Elementos de la Auditoría de Gestión

For kinetic electron emission, the source of energy for the emitted electron has never raised any doubts, namely, the kinetic energy of the ion. This is true whatever is the energy transfer mechanism, which has remained obscure until now. KEE is universal; it occurs when various solids are bombarded by particles of very different properties, and

becomes important whenever < 0. Contrary to the PEE,

which has been successfully treated theoretically by Shekter and Hagstrum, the phenomenon of KEE is not well understood. In a quite recent review on the subject, K. H. Krebs [30] concluded that the state of theoretical descriptions of KEE at present is insufficient, and added that "the development of a comprehensive theory is far away and may be

impossible".

The kinetically ejected electrons have several interesting properties:

(a) The yield coefficient ( ^n> is greatly influenced by the state of the target cleanliness [21,22,29]: like in the PEE, clean surface will produce lower yield than from a contaminated one.

(b) y, . varies with ion velocity (and hence, ion 'kin

Fie*

ion velocity (cm/s)

, Schematic variation of KE3 yield coefficient a function of ion velocity.

for KEE to occur, the ion must possess velocity higher than 7

a certain threshold of about 0 . 6 x 1 0 cm/s.

(c) F o r the same velocity of the ion, the yield

coefficient has been found experimentally to be independent of the ion charge [2 1 ,2 2 ].

(d) The yield coefficient has an oscillating

Z^-dependence, where is the ion's atomic number [30], as

shown in Fig. 2 .7 . This behaviour is related to the

inelastic energy transfer, for which the electronic stopping power (S ) is found to have oscillating Z .-dependence as

e 1

well [9].

(e) Given the same ion-target combination, surface orientation with greater transparency will produce lower yield coefficient [2 1 ,2 2 ].

(f) With a polycrystalline target, the yield

coefficient C ^ n) shows a sec 6 ^ — dependence on the angle of incidence (6 ^) measured with respect to the surface normal [21,33,34] .

(g) The yield coefficient is found to be independent on the target temperature [21,35].

(h) The ejected electrons have energy distribution peaks at about 2 eV and a monotonica1ly decreasing tail. The peak's FWHM is found to increase slowly with the ion's

energy [2 2 ].

(i) The ejected electrons have spatial distribution which obeys the cosine law.

Several theories have been proposed for the mechanism of !’E E . Among the old theories (presumably forgotten) are: the "thermal emission theory" of Kapitza (1923), the

Pig. 2.7 » The variation of KEE yield coefficient from stainless steel with the ion atomic number at 26 keV . (After Krebs (Ref. 50))

"shaking theory" of Frenkel (1941) and the "radiation theory" of Izmailov (1955) [21.22].

Ploch laid the foundation of the so-called "standard" theories of K E E . Based on the close relationship between the energy dependence of the electron yield and the cross

section for ionisation of an atom by ion impact (a^); he suggested that the electrons were formed by a process of ionisation of the lattice atom by the incident ion [2 1 ]. Three KEE theories which have been principally based on this

assumption are those of von Roos and Pari 11is-Kishinevskii [36] for low velocity ions, and of Sternglass [37] for high velocity ions. In a recent review on this subject. N.

Benazeth [38] pointed out three areas in which these

theories may differ: (i) mechanism of calculating the energy transfer, which can be either through inelastic collision cross-section, or electronic stopping power, (ii) liberated electron slowing-down in the solid, which may be approached either by mean free path or by electronic stopping power, and (iii) inclusion or exclusion of electronic emission due to energetic recoil target atoms.

In von R o o s 's theory, the solid is treated as a free "gas of lattice atoms" which obeys the Boltzmann

distribution function. Electrons are liberated by these "free" atoms during ionising collision with the incident ions; no contribution from the atoms recoil energies is taken into account. The number of electrons liberated in the

collision is calculated using ionisation cross-section, ;

and the number of electrons finally escape from the solid is calculated using a simple velocity dependent escape

probability, ignoring the possibility that some of the electrons being absorbed by the lattice.

To calculate the number of electrons liberated in the collision, Sternglass used the concept of mean energy loss per secondary formed (E) and total stopping power (dE/dx). Since dE/dx is a function of ion energy (E) , and hence its distance from the surface (x), the number of electrons

formed in the collision is also a function of E and x, i.e., n(E,x). He rightly ignored the contribution from the recoil energies because at high velocities nuclear stopping power is negligible. The number of electrons eventually leave the surface is calculated by using an exponential escape

probabi1 ity

P(x) - P.A exp(-x/L )

1 s

where L is the characteristic length of the attenuation

s

process, x is the perpendicular distance of the electron from the surface, P^ and A are constants. This means that the yield from a thin layer of thickness dx located at a depth x is given by

dy - n ( E ,x)P(x)dx.

Parilis and Kishinevskii assumed that the collision between the incident ion and a lattice atom results in the

ionisation of the latter with a hole in its filled band, and considered that the process has the same cross-section as for the formation of an electron-hole pair. As for the process of energy transfer, Parilis and Kishinevskii apply the Firsov's calculation of energy loss, which is based on a friction model. They then treated the ejection of electron from the surface as a result of an Auger recombination of a

conduction electron with the hole. To calculate the electron yield coefficient they used exponential escape probability, as follows:

y - c t(u) w (<5) N exp(-x/A) dx

where N is target atomic density, xn the depth at which the ion still retain the ability to ionise, o(u) is the cross- section for the formation of an electron-hole pair, u the

ion velocity, and w(6) the probability of the Auger process for a hole and 6 is its depth.