Carbon Nanotube-Based Field Emission X-ray Technology

Authored by: Lei Zhang , Jianping Lu , Yueh Lee , Sha Chang , Otto Zhou

Handbook of X-ray Imaging

Print publication date:  December  2017
Online publication date:  December  2017

Print ISBN: 9781498741521
eBook ISBN: 9781351228251
Adobe ISBN:


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Field emission is an alternative mechanism to classical thermionic emission for electron generation (Wood 1897). It describes the phenomenon of electron tunneling from the surface of a material, typically metal, into vacuum under an electric field. As illustrated in Figure 4.1, the combined effect of image force potential and the strong external electric field narrows the effective potential barrier, so that electrons around the Fermi level would have a meaningful probability to escape from the surface to the vacuum level through the quantum tunneling effect. The stronger the external electric field, the narrower the energy barrier is. The emission current is mainly determined by the strength of the electric field and the type of material, and is quantified by the Fowler–Nordheim equation (Fowler and Nordheim 1928; Nordheim 1928a,b) as follows: I = aV 2 exp ( − b Φ 3 / 2 β V ) where a and b are constants, I is the emission current, V is the applied voltage, Φ is the work function of the material and β is the field emission enhancement factor. The work function typically ranges from 2 to 5 eV for metals and depends strongly on the surface crystallographic structures (Hainfeld 1977). Detectable field emission starts at an extremely high local electric field, about 107–108 V/cm. In order to achieve such a high local field, a geometrically sharp tip or protrusion is commonly used to produce a largely intensified local electrical field (Fursey 2005). This geometrical effect is characterized by the field enhancement factor β, which is the ratio between the local and applied electric fields. The larger the β is, the higher the field strength enhanced at the emitting surface and, therefore, the lower the required applied voltage is for emission (Cheng and Zhou 2003).

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