8 Laser post-ionisation— fundamentals

1

J.C. Vickerman and D. Briggs, ToF-SIMS: Surface Analysis by Mass Spectrometry, 2nd Edition© 2012 IM Publications LLP and SurfaceSpectra Limited, doi: 10.1255/tofch8

8 Laser post-ionisation—fundamentals

Andreas WucherFaculty of Physics, University of Duisburg-Essen, Germany

8.1 IntroductionOne of the major disadvantages of the SIMS technique is the fact that the secondary ion formation probability — i.e. the probability that a sputtered particle is emitted in a positive or negative charge state — extremely sensitively depends on the chemical environment at the investigated surface. Moreover, in many cases of practical analytical interest, this probability is very small and, therefore, the majority of sputtered particles are emitted as neutrals. In the context of quantitative surface anal-ysis, it is therefore very desirable to detect the sputtered neutral particles as well, thereby increasing both the sensitivity of the ToF-SIMS method and the ability to quantify the measured data. For this purpose, the sputtered neutral particles (atoms or molecules) must be post-ionised (i.e. ionised well after leaving the surface) in order to render them accessible to mass analysis and detection. The fundamental difference to secondary ion formation is that the post-ionisation process occurs far away from the sample and, hence, the post-ionisation probability can be considered to be practically inde-pendent of the chemical state of the surface, thus eliminating the matrix effect inherent in the SIMS technique. Secondary neutral mass spectrometry (SNMS) is therefore expected (and has in many cases been demonstrated1) to allow a much easier quantitation of measured data and has consequently been developed as an invaluable add-on to ToF-SIMS instruments. Due to the inherently pulsed nature of the ToF spectrometer, it is advisable to employ a pulsed post-ionisation method, which can be implemented in the most efficient way by photoionisation using an intense pulsed laser beam.a The resulting technique has been frequently termed laser (post-ionisation) SNMS, and this generic term will therefore be used throughout the remainder of this chapter. In the following, we will briefly outline the experimental setup of a laser SNMS apparatus and point out a few sensitive points that are different with respect to ToF-SIMS. The subsequent discussion will then touch on a fundamental description of the signal measured with this technique as well as its dependence on various experi-mental parameters.

a It should be noted that the acronym SNMS was originally introduced by Oechsner et al. to describe a method using electron gas post-ionisation.2 In the context of ToF spectrometry, post-ionisation by electron impact using a pulsed electron beam has also been realised3 but is far less efficient due to the low (space charge limited) achievable electron density in the beam.

2 Chapter 8 Laser post-ionisation—fundamentals

8.2 Experimental considerationsThe basic setup used in a laser SNMS ToF experiment is sketched in Figure 1. A reflectron type spectrometer is shown, since it is the simplest ToF device and therefore used in many commercially available ToF-SIMS instruments. However, the discussion is equivalent if other ToF spectrometer types are employed. The plume of neutral particles sputtered from the sample surface is intersected by a laser beam which is directed parallel to the surface and positioned at distances of, typically, 1 mm or less above the surface. Positively charged photoions created in the interaction region are accelerated into the mass spectrometer by an elec-tric field which is normally generated by putting the sample on a high positive potential. Alternatively, the sample can be kept at ground potential but, in this case, the extraction electrode as well as the whole field-free drift region of the mass spectrometer must be floated with respect to ground. In principle, it is possible to use a cw extraction field (as is frequently done in ToF-SIMS mode), thereby accepting the fact that the primary ion beam is deflected in this field. Alternatively, the sample can be kept at ground potential during the primary ion pulse and the extraction field is switched on with a controlled delay by means of a fast high voltage switch. This technique is often used in ToF-SIMS in order to improve the time refocusing proper-ties by “time lag focusing”. Moreover, it makes the SIMS spectra independent of the primary ion pulse width and can therefore act to enhance the measured signal. It is of particular importance in laser SNMS, since it allows the ionising laser to be fired before switching on the extraction field, thereby eliminating the flight time resolution limit imposed by the temporal duration of the laser pulse.

Detection of the post-ionised neutrals is accomplished by the same microchannel plate device as used in the ToF-SIMS mode. There is, however, a significant difference with respect to the signal acquisition technique which arises from a simple duty cycle argument: In a laser SNMS experi-ment, the pulse repetition rate (laser shots and sputtering/acquisition cycles) is generally limited by the specification of the ionising laser. To date, the fastest systems which are commercially available feature maximum repetition rates around 1 kHz, which is far below the typical value of about 10 kHz employed in a ToF-SIMS experiment. Therefore, in SNMS mode, the system is generally operated under conditions where many (up to several thousand) photoions of the same mass are generated in one single laser shot. It is evident that this signal cannot be recorded using single ion counting techniques in combination with time-to-digital converters as usually employed in ToF-SIMS mode. Instead, transient digitisers are generally used in order to record the time-of-flight spectrum of

Figure 1. Basic experimental setup for time-of-flight laser post-ionisation SNMS.

8.3 Photoionisation mechanisms 3

post-ionised sputtered neutrals. While this direct digitisation leads to an enormous amount of recorded data (every time bin takes a data byte, even if there is no detected ion in the respective flight time interval), it offers the great advantage that a complete mass spectrum can be taken in one single acquisition cycle. In particular, this opens the possibility of fast parallel imaging of many masses in order to perform high resolution three-dimensional microanalysis.

