Ionization probability of Si+ ion emission from clean Si under Ar+ bombardment

Article abstract of DOI:10.1088/0953-8984/9/43/025

The secondary-ion intensity of sputtered Si has been measured as a function of the emission energy using a previously calibrated mass analyser. From the Sigmund-Thompson energy distribution for neutrals, the ionization probability R⁺ for Si⁺ ions is inferred. It is found that the behaviour of R⁺ at high emission energies is consistent with neutralization via the electron tunnelling mechanism (resonant electrons tunnelling from the substrate to the outgoing ions). The possibility of electronic excitations induced by the collision cascade in Sroubek's model is also considered.

Full text of DOI:10.1088/0953-8984/9/43/025

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J. Phys.: Condens. Matter 9 (1997) 9427–9433. Printed in the UK
PII: S0953-8984(97)82256-4
Ionization probability of Si+ ion emission from clean Si
under Ar+ bombardment
M H S Low, C H A Huan†, A T S Wee and K L Tan
National University of Singapore, Department of Physics, Kent Ridge, Singapore 0511
Received 3 March 1997
Abstract. The secondary-ion intensity of sputtered Si has been measured as a function of the
emission energy using a previously calibrated mass analyser. From the Sigmund–Thompson
energy distribution for neutrals, the ionization probability R+ for Si+ ions is inferred. It is
found that the behaviour of R+ at high emission energies is consistent with neutralization
via the electron tunnelling mechanism (resonant electrons tunnelling from the substrate to the
outgoing ions). The possibility of electronic excitations induced by the collision cascade in
Sroubek’s model is also considered.
1. Introduction
When solid surfaces are bombarded with ion beams, atoms and molecules are ejected from
the surface in various charge states. In the case of a clean metal surface the fraction of
particles escaping as singly charged positive ions is very small, commonly ranging from
10−5 to 10−3. The formation and escape of secondary ions is probably the least understood
aspect of the sputtering process. Measurements of the dependence of secondary-ion intensity
on emission kinetic energy have indicated that the ionization probability (R+) approximately
follows an exponential dependence on the escape velocity [1–4], of the form
ꢀ
ꢁ
A
R+ ∝ exp −
(1)
v
⊥
where A is a constant that is dependent on the electronic environment of the ion and substrate
and v is the normal component of the ion emission velocity. The value of A is typically
⊥
in the range 1 × 103–1 × 105 m s−1 [1–4].
On the basis of observations on the emission energy dependence, various models
have been proposed to describe the ionization process and hence to provide quantitative
expressions for the ionization probability. The exponential dependence of R+ is most
consistent with the electron tunnelling model. This model describes ionization, on an atomic
level, as resulting from resonance-like transitions of electrons between atomic electronic
levels of the escaping sputtered atom/ion and substrate continuum states [5–8]. All electronic
excitations generated by the ion bombardment are assumed to dissipate rapidly so that the
substrate electron temperature (Te) is equal to zero. The theoretical treatment in this model
assumes that the sputtered particle leaves the surface as an ion, and calculates the probability
of neutralization by electrons from the substrate. Hence, the first ionization potential (Ip)
plays a major role in positive ion emission. Owing to the screening by electrons in the
† Fax: 65 777 6126.
c
0953-8984/97/439427+07$19.50 ꢀ 1997 IOP Publishing Ltd
9427

