pubs.acs.org/NanoLett
Coulomb-Controlled Single Electron Field Emission via a Freely Suspended Metallic Island Chulki Kim,* Hyun S. Kim, Hua Qin, and Robert H. Blick Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706 ABSTRACT We observe Coulomb blockade in the field-emission current of a metallic island between two electrodes freely suspended by thin tunneling barriers. A third electrode serves as a gating contact to trace the Coulomb staircase of the device. Coulomb blockade is revealed at 77 K in conjunction with field emission. The measurements are in very good agreement with a theoretical model, taking into account orthodox Coulomb blockade and field emission. KEYWORDS Coulomb blockade, field emission, tunneling
A
recently CB was also demonstrated in nanoparticles at around 77 K,8,9 while Raichev11 was the first to suggest the simultaneous occurrence of CB and field emission (FE). This would allow the realization of FE devices in which the emission of electrons is controlled one by one. Such a technique has similarities to single photon on demand devices,10 in which the emission of single quanta can be precisely triggered. Here we are following this line of thought and present measurements of single electron field emission via an electron island, which is controlled by the Coulomb interaction. A third electrode serves as a gating contact to trace the Coulomb staircase of the device. Coulomb blockade is revealed at 77 K in conjunction with field emission. We connect this to the recently developed theoretical model by Raichev.11 The metallic island is placed between three electrodes functioning as emitter (cathode), collector (anode), and gate as shown in Figure 1a. The electrodes are defined by electron beam lithography and deposition of a 60 nm thin gold layer on top of silicon-on-insulator (SOI) material. A series of CF4 and SF6 plasma etch12 steps are then performed to mill down the SOI-substrate around the gold electrodes. The gold itself withstands this dry etch, leaving a conducting island disconnected from the underlying substrate but attached to the leads (see Figure 1a). The peculiar feature of this etch step is that we are able to reproducibly remove the SOI from beneath the electron island and to suspend it freely. The island is only connected to the surrounding electrodes by thin layers of CF2, that is, Teflon components. It is known that Teflon is produced during CF4 plasma treatments,13,14 as such a layer apparently lowers the work function of the coated material.14,15 We note that the island is placed at distances of 12 and 26 nm toward source and drain, respectively (see Figure 1b). The gating electrode is placed at a slightly larger distance away of 35 nm.
t the heart of many applications, such as thin film displays, microwave sources, and sensors, one finds field emitters.1 Field emission itself is a well-studied phenomenon for which in the early days of quantum mechanics a model was developed by Fowler and Nordheim.2 The model is based on electron tunneling through a vacuum barrier, although quite general in the assumptions, it beautifully explains the main features of the experiment. Apart from this theoretical approach, which only treats the emission from flat surfaces, it is obvious that the actual shape of the field-emitting surface is crucial. In 1968, Spindt3 noted that the field emission current can be considerably enhanced when a fine tip is used as an emitting contact. Most applications now make use of these so-called Spindt-tips. A new regime of field emission is discovered when emission via an isolated metallic island is considered. Placing such a small metallic grain between anode and cathode gives rise to strong deviations from the traditional Fowler-Nordheim (FN) behavior, as demonstrated earlier.4 Essentially, it was shown that field emission through a metallic grain placed on a cantilever tip between source and drain electrodes leads to a modulation of the emitted current. Such a “throttling” behavior represents a valuable new control mechanism for field emitter tips. Similar results were found in another realization of this experiment, where the gold island is placed on a nanopillar between a source and drain electrode.5 The question arising now is whether a diameter of the metallic grain of below 100 nm can result in single electron effects, such as the so-called Coulomb blockade (CB). CB of electron transport was first demonstrated in single electron transistors by Fulton and Dolan in a seminal paper.6 For more details, we refer to a review by Likharev.7 More * To whom correspondence should be addressed: E-mail:
[email protected]. Received for review: 10/31/2009 Published on Web: 01/08/2010 © 2010 American Chemical Society
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DOI: 10.1021/nl903644u | Nano Lett. 2010, 10, 615-619
FIGURE 2. Coulomb-staircase in the direct current IDS vs bias voltage VDS for gate voltages (a) VG ) 0 V and (b) VG ) 50 mV at 77 K. The staircase is identified in both cases, but shifted in (b) due to the gate voltage potential variation. Inset in (a) gives the level diagram with the island placed between cathode (C) and anode (A).
