It is proposed that superionic conductors would be worthy of study as electron emitters. 1. Introduction. Electrons are emitted into a vacuum from flat borosilicate ...
JOURNAL DE PHYSIQUE Colloque C6, suppl6ment au nO1l,Tome 48, novembre 1987
MODELS OF FIELD INDUCED ELECTRON EMISSION FROM ELECTROLYTIC CONDUCTORS
D. Brynn Hibbert Department of Analytical Chemistry, University of New South Wales, PO Box 1, Kensington, New South Wales, Australia 2033
Abstract: A theory of field induced electron emission from electrolytic conductors is proposed in which an electron associated with an immobile anion at the surface is destabilised as a cation moves into the bulk. This electron may be thermally emitted over a field-lowered barrier. Equations are developed for the potential barrier that must be surmounted by the electron and the form of the current versus voltage relation is investigated for the cases of a cation near the surface and one removed into the bulk. It is proposed that superionic conductors would be worthy of study as electron emitters. 1. Introduction
Electrons are emitted into a vacuum from flat borosilicate glass cathodes subjected to electric fields of about 5 x lo6 V m-l [I-31. Although the emission is noisy it may be sustained for long periods and under conditions of ultra-high vacuum [3]. The emission is strongly dependent on temperature and apparently follows a Schottky-like equation [I]
N is a constant related to the number of emission sites, j is the energy of the site (about 1 eV) and a is a constant that determines the extent of lowering of the potential barrier to ' l ~ was emission. Experimentally a was found to be 1.5 - 2 x 1 0 - ~e V ( ~ m - ~ ) -which eV(Vrn-') -'I2 that may be somewhat greater than the theoretical value of 8.5 x deduced from a simple model in which the departing electron is attracted to the positive site remaining in the glass surface
.
E IS the relative permittivity of glass (4.8) and E the applied electric field.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987601
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This theory is sufficient to explain the general features of the emission but is deficient in two respects: 1) In earlier thermionic emission [5] and photoemission [6] studies the energies of the emitted electrons were never less than -4 eV. It may be that very weakly bound electrons could not be detected in these experiments (see for example [7]for an account of 0.7 eV exoelectrons in glass surfaces); but it is not clear with what features of the known electronic and atomic structure of glasses could 1 eV electrons be associated. 2) No account is taken of the electrolytic conduction that must occur in glasses of this type. A model of an emitted electron interacting with a cation in the surface must assume that movement of the cation is prohibited until after emission. Even in the absence of electron emission an electric field causes movement of ions in glasses, a phenomen known as an absorption current. 2.
lon-hopping-electron-destabilizationtheory The model that we develop here is shown graphically in Fig. 1.
glass
vacuum
glass
vacuum
Fig. 1: Potential of an emitted electron near the glass-vacuum interface (a) In the absence of a field (b) With applied field E ~ r n - '
In an electric field that would not be sufficient of itself to admit an electron a positive ion initially in the surface of the glass and associated with an oxygen anion in the silica (SOq) lattice (-Si-0- Na+) migrates into the bulk. This has the effect of destabilizing the electron causing its energy to move nearer the vacuum level, and rendering it likely to be emitted by thermionic emission over a field-lowered barrier. A realistic model of the force between ion and surface electon is of Coulomb attraction shielded by a Yukawa potential [8]
exp(-blxb
+
(be + x)
I-
x is the distance into the vacuum and xo is the Yukawa shielding distance
Equation (3) has the failing that at the surface (x=O) V(x) becomes --. We adopt the formula of Seitz [9] that allows the image potential part of (3) to go to some value cp'. Now
2
where
6
=
-
e (e- 1)
4m0 (E + 1) 9'
At the surface of the electrode the energy of the electron is 2
eV(x=O) = -cpl
-
e exp(-b/xo)
4m0 be
This is the energy from which an electron is emitted in the absence of a field and thus would be determined in a thermionic or photoelectric experiment with b=bo the average interionic separation (taken as the sum of the Pauling or Goldsmidt radii of Na+ + 0-). The second term goes to zero as the ion hops into the bulk, lowering the energy to -9'. Equation (4) may be differentiated and set to zero to determine the position of the barrier although the resulting equation in xmax may only be solved maximum, x,, numerically. The movement of the cation into the bulk causes a shift of xm, nearer the surface with a lowering of the barrier.
