4.2. Mechanism of Metal Hydride Secondary Ion Formation
Cluster secondary ions can theoretically form on the surface or just above it during the sputtering process, or in the plum of the sputtered particles in the vacuum after completion of the sputtering process while colliding with gaseous atoms and molecules. Previous studies indicate that the recombination process indeed happens on the surface [
56,
57,
58] or just above it [
56,
59,
60], and similar conclusions can be obtained from the results of the hydrogen flooding experiments. Firstly, the formation of high-intensity secondary ions such as TiH
3– in the vacuum would require a high-rate occurrence of successful three-particle collision reactions, which is highly unlikely. In the case of atomic H, a three-particle reaction would be partially required for the formation of dihydride ions as well, although not completely necessary due to the incomplete dissociation of hydrogen. If the in-vacuum formation of cluster secondary ions would indeed be their main formation pathway, then, according to the particle collision reaction, dissociation of hydrogen would most significantly increase the intensity of the monohydride secondary ions. This is not the case since H
2 dissociation results in the most pronounced intensity increase of hydride secondary ions composed of numerous H atoms/ions. Already based on this, we can conclude that the formation of hydride cluster secondary ions originating from the metallic surfaces primarily does not occur in the vacuum.
The next argument against the in-vacuum formation of hydride cluster ions is the time scale of collisions and the time available for the successful reaction to occur. The latter corresponds to the time frame between the primary ion pulse and the end of the extraction into the analyzer, which is a few µs at most. The average time, required for the collisions to occur, can be calculated via the kinetic theory of gases. The root mean square (RMS) speed of the gas can be calculated via Equation (2)
where
vRMS is the RMS speed of the gas particle,
R is the molar gas constant of 8.31 J/molK,
T is the temperature in K, and
M is the molar mass. The thermal temperature of hydrogen molecules exiting the hydrogen atom beam source depends on the heating power and can be up to 2200 K. When H atoms or H
2 molecules hit the recombinator they lose some of their kinetic energy and they cool down. The same thing happens when molecules hit the chamber walls. Therefore, it is practically impossible to determine the temperature of the molecules when they reach the sample. Nevertheless, if we estimate the gas temperature of approximately 1000 K, the speed of H
2 molecules can be calculated as approximately 3500 m/s and the speed of H atoms as 5000 m/s. According to Equation (3)
the mean free path of the gaseous particle can be calculated as well. Here,
l denotes the mean free path,
kB the Boltzmann constant of 1.38 × 10
–23 J/K,
d the diameter of the colliding particles, and
p the pressure in Pa which was 7 × 10
–5 Pa. Since the collisions of H
2 molecules or H atoms with metal atoms are of interest,
d1 and
d2 should correspond to the diameters of the metal atom and H
2 molecule or H atom. There are also possible deviations in diameters due to the ionization of any of the atoms or molecules, but for the purpose of this discussion, these will be disregarded. Fe, with an atomic diameter of 248 pm [
61], can be chosen as a common example of a metal atom. Kinetic and van der Waals diameters of the H
2 molecule and H atom are 289 [
62] and 220 pm [
63], respectively. Therefore, the mean free paths of 610 m for the H
2 molecules and 800 m for the H atoms can be calculated. The average times required for the metal – H
2/H collision (
t) can be determined via Equation (4)
The values of 170 ms (H2) and 160 ms (H) are more than four orders of magnitude larger than the time frame during which the collision reactions can occur. This is another indicator of the low probability that in-vacuum collision reactions represent a significant pathway of the metal hydride cluster ion formation.