presented in the following were performed at 77 K, that is, at a thermal energy of Eth ≈ 6.7 meV. The sample was placed in a radio frequency probe station (DC, 50 GHz) under vacuum (e10-5 mbar) with a cooled sample stage. We recorded the field emitter’s tunneling current through the suspended island under variation of bias and gate voltages with a sensitive current preamplifier, a setup similar to the one used in earlier experiments.17,18 The device temperature is maintained at 77 K during the course of the measurements. Electrons tunnel over the gaps between source-to-island and drain-to-island with the Teflon glue effectively lowering the barrier work function.14 In addition, the geometry of the structure enhances the local electric field further lowering the absolute bias voltage required to add electrons onto the island. To underline this, we show in Figure 1c the electric field distribution around the island and electrodes obtained from a finite element simulation.19 The resulting high field intensity indicates that electron tunneling is strongest on the island-source contact. The fundamental finding of our work is shown in Figure 2, where we plot the measured direct current versus bias voltage for a gating voltage of VG ) 0 V. The trace shows an onset of current flow at around 1.65 V and then a stepwise increase of the current. This staircase pattern is similar to the expected CB-staircase.11 The offset stems from the fact that the electrons first have to overcome the metal-Teflon barrier before the Coulomb interaction will regulate the stepwise increase of the island charge one by one. The total energy required for electron transport over the island thus is the sum of the Coulomb energy and the reduced work function EC + eΦ. In Figure 2b a similar graph at a gate voltage of VG ) +50 mV is depicted. As seen, this leads to the expected shift of the staircase and to a variation of the step widths. CB occurs when electrons are emitted from the cathode but prevented to tunnel toward the island. Once the electrons can overcome the addition energy ∆EN the island’s
FIGURE 1. (a) Freely suspended metallic island glued between source (S), drain (D), and gating (G) electrodes. The island with dimensions of 80 nm × 80 nm × 60 nm (length × width × height) is attached to the electrodes by a thin layer of CF2, that is, a Teflon compound (white). Scale bar, 300 nm. (b) Top view of the suspended device, indicating the close proximity to the source electrode. The CF2 layer appears as a white film. Scale bar, 100 nm. (c) The resulting electric field enhancement around the source electrode modeled by finite element simulations. Red indicates the highest electric field intensity and blue the lowest. We note that the simulation is performed including the glue, that is, a relative permittivity of εr ) 2.1.
It has to be stressed that complete removal of the surrounding SOI-material considerably alters the electromagnetic environment, since we do not have to take into account a relative dielectric constant of silicon (εr ) 11) any longer. This has remarkable consequences when it comes to Coulomb blockade effects. Using the orthodox model,16 we define the total charging energy as EC ) e2/Ctot, where the energy required to add the Nth electron to the metallic island is the addition energy ∆EN. Ctot ) ΣiCi refers to the total capacitance, that is, includes anode to island Can, cathode to island Ccat, and the gate to island capacitance CG. For a simple estimate the capacitance of a sphere Ctot ≈ Cs ) 4πεrε0r can be used with a radius r ) 40 nm taken from the graph in Figure 1b. This yields a capacitance of Cs ) 4.65 aF and following from this a charging energy of EC ) 34.4 meV. However, since the metallic island is “glued” to the electrodes by thin Teflon layers, we need to take a relative permittivity of εr ) 2.1 into account. This dielectric layer modifies the charging energy to EC ≈ 17.2 meV (see Figure S1 in Supporting Information). The addition energy is smaller than the thermal background energy at room temperature Eth ) kB × (300 K) ≈ 26 meV. Hence, all measurements © 2010 American Chemical Society
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FIGURE 3. (a) The variation of the step width at different gate voltages. Error bars were extracted from full width at half-maximum of the corresponding transconductance peaks, that is, G ) dIDS/dVDS. A Coulomb diamond is sketched indicating the linear variation of the Coulomb gap with gate voltage variation. The dashed line is a guide to the eye, connecting the data points (red). (b) Current IDS vs voltage VDS at 20 mV gate voltage; the data trace (red) has been fitted according to eq 4. The current determined in the model calculation (black) is switching between two stable states at around 1.725 V. The inset shows the conductance dI/dV vs voltage VDS.
