Paradox of low field enhancement factor for field emission nanodiodes in relation to quantum screening effects
© Cheng et al; licensee Springer. 2012
Received: 5 October 2011
Accepted: 14 February 2012
Published: 14 February 2012
We put forward the quantum screening effect in field emission [FE] nanodiodes, explaining relatively low field enhancement factors due to the increased potential barrier that impedes the electron Fowler-Nordheim tunneling, which is usually observed in nanoscale FE experiments. We illustratively show this effect from the energy band diagram and experimentally verify it by performing the nanomanipulation FE measurement for a single P-silicon nanotip emitter (Φ = 4.94eV), with a scanning tungsten-probe anode (work function, Φ = 4.5eV) that constitutes a 75-nm vacuum nanogap. A macroscopic FE measurement for the arrays of emitters with a 17-μm vacuum microgap was also performed for a fair comparison.
Keywordsquantum screening effects field emission vacuum electronics Fowler-Nordheim tunneling silicon nanostructures
Recently, micro-/nano-fabricated field emission arrays [FEAs] have attracted a great deal of attention since they have been seen as outstanding electron sources operating with high efficiency, high currents, and fast turn-on times [1–4]. Much effort has been directed toward FEAs' commercial applications in vacuum electronic devices and components, including vacuum lamps and lighting , high-power microwave amplifiers , thermoelectric cooler , microscopes and visualization equipments, parallel e-beam lithography  and, of particular interest, the next-generation flat panel displays . With the rapid advent of nanotechnology, various low-dimensional nanomaterials with extreme aspect ratio and high density, like carbon nanotubes [CNTs] , zinc oxide nanowires , and silicon carbide nanowires , have been successfully fabricated with different synthesis methods, and their excellent field emission properties have been widely reported in the literature. It has been known that field emission [FE] properties are highly sensitive to characteristic material properties, like morphology, emitter density, aspect ratio, and electron work function.
Among versatile nanomaterials, silicon nanomaterials are of particular interest due to their excellent compatibility to very-large-scale integration [VLSI] integrated-circuit processes. However, the emission currents from conventional FE cathodes with a large vacuum gap, usually larger than hundred micrometers, are insufficient for practical and realistic electronic applications, and the large operating voltages are far too high for being integrated into the standard CMOS electronic devices. However, following Moore's law for microelectronic devices, within the ever-improving VLSI/USLI technology, nanodiodes with a nanogap may be envisioned in the very near future, and they may bring advantages of lower power consumption and high-current output for the next-generation vacuum nanoelectronics. When aggressively squeezing the vacuum electronic devices to the nanoscale level, many challenging and anomalous physical effects will emerge, such as the space charge effect , energy accumulation that increases the burnout resistance, and vacuum sealing; these are, however, ignorable in conventional FE microdevices. The most striking effect, which is, however, largely ignored in previous literature, is the relatively low field enhancement factor obtained from the experimental Fowler-Nordheim [FN] plot. The field enhancement factor may describe the ability of specific emitters to amplify the macroscopic field, which in turn determines the total emission current. In many experiments of nanoscale FE characterizations (usually apply a tungsten [W]-probe anode with its work function, Φ = 4.4eV ) for a single carbon nanotube , nanofiber, or nanoflakes  with a work function of Φ = 5.1 ∓ 0.1eV, the reported field enhancement factors for nanogaps of d = 60 to approximately 380 nm are in the range of 90 to approximately 380 nm . These values are, however, much lower than those obtained from FE microdiodes with a vacuum gap larger than a few hundred micrometers, of which the field enhancement factor is usually in the order of 103 to 104 . These values are already conservative, and if we consider a more realistic scenario, the electrostatic screening effect  implies that the field enhancement factor for the arrays of nanoemitters should be strongly dependent on the density and arrangement of nanoemitters. It is therefore relevant to explain the anomalously low field enhancement factor in vacuum nanodiodes. For such small vacuum nanogap, the simple electrostatic explanation may not be sufficient, and a careful look into a quantum level is necessary by considering all energy levels of nanodiode structures, including the effect of anode. It is rather illustrative to use the energy band diagram to study how the field enhancement factor may be affected by a quantum effect due to the work function difference between the emitters and anode, especially when the work function of the field emitter (i.e., CNT emitters) is higher than that of the anode (i.e., W-probe) .
