Research Express@NCKU - Articles Digest

ield-emission devices combining the advantages of vacuum tubes and solid-state fabrication techniques are very attractive for their potential applications as flat panel displays. The discovery of carbon nanotube (CNT) has drawn a lot of attention due to their unique physical properties and various potential applications. Owing to their high aspect ratios and small radii of curvature, CNTs exhibit excellent field emission characteristics. Hence, they are very promising candidates as field emitters. In addition to CNTs, the recent advance of nanotechnology also provides other efficient field emitters through a wide range of nanostructures, including nanorods, nanotubes and nanowires, of different materials. Although these one-dimensional (1-D) nanostructures have excellent field emission properties, they are often grown on silicon (Si) substrate for future integration into a whole device. Accordingly, the interface between the substrate and the nanostructure will play an important role in the overall field emission properties. The emission current from the nanostructure will be tailored by the junction effect.

In our previous work, a classical carrier transport model is established to study the field emission currents affected by the junction effects for the narrow- and wide-band-gap single 1-D nanostructure (undoped) grown on both n-type and p-type doped Si substrates.¹ Our simulation results agree with the experiments qualitatively and provide a perspicuous explanation for the junction effects by using the energy-band structure theory. However, the field emitters are generally composed of an array of 1-D nanostructures. Hence the field emission characteristics of any emitter in the array will be influenced by the screen effects due to the appearance of the neighboring emitters. The field emission characteristics changed by the screen effects for the conducting CNTs have been studied extensively. But the field emission currents influenced by the screen effects in an array of semi-conducting 1-D nanostructures were seldom discussed. In this study, the screen effects of an array of 1-D nanostructures grown on doped silicon substrates are investigated.

The configuration and dimensions of the field emission device investigated in this study are shown in Fig. 1. The one-dimensional carbon nanotubes (CNTs) are grown on n- and p-type Si substrates are discussed. The field emission properties of the equal-height 1-D nanostructure array will be examined first. The height of the nanostructures is 0.45μm. Figure 2 presents the F-N plots, i.e. the Log(I/V²) vs. 1/V curves, for CNTs grown on both n- and p-type Si substrates. Figure 2 indicates that, in the high anode voltage region (i.e. in the small 1/V region), CNTs deposited on n-type Si have larger emission currents. And the F-N plot for CNTs deposited on p-type substrate deviates from the ideal F-N equation in the high anode voltage region. The presented F-N plot of CNTs deposited on impurity doped Si substrates can be explained by the metal-semiconductor junction effect formed at the CNT-Si interface. (The band gap of CNT is much smaller than that of Si, hence CNT can be viewed as metal when a CNT-Si junction is formed.) The typical current-voltage characteristic of the metal-semiconductor contact can be expressed as

, where J_s is the reverse saturation current density and the applied voltage V is positive for forward bias and negative for reverse bias.2 In the field emission process, the emitted electrons are transported across the CNT-substrate interface followed by tunneling from CNT to vacuum. Applying a positive voltage to the anode is equivalent to add a forward bias to the CNT-Si(n-type) junction, accordingly the electrons is not hindered to pass through the interface and the emission current is determined only by the field emission behavior of the CNT. However, the CNT-Si(p-type) junction is biased reversely when the positive anode voltage applied. The current passing through the junction will be limited by the reverse saturation current Js. The emission current is saturated for CNT grown on p-type Si and the carriers in CNT are depleted in the high-voltage region.

Fig. 1 Simulation structure and dimensions.

Fig. 2 F-N plots for an array of 1-D CNTs grown on n- and p-type Si substrates with equal heights.

Next, the screen effects of the 1-D nanostructure array with different heights grown on impurity doped Si substrates are investigated. Our simulation model has been shown in Fig.1 with the central 1-D nanostructure 0.1μm higher than the side 1-D nanostructures. The distance between two neighboring emitter is 0.1μm. Figure 3 depicts the F-N plots of CNTs deposited on n- and p-type Si substrates. Figure 3 exhibits that the emission characteristics of the central (higher) CNT are very similar to those of the equal-height CNT array (Fig. 2), that is, the emission characteristic follows the ideal F-N plot for n-type Si substrate but deviates from the ideal F-N plot in the high-voltage region for p-type Si substrate. But because the central CNT is closer to the anode, the emission currents from the central CNTs are larger. The emission characteristic of the side CNT is very different from that of the central CNT in Fig. 3.

Fig. 3 F-N plots for an array of 1-D CNTs grown on n- and p-type Si substrates with different heights CNTs.

The emission current from the side CNT on p-type Si does not saturate and is even larger than that from the side CNT on n-type Si in the high-voltage region. Figures 4(a) and 4(b) plot the electrostatic potential contours for CNTs grown on n- and p-type Si, respectively, with the applied voltage of 400 V [i.e. 1/V = 0.0025 in Fig. 3, where the F-N plot of the central CNT on p-type Si has enter the saturation region]. Figure 4(a) indicates that, for n-type substrate, the equal-potential lines are blockaded from the emitters for both the central and the side CNTs. But owing to the higher central CNT, the equal-potential lines are compressed around the top of the central CNT. The equal-potential lines around the top of the side CNT then become sparser, because of the screen effect from the central CNT. According to this result, for n-type Si, the electric field on the top of the side CNT should be smaller than that on the tops of the equal-height CNT array. This kind of screen effect is very like the screen effect of conducting CNT array with different heights, which has been studied in the literature. Conversely, Fig. 4(b) exhibits that the equal-potential lines penetrate into the central CNT but still are blockaded from the side CNT for p-type substrate at the anode voltage of 400 V (the F-N plot of the side CNT has not entered the saturation region yet.) This will cause the equal-potential lines denser around the top of the side CNT and the electric fields enhanced on the surface of the side CNT (i.e. for p-type Si, the electric field on the top of the side CNT should be larger than that on the tops of the equal-height CNT array). As a result, the current emitted from the side CNT on p-type substrate is slightly larger than that on n-type substrate in the high-voltage region, as shown in Fig. 3. This kind of screen effect due to the carrier depletion and the equal-potential lines penetrating into the higher emitters is very different from the screen effect of the conducting emitters.

Fig. 4 Electrostatic potential contours for an array of CNTs with different heights grown on (a) n-type and (b) p-type Si substrates. The anode voltage is 400 V.

In conclusion, the field emission properties of the 1-D nanostructure array grown on doped silicon substrate influenced by the screen effects have been studied via computer simulation. For an array of 1-D nanostructures with different heights, the field emission characteristics of the higher 1-D nanostructures are very similar to those of the equal-height 1-D nanostructure array. But the field emission characteristics of the shorter 1-D nanostructures are contrary to those of the higher ones. These anomalous phenomena for the shorter 1-D nanostructures are induced by the electric fields enhanced on the surface of the side emitter due to the equal-potential lines penetrating into the higher emitters and reduced on the surface of the side emitter due to the equal-potential lines are compressed by the higher emitters. The equal-potential lines penetrating into or blockaded from the emitters are caused by the junction effects of the nanostructure-Si interface.

References:

1. Y. C. Lan, M. X. Yan, W. J Liu, Y. Hu and T. L. Lin, J. Vac. Sci. Technol. B 24, 918 (2006).
2. S. M. Sze, Semiconductor Devices Physics and Technology, 2^nd Ed., John Wiley & Sons (2001).