Re: Breakdown voltage at submillimeter distances?

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: Robert Clark <bobbygc2001@xxxxxxxxx>

 Thanks for the detailed response. I was thinking of
creating small capacitors using very small gap spacing
based on the idea that the breakdown voltage would
start rising again at the left end of the Paschen
curve. Your references seem to put the scotch on that
idea.
 However, I've read that the shape of the electrodes
has an effect on the measurements: pointed ones give
off more electrons than flat ones.
 What would be the result if we used flat plates
(atomically flat even)?


   Bob Clark

--- Tesla list <tesla@xxxxxxxxxx> wrote:

> Original poster: Bert Hickman
> <bert.hickman@xxxxxxxxxx>
>
> Tesla list wrote:
>
> >Original poster: Robert Clark
> <bobbygc2001@xxxxxxxxx>
> >  Actually I'm interested in the results at a few
> >microns. I found this after a web search:
> >"Under constant atmospheric conditions, it is found
> >that the breakdown voltage of a uniform field gap
> may
> >be expressed in the form:
> >  V = A*d + B*SQRT(d)   where d is the gap spacing
> >[i.e., in centimenters - Bob]
> >  For air under normal conditions:
> >  A = 24.4kV/cm
> >  B = 6.29kV/cm^1/2"
> >  Anyone know if this formula would apply or know a
> >more accurate formula at the micron scale?
> >
> >    Bob Clark
> >
>
> Hello Bob,
>
> There are a few recent experimental studies that
> indicate that, for gap distances of less than
> ~4-6 microns in air at STP, breakdown voltage
> diverges from the climbing curve seen in the left
> half of the Paschen curve. Instead of climbing,
> breakdown voltage declines for decreasing gaps
> for gaps smaller than ~4-6 microns (at about the
> Paschen minimum of 325 volts).
>
> One study (1) shows an approximately linear
> decline, while another (2) shows a linear ( for
> gaps of less than <2.5 microns) or a logarithmic
> decline (gaps between 2.5 to 40 microns). The
> source of electrons supporting avalanche
> breakdown is apparently field emission
> (Fowler-Nordheim tunneling) from the cathode due to
> the extremely high E-field.
>
> Reference 1 estimates breakdown voltage in the
> region between 0 - 4 microns as:
>
> Vb = K1*d
>
> where K1 is between 65 and 110 V/micron and d is in
> microns.
>
>
> Reference 2 estimates breakdown (for gaps greater
> than 2.5 microns) as:
>
> Vb = 120*ln(d) + 62  (for 2.5 < d < 40 microns)
>
> and
>
> Vb ~ 70*d (for d <= 2.5 microns
>
> Reference 3 showed variations in the breakdown
> voltage curve depending on electrode material
> (the study used nickel, brass, iron, copper, and
> aluminum electrodes).
>
> The references are:
> 1. Slade, P.G.; Taylor, E.D., "Electrical
> breakdown in atmospheric air between closely
> spaced (0.2 μm-40 μm) electrical contacts",
> Electrical Contacts, 2001. Proceedings of the
> Forty-Seventh IEEE Holm Conference on Publication
> Date: 10-12 Sept. 2001, Pages 245 - 250. Shows
> fairly linear decline for 5 micron gaps or less.
>
> 2. Lee, R. T.; Chung, H. H.; Chiou, Y. C., "Arc
> erosion behaviour of silver electric contacts in
> a single arc discharge across a static gap",
> Science, Measurement and Technology, IEE
> Proceedings, Jan 2001, Volume 148, Issue 1, pages
> 8-14
>
> 3.  J-M Torres and R S Dhariwal, "Electric field
> breakdown at micrometre separations",
> Nanotechnology, 1999, Vol 10 102-107
>
> Bert
> --
>