Low-field electron emission from nano-carbons
Al. A. Zakhidov*, A. N. Obraztsov, A. P. Volkov, D. A. Lyashenko
Moscow State University, Physics Department http://carbon.phys.msu.ru
Moscow 119899, Russia
Motivation FE site model for nC materials Energy band diagram
Electron field emission (FE) from surface of conductive materials induced by of strong electric field has great importance for
fundamental and applied science. Various carbon related materials show low-field electron emission and are therefore highly
attractive as replacement for metals and semiconductors in FE cold cathodes. For example nano-carbon cathodes can be
extensively used in various types of cathodoluminescent lamps [1-2]. One of the main advantages of carbon materials for FE
applications is in extremely strong interatomic covalent forces bonding providing highest mechanical strength and chemical
inertness appropriate for cathode material operating in vacuum devices under intense electric field in order of 10 7-108 V/m and in
the harsh conditions of residual gas ion bombardment. bonds
An phenomenological model of FE sites and corresponding
mechanism of FE has been proposed in our recent publications for nano- DOS
carbon materials allowing explanation of the experimental observations
mentioned above. This explanation assumes that two kinds of FE may bonds
exist in carbon emitters: (i) first type takes place at high electric fields
similar to that for usual metallic emitters (FN emission) and (ii) second
type takes at low electric fields with threshold values much lower than
those predicted by the FN theory. The latest type abnormal low-field
emission is specific for some nanostructured carbon materials only. This DOS k
specificity, in fact, originates from the possibility of carbon atoms being
arranged both sp3 (diamond-like) and sp2 (graphite-like) hybridization.
These two different carbon phases may be combined with a very narrow
interface providing immediately high electrical conductivity and
significant reduction of the potential barrier for electrons escaping into
vacuum. Our phenomenological model and mechanism of cold emission Color FE display prototype Schematic energy band diagram presentation of vacuum-cathode interface without (a) and with (b) external field. The straight
have universal character since the discussed nanostructured species do lines show simplified two-barrier structure including rectangular barrier between two carbon phases and outer potential
exist in various carbon materials. However this explanation of low-field barrier. The dashed lines show quantum wells corresponding to separate carbon atoms in the presurface layer with graphite
electron emission requires additional theoretical and experimental properties and surface cluster with diamond-like properties similar to WBG semiconductor having gap in density of electron
confirmations. states between highest occupied state (HOS) and lowest unoccupied states (LUS). The electron states in the quantum wells
In this work we performed analysis of a probability for electrons to be emitted from FE site model for nanostructured graphite-like carbon are shown by gray and resonance electron states (RES) in HOS-LUS gap are shown by black. The height of rectangular
barrier and work function of surface cluster (Evac-EF) is about 4.5 eV. When external field is applied to the cathode the
nanocarbon cathode surface through heterogeneous sp2-sp3 surface layer. with curved graphite sheets: bended part of crystallite
contains chain of atoms with de-overlaped bonds, electron states in quantum well corresponding to the surface cluster are shifted down due to voltage drop.
1. A.N. Obraztsov, Catholuminescent light source, PCT/RU 02/00175 providing local reducing of WF.
2. A.N. Obraztsov, A.P. Volkov, Al.A. Zakhidov, D.A. Lyashenko, Yu.V. Petrushenko, O.P. Satanovskaya, Field emission
characteristics of nanostructured thin film carbon materials, Appl. Surf. Sci. 215(2003)214-221
Electron tunneling trough sp2-sp3 heterogeneous Results Discussion and Conclusions
surface layer. Expression for the phase ratios in the brackets has simple analytical form for a case of two rectangular barriers. And the
brackets in second term is equal to zero when Fermi level coincident with energy levels in the quantum well between the
1.The presence of the resonance electronic states (RES) in the quantum well
potential barriers. These conditions can naturally be called “resonance tunneling”. The main input into transmission corresponding to the WBG layer is an important feature which provides
A general expression for FE current of electrons tunneling through the (1) coefficient value at the resonance conditions is going from forth item in (4) which contains multiplication of tunneling low-field and intensive electron emission.
