# Field Emission

1. Jun 28, 2013

### grandmessage

Hello everyone,

a number of books and web articles says that the minimum field required is ≈$10^7V/cm$ for electrons field emission/tunneling from the surface of metals.
But fowler-nordheim formula shows that there is still considerable amount of field emission
current density (mA/cm2) even at lower fields of order $10^4V/cm$, for the same
tunneling barrier.

What is the truth..??

Any answers would be greatly appreciated!

2. Jun 28, 2013

### erst

Two very different things. Field emission from the surface of a metal involves ejecting the electron to the vacuum level, i.e. it becomes entirely free from the metal and goes off into the environment. This a large energy compared to the thermal energy so a electric strong field is needed.

Fowler-Nordheim tunneling refers to tunneling from the metal to either a semiconductor or another metal, i.e. this is material to material NOT material to vacuum. This is usually a much lower energy. You just have to overcome some tunnel barrier like an insulator or the semiconductor's Schottky barrier. If the barrier is thin and/or low, then a strong field is not needed.

3. Jun 28, 2013

### grandmessage

Hello sir,

Where we can find simplified form of Fowler-Nordheim equation here also they says the minimum field required is $3×10^7 V/cm$.
But for a metal of work function ∅=5eV and local electric field(E-local) $10^4V/cm$
it gives a minimum filed emission current density $0.1mA/cm^2$..
Is this true..??

4. Jun 29, 2013

### ZapperZ

Staff Emeritus
Back up a bit, because there's a bunch of things I don't quite understand here.

First of all, there is no "required field". By definition of tunneling, it can occur even at zero field. It is just that it is highly unlikely that it will occur in that situation. So, in principle, field emission current can occur over a large range of field. It is just that, based on the type of electron detection scheme used, there may not be any significant reading until it gets to some value. This may be what they meant by the "minimum field emission current".

And erst is not correct. Fowler-Nordheim does apply to metal-vacuum interface. If not, the hundreds of papers published in accelerator physics studying high-gradient structures are all wrong. There's also nothing inherent in the FN model that demands that it must be metal-semiconductor or metal-metal interface. In fact, it is this field-emission current that is the leading cause that initiates vacuum breakdown in high-gradient accelerating structures.

Zz.

Last edited: Jun 29, 2013