charge changes from an N- to an (N + 1)-electron state. The decisive tunneling event from the island is due to field emission tunneling according to the FN model. The potential barrier is deformed by the external electric field, evidenced in our data by the high turn-on voltage (∼1.65 V) and the exponential increase in current. In addition we found that field emission is controlled by one electron at a time in low bias, as predicted by Raichev.11 Above the fifth step (∼1.85 V) strong field emission washes out CB effects. It might be argued that the electron wave functions interfere in the small junction leading to current oscillation, so-called Gundlach resonances.20,21 However, taking into account the small Fermi wavelength of the electron (e2 nm) within the Teflon junction and comparing this to the actual gap of ∼26 nm, such interference is not very likely. In addition, we find gate voltage variations of the staircase, as will be discussed in the following. The most crucial test for single electron transport through the island is given by controlling the charging via a gate electrode. Figure 2 presents already two gate voltage variations; as expected, the width of the steps as well as the position is shifted. In Figure 3a, the width of the first step of the staircase (solid red lines) is given for a variety of gate voltages. The black arrows define the error bars in determining the absolute step width. The error bars were obtained from the transconductance peaks’ (G ) dISD/dVSD) widths at half-maximum. Naturally, the “rounding” of the steps varies according to temperature. The overall change of the CB staircase width is clearly visible. The stair widths of the other plateaus follow the same behavior, that is, the minimum is at around VG ) 25 mV (see Figure S2 in Supporting Information). We can now apply the orthodox model of CB to estimate the capacitances of the island to gate, anode, and © 2010 American Chemical Society
cathode; from the slopes (solid black lines) in Figure 3a we can extract these capacitance values. We then obtain CG = 2.7 aF, Ccat = 3.4 aF, and Can = 3.1 aF. This gives us a total capacitance of Ctot = 9.2 aF and finally a charging energy of EC = 17.4 meV, which agrees very well with our previous estimate. To accurately model the results in more detail we adopt Raichev’s approach11 on the combination of field emission and Coulomb blockade. We find similar barrier conditions as they are assumed in this model, that is, that the island is closer to the cathode than to the anode, as seen in Figure 1b. This assumption is also supported by finite element simulation in Figure 1c; for such a configuration the total current is given by the sum over all currents IN for a particular number of electrons N on the island, weighed by the probability PN to find N electrons on the island, J ) Σi ∞) N(PNIN). The probability is given by PN ) Z-1 exp(-βEN) where β-1 ) kBT with the energy of the island with N-added electrons EN being defined by
EN )
(
CanVDS e2 N2Ctot e
)
2
(1)
and the partition function given by Z ) ΣN exp(- βEN). The energy to transfer a single electron from the cathode to the island is given by ∆EN ) (e2/Ctot)[N - 1/2 - CanVDS/e]. Since we found Ccat > Can, the island-anode link finally determines the flow of electrons from cathode to anode via the island. Consequently, we find that the plateau width at VG ) 0 is given by ∆VDS ) e/Can ) 51.3 mV, which agrees with Can ) 3.1 aF found above. Tuning the gate voltage to VG ) 25 mV, 617
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FIGURE 4. (a) Current IDS vs VDS with gate voltage fixed at VG ) 0 V, plotted in a Fowler-Nordheim (FN) representation. The Coulomb blockade and FN (orange) regimes overlap. The high voltage region is well fitted by the isolated emitter model (blue), while a Child-Langmuir approximation (green) only predicts the upper boundary correctly. (b) A magnified view of data (red) in the crossover of Coulomb blockade and field emission regimes with gate voltage fixed at VG ) 20 mV with the Raichev model fit (black).
