# breakdown voltage in vacuum

I was trying to use the paschen's law to calculate the breakdown voltage for our vacuum chamber. Our pressure is 10^-8 torr, and distance was 3mm. However, I cannot do it because Paschen only worked at higher pressures (>several Torr).

Any other way that I can calculate the breakdown voltage in low pressure?

• What you would get by extrapolating from Paschen curves is probably not very useful for estimating the real breakdown. Instead of being a gas/volume question, it will be a surface finish and surface contamination question. This makes it almost impossible to come up with an analytical solution. You may need in situ plasma cleaning and/or conditioning runs to get maximum breakdown voltages. – Jon Custer May 26 '17 at 20:23

As you raise the voltage (before breakdown) you should be able to measure the increase in field emission current; the slope of that curve (Plotted as a Fowler-Nordheim plot) can be used to estimate the $\beta$ value which is an indication of the surface smoothness. As you condition the surface, $\beta$ will decrease.