P.; Chen, S.; Zheng, J.; Liu, G.-Y., "Size-Independent" Single-Electron Tunneling. The Journal of Physical Chemistry Letters 2015, 6, (24), 4986-4990. 13. Radojkovic, P.; Schwartzkopff, M.; Enachescu, M.; Stefanov, E.; Hartmann, E.; Koch, F., Observation of Coulomb Staircase and Negative Differential Resistance at Room


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