The hydride cluster ion formation on the surface of sputtered samples will be consequently considered in the following. A comparison of the monolayer formation via gas adsorption and its removal via sputtering indicates a high probability of this mechanism being the most important one. While continuing the analysis considering iron, its numerical density of 8.5 × 10
28 atoms/m
3 can be calculated via Equation (5)
where
ρN represents the numerical density,
ρm the mass density, and
NA the Avogadro constant of 6.02 × 10
23 mol
–1. The number of Fe atoms per meter can be obtained from the
ρN and it is 4.4 × 10
9 atoms/m. This value can be further transformed to the size of the atom, although, due to the arrangement of the atoms in the crystal structure of the metal, it is closer to the thickness of the monolayer which is 230 pm. Due to the tightly packed atoms in the solid Fe, this value corresponds appropriately to the slightly larger diameter of the Fe atom of 248 pm [
61]. The sputter rate of iron in the H
2 atmosphere with 1 keV Cs
+ ions and under the same analysis conditions was measured to be 84 pm/s, which can be translated to 0.37 monolayer/s. Therefore, approximately 2.7 s are needed to sputter one monolayer of Fe with adsorbed hydrogen.
The time needed for the complete formation of hydrogen monolayer can be determined as well. If the sticking coefficient of 1 (each atom that hits the surface is also adsorbed) and adsorption of one gas particle per atom on the surface are assumed, then Equation (6)
can be applied.
τ is the time needed for the monolayer formation, and
D is the dose of gas particles that, by the assumption, equals the surface density of Fe atoms (1.9 × 10
19 atoms/m
2). At a temperature of 1000 K and a pressure of 7 × 10
–5 Pa,
τ equals 4.3 s for the H
2 molecules and 3.0 s for the exclusively H atoms. Equation (6) is derived from Equation (7)
where
j represents the current of gas molecules and is defined via Equation (8) as
vRMS is defined by Equation (2) and
ρG is the density of the gas in particles/m
3 defined by Equation (9)
In the case of the opened recombinator of the hydrogen atom beam source, Equation (6) does not describe the process of adsorption completely since gas is introduced via the point source. However, considering the distance from the source to the sample and the driving pressure of the atom beam source in relation to the previously measured gas currents [
64], it can be concluded that the gas current of this system is even lower if the point source is considered instead of the random distribution. The latter gives the value of
j in the range of 10
18 m
–2s
–1 while the calculation via point source approximation has the
j value in the range of 10
17 m
–2s
–1. A lower current of gas molecules
j results in even loner monolayer formation time
τ.
Furthermore, the assumption of dose
D being equal to the surface density of the metal ions is not necessarily correct. The comparison with Equation (10)
which represents an approximation of the time needed for gas molecules to form one monolayer, that is monolayer formation time [
65], is consequently sensible. Approximation Equation (10) also assumes the sticking coefficient of 1. At the pressure of 7 × 10
–5 Pa,
τ calculated via Equation (10) equals 4.6 s for both H
2 and H. The monolayer formation time is in this case slightly longer than while assuming equal values of gas dose and surface density of metal ions. It is consequently possible to conclude that slightly more than one H atom gets adsorbed to each Fe atom. Such a conclusion corresponds to the notable size difference between Fe and H atoms. Furthermore, although hydrogen is a relatively reactive gas and freshly sputtered surfaces are proven to adsorb gaseous species at a high rate [
66], the sticking coefficient of 1, especially in the case of H
2, is too high. Since the dissociation ratio of H
2 molecules reaches approximately 30%, a sticking coefficient below 1 can be expected during SIMS analyses in combination with the hydrogen atom beam source as well.
The consequence of a lower sticking coefficient is even longer monolayer formation time. When accounting for all of the above effects, it is possible to conclude with a relatively high degree of certainty that monolayer formation time at the given conditions, especially concerning H2 molecules, is notably longer (almost 2-fold) than the time needed for the removal of one monolayer of Fe with adsorbed hydrogen which accounts for 2.7 s. Dissociation accelerates the monolayer formation by adsorption of more reactive H atoms with a higher sticking coefficient, therefore creating a larger portion of the monolayer before the latter is sputtered away. Since molecule dissociation also causes an increase in the intensity of metal hydride secondary ions, it can be concluded that a higher degree of hydrogen adsorption and a higher percentage of hydrogen monolayer formation increase the formation rate of hydride secondary ions. This correlation proves the importance of the adsorbed species and indicates that cluster secondary ions are preferentially formed on the surface or just above it during the sputtering process with a mechanism being the recombination of sample particles with pre-adsorbed atoms and molecules.