9428
M H S Low et al
metal conduction band, the positive ion leaving the sample surface has its atomic level
(ε(z)) shifted by an image potential, that is inversely proportional to the ion–image distance
(z), with respect to its value in free space (the maximum shift taking place at small distances,
while for very large distances ε(∞) = Ip). As the sputtered ion leaves the surface there
exists the possibility that ε(z) coincides with any of the occupied electronic energy levels
(below the Fermi energy). This allows resonant electron tunnelling between the outgoing
ion and the target surface to occur, which leads to neutralization of the outgoing ion. The
ionization probability based on this mechanism can be calculated from first principles for
certain ε(z) dependences. [5] and [6] have obtained R+ in the form
ꢀ
ꢁ
C(Ip − φ)
R+ ∝ exp −π
(2)
h¯γ ν
⊥
which is consistent with the experimental result in (1). The constant C accounts for the
variation of the respective atom/ion and substrate electronic levels as the atom/ion moves
away from the surface, φ is the work function, γ is the decay length for the half width of
the atomic level, typically of the order of 2 A−1, and ν is the normal component of the
˚
⊥
ion emission velocity.
In this study R+ has been determined for Si atoms sputtered from Si(100) via
measurements of the energy distributions of Si+ ions. The results indicate a strong
dependence of the ionization probability on emission velocity that is in agreement with
(2), particularly over the higher-emission-energy range. Deviation from this dependence is
observed at lower emission energy and a possible reason for this is discussed.
2. Experimental details
A schematic view of the set-up is presented in figure 1. The UHV chamber is pumped by
a 240 l s−1 turbomolecular pump, giving a base pressure of 10−9 mbar with the help of a
titanium sublimation pump and baking. Primary Ar+ ions are produced from a VG EX05
ion source with raster scanning of the beam. During operation of the ion gun, the analysis
chamber is maintained at 1 × 10−8 mbar pressure. The angle of incidence of the primary
beam used in the experiment is 45◦ with respect to the sample surface normal. The primary
ion energy and current density are fixed at 4 keV and 0.33 µA mm−2 respectively. A
mirror-polished B-doped Si(100) wafer is used as the sample.
Secondary ions are extracted perpendicularly to the sample surface and mass analysed by
the Hiden Analytical EQS300 mass spectrometer which includes a 45◦ electrostatic energy
analyser (ESA) for ion energy analysis. The resolution of the ESA is ±0.8 eV. The target
is kept at earth potential and the energy scanning is performed at constant pass energy in
the ESA, so that all ions enter the mass analyser at the same energy.
The measured secondary-ion energy distributions, Nm+(E), are divided by the instrument
transmission function, T (E), to correct for the increasing degree of discrimination that
the instrument imposes on secondary ions of greater emission energies. Details of the
secondary-ion energy calibration are described elsewhere [9] and the transmission function
for our instrument has been found to take the form
T (E) ∝ E−β
(3)
for ion energies E above 6 eV with β = 1.50 ± 0.01. This has been determined
experimentally by using the method proposed by Garrett et al [2], which involves measuring
the K+ secondary-ion energy distribution of a potassium adsorbate sputtered off a Cu target
surface, and also independently confirmed by simulating the trajectories of secondary ions
emitted from the target surface to the analyser with the help of the SIMION [10] software.

Secondary-ion intensity of sputtered Si
9429
Figure 1. Schematic diagram of UHV–SIMS system.
3. Results
We have investigated the energy distribution of Si+ from Si(100) under 4 keV Ar+
bombardment at 45◦ incidence. The sample surface is first cleaned by prolonged Ar+
bombardment before obtaining the energy spectrum, so as to remove adsorbed gases and
other contaminants that might affect the secondary-ion yield. The uncorrected energy
distribution of Si+ ions is shown in figure 2 up to 25 eV. Above that, the spectrum contains
too much noise to be useful. The most probable energy, Em, occurs at about 4.5 eV, while
the results of Wittmaack [11] show that Em ≈ 5 eV for Si bombarded with 4 keV Ar+ at
normal incidence.
The energy dependence of the ionization probability R+ is simply determined by
dividing the corrected ion energy distribution of Si+, Nc+(E), by that of neutral Si, N0(E),
i.e.
Nc+(E)
N0(E)
Nm+(E)
N0(E)T (E)
R+(E) =
=
.
(4)
N0(E) is assumed to follow the well established Sigmund–Thompson relationship [12, 13]
E
N0(E) ∝ cos θ
(5)
(E + U)3
where θ is the angle of ejection with respect to the surface normal and U is the surface
binding energy of the Si atom. This empirically derived relation has been shown to be
capable of accurately predicting the secondary-neutral energy distributions for a number of
elemental matrices such as Cu, Ag and Zr [14–16]. U is approximated in this study by the
sublimation energy of silicon (4.67 eV).
Figure 3 also shows the behaviour of the experimentally derived R+ as a function of
1/ν . The validity of the R+ curves at low energies is limited because the transmission
⊥