8.3 Photoionisation mechanismsIn laser SNMS, post-ionisation of sputtered neutrals is accomplished by absorption of one or more photons from an intense laser field. Figure 2 illustrates the different photoionisation schemes which can be employed. Conceptually, the most simple process is single photon ionisation (SPI), where the absorp-tion of one photon is sufficient to overcome the ionisation potential (IP) of the sputtered neutral species. Since typical IP values lie in the range between 5 eV and 15 eV, this requires UV or even VUV radiation in order to provide high enough photon energies. For species exhibiting ionisation potentials up to 8 eV, gas lasers such as excimer (hn ≤ 6.4 eV) or fluorine lasers (hn = 7.9 eV) represent promising systems that are capable of delivering UV/VUV radiation with enough intensity to drive the photoionisation process into saturation (cf. Section 8.4). The range above 8 eV, which is of particular interest for most organic molecules, can only be reached with exceedingly complex laser systems employing, for instance, non-linear optical processes in gases. If the photon energy is below the IP, absorption of more than one photon is needed for post-ionisation. This leads to multiphoton ionisation (MPI) schemes which may either employ resonant or non-resonant intermediate steps. Resonance enhanced multiphoton ionisa-tion (REMPI) utilises one or more resonant transitions to excite the sputtered neutral species into a high lying state, from which it is then ionised using either a non-resonant transition into the continuum or by another resonant transition into an auto-ionising state. The corresponding technique has been intro-duced as resonance ionisation (mass) spectrometry (RIS or RIMS).4 It is clear that REMPI schemes work (i) extremely efficiently due to the generally large cross sections of the resonant transitions involved and (ii) extremely selectively with regard to the detected species and its electronic state. They are, therefore, mainly used in cases where extreme detection sensitivity and/or species selectivity is desired (for instance

Figure 2. Multiphoton ionisation schemes employed in laser SNMS.


in ultra-trace analysis applications). Non-resonant multiphoton ionisation (NRMPI) schemes, on the other hand, utilise direct multiphoton transitions into the ionisation continuum without resonant intermediate steps. In connection with surface analysis, this technique has been introduced as surface analysis by laser ionisation (SALI).5 NRMPI processes are sometimes characterised to proceed via virtual intermediate states with extremely short lifetimes (cf. Section 8.4.2). In order to be efficient, these schemes therefore require relatively high photon flux densities which are only achievable with powerful laser systems. A promising strategy, in this respect, is the use of ultrashort laser pulses, which give access to peak power densities up to 1015 W cm–2 and above. At these laser intensities, the electric field imposed by the laser pulse becomes comparable to the Coulomb field experienced by the valence electrons in the atom or molecule and the photoionisation mechanism gradually changes from MPI to field ionisa-tion (FI). Moreover, short laser pulses with sub-picosecond duration may be particularly important to reduce photon induced fragmentation which may occur during MPI of sputtered molecules. The great advantage of non-resonant techniques such as SPI, NRMPI and FI is that the post-ionisation process is far less selective than with REMPI schemes and these methods, therefore, open the possibility to analyse samples of an a priori unknown composition.

8.4 Photoionisation probabilityDepending on the peak power density of the laser field, the photoionisation process can be classified into two asymptotic regimes. At low laser intensity, ionisation proceeds via the (sequential) absorption of photons, until the excitation energy exceeds the ionisation potential. In this regime, the process can be treated in terms of perturbation theory, leading to the well-known multiphoton absorption characteristics outlined below. In the limit of high laser intensity, on the other hand, the electric field imposed by the laser becomes comparable to intra-atomic fields and the photoionisation process must be viewed in terms of field ionisation phenomena.

8.4.1 Single photon ionisationThe quantitative description of the photoionisation probability depends on the photoionisation scheme employed. In SPI schemes, where only one photon is absorbed by the sputtered neutral particle, the resulting electronic transition can be described by a conventional photoabsorption cross section sa, which will, of course, depend on the ionised species as well as on the spectral characteristics (wavelength and spectral linewidth) of the ionising laser. In order to demonstrate the typical range of magnitudes, Figure 3 shows values of sa which have been measured for different sputtered neutral atoms under irradiation with a wavelength of l = 157 nm (hn = 7.9 eV). In the general case, the transition will be non-resonant and the resulting cross section falls in the range of 10–19–10–17 cm2. In favourable cases, the employed laser wave-length may incidentally match a resonant transition into an autoionising bound state above the ionisation threshold, and the resulting cross section may, therefore, be significantly enhanced (see, for instance, the value depicted for Mo in Figure 3). As a rule of thumb, such an enhancement is expected if the condition6

h IP En

ν ≅ +( ) −

* 11

2 (1)

is fulfilled [E *: excitation energy of an excited ionic state; n: (large) integer number]. For atoms, absorption of one photon will inevitably lead to ionisation and, hence, the ionisation cross section si is

8.4 Photoionisation probability 5

equivalent to sa. For sputtered molecules or clusters, sa is generally found to increase with increasing molecular size7 and may reach values around 10–16 cm2. In this case, dissociative ionisation may occur as soon as the photon energy exceeds the sum of ionisation potential and dissociation energy and, there-fore, the absorption cross section must, in this case, be multiplied with a branching ratio si / sa for direct ionisation. In this context, it is important to note that sputtered molecules may contain a relatively large amount of internal energy8 which lowers the effective dissociation threshold. The ionisation rate is then simply described by

