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High Current Density Advanced Cold Cathode Facility *
ECE Department, University of Wisconsin,
He ,
Scharer ,
Booske ,
Madison ;
Sengele ,
University of
Vlahos ;
Michigan,Ann Arbor
Jordan ,
TMM Method Model
We report measurements and analyses of field emission from both copper
and aluminum cathodes. The copper cathodes have been micromachined to
have raised ridges or knife edges to enhance the surface electric field. Raised
ridges have also been formed into the aluminum cathodes, using Ablation Line
Focus (ALF) laser-micromachining, developed at the University of Michigan.
Experimental result from CKE
cathode fitted with FN model
Work function Φ=4.5 eV
Effective Local Field Enhancement
Factor βeff = Esurface / Egap =602
The measurements are conducted in the Madison Cathode eXperiment
(MACX) facility after baking and processing to a UHV base pressure of 10-10
Torr. The anode-cathode gap is variable from 0-10 mm with 50 μm accuracy
and the cathode voltage is variable from 0 – 20 kV (negative). Pulse lengths
are variable between 1 μs – 500 ms. The MACX facility also provides the
ability to heat the cathode from ~ 300 – 650 oK while measuring electron
emission currents.
The experimental data is investigated with an accurate TMM (Transfer
Matrix Method) model. With this model we can predict the entire range of
emission from thermionic to field emission by varying the surface electric
field. A new definition of TE (thermionic emission), FE (field emission)
and ME (mixed emission/transition range) is provided.
Emission Area Ratio
Experimental result from CKE
cathode fitted with TMM model
Cathode Electrical Test Facility System
Cathode Anode Structure
Work function Φ=1.73 eV
Effective Local Field Enhancement
Factor βeff = Esurface / Egap =7
Research Objectives
Height (m)
UHV (10-10 Torr) facility for high current density cathode research
Develope TMM model to predict the entire range of emission from
thermionic to field emission and mixed emission (field + thermionic)
Emission Area Ratio
Analyze the experimental data with TMM model codes
Design high-current density cathode with high local field enhancement
factor (β=Eloc/(V/d)) and low work function
Temperature=330 ºC
Position (m)
1.25 cm diameter ALF cathode with β ~4 which works well on UM HPM (Several Hundred MW) magnetron.
University of Michigan Collaboration Cathode Structure
Vacuum System Introduction
Vacuum System: A scroll pump, turbo pump and a VacIon pump are used
to bring the whole system to 10-10 Torr with the system baked to 450 ºC.
Cathode and Anode: The cathodes are made of Al, Cu, C or Mo and may
be coated with CsI. The anode is made of stainless steel. It is a tube about 1cm in diameter and 8-cm long. A tiny second anode is applied to measure the
emission current density distribution.
TE, FE and ME Regime
[email protected]=E0,T=T0; [email protected]=E0,T=0 K;
[email protected]=0,T=T0
Electrical System
1. -0.1~ -20 kV, 1 μs -500 ms long duration with <60 ns rise time are
applied between the cathode and anode.
2. To reduce the transient current spike, a high-voltage current limiting
resistor and two forward /reverse Schottky power diodes in parallel are added.
3. At low current level,(<1 μA), a three stage operational amplifier is
utilized to provide 1000 times of amplification in amplitude. A three stage low
pass filter is used to improve the SNR (Signal-Noise Ratio) when necessary.
9.06 mm
High electric field required for
transition at high temperature
Copper Knife Edge (CKE) Cathode Fabrication Structure
TMM Method Model
Experimental result can be explained by the TMM model well
Unique and physically reasonable cathode parameters like
effective beta, βeff , effective work function Φ, and emission area
ratio R are obtained with TMM model
TMM code shows good agreements with Fowler-Nordhem law
and Richardson law at very high or very low electric fields
TMM Model
1. Assumes a Fermi-Dirac distribution with a non-zero temperature in
electron supply
2. . Electron tunneling is calculated exactly (within a 1D assumption) using
a transfer matrix method to solve the steady-state Schrödinger’s equation
(without WKB approximation)
3. The entire range of emission from thermionic to field emission and mixed
emission (field + thermionic) is obtained
4 Experiments on a copper knife-edge cathode show close agreement with
the TMM model.
Bench mark with Fowler-Nordheim and Richardson’s law
(1) R.H.Fowler and L.W.Nordheim, Proc. Roy.Soc, (London), A119, 173 (1928)
(2) E.L.Murphy and R.H.Dood, Phys Rev, 102, 1464, (1956)
(3) Kevin L. Jensen, Patrick G. O’Shea, and Donald W. Feldman, Appl. Phys.
Lett. 81, 3867, (2002)
(4) Kevin L. Jensen, Marc Cahay, Appl. Phys. Lett, 88, 154105 (2006)
(5) Kevin L. Jensen, J. Vac. Sci. Technol. B 21, (2003)
Research Supported through AFOSR by a USDOD MURI05 grant on the Nano-physics of High Current Density Cathode and Breakdown