9430
M H S Low et al
Figure 2. Uncorrected energy spectra of Si+.
function of our analyser has been determined only for E > 6 eV [10]. In the region around
9 eV, a local minimum is observed. Similar results have been reported by Wucher and
Oechsner [17] and were ascribed to the effect of the image charge potential energy which
the sputtered ions must overcome before they finally reach the detector. The image force
is a consequence of the attraction between the leaving ion and an equal induced charge of
opposite sign in the metal, and acts to reduce the velocity of the leaving ion. Hence, there is
a principal difference between the actual energy of the sputtered particle during ionization,
i.e. close to the surface, and the experimentally obtained ion energy at a large distance
from the surface. The effect of the correction leads to a shift in the observed secondary-ion
energy spectrum relative to the neutral spectrum and is expected to be most prominent for
the low-energy ions, but negligible for E > 12 eV [1].
4. Discussion
Fitting the data for R+ to the electron tunnelling relations in (1) and (2), we obtain the
full line in figure 3. R+ is then seen to exhibit exponential behaviour for large velocities
(v > 1.1 × 104 m s−1 ≡ 19 eV) with A = 2.1 × 104 m s−1. The electron tunnelling process
requires the Si(Ip) level to lie in the energy region of the Si valence band where the density
of electronic states is non-zero, to allow for electrons tunnelling from the target surface
to the outgoing ions. Recent characterizations of the valence band structure of the clean
Si(100) surface using XPS [18] have shown three peaks in the energy region of the Si(Ip)
level, corresponding to the L3(I), X4(I) and W2 + 61min bands, which allows the possibility
of electron tunnelling. A number of experimental results have shown that R+ obeys the
exp(−A/v) dependence in metals. Vasile [1] has found values of A ranging from 3 to
6 × 104 m s−1 for ions sputtered from Cr, Ag, Cu and Zr, while MacDonald and Garrett
[19] report values in the range (2.5–4) × 104 m s−1 for Fe+, Ni+ and Cr+ from stainless
steels.

Secondary-ion intensity of sputtered Si
9431
Figure 3. Ionization probability R+ of Si atoms fitted according to (1).
Figure 3 shows a deviation of R+ from the exponential dependence at lower velocities
(v < 1.1 × 104 m s−1 ≡ 19 eV). The smaller velocity dependence observed is difficult to
reconcile with (1) and (2) and cannot be fully explained by the image force correction to
the measured energies, since the application of this correction on experimental results is
only important for the low-energy particles (<8 eV) [1].
A possible explanation for this discrepancy could be that the electronic excitations
induced in the semiconductor by bombarding particles may significantly influence the charge
state of sputtered particles. Hence, the assumption Te = 0 leading to (2) breaks down,
making the model not applicable for lower emission energy. According to Sroubek [20],
electronic excitations in real systems would only influence the charge state of sputtered
atoms under conditions of high electronic temperature, i.e. Te ꢁ h¯ γ ν/k. By estimating
the electronic energy density dissipated by the primary ions in the collision cascade and
equating to the energy density of the excitations, he is able to obtain values of Te. Such
numerical results obviously depend on the choice of the thermal diffusion coefficient D.
When D is taken to equal 1 cm2 s−1, the corresponding temperatures of Te are around
1000 K for Cu, 2600 K for Si and 4400 K for GaAs. The key question is whether such
high electronic temperatures can exist in the bombardment region. If so, the condition of
Te ꢁ h¯ γ ν/k in Si would be fulfilled for emission energies E well below 40 eV if we
−1
˚
assume γ = 2 A
.
By assuming that the electrons in the sputtering site are excited to a high electron
temperature, Sroubek also formulated the semiphenomenological electronic excitation model
of secondary-ion production [20–23]. He showed that the ionization probability can be
approximately given by
ꢀ
ꢁ
ꢀ
ꢁ
210
ε(z∗) − φ
R+ ∝ exp −
+ exp −
(6)
h¯ γ ν
kTe
⊥
where 10 is the original width of ε(z) and z∗ is the distance from the surface where the
positive ion is formed. As expected, the expression in (6) reduces to the functional form
of (2) when Te = 0. The first term decreases rapidly with decreasing ν and thus the
⊥