Ri = IL · si, (2)

where IL denotes the photon flux density which is calculated from the laser power density PL (in W cm–2) by IL = PL / hn and hn denotes the photon energy. Due to the use of a pulsed laser, IL will, in general, be time dependent and, therefore, Equation (2) must be integrated over the temporal laser pulse profile F(t). For the sake of simplicity, we will in the following assume a rectangular pulse, where IL is taken to be constant throughout an effective interaction time ti determined by

t F t dti = ( )∫ (3)

Then, the total photoionisation probability is given by

p I tii

aa L i= − ⋅ ⋅ ( )σ

σσ1 exp (4)

Note that the first term on the right-hand side of Equation (4) is unity for sputtered atoms. In the limit of low IL, the exponential function can be expanded and pi is proportional to R i and, hence, proportional to IL. In the limit of high laser intensity, on the other hand, pi becomes independent of IL and approaches a constant value. Provided the achievable laser intensity is high enough, the photoionisation process can therefore be driven into saturation, a condition which is very desirable for quantitative analysis since it eliminates the influ-ence of different photoionisation cross sections on the detection sensitivity of different species.

The laser intensity dependence predicted by Equation (4) can easily be verified experimentally. As an example, Figure 4 shows the post-ionisation probability measured for atoms and clusters sputtered from

1 2 3 4 5 6 7 8 9 1010-19

10-18

10-17

10-16

10-15

T a

Ag

G e

157 nm Mo

NbNi

C r

F e

T i

Al

cros

s se

ctio

n (c

m2 )

Figure 3. Single-photon absorption cross section of different neutral atoms under irradiation with 157 nm radiation from an F2-laser.


clean metallic and semiconductor surfaces. The dotted lines represent least square fits of Equation (4) to the data using sa and the saturated signal as fitting parameters. It is seen that the theoretical dependence is nicely reproduced by the experimental data, a finding which is characteristic for SPI and very much in contrast to most published data on MPI processes. It is seen that the non-resonant SPI process saturates at laser peak power densities of the order of 106–108 W cm–2.

0 2 4 6 8 10 12 14 16

T i

Al

C r

sign

al (

a.u.

)

0 0.5 1.0

las er power dens ity (106 W cm-2)

Mo

0 5 10 15 20 25 30 35

G e2

G e

= 157 nm

Figure 4. Laser intensity dependence of photoion signal measured for neutral atoms and clusters sputtered from clean surfaces.


8.4.2 Multiphoton ionisationThe theoretical description of a resonance enhanced multiphoton ionisation process has been developed in detail elsewhere.9 Ignoring coherent effects,b simple rate equations, analogous to Equation (2), can be used to describe the efficiency of the different steps. For the simplest case of a two-step process involving one resonant transition, the total ionisation probability is given by6,10

pR R e e

iexc i

t ti i

=⋅−

⋅−−

−

⋅ ⋅

λ λ λ λ

λ λ

1 2 1 2

1 21 1 (5)

with

λ1 2 2

22

1 14

2, =

+ +⋅ − ± −

+ +( )

R R R R RR R R

i loss exc exc i

i loss exc

. (6)

Here, Rexc = sexc · IL1 and Ri = si · IL2 denote the rates of excitation into, and ionisation from, the interme-diate state, Rloss describes the loss rate generated by spontaneous emission from the excited state, and IL1 and IL2 denote the intensities of the excitation and ionisation laser, respectively. In many practical applica-tions, the excitation step will be tuned to a resonance and, therefore, be saturated [IL1 >> 1 / (sexc·ti)]. Under these conditions, Equation (5) reduces to a dependence on IL2 which is similar to that of an SPI process [Equation(4)] with typical ionisation cross sections si of the same order as those depicted in Figure 3.

The description of non-resonant MPI processes depends on the laser intensity employed. In the regime of low laser intensity, a quantum mechanical treatment based on lowest order perturbation theory leads to an ionisation rate of the form11

Ri = si(n)·(IL)

n, (7)

where n denotes the minimum number of photons required to overcome the ionisation potential. The proportionality constant si

(n) can be regarded as a generalised cross section that depends on the ionised species and the spectral characteristics of the ionising radiation. It should be noted that the dimension of s i

(n) depends on the photon number n. The value of such generalised cross sections depends critically on the presence or absence of nearby resonances and may, therefore, vary over many orders of magnitude between different species and laser wavelengths. For a truly non-resonant process, a rough estimate can be given by regarding the non-resonant multiphoton transition as a sequence of one photon transitions proceeding through “virtual” intermediate states, the lifetime ti of which can be estimated from a typical electron orbit frequency (~ 1015 Hz). The generalised cross section can then be written in the form11

s i(n) @ s1t1 · s2t2 · ··· · sn – 1tn – 1 · sn, (8)

where sk denotes the cross section of the k-th transition. Taking average values tk ~ 10–15 s and sk ~ 10–17 cm2 (cf. Figure 3), we arrive at

s i(n) ~ 10–(32n – 15)cm2nsn – 1. (9)

b This is generally justified since the coherence times of multimode lasers typically employed in Laser SNMS are smaller than the pulse duration.


