Field emission is one of the earliest confirmations of electron tunneling as predicted by the quantum theory in the 1920's. By applying a large electric field (E-field) to a cold cathode, it makes the electrons tunnel from the cathode through the potential barrier (modified by the E-field) into the vacuum. Field emission technology is a conventional experimental method for studying the electronic structure of materials, such as the work function of metal surfaces. Moreover, this technology has also shown huge potential in many applications such as flat-panel displays and highly spin-polarized electron sources. In previous studies, some theoretical methods based on simplified models were used to simulate the process of field emission and try to explain the field emission experimental results. The well-known Fowler-Nordheim (F-N) theory gave an analytic dependence of the emission current on the applied field and the work function, by assuming that the emitter is a free-electron-like metal. But these conventional methods failed to interpret some unique properties of the field emission, especially for the nano-material emitters that have been studied in recent years. In the last thirty years of the 20th century, various theoretical calculation methods based on first-principles techniques have been rapidly developed, which makes it possible to simulate and analyze the field emission with full knowledge of the electronic structure at the atomic level for the emitter materials.
We tried to combine the classical wavefunction matching method and current band structure calculation techniques to simulate the field emission. The plane-wave expansion vectors of the wavefunctions of emitter states are matched to Airy functions that are solutions of the classical triangular potential barrier problem, and then the emission current can be computed from our first-principles calculation results for the emitter. The following two examples illustrate some unique properties of the field emission from nano-materials.
1. Nanographite ribbons:
A nanographite ribbon has some unusual electronic properties, such as its edge state and dangling bond state that are both dependent on its edge type. Also, it is a simple model for studying some properties of carbon nanotubes. We have calculated the band structures and eigen-state wavefunctions of four types of nanographite ribbons with different edges under an E-field, and used these data to compute field emission current.
In the total energy distribution (TED) curve of the emission current for the pristine zigzag ribbon, the main current peak is located at the Fermi level (EF) and results from the dangling bond states. But in the TED curve of the emission current for the H-terminated zigzag ribbon, the main peak appears far from EF, because the dangling bond states are removed in this case. The edge states at EF contribute little to the total current since they are far from the G point in the Brillouin zone (BZ). For two types of armchair ribbons, the main peaks in the TED curves are all located at EF and result from the highest occupied bands. Because of the p-bond character of the highest occupied states, most of the emission current is not from the G point in the BZ, but from the off-zone-center states in this band. This property is different from that in two cases of zigzag ribbons, and so the dependences of the field emission current on the energy, k-point and wavefunction symmetry are revealed clearly in our calculations and discussions for the ribbon cases.
On the other hand, the effect of the inter-ribbon distance Dx on the emission current from the ribbon array has also been studied. It is found that the emission current densities increase with increasing Dx for the pristine ribbons, but initially decrease with increasing Dx for the H-terminated ribbons, independent of whether the edge is zigzag or armchair. This interesting property is due to the edge dipole moment effect: whether the ribbon is H-terminated or not determines the direction (or sign) of the edge dipole moment P, and so affects the dependence of the work function f on Dx; such a change of f due to the change of P causes the initial increase (decrease) of current for the pristine (H-terminated) ribbon according the F-N formulae.
F-N analysis has been also used in this case. The work function obtained by fitting a linear F-N plot is compared with the actual work function from the first-principles calculation. We found that the work function deduced from the F-N plot, as used by general experiments, may be larger than the actual work function because the states contributing most of the emission current are possibly far from EF.
2. Pseudomorphic Fe ultrathin films on W(001) surface:
The magnetic nano-films have always attracted much research attention because of their importance in the study of strongly correlated systems. Moreover, they are also expected to provide highly spin-polarized electrons that are useful in many fields. We have calculated and discussed the spin-polarized field emission from pseudomorphic Fe ultrathin films on W(001) surfaces.
First, the layer-resolved densities of states for these ultrathin films showed that they are all dominated by minority spin electrons in the topmost layer and near EF. This means that the spin-polarized field emission current is possibly produced from these Fe ultrathin films.
Our computed results show that the electron spin-polarization (ESP) of the field emission current from two and four layers of pseudomorphic Fe films on W(001) can reach -99% and -98% (minority spin electron dominated) respectively. It is found that in the former case, the majority (minority) spin electrons emit from the bulk states of the whole Fe/W system (the Fe quantum well states), and in the latter case, the majority (minority) spin electrons emit from the W substrate states (the surface resonance states mainly localized in the Fe film).
On the other hand, the ESP of the field emission current from three and five layers of pseudomorphic Fe films on W(001) is not so high as that of the above two cases, but there exists an interesting property: they are sensitively dependent on the external E-field. The energy difference between the eigen-states with two spins contributing most of the emission current should be responsible for this property.
The workfunctions of the two and four layers of pseudomorphic Fe films on W(001) were found to be lower than that of the W(001) surface, which is favorable for the field emission. This is related to the charge transfer between different layers. Moreover, the total energy calculation showed that among the pseudomorphic Fe ultrathin films on W(001), one and two layers of Fe films are both stable, four layers of Fe film is metastable, and three layers of Fe film is thermodynamically unstable. These stability results are consistent with recent experiments.