In order to obtain the exact work function (Φ) of SiNTs, which could be very different from the bulk silicon, the scanning Kelvin probe microscopy (NT-MDT Solver P47, NT MDT Co., Zelenograd, Moscow, Russia)  was applied to measure the work function (Φ) of SiNTs. Here, an AC voltage (75.2 kHz) was first applied to the SiNTs sample, inducing an oscillating electrostatic force between the conductive atomic force microscope tip and the sample. Then, the compensation of electrostatic forces at this frequency was achieved by adjusting a DC bias to match exactly the contact potential difference [CPD] between the tip and the sample. Since the work function of the cantilever is known, the value of CPD can be determined by Φsample = Φcantilever + CPD. Here, the measured work function of SiNW emitters is 4.94 eV.
Results and discussion
Field emission properties of P-SiNT emitter with W-probe or -plate anode at different separations
(V/μm, at J= 10 mA/cm2)
In order to explain our experimental results, a quantum screening effect model is proposed here. A schematic diagram about energy band distribution in the vacuum gap is shown in Figure 2. In the vacuum region in Figure 2b, the dashed lines represent the potential contours for a FE microdiode with the anode located at a long distance (usually larger than several micrometers and not shown in this figure) such that its influence on electron emissions in the near-field region of emitter surface may be neglected. The solid line in Figure 2a represents the one for a very short anode-to-cathode distance, where the potential barrier seen by an electron tunneling through a vacuum gap is dramatically increased; thus, an electron may need more energy or a higher applied field for tunneling through the potential barrier compared with electron emission at a large anode-to-cathode distance. From Figure 3a, it is quite evident that the microdiode requires much lower turn-on field due to the absence of the quantum screening effect. As a result, except for the electrostatic screening effect depending on the emitter's density and sharpness, the vacuum gap height is also important when considering the effect of potential barrier on the transport of electrons.
It is interesting to note that for high applied fields, the flattening of FN plot (also known as the saturation effect) is observed. Figure 3b is similar to Figure 3a, but for a higher electrostatic bias field, showing that the conduction band of p-type field emitter will be degenerated at the surface, and the green shaded region in Figure 2b indicates a depletion region between the p-type interior and the n-type surface, of which the Fermi level lies in the middle of the energy gap. This leads to a minimum concentration of electrons and holes in such region, in some sense similar to the reverse-biased condition in a p-n junction . We also notice that due to the space charge in the vacuum region , even the applied field is very strong, potential barrier at the surface remains much higher than that of microdiodes, and therefore, the quantum screening effect is hardly eased. In the linear region (before the saturation occurs) of FN plot, the field enhancement factors calculated from the slope of FN plot are respectively 436 and 616.2 for the nanodiode and the microdiode with W-plate from our experimental results, as have been observed in many nanoscale FE measurements. As described in previous papers [3, 5, 19], the field enhancement factor is usually defined as the local field (F) over the applied field (E0), where the applied field is usually taken as the applied voltage over anode to the bottom of cathode separation D (as shown in Figure 2), or γ = F/E0, where E0 = V/D. According to our quantum screening effect model, as anode to the top of cathode separation d (like the top of our P-SiNT) approaches to nano-distance, the local field will decrease because of the quantum screening effect, but the applied field did not decrease because the separation of anode to the bottom of cathode is still large. It is quite evident that the quantum screening effect may decrease the field enhancement factor. Besides, comparing with the field emission properties of SiNTs with W-probe and with W-plate, the results showed that the enhancement factor of SiNTs with W-plate is larger than with W-probe, and the turn-on field of SiNTs with W-plate is less than with W-probe. In our experiment, the SiNTs array is not too dense so that the SiNT emitters' array with W-plate anode geometry can be served as a parallel circuit without considering the space charge effect so that it can decrease the turn-on field. Besides, according to Wang's model , more electron emission emitters with certain density will increase the field enhancement factor, so the SiNT emitters' array with W-plate have larger field enhancement factor than the SiNT emitters' array with W-probe in this paper.
In summary, we have experimentally demonstrated that in FE nanodiodes, the quantum screening effect may significantly increase the turn-on field and reduce the field enhancement factor and, therefore, deteriorate the electron emission efficiency. Furthermore, the experimental evidence is supported by a simple band diagram analysis. This quantum screening effect, which describes the relatively low field enhancement factors and higher turn-on field in most nanoscale FE experiments, is particularly crucial for vacuum nanoelectronic devices.
The authors would like to thank the support of the National Science Council (NSC) of Taiwan under contract number NSC-99-2221-E-151-015 and the equipment support of the National Nano Devices Laboratories (NDL) of Taiwan.
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