In order to be efficient, the ionisation rate [Equation (7)] must become comparable to the inverse laser pulse duration (Dt)–1. Inserting Dt of the order of 10 ns, this requires peak laser power densities in excess of about 1010 W cm–2 (for a two-step process) to approximately 1013 W cm–2 (for large values of n). Note that these values become significantly larger if shorter laser pulses are employed, leading to 1015–1018 W cm–2 at Dt ~ 100 fs.

In analogy to Equation (4), the saturation behaviour of a non-resonant MPI process can be formally described by

pi = 1 – exp si(n) · (IL)

n · ti, (10)

where the effective interaction time ti is now determined by

ti = òF(t)ndt. (11)

The laser intensity dependence predicted by Equation (10), however, is quantitatively observed only in very few cases. There are several reasons causing the frequently found deviations. First, the ionisa-tion process is, in many cases, enhanced by nearby resonances, which makes the description according to Equation (5) more appropriate.6 Second, for the specific case of sputtered atoms, even the predicted proportionality to (IL )

n in the regime of very low laser intensity is often not observed. This effect, which is not so prominent for thermal gas-phase atoms, has been shown to be due to dissociative ionisation of sputtered clusters, which is often resonance enhanced and may significantly contribute to the measured atom signal.12 Moreover, deviations are expected to occur for very high intensities where the electric field induced by the laser becomes comparable to the interatomic fields. As illustrated in Figure 5, this leads to a principal transition from multiphoton absorption to a field ionisation process, where the electron is released simply by the action of the laser-induced field. The intensity at which this ionisation mechanism becomes important can be estimated from the Keldysh parameter13

γ =IPU p2

(12)

with

Figure 5. Photoionisation at very high photon flux density.


Ue Em

Ppe

L= = ⋅ ⋅ ⋅−2

02

220 2

49 3 10

ωλ. eV (PL in W cm–2, l in nm)

being the ponderomotive potential of the electron in the laser field of amplitude E0 and angular frequency w. More specifically, the value of g, as defined by Equation (12), measures the ratio between the tunnelling

time (defined by the time an electron of average orbital velocity v ~ / eIP m needs to tunnel through a barrier of length l ~ IP / eE0) and the laser field period and, therefore, represents a measure of the adiaba-ticity of the field ionisation process. A value of g << 1 indicates that tunnel ionisation may occur with appreciable efficiency, whereas the MPI regime is characterised by g >> 1.

The field ionisation probability can be roughly described by Ammosov–Delone–Krainov14 (ADK) theory, which predicts the ionisation rate for a hydrogen-like state with binding energy Eb, effective quantum number n* = Z *(13.6 eV / Eb)

1/2 and angular momentum (l,m) as

R t C fi p n lmp

t

n

t

p

( )=

−

ωω

ωωπω*

*

2

2 1 14 2

2243

exp −

ω

ωp

t

(13)

where ω pbE

=

, ωte

eF t

m IP=

( )( )2 1 2/ , C n n nn

n*

* * * *2 2 12 1= +( ) ( )

−Γ Γ , f

l l m

m l mlm m=+( ) +( )( ) −( )

2 1

2

!

! !

and F(t) denotes the time dependent laser field. The parameter Z * describes the charge of the created ion. For single ionisation we have Z * = 1, Eb = IP, n* » 1 and l,m = 0 ® flm = 1. The ionisation probability is then calculated by integrating Equation (13) over time

p R t dti i= − − ( )

∫1 exp (14)

The resulting ionisation probability calculated for a particle with IP = 5 eV, 10 eV, 15 eV and 20 eV assuming a Gaussian-shaped laser pulse of 100 fs duration (FWHM) is shown in Figure 6. It is seen that

Figure 6. Photoionisation probability of atoms vs laser peak power density as calculated from ADK theory for three different values of the ionisation potential.


the field ionisation process exhibits a relatively sharp threshold at peak power densities of the order of 1012–1014 W cm–2 and saturates below 1015 W cm–2 for all cases of practical interest here. Defining the saturation intensity by means of 90% ionisation probability, one finds a relationship between Psat and IP as shown in Figure 7, which can, in principle, be used to determine an unknown IP value. However, care must be taken since Psat depends on the laser pulse shape, so the same laser must be used for comparison. As a general characteristic of ADK theory, the predicted ionisation efficiency does not depend on the laser wavelength, although the Keldysh parameter does. The theory appears to be fairly accurate for rare gas atoms,15 which are, therefore, frequently used to calibrate the laser intensity axis. It fails to describe more complex phenomena such as multiple ionisation arising from non-sequential processes, where the liber-ated electron re-collides with the ion due to the oscillating laser field.16 Several extensions of the tunnel-ling theory have been published for molecules,17,18 where an additional complexity arises from their more complex electronic structure, geometrical configuration and orientation with respect to the laser field. Therefore, molecules often appear to be harder to ionise than atoms. It was found, however, that the larger geometric extension may lead to smaller Keldysh parameters and larger tunnelling rates.18 Particularly for organic molecules, it was found that longer wavelengths produce more efficient ionisation along with less fragmentation,19,20 indicating that short-pulse infrared irradiation may be a suitable choice for post-ionisation of such species.

If the field strength becomes large enough to completely suppress the tunnelling barrier, the ionisation probability should become unity regardless of the laser pulse duration. The laser intensity necessary to fulfil this condition critically depends on the shape of the potential. For a Coulomb potential with effective core charge Z *, barrier suppression ionisation (BSI)15 sets in at a field strength of 0.0174 IP 2 / Z * V Å–1, corresponding to a peak power density of 4.0 × 109 IP 4 W cm–2 for Z * = 1 (IP

Figure 7. Saturation intensity (i.e. laser peak power density where field ionisation yields 90% single ionisation probability) vs ionisation potential as predicted by ADK theory using a 100 fs Gaussian-shaped laser pulse.

