Theoretical modeling of electron emission from graphene
- PDF / 612,487 Bytes
- 6 Pages / 585 x 783 pts Page_size
- 57 Downloads / 293 Views
troduction Electron emission from a solid is a fundamental process underlying the release of electrons into the vacuum under the action of heat, an electric field, or photons, termed thermionic emission, field emission, and photoemission, respectively (Figure 1). Thermionic emission is based on changing the energy distribution of electrons in the solid by elevating the temperature (T), thus increasing the number of electrons that are energetic enough to overcome the surface barrier Φ. Thermionic emission was first described by Richardson in 1901,1,2 now known as the Richardson–Dushman (RD) Law: JRD = A × T 2exp(–Φ/kBT), where JRD is the thermionic emission current density, A is a constant depending on electron mass, and kB is the Boltzmann constant. Field emission is based on free electrons tunneling through the surface barrier by having a strong electric field to reduce the barrier’s height and width. A description of field emission was first developed by Fowler and Nordheim in 1928,3,4 now known as the Fowler–Nordheim (FN) Law: JFN = a × F 2exp(–b/F), where JFN is the field-emission current density, and a and b are constants dependent on the work function of the material. Here, F is the surface electric field that can be modified with an enhancement factor β (>1) to account for geometrical effects on the surface. Photoemission is similar to thermionic emission in the sense that it relies upon electrons in the cathode
material being energetic enough to overcome the surface barrier. In the most basic form of photoemission, a single photon imparts energy to an electron on the surface such that the kinetic energy of the electron can overcome the work function, which is the famous photoelectric effect explained by Einstein in 1905.5 Photoemission is best described by the Fowler– DuBridge (FD) Law, developed in 1930s.6,7 These three classical models were later combined into a generalized model.8 All of these models assumed that the electron dispersion in the bulk solid is a parabolic type function. However, this may not be valid for new, novel materials such as graphene and other two-dimensional (2D) Dirac materials in which the transport electrons follow relativistic energy dispersion. Monolayer graphene9 was formed experimentally by exfoliation in 2004, and subsequently, many of its unique properties10 have been reported, such as linear band structure, ultrahigh mobility,9 excellent optical,11,12 electrical,13 and thermal14,15 conductivities, which indicate that graphene may be a suitable material for electron emission. An electron in graphene is described by a peculiar “linear band structure,” where the electron’s energy and momentum are related by linear energy-momentum dispersion given by E ∝ p, where E is the electron energy and p is the electron momentum.16,17 Such unusual energy-momentum relation coincides with that of the ultrarelativistic massless Dirac fermion in high-energy physics.
Y.S. Ang, Singapore University of Technology and Design, Singapore; [email protected] Shi-Jun Liang, Singapore University of Techn
Data Loading...
