Designing efficient field emission into ZnO
Field emission (FE) is a unique quantum-mechanical effect where electrons tunnel from condensed matter into a vacuum. Unlike the circumstances where there is a hot filament, in FE electrons are freed by tunneling under a strong electric field: for this reason the phenomenon is also called cold-cathode emission. FE is of great commercial interest in flat panel displays, x-ray sources, and other vacuum microelectronic devices. In past decades, research in this area mainly focused on carbon-based materials because of their high mechanical stability, good conductivity and negative electron affinity. One-dimensional (1D) nanostructured materials—such as carbon nanotubes (CNTs)1,2 —were particularly thought to be good candidates for FE: they have the added advantages of high aspect ratio, which enhances the electric field on the sharp end of their structures. However, it has since been shown that CNTs can operate either as conductors or semiconductors depending on how they have been rolled.3 This results in varied voltage drops across conducting and seminconducting CNTs and, thus, varied effective fields on the emission tips of conducting and semiconducting CNTs.
Zinc oxide (ZnO), a wide-direct-bandgap semiconductor, has been intensively investigated recently4–6 because of its promise for short-wavelength light-emitting and laser diodes. Various 1D ZnO nanostructures—such as nanowires and nanoribbons—have been fabricated using various methods.7–11 In fact, ZnO has demonstrated the richest nanostructures of all known materials. With its structural similarity to the CNT,12 1D nanostructural ZnO is a potential alternative for producing field emission with low threshold and high efficiency: it is an oxide material that is thermally stable and intrinsically oxidation resistant. Moreover, it has no 'rolling' problem.
Field emission properties from nanostructural ZnO with various morphologies have recently been reported,12–16 but to compete with CNTs, further improvement will be required. We present here some approaches to lower the FE threshold, increase the emitting current, and enhance the efficiency by geometrical optimization and doping. 17,18
To understand our approach, it is necessary to have some idea of the theory behind it. Electrons in solid materials are confined by a potential-energy barrier. The potential energy of a planar cold cathode with micro-roughness can be written as:19
where x is the distance away from the emitter surface, EF is the energy of Fermi level of the cathode material, φ and is the potential barrier for electron, e is the charge quantity of an electron, and E is the electric field strength directly on the emitter surface. The factor β is introduced to describe the geometric effect of the microroughness on the electric field. Sharp geometry and large β come hand in hand: Figure 1 shows that—with a microtip emitter—the emission barrier width reduces as compared to a planar surface.
The relationship between FE current density and the applied electric field is described by the Fowler-Nordheim (FN) equation:13
where A and B are constants with values of 1.56 × 10-10 (AV-2eV) and 6.83 × 103 (VeV-3/2μm-1), respectively. The field enhancement factor β in the FN equation reflects the degree of FE enhancement of any tip over a flat surface: it represents the true value of the electric field at the tip compared to its average macroscopic value. For a nanostructural emitter, the β value is related to the geometry, crystal structure, conductivity, work function, and nanostructure density.
According to the equations above, an effective approach to achieving strong electric fields is to employ sharp tips as electron emitters.In addition, lowering the electron barrier is beneficial to FE. Doping is an effective approach to adjusting the Fermi energy level for semiconductors. The relationship between electron concentration and the Fermi level can be written as:20
where n is the electron concentration, m* is the electron effective mass, k is Boltzmann's constant, h is Planck's constant, T is the absolute temperature, and EF and EC are energies at the Fermi level and the bottom of conduction band, respectively. This indicates that the FE performance can be improved through n-type doping because the Fermi level is lifted and, hence, the work function is reduced. It is even possible to realize negative electron affinity—very advantageous for electron emission—through heavy doping under certain conditions.21
The samples for FE were fabricated by the vapor-phase transport method as reported in our previous papers.17,18 Intially, random ZnO nanowires were obtained, as shown in Figure 2(a). However, by controlling the growth in a two-step process,17 the nanopin morphology was produced: see Figure 2(b).
Because it is an n-type dopant in ZnO, heavy doping with gallium allows the material to be used as a transparent conductor for display applications: gallium doping lifts the Fermi level. When we fabricated Ga-doped ZnO fibers using the vapor-phase transport method (see Figure 3),18 our quantitative analysis showed that the gallium doping concentration was about 0.73%. The carrier concentration and resistivity of the Ga-doped ZnO were -3.77×1020/cm3, and 8.90×10-4 Ω cm, respectively.
Figure 4 compares the FE characteristics of the ZnO nanowire and nanopin. The threshold electric field is 4.30V/μm for nanowires and 1.92V/μm for nanopins at a current density of 0.1μA/cm2. According to the FN equation, the field enhancement factors β were estimated from the slope of the ln(J/E2)-1/E plot inserted in Figure 4. The β values of the nanopins and nanowires were 657 and 189, respectively. The higher field-enhancement factor of the nanopins is attributed to the sharp tips.12–15
In a Ga-doped ZnO nanofiber array, the doped gallium has two beneficial effects: the reduced resistivity reduces the voltage drop along the nanofiber, resulting in enhancement of the effective field at the nanofiber tips; and n-type doping enhances FE by lifting the Fermi level and lowering the work function. Figure 5 illustrates the latter effect. Here, the estimated Fermi level is just 0.12eV below the conduction band18 according to Eq. 3. Figure 6 shows the dependence of emission current density on the applied electric field. Similarly, we obtained some critical parameters for field emission: the threshold electric field is 2.4V/μm to obtain an emission current density of 0.1A/cm2; the current density reaches at 1μmA/cm2 at 6 V/μm; and the estimated β value is 2991.
We have shown that 1D ZnO nanostructures can be engineered through morphological and electronic design for FE applications. Such designs can easily be realized, implying great potential for employing 1D ZnO field emitters. The remaining challenge is how to fabricate uniform 1D ZnO nanostructures over a large area. Sample size is generally quite small using the vapor-phase transport method as we have here. However, we can use the hydrothermal decomposition method instead.22 Moreover, this way, fabrication can be done at low temperatures (<100°C), implying a much wider choice of substrates. Work in this direction is currently under way.
Thanks to C. X. Xu for his contributions to the work reviewed in this article. We acknowledge the financial support by the Agency for Science, Technology, and Research of Singapore.