8.5 Measured signal 11

in eV). As seen in Figure 7, this is almost exactly where ADK theory predicts the tunnel ionisation effi-ciency to saturate. It has been shown that the BSI threshold can be reduced if more realistic potentials reflecting the electronic structure of the neutral particle are invoked, a finding which is particularly important for molecules.18,19

An interesting approach21 to describe intense-field photoionisation in a unified picture is based on the idea that m photons of energy Eph arriving within a typical electronic response time Dtm = h / Em are effectively equivalent to a single photon of energy Em = mEph. The basic idea is then to treat multiphoton excitation in terms of known single photon absorption cross sections sm at the virtual photon energy Em , where each m above the minimum number (n) of photons required to surpass the ionisation poten-tial constitutes an alternative ionisation channel. Using Poisson statistics describing the probability for absorption of a certain number of photons, this yields an analytical expression for the photoionisation probability21

pm m P P

miL sat m

m

≈ −( )

( )

∏1Γ

Γ

, , , with PE eV

cmsat mm

m, .= ×

( )( )−

2 0 1010

132

16 2

Wcm2 σ

, (15)

which is shown to reproduce both MPI and field ionisation behaviour at low and high laser intensity, respectively. Using published data on sm, it was shown that this model is able to reproduce the suppressed ionisation of N2 and O2 with respect to Ar and Xe, respectively,c which is difficult to explain by tunneling models.23

8.5 Measured signalIn ToF-SIMS, the measured signal, i.e. the number of detected ions per data acquisition cycle, is deter-mined by the number of secondary ions sputtered during a primary ion pulse multiplied by the transmis-sion of the spectrometer. Compared to ToF-SIMS, a laser post-ionisation experiment suffers from the additional complexity that a pulsed post-ionisation medium (the laser beam) is employed that must inter-sect the flux of sputtered neutral particles at a given time and position in space. One major implication of this is the fact that, in laser SNMS, the primary ion beam must not necessarily be pulsed, since the time resolution needed for the ToF analysis is, in principle, provided by the pulsed nature of the post-ionisation process. As outlined in section 8.6.1, one will, in most cases, still work with a pulsed ion beam in order to optimise the useful yield, but the temporal width of the primary ion pulse will, in general, be very much different from those employed in ToF-SIMS mode. In order to optimise the analysis with respect to detec-tion sensitivity, useful yield etc., it is necessary to develop a theoretical understanding of the measured signal, i.e. the number of detected photoions of a certain sputtered neutral species per data acquisition cycle (primary ion pulse and laser shot), as a function of the various experimental parameters. Such a description can be roughly divided into three steps. First, we determine the number of sputtered neutral particles that is intersected by the laser beam and, hence, is in principle accessible to post-ionisation. Second, it is necessary to determine the effective post-ionisation probability of these particles. In a third step, the detection probability of created photoions needs to be characterised. In this context, we will dwell on the definition of an effective ionisation volume. Putting the three steps together, we will then develop

c N2 and O2 have IP values almost identical to those of Ar and Xe, but exhibit lower ionisation probabilities at the same laser intensity.22


a fundamental equation describing the signal measured in a laser post-ionisation SNMS experiment. Due to the complexity of Equations (13), (14) and (15), we will use the simplified MPI model [Equation (10)] as a reasonable means to at least qualitatively describe a non-resonant photoionisation process in the entire range of laser intensities.

8.5.1 Number of sputtered neutral particles accessible to post-ionisation

Consider the situation depicted in Figure 8. During the primary ion pulse of width tp, the sample is bombarded with a constant primary ion flux Ip. At a given time t ¢, a number of Ip · YX · dt ¢ particles of a species X are sputtered during the time interval dt ¢. The quantity YX denotes the partial sput-tering yield of X which is related to the presence of X at the surface and, hence, carries the desired analytical information.d In principle, only neutral particles which are located inside the ionisation

d We ignore for the moment the (usually small) fraction of secondary ions and treat all sputtered particles as neutrals.

Figure 8. Geometrical (a) and temporal (b) setup of ionisation laser.


volume DV with lateral cross section DA and extension Dr along the particles’ flight path [see Figure 8(a)] at some time during the laser pulse of width Dt can interact with the laser and are therefore eligible for post-ionisation. It is clear that this number must depend on the geometrical parameters as well as on the relative timing of both pulses which, in turn, may be characterised by the delay time t between primary ion and laser pulse [see Figure 8(b)]. More specifically, only parti-cles which are ejected into the solid angle interval DW = DA / r2 with velocities around v = r / (t – t ¢) fulfil this condition. Moreover, it is important to realise that sputtered particles are emitted from the surface with statistically distributed emission direction and velocity. In order to account for this, we define probability distributions f (q,j) and f (v) with respect to the polar and azimuthal emission angles q and j and the emission velocity v. The number of neutral particles accessible to post-ionisation can then be described as the sum of two contributions. First, we must count all particles which are inside DV at the time the laser pulse is fired. Provided DA and Dr are suffi-ciently small, this is given by

