# Range of Nordheim parameter y

1. Aug 27, 2009

### pafcu

Hi,

The current density due to field emission on a surface is described by the Fowler-Nordheim equation
$$J = t(y)^{-2}a\phi^{-1}F^2\exp(-v(y)b\phi^{3/2}/F)$$

where $$v(y)=1 - y^2+ (1/3)y^2ln y$$ and $$y=cF^{1/2}\phi^{-1}$$
$$F$$ is the applied electric field above the surface.

(See for example "Simple good approximations for the special elliptic functions in standard
Fowler-Nordheim tunneling theory for a Schottky-Nordheim barrier" by Forbes)

Anyway, my specific problem is that y should be in the range [0,1] as stated in the paper. However, y is clearly proportional to the field strength. Is there some limiting factor that forces the applied field to be small enough so that y is never larger than 1? Or is it simply the case that once y=1 it doesn't grow anymore, no matter how powerful the electric field F gets? This doesn't seem to be explained anywhere, and many papers don't mention the range of y at all.