The Ionization Probability

The formation of secondary ions is the most difficult feature in SIMS. Whereas sputtering is relatively well understood, the process of sputter ionization is not, and a theory that describes the process of secondary ion formation satisfactorily does not yet exist. However, a number of trends can be rationalized. 

The ionization probabilities Rr1 vary over some five decades across the elements in the Periodic Table. In addition, they vary with the chemical environment of the element. This effect - which usually is referred to as the matrix effect - makes quantitation of SIMS spectra extremely difficult. As shown in Table 4.1, positive secondary ion yields from metal oxides are typically two orders of magnitude higher than those of the corresponding metals. A similar increase in yields from metals is observed following the adsorption of gases such as oxygen or carbon monoxide. 

As noted previously, the ionization probability - which accompanies sputtering - is at best qualitatively understood. Several attempts have been undertaken to develop models for secondary ion formation, and in this respect the interested reader may consult the literature for reviews [2, 4]. Here, we will briefly describe one model that accounts quantitatively for a number of observations on metals -the perturbation model of Norskov and Lundquist [12]. This model assumes that the formation of a secondary ion occurs just above the surface, immediately after emission. Then  

Both ion formation and neutralization just above the surface are more likely if the velocity, v, of the departing particle is small, or in other words, when its residence time in the interaction zone just above the surface is long. 

These features are recognized in the following expression for the ionization probability  

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Local Thermodynamic Equilibrium (LTE). This LTE model is of historical importance only. The idea was that under ion bombardment a near-surface plasma is generated, in which the sputtered atoms are ionized [3.48]. The plasma should be under local equilibrium, so that the Saha-Eggert equation for determination of the ionization probability can be used. The important condition was the plasma temperature, and this could be determined from a knowledge of the concentration of one of the elements present. The theoretical background of the model is not applicable. The reason why it gives semi-quantitative results is that the exponential term of the Saha-Eggert equation also fits quantum-mechanical expressions. 

The element sensitivity is determined by the ionization probability of the sputtered atoms. This probability is influenced by the chemical state of the surface. As mentioned above, Cs" or OJ ions are used for sample bombardment in dynamic SIMS, because they the increase ionization probability. This is the so-called chemical enhancement effect. 

The power dissipated at two different frequencies has been calculated for all reactions and compared with the energy loss to the walls. It is shown that at 65 MHz the fraction of power lost to the boundary decreases by a large amount compared to the situation at 13.56 MHz [224]. In contrast, the power dissipated by electron impact collision increases from nearly 47% to more than 71%, of which vibrational excitation increases by a factor of 2, dissociation increases by 45%, and ionization stays approximately the same, in agreement with the product of the ionization probability per electron, the electron density, and the ion flux, as shown before. The vibrational excitation energy thresholds (0.11 and 0.27 eV) are much smaller than the dissociation (8.3 eV) and ionization (13 eV) ones, and the vibrational excitation cross sections are large too. The reaction rate of processes with a low energy threshold therefore increases more than those with a high threshold. 

All elements can be detected and measured with a sensitivity of the order of 1 ppm. The analysed volume is typically 0.1 cubic micrometers, so a sensitivity of 10 19g is possible. Different isotopes can be distinguished, but the ionization probability is matrix dependent, which makes quantitative analysis difficult. 

The interaction will become weaker as the electron wavelength becomes greater or less than the molecular diameter with a consequential decrease in the cross section. This leads to an expression for the ionization probability as a function of electron energy, giving the shape of the ionization efficiency curve,... 

The essential quantities that determine the yield of secondary ions in a SIMS spectrum are thus the sputter yield Y and the ionization probability R . 

In SNMS, sputtered neutrals are post-ionized before they enter the mass spectrometer. In contrast to SIMS, SNMS does not suffer from the matrix effects associated with the ionization probability of sputtered particles. Here, the sensitivity for a cer-... 

The initial low rate of increase of all negative ion yields with exposure is again indicative of an increasing work function which generally reduces the ionization probability for negative ions—an effect opposite to the initial increase in ionization probability observed for positive ions. 

The probability of ionization is given by the geometrical probability, i.e. by the ratio of that effective area to the total area considered, which is unit. That is why (3b) gives the ionization probability of the i element per incident electron for the excited volume of our thin layer. Although the concentration dependence described in (3a) is identical to that given in (3b), it is expressed simpler in (3b), which describes a linear dependence on its variable (c ) than how it is expressed in (3a) where both the numerator and the denominator depends on the variable (c ). 

To increase the ionization probability, a homogeneous weak magnetic field is used to keep the electrons on a spiral path. At the end of the ionization chamber, electrons are collected in a positively charged trap, where the electron current is measured and kept constant by the emission regulator circuitry. 

Fig. 4. The dependence of the ionization probability for the He ion on the strength of the external electric field. The points are the experimental data [ 14] and the line has been calculated using eqn. (8) with / = 0.076 eV and A = 0.3.

Second, the cross section curves for He(2 S)-N2,Kr,Xe are very similar to the He(2 S)-Ar curve shown in Fig. 6. Also, they lie in an energy region where (oo) D+—because no decrease as predicted for the region (oo) [equation (11.14)] is observed at low collision energies— however, they are also not described by (11.17), which predicts a linear increase as observed for the triplet systems. Only at the lower velocities a nearly linear increase is observed. The deviation from the behavior predicted by (11.12) at higher velocities is probably caused by the fact that the ionization probability per collision in the relevant impact parameters range is already close to unity whereas P(b)< 1 was assumed in the derivation of... 

Analyzing the data on molecular gases irradiated by vacuum UV emission,60 Platzman2 has noted that for certain gases the probability of ionization 77 (Eph) is smaller than unity when Eph exceeds Ix by 10 eV or more. This was confirmed in his subsequent study of molecule-noble-gas mixture,61 done in collaboration with Jesse. They have also observed an isotopic effect the substitution of deuterium for hydrogen increases the ionization probability. Platzman thus concluded that in such discrete states with E>lx the predissociation efficiently competes with autoionization. Platzman has named them the superexcitation states (SES). The SES were discussed in a special issue of Radiation Research62 (see also Refs. 25 and 63). 

Only a small fraction of the sputtered material will actually be ionized. The ionization probability depends on the element species and on the matrix material. 

From the ionization probabilities P s one can recover the average number of escaped electrons = f k kPt and an estimate of the corresponding variance A= Y)i k2Pk - [fir. klf)2 Ionization cross-sections can also been evaluated from the knowledge of the Pk,s [32],... 

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