∆ ∆Ω ∆N I Y dt f f vvr

rdensp X

( ) ,= ′ ⋅ ( ) ⋅ ( )∂∂

θ φ , (16)

which is proportional to the number density of sputtered particles within the ionisation volume and will therefore be in the following termed density contribution. Second, we must count those particles which are located outside DV at the time the laser is fired, but enter the ionisation volume at some time during the finite width of the laser pulse. This is given by

∆ ∆Ω ∆N I Y dt f f vvt

tfluxp X

( ) ,= ′ ⋅ ( ) ⋅ ( )∂∂

θ φ , (17)

which is proportional to the flux of sputtered particles across DA and will therefore be termed flux contri-bution. Integrating over the primary ion pulse, we determine the total number of sputtered neutral particles which are accessible to post-ionisation as

∆ ∆Ω ∆ ∆N t I Y f f vvr

r v t dttotalp X

t p

( ) ,( )= ⋅ ( ) ⋅ ( ) +[ ] ′−∫θ φ0

. (18)

In order to judge the balance between the two contributions, we define a critical velocity by

vcritrt

=∆∆

(19)

It is seen that the density contribution dominates for emission velocities v << vcrit while for v >> vcrit the flux across the ionisation volume may become important (cf. Section 8.5.2).

8.5.2 Post-ionisation probabilityAs described in Section 8.4, the post-ionisation probability of a given particle is determined by the time ti during which it interacts with the laser via

ptti

i

sat

= − −

1 exp , (20)


where the definition of the generic parameter tsat depends on the nature of the photoionisation process [see Equations (4), (10), (14) and (15), respectively].e In order to proceed, it is therefore necessary to determine ti for the particles of each contribution separately.

Let us, for the moment, assume that v ≤ vcrit. As sketched in Figure 9, particles belonging to the density contribution, i.e. which are present within the ionisation volume at the time the laser pulse starts, can then be divided into two categories. First, all particles which are located farther away from the exit cross section than vDt (the maximum distance a particle can travel within the duration of the laser pulse) will experience an interaction time which is equivalent to the laser pulse duration. These particles, which constitute a total fraction 1 – v / vcrit of the density contribution, will therefore be post-ionised with probability

α0 1= − −

exp

∆ttsat

. (21)

Here, Dt denotes an effective pulse duration as calculated by Equations (3), (11) or (14), respectively. Particles located within vDt from the exit cross section, on the other hand, will leave the ionisation volume at some time during the laser pulse and, hence, experience shorter interaction times. For Dt << tsat, i.e. if the ionisation process is far from being saturated, it is obvious that this leads to an average ionisation prob-ability of these particles which is given by a0 / 2. The effective post-ionisation probability of particles from the density contribution is under these conditions given by

pv

vv

videns

crit crit

( ) = −

⋅ + ⋅1

20

0

αα

(22)

as long as v ≤ vcrit. If, on the other hand, v > vcrit, the maximum interaction time is determined by Dr / v and Equations (21) and (22) must be replaced by

α0 1= − −⋅

exp

∆rv tsat

(23)

and

pidens( ) =

α0

2. (24)

e Under barrier suppression conditions tsat should formally go to zero.

Figure 9. Schematic view of ionisation volume and particle fluxes.


At the same time, particles from the flux contribution enter the ionisation volume at different times during the laser pulse. It is easy to show that these particles are post-ionised with the same average prob-ability of

piflux( ) =

α0

2. (25)

Combining Equations (22) or (24) with (25), it is seen that at low laser intensity the number of (flux contribution) particles which enter DV during Dt and are ionised exactly balances that of (density contribution) particles which escape from the ionisation volume without being ionised. By explicit inte-gration of Equation (20), it can be shown that this also holds true for Dt ≈ tsat, i.e. if saturation ionisation is approached. This implies that for all experimental conditions where the photoionisation process is not driven far into saturation (which will be true for the vast majority of all laser SNMS experiments), the signal measured for a post-ionised species X can be described as

S I Y f f vvr

r dt TX p X

t

X

p

= ⋅ ( ) ⋅ ( ) ′ ⋅ ⋅∫θ φ α, ∆Ω ∆ 0 (26)

just the same as if the sputtered particles were not moving at all. The quantity T denotes the mass spectrometer transmission, i.e. the probability to actually detect a photoion which has been created by post-ionisation.

Under conditions far into saturation, on the other hand, which are characterised by Dt >> tsat, the effective ionisation probability of both density and flux contribution approaches unity. Therefore, under these conditions (and only then!), the flux contribution explicitly enters the measured signal, which is then described by

S I Y f f vvr

r v t dt TX p X

t

X

p

= ⋅ ( ) ⋅ ( ) +[ ] ′ ⋅ ⋅∫θ φ α, ∆Ω ∆ ∆ 0 . (27)

If, in addition, the flux contribution largely overweighs the density contribution (i.e. v >> vcrit), the character of the SNMS experiment changes from a particle density detector into a particle flux detector.

