FIELD EMISSION FROM LOW BARRIER SURFACE CATHODES

V. Semet, Ch. Adessi and Vu Thien BinhEquipe Emission Electronique, LPMCN -UMR CNRS

University Lyon 1, 69622, Villeurbanne, France.

Corresponding author: Vu Thien Binh, yuthien.binhaJpmcn.univ-lyonI rTechnical Digest 19th IVNC & 50th IFES, 17-20 July 2006 - Guilin, China

INTRODUCTION

In most cases, analyses of experimental field emission I-V characteristics (FE current vs voltagevariation) for extracting information about the cold cathode emission behavior and the work function (P of theemitting surface, use the conventional analytic Fowler-Nordheim (FN) relation [1]

I= 1.54xlo-6 X [ (j2V2 A) / ((P t2(y))] x exp { -6.83X10 [((P312 v(y)) / (fV) ] } (1)

where I is the FE current in A, (P is the cathode work function in eV, V is the applied FE voltage in V, A is theFE surface area in cm2, 1 is a geometrical factor in cm-' determined by the geometry of the electron emitter andother electrodes and gives the applied local field F = PV. v(y) and t(y) are the Nordheim functions of theNordheim parameter y = 3.7947x 10-4 F"X2 / (P, which take into account the lowering of the potential barrier dueto the image potential, also called the Schottky effect. It's one property is the simplicity related to an analyticalrelation and the possibility to state, with high probability, on a tunnelling mechanism for the emission when itsln(INV2) vs 1/V plot is a straight line. However, many new experimental measurements have stimulated anotherlook on the relevance of the FN approach for low values of (P [2,3] for which electron emission no longer takesplace solely by tunnelling, through the triangular barrier, but occurs partly or dominantly by direct emissionover the top of the barrier that has been pulled down below the Fermi level by the Schottky effect.

1. THE METHODOLOGY

In this work we will address only the current density J versus applied local field F, in order to put asidethe field enhancement factor 1, and to point out the relations between the J-F characteristics and the differentemission mechanisms, namely tunnelling, thermoinic and ballistic.

The current density is computed using the transmission probability for an electron to cross the barrierbetween the electron sea of the cathode and the vacuum [4]. The basic equation used is the following:

J = (me/4nh3) x kBT x J T(E) x ln (1 + exp [(EF -E)/kBT] dE) (2)

where m is the mass of the electron, kB the Boltzmannn constant, T the temperature, EF the Fermi level, E theenergy of the electron and the integration is done from the energy of the bottom of the conduction band toinfinity. The main point of the method is the calculation of the transmission coefficient T(E). It is computed bysolving the ID Schr6dinger equation with values of the effective potential constant inside the cathode,corresponding to the applied bias corrected with the image potential between the cathode and the anode thenfinally equal to the applied bias inside the anode. The Schrodinger equation is solved first for a bare systemwithout the image potential. The image potential is then introduced by mean of the self-consistent Lippman-Schwinger equation [5], which is resolved by spatial discretization [6]. This method allows computing the exactcurrent with the image potential. However, it corresponds to a zero emitted current approximation.

Three parameters are extracted from the numerical calculations for each set of variables ((P, F, T). Theyare the total current density, the current density per energy (i.e. the total energy distribution spectrum) and thepotential energy distribution.

1-4244-0401-0/06/$20.00 ©2006 IEEE 25

2. THE RESULTS

The Figures 1 and 2 are examples of the results for CD = 1.2 eV at T = 300 K. The lower limit of theapplied local field (0.025 V/A) is defined as the value to obtain a total current in the range of pA from a

lOOx100 nm2 emission area, i.e. for a current density of about a few mAJcm2. The upper limit for the currentdensity is in the range of 109 A/cm2 for F = 0.3 V/ A.

10

5

0

-5

0

O.$0.0

1

7iiC:

0

QL-0.5

-1.0I

Figure 1: J-F characteristics of a low workfunction cathode. The ln (J/F2) vs 1/F plotshows an approximatively linear variationonly for the interval of field between 0.035and 0.09 V/ A. The insert is the linearrepresentation J vs F of the same data.

10 20 30 40

F (VIan~gstro"m)-'

Current density per unit energy (normalized)O.0O 02 0.4 0.6 0.8 1.0 1.2

0 10 20 30 40 50 60Distance from the surface (angstr)

0.5

0

0.0 :-m

oc

0

-0.50

-1.0

Figure 2: Potential energy diagrams and total energy distribution spectra for four different applied local field F indicated inFig. 1 above (for 1 to 4). The Fermi level of the metallic cathode is taken as the energy reference. The TED spectra arenormalized to allow comparison.

A systematic study was done in order to relate the J-F characteristic variation with the three emissionmechanisms, tunnelling, thermionic and ballistic. All three are now effective during the field emission fromsurface with low work function. Empirical relations will be given to extract some cathode properties from themeasured J-F characteristics.

1 R.H. Good and E.W. Muller, Handbuck der Physik 21, 176 (1956). A.G.J. van Oostrom, Validity ofthe Fowler-Nordheim modelforfield electron emission, Thesis 1965, Univ Amsterdam2 K.L. Jensen, J. Vac. Sci. Technl. B 17, 515 (1999).3 R. Forbes, Ultramicroscopy 79, 11 (1999).4 K.L. Jensen and M. Cahay, Appl. Phys. Letters 88, 154105 (2006).5 E.N. Economou, Greens 'sfunctions in quantum physics, Springer-Verlag, Berlin, 1990.6 Ch. Adessi and M. Devel, Ultramicroscopy, 85, 215 (2000).

26

'-,(4U-

CZ

-1 0

-15