Re: Breakdown voltage at submillimeter distances?

["Tesla list" <tesla@xxxxxxxxxx>]

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
--
***************************************************
We specialize in UNIQUE items! Coins shrunk by huge
magnetic fields, Lichtenberg Figures (our "Captured
Lightning") and out of print technical Books. Visit
Stoneridge Engineering at http://www.teslamania.com
***************************************************