8.5.3 Ionisation volumeIn order to illustrate the dependence of the measured signal on the size of the ionisation volume DV, we insert DW = DA / r 2 into Equation (26) and obtain

S A r

V

I Yf

rf v

vr

dtX p X

t p

= ⋅ ⋅ ⋅( )

⋅ ( ) ′ ⋅∫∆ ∆

∆

θ φ

ρ

α,

2 XX T0 ⋅ . (28)

Since a0X and T are dimension-less quantities, it is apparent that the second term in Equation (28)

describes the number density r of sputtered particles at the point (r,q,j), which is taken to be constant across the entire ionisation volume. So far, we have regarded both the ionisation volume DV and the instrument transmission T as constants. In reality, however, both quantities critically depend on the


experimental conditions. Probably the most crucial parameter in this context is the spatial profile of the laser field which can be characterised by the spatially resolved intensity IL(r). In connection with Equation (10), this leads to a position dependent post-ionisation probability

α σX in

LnI t0 1r r( )= − − ( ) exp ( ) ∆ . (29)

Moreover, the ToF spectrometer will, in general, accept ions starting from different locations with different probability, thus leading to a position dependent transmission T(r). The actual signal is then formally described by three-dimensional integration

S T d rX X= ( )⋅ ( )⋅ ( )∫∫∫ ρ αr r r0 3 . (30)

In principle, the r-dependence of all three quantities in the integrand is important and it is therefore not possible to determine DV, a0

X and T independently from each other. Depending on the laser focusing conditions, however, some limiting cases may be discussed.

In the case of a tightly focused ionisation laser, the r-dependence of the integrand in Equation (30) will predominantly be determined by a0

X(r), and the product

∆V d rX X⋅ = ( )∫∫∫α α0 0 3r (31)

may therefore be separated from the instrument transmission T which, in this case, can be taken as constant across the relatively small ionisation volume. It is important to note that under these conditions, which are generally employed in NRMPI and intense-field applications, the size of the effective ionisation volume may strongly depend on the laser intensity. This is of particular importance at high intensities where saturation of the ionisation process is approached. In this case, the effective ionisation volume will expand with increasing laser intensity due to increasing signal contributions from the wings of the laser intensity profile and, hence, no saturation plateaus such as those visible in Figure 4 will be observed.24,25 Instead, in cases where DV is entirely determined by the laser focal properties (i.e. beam waist and Rayleigh range), the volume size effect leads to an apparent laser intensity dependence of the measured signal which varies proportional to IL

3/2 in the saturation regime.26 Often, however, the ion-optical acceptance of the spectrometer is restricted to a length significantly smaller than the Rayleigh range. Under these “parallel beam” conditions, the post-ionisation signal can be plotted in a lin–log fashion as shown in Figure 10. Using Equation (10) along with a Gaussian laser radial intensity profile of peak intensity I0 and intensity I0 / e at radius R, the integral in Equation (31) can be calculated analytically, yielding an asymptotic behav-iour according to27

∆ ∆V R ln

t IXn⋅ → ⋅ ( )+

+ ( )

( )α π σ0 20

10 577ln . ln (32)

in the limit of large laser intensity. For the specific example of Figure 10, n = 8 and s(n) = 10–99 W–n cm2n s–1 were chosen in connection with a 20-fs square temporal pulse and MPI ionisation rate, but it can be shown27 that other intense-field ionisation mechanisms predict a similar relationship as well. It is seen that the limiting slope of this plot yields the effective ionisation volume DV = pR 2l. Moreover, the post-ionisa-tion probability aX

0 can be determined at each laser intensity as the ratio between the slope at this point and the asymptotic slope. As a consequence, the saturation behaviour can be measured even though the ionisa-tion volume expands as a function of laser intensity. If the asymptotic linear behaviour is extra polated to


the laser intensity axis, one obtains a “saturation intensity” Isat which provides a very convenient parameter describing the ionisation efficiency.f

In the limit of a largely defocused laser, on the other hand, the laser intensity and, hence, the post-ionisation probability can be regarded as constant and the ionisation volume is defined by

∆V T d r⋅ = ( )⋅ ( )∫∫∫ρ ρ r r 3 . (33)

Conditions of this kind are often established during SPI or REMPI experiments. It should be empha-sised that only in this limit DV and aX

0 are rigorously decoupled from each other and, therefore, the laser intensity dependence of the measured post-ionisation signal directly reflects the saturation behaviour of the photoionisation probability.28 In cases where r(r) can be taken as constant, the effective ionisation volume may, under these conditions, be entirely determined by the sensitive volume accepted by the ion optics of the employed ToF spectrometer. In principle, it is possible to map out this volume by scanning a tightly focused and largely attenuatedg laser beam in directions parallel and perpendicular to the surface, thereby recording the SNMS signal as a function of the lateral beam position. Figure 11 shows the result of such a measurement which was performed on a typical reflectron ToF spectrometer. It is seen that the diameter of the sensitive volume accepted by this particular instrument has an extension of about 1 mm in both directions perpendicular to and along the ion optical axis. While the first result is easily understood as a simple ion optical effect, the latter finding seems to be surprising at first sight. A close inspection reveals that the apparent restriction of the sensitive volume along the ion extraction axis is caused by the time refocusing properties of the ToF spectrometer. In order to illustrate that, Figure 12 shows the flight

f Note that barrier suppression ionisation would directly predict the extrapolated straight line behaviourg Important to avoid saturation effects

50 100 2000

5

10

15

phot

oion

sig

nal (

arb.

uni

ts)

laser peak power density (TW/cm2)

Figure 10. Dependence of the post-ionisation signal under intense-field conditions on laser intensity under parallel beam irradiation conditions (data reproduced from Reference 27).


time of the photoions as a function of their starting coordinate along the extraction axis, as calculated for the instrument used to record the data presented in Figure 11.h It is seen that only those photoions which are generated within approximately 1 mm around the centre of the ionisation volume (shaded area) are detected in the sharp, refocused ToF peak of about 20 ns width, while ions produced outside this range become strongly dispersed in flight time and, therefore, only contribute to the (structure-less) background of the recorded ToF spectrum.