we obtain a reduced value of ∆VDS ) e/(Can + Ccat) ) 20 mV, which is also expected using the previously found capacitance values. This is different to the orthodox model of CB, since we have to take field emission into account here.11 Finally, the total current can thus be given as
J ) Z-1
∑ IN
exp(-βEN)
This equation allows us to model the measurements as shown by the dashed (black) line in Figure 3b. The general shape of the CB staircase in the IV-trace can be reproduced as well as the threshold for current flow. Toward higher voltages the simulation shows a double occupancy, that is, the current is switching between two stable states. This is in accordance with the fact that field emitted electrons will dominate the current flow at high bias and CB effects will be washed out. To compare the results better with conventional field emitters,thedata(red)isgiveninFigure4inaFowler-Nordheim manner. Comparing the actual current through the island with the standard FN-approximation (orange) in Figure 4a we find that the FN-curve reproduces the low bias region but overshoots the high field data. On the basis of the slopes in FN fitted regions, the enhancement factors were calculated as ζ(a) ) 128 and ζ(b) ) 64. The blue trace is obtained modeling field emission through an isolated emitter (IE), as we found previously.4 While this IE model describes the saturation at large biases, both models do not account for the steps in the low-bias region due to CB. In Figure 4b a low bias regime is magnified; evidently the FN-trace correctly predicts the overall trend in this region, while the IE model overestimates the current here. The solid black trace gives the result according to eq 4, assuming for the temperature T f 0. As seen it can properly estimate the CB modified field emission current. In the low-bias regime the electron island regulates the flow of charge one electron at a time. As discussed before, the model also takes into account switching between two states on the electron island, for example, (N + 1) T (N + 2). This switching indicates that it is “easier” for electrons to escape from the island toward
(2)
N
Each current IN for a specific number of electrons N is described by the classical Fowler-Nordheim equation2 as
IN ) κSFN2 exp(-Λ/FN)
(3)
where the material constant is κ = |e|3(εF/W)1/2/(4π2p(εF + W)) is expressed through the work function W ) eΦ and the Fermi energy εF of the emitting material. The emitter’s effective surface area is given by S. The “built in” electric field is described by Λ ) 4(2m)1/2W3/2/(3|e|p) with m giving the electron mass. F in general is denoting the applied electric field between the island and the source electrode including the geometric enhancement. The effective electric field FN for the island depending on the electron number N is FN ) ζ(1)/(4πε0)(N|e|)/(R2) where ζ is the geometrical enhancement factor. This in combination with eqs 1s3 gives us the final current
J ) Z-1
∞
∑ κSFN2
( )
exp -
N)1
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Λ exp(-βEN) FN
(4)
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(2)
the anode at higher bias, due to the exponential increase of the field emission current. Apart from lowering the field emission energy the Teflon anchors’ mechanical flexibility might also lead to so-called electronshuttlingfromsourcetodrain,asdiscussedbefore.4,5,22 For comparison to nanoelectromechanical shuttles, we traced the direct current versus radio frequency voltage. However, only a very weak mechanical response was evident (see Figure S3 in Supporting Information). This can be attributed to the mechanical stiffness of the Teflon layer, which possess a Young’s modulus a factor of 4 larger than the one of silicon.23 In summary, we found that field emission of electrons over a small metallic island can be controlled by Coulomb blockade. The results follow model calculations taking into account classical field emission and control of single electron transport. These results open a broad range of possible applications in field emission devices, but they will also have great impact on single-electron-on-demand applications.
(3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)
Acknowledgment. The authors like to thank DARPA for support through the NEMS-CMOS program (N66001-07-12046) and the University of Wisconsin-Madison for support with a Draper-TIF award.
(17) (18) (19)
Supporting Information Available. This material is available free of charge via the Internet at http://pubs.acs.org.
(20) (21) (22)
REFERENCES AND NOTES (1)
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Fursey, G. Field Emission in Vacuum Microelectronics; Kluwer Academic/Plenum Publishers: New York, 2005.
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DOI: 10.1021/nl903644u | Nano Lett. 2010, 10, 615-619