For some values of E, cp and b, ,x, may become zero or negative.The latter condition, which appears to indicate that the barrier is behind the surface, arises from the penetration of the field in the dielectric and is depicted in figure 2. In an earlier publication [4] we suggested that this situation occurred with a zero activation for electron emission. This is incorrect, as may be seen from figure 2. Once the cation has hopped sufficiently far into the bulk the barrier becomes (from 6 ) simply 9'.
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vacuum glass Fig. 2: Potential of an electron near the glass - vacuum interface with a cation far into the bulk 3. Discussion - 3.1 - MODEL OF EMISSION -We propose the following model for electron emission from an electrolytic conductor. 1. When an electric field is f i t applied to the conductor cations move into the bulk towards the cathode. This is coincident with the observation of field stimulated exoelectron emission 171. 2. A steady state is reached after a few seconds or minutes with cations depleting the vacuum-glass interface. The Yukawa potential experienced by an electron in the surface is - e/4m0 exp(-blx,) ,where b is an average interionic separation that is greater than that in the absence of a field (b,). 3. The position of the maximum of potential that an electron must surmount is given by differentiating (4) . The height of the barrier cp(F) is then eV(x= xm, ) - eV(x=O) . A calculated emission curve plotted as equation (1) is given in Fig. 3 for the extreme cases of b=b,and b==. The pre-exponential factor has been adjusted in each case to give the same current at E = l x lo5 . Whether on average a cation is relatively near to the surface (and thus to 0-) or far into the bulk when an electron is emitted may be seen by the slope of the log I versus E ~ / ~ curve. Theory predicts [4] a linear term in E in the expression for V(x= xmax )in addition to that in E~~~ This is seen to be only a small perturbation at high E. As b goes to = , however, the remaining image term is much smaller than that arising from the interaction with a positive ion in the surface(about 2.5 times less in Fig 3.)
Fig. 3: Calculated current - voltage curves plotted as Eq.(1) for cation at surface (b = bo) and removed into the bulk (b = =).
- SUPERIONIC CONDUCTORS AS ELECTRON EMllTERS - Electron emission is limited from borosilicate glasses by the poor electrolytic conduction of these materials. A greater emission current should be seen from materials having greater conductivity. An obvious candidate for investigation is the class of superonic conductors [lo]. For example RbAg415 has a room temperature conductivity of 0.2 S cm-' [ l l ] with an activation energy for conduction of 0.1 eV. How the stability of I- is affected by the movement of not clear; the low activation energy for conduction is a function of the many equivalent sites available to an ion. 3.2
is
3.3 - LIFETIME OF ELECTROLYTICEMITTORS - The phenomenon of electron emission from
glasses and electrolytic conductors is irreversible - electrons are not returned at the cathode, instead cations are probably discharged. Ultimately the material itself will lose structural coherence. In a similar experiment in which electrons were collected by a thin conducting anode at the surface of a glass [I21 oxygen was seen to outgas. However a simple calculation shows that at a current density of 10 pA cm-2 measured from a Pyrex emitter the rate of removal of 0-from a surface is 30 pm s-I . An hypothetical lmm thick emitter running at 1 pA cmB would be consumed in about 100 hours.
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References 1. HIBBERT, D. B . and ROBERTSON , A .J.B . , Proc.I?. SOC.A54 (1976)85. 2. HIBBERT,D.B. and ROBERTSON ,A. J .B. , Int J. Electron 48 (1980)301. 3. HIBBERT, D. B. , Proc.27th lnt. Field Emission Symp., Tokyo (1980) 138. 4. HIBBERT, D.B., ROBERTS, T. M. and BHOTE, S .H., J.Phys.D:Appl.Phys. 18 (1985) 1833. andFLETCHER,P.C., J. Appl. Phys. 40 (1969)3927. 5. BODE ,W. 6. ROHATGI, V.K. ,J.Appl.Phys. 28 (1957) 9.51. 7. HIBBWT, D.B. and ROBERTS,T.M. , Nature 297 (1982)42. 8. MARTIN, P.A., STREETMAN ,B.G. and HESS K., J.Appl.Phys, 52 (1981)7409. 9. SEITZ,F. "Modern Theory of Solids " ,McGraw-Hill, London (1940). 10. CHANDRA, S., "Superionicsolids" ,North Holland Press, Amsterdam (1980). 11.BRADLEY, J.N. and GREENE, P.D., Trans Faraday Soc., 62 (1966)2069. 12.LINEWEAVER, J.A., J. Appl. Phys., 34 (1963)1786.