8.5.4 SNMS equationAs already mentioned in Section 8.5.2, the SNMS signal measured under practically all relevant experi-mental conditions can be expressed by Equation (26). Substituting the integral over t ¢ into an integral over the emission velocity, this yields

h For technical reasons the ToF spectrometer was operated under first order focusing conditions in this particular experiment.

-2 -1 0 1 20.0

0.2

0.4

0.6

0.8

1.0

1.2 mm

sign

al (

a.u.

)

x-pos ition (mm)0 1 2 3 4 5

1.0 mm

z-pos ition (mm)

Figure 11. SNMS signal of post-ionised sputtered neutral atoms vs lateral and vertical position of the tightly focused ionisation laser beam.


S I Y fV

rT

f vv

dvX p X X

v

v

X

= ⋅ ⋅ ⋅ ( )⋅ ⋅ ⋅( )

∫α θ φ

η

02

0

,min

max∆

(34)

with

vr

t t pmin = +

and vrtmax = .

Casting the last four terms into a geometry and transmission factor h 0X , Equation (34) is equivalent to the

well-known SNMS equation

S I YX p X X X= ⋅ ⋅ ⋅α η0 0 . (35)

There is, however, an important difference to other SNMS techniques which usually work with cw post-ionisation, where the measured signal represents a flux of post-ionised particles. Laser SNMS, on the other hand, employs a pulsed post-ionisation process, and SX in Equation (35) therefore denotes an absolute number of post-ionised particles per data acquisition cycle. In contrast to the formally similar electron impact SNMS equation published by Oechsner and coworkers many times1 (where h 0X denotes a dimension-less factor), the quantity h0 X in Equation (35) must therefore possess the dimension of a char-acteristic sampling time. In order to give a rough estimate of its value, it is necessary to introduce explicit functional forms of the probability distributions with respect to the emission angle and velocity of the sputtered neutral particles. For simplicity, we use a normalised cosine polar angle distribution29

f θ φπ

θ, cos( )= ⋅ ( )1 (36)

0 1 220.36

20.38

20.40

time

of fl

ight

(μs

)

s tart pos ition z (mm)

Figure 12. Flight time of extracted photoions across a typical reflectron ToF spectrometer vs starting position along the extraction axis.


and a normalised Thompson velocity distribution30

f v vv

v vb

b

( )=+( )

4 23

2 2 3 (37)

with a characteristic emission velocity

vUmb

X

X

=2

(38)

being determined by the surface binding energy UX of the sputtered species X with mass mX. It should be noted, at this point, that Equation (37) provides a reasonable description for sputtering in the “linear cascade“ regime (i.e. with atomic primary ions). It may not be suitable to describe sputtering under cluster ion bombardment, as is now frequently employed in ToF mass spectrometry since, under these conditions, sputtering occurs in the “spike regime”, where the emission energy distribution is dominated by a low-energy contribution peaking at energies of the order of 0.1 eV.31 For the present purpose, however, we still use Equation (37) even for these cases in connection with an accordingly low value of the effective surface binding energy UX.The maximum possible value of the velocity integral in Equation (34) is obtained by setting vmin = 0 and vmax = ¥. Using Equation (37), we then obtain

ηθπ

πX

b

TV

r v0

2 4max

cos= ⋅

( )⋅ ⋅∆

. (39)

Moreover, in order to sample as large a solid angle as possible, it is common practice to bring the laser beam as close to the surface as possible. This is generally done by approximately matching the laser focus diameter (and, hence, the width Dr of the ionisation volume) with the distance r thus giving DV µ r 2 · l. The extension of the ionisation volume along the direction of the laser beam, on the other hand, is either determined by the Rayleigh range of the laser focus or by the lateral extension of the sensitive volume (whichever is shorter). For a typical value, we insert l ~ 1 mm. With upper limits of cos(q) = 1 (normal emis-sion) and T = 0.1 in connection with a typical vb of the order of 105 cm s–1, this yields h0

X|max ~ 25 ns (atomic projectiles) or ~ 100 ns under cluster bombardment.

8.6 Experimental parametersThe goal of this section is to elucidate the role of different adjustable parameters with respect to the detec-tion sensitivity and useful yield of a laser post-ionisation experiment. Probably the most important issue in this context regards the timing of the different pulses and, therefore, a separate sub-section will be devoted to this subject. Besides that, the chapter will be organised according to the different components of the experimental setup.

8.6.1 Timing considerationsThe timing sequence of the different pulses involved in a laser post-ionisation experiment represents one of the fundamental problems of the technique. The crucial parameters are the primary ion pulse width tp and the relative delay t between the primary and the ionising laser pulse. It should be

8.6 Experimental parameters 21

emphasised again that the role of tp is very much different from that in ToF-SIMS, where this quantity primarily determines the flight time (and mass) resolution of the technique. In SNMS mode, tp has no influence on the mass resolution. Instead, the interplay of tp and t determines the character as well as the magnitude of the measured SNMS signal. In order to illustrate this, Figure 13 