9432
M H S Low et al
second term dominates at low ν when Te = 0. By further assuming that ε(z) has a linear
⊥
dependence on z, the second term in (6) translates into a simple power law which has a
weaker energy dependence. Rewriting (6) then gives
ꢀ
ꢁ
ꢀ
ꢁ
ꢀ
ꢁ
ꢀ
ꢁ
n
n
210
h¯ γ ν
Z+
Z0
h¯ γ ν
A
ν
⊥
⊥
R+ ∝ exp
−
+
−
∝ exp
−
+ C
(7)
(8)
210
ν
⊥
A
⊥
where
4πε0(I − φ)2
n =
kTee2γ
and Z+, Z0 are the partition functions of the ion and of the atom respectively.
We have attempted to fit R+ over the range of 12–25 eV according to (7) using C and n
as fitting parameters. The value of A is retained as 2.1×104 m s−1 since at large velocities
expression (7) approaches an exponential dependence. The best fit to the experimental data
(see figure 4) is obtained for C = 6.3 and n = 1.47. Thus by including electronic excitation
effects, the fit to R+ is improved from 19 eV down to 12 eV. Further deviation of R+ from
(7) below 12 eV can then be attributed to the image charge effect as explained above.
Figure 4. Ionization probability R+ of Si atoms fitted according to (7).
Quite apart from improving the fit, the additional term due to electronic excitations also
yields the electronic temperature Te through the power factor n in expression (8). Using
values for the ionization energy Ip(Si) = 8.15 eV, the work function φ(Si) = 4.91 eV
−1
˚
and γ = 2 A [5], we obtain Te = 2900 K. This value of Te is in good agreement
with Sroubek’s theoretical estimate which effectively means that the electronic excitation
mechanism will have some influence at velocities much less than 2 × 104 m s−1 ≡ 50 eV,
as seen from the condition Te ꢁ h¯ γ ν/k. This also agrees with the inclusion of electronic
excitations to the fit for ion emission energies less than 19 eV.
It must be mentioned that the analysis of R+(E) is heavily dependent on the neutrals
distribution N0(E) in expression (5) being correct. Although no direct measurement for
Si has ever been made, early work by Zalm [24] on the sputtering yield under noble gas

Secondary-ion intensity of sputtered Si
9433
ion bombardment seem to indicate that the sputtering process in Si conforms to the linear
cascade theory. More recent angle resolved Si+ emission by Pellet et al [25] also confirms
the linear cascade behaviour to some degree. The linear cascade theory has been applied to
several metals by Vasile [1] with a wide range of surface binding energies.
For the present set of data, the effect of the linear cascade expression on the ionization
probability has been examined. Two other values for the power factor of the denominator in
expression (5) have been used, namely 2.75 and 2.5. The procedure for fitting the spectrum is
the same as before, i.e. by first fitting the high-energy part of the spectrum to expression (1)
and obtaining the value of A in the exponential, and then fitting with expression (7) to
obtain n. In both cases, the value of A obtained is 2.0 × 104 m s−1, close to that obtained
above. The lack of sensitivity in A to the neutral distribution has also been noted by Vasile
[1]. However, the values of n obtained show quite a large variation. For the power factor
of 2.75 the value of n is 1.16, giving Te = 3700 K, while for the power factor of 2.5 the
value of n is 0.73, giving Te = 5800 K. Thus it appears that high temperatures persist in
the electronic excitations and that Sroubek’s estimate of 2600 K may be somewhat low.
5. Conclusion
In conclusion, the charge exchange process in Si+ secondary-ion emission from Si(100)
was found to exhibit a strong dependence on escape velocity, particularly over the high-
emission-energy portion (>19 eV). Such a trend is consistent with the electron tunnelling
model which is based on the electronic interaction of the sputtered ion with an undisturbed
metal band structure (Te = 0 K). At lower emission energies (<19 eV), the ionization
probability for Si+ exhibits a reduced velocity dependence. Agreement between experiment
and theory can be improved if electronic excitations in the collision cascades are considered.
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