potential barriers is expressed by formula: probabilities for two separate barriers. In this case we may omit other items except forth in the expression for the
transmission coefficient. Let us analyze this special resonance case for our two-barrier model. By assuming 4-'4=2n (n=
where k is a wave vector of electrons, Еz – energy of electrons, F – external electric field near the cathode surface, e – electron 0, ±1, ±2, ±3….) we obtain for the transparency coefficient which is determined mainly by second term in (4).After some
charge, h – Plank constant vz - electronic group velocity normal to surface, and T(Ez,F) – transparency of potential barrier simple simple analysis we have obtained formula for FE current:
2.The efficient electron tunneling requires the special energetic position of
these RES near Fermi level and slightly above it to explain the existence of
There are some uncertainties in the determination of the shape of the first barrier between sp2 and sp3 carbon phases in the cathode nonzero FE thresholds.
surface. For the simplest approximation with a barrier height
V and width w the corresponding
transmission coefficient (and tunneling (2) 3.FE current increases in order of 4 in case of tunneling though RES at the
probability P1) is 
same electric field.
The Wentzel-Kramers-Brillioun (WKB) approximation may be used for the second barrier on cathode-to-vacuum interface 4.FE resonance current exponentially depends on width of WBG layer w.
assumption on its simplest triangle shape.
The corresponding transmission This formula is different from usual Fowler-Nordheim It should be mentioned that the two-barrier mechanisms are well known in the analysis of electron emission
coefficient has a form of  (3) law by second additional term in exponent function. phenomena. For example, two-barrier structure of potential barrier on cathode surface may be formed due to presence of
This new term ( 1/2w) may lead to significant increase additional levels in density of electronic states related to adsorbed gas molecules or structural defects. But in this case
where P2 is tunneling probability, Е0 – energy of electrons in vacuum near
in the current density.Using for estimation =4.5eV and emission current intensity and stability are very low due to strong localization of such states in contrast to carbon cathodes
the surface. where according to our model it is assumed that two-barrier structure is formed on essentially sp2 highly conductive
w =4 Å, as it was proposed above, we will have current
density increase on 4 orders for the same fields in carbon surface due to presence of extended sp3 insulator carbon clusters. These clusters provide delocalized electron states
Following to  an expression for two-barrier transmission coefficient may be obtained combining formulas for T 1(Ez,F)and comparison with values predicted by FN for metal but remain transparent for tunneling electrons in contrast to other two-barrier models of FE, which are proposed for
T2(Ez,F) as: emitters. Fig on the right shows for the same values of interfaces of two materials with different energy band structure. The last one may be realized, for instance, on interfaces
=4.5eV and w =4 Å and for =4.5 eV current-versus- of well conductive materials (metals, graphite) and wide band gap (WBG) semiconductors. But even in the case of very
(4) field dependences obtained using usual FN theory and thin WBG material layers their thicknesses and interface region dimensions are much large in comparison to sp3 clusters
using formula (5) for the two-barrier model. The on sp2 carbon surface and therefore corresponding efficiency of electron emission is much lower than experimentally
dependences clearly show reduction of the threshold observed for nano-carbon cathodes. In contrast to formal speculation about resonance tunneling via electronic states in
where in the brackets we have phase ratios for every term. Taking into account that thickness of an internal barrier is much smaller
field and dramatic increase of the current density for the WBG material with unknown structure our model allows self consistent explanation of the mechanism of low-field
than that for outer one, the transmission coefficient T1 should be much larger than T2. It allows us to neglect in formula (4) by
two-barrier emitters with resonance electron states. emission and of the nature of two-barrier structure and the resonance states.
items other than second and forth.
Current-vs.-field dependencies for electron emission calculated in accord with FN low (dots
3. L.D. Landau, E.M. Lifshic, Quantum mechanics. Nonrelyativistic theory. “Nauka”, Moscow, 1989. line) and with respect of two-barrier model using formula (5) (straight line)
4. E.O. Kane, Theory of Tunneling. J. of Applied Physics, 32 83-91 (1961)
This work has been supported in part by INTAS
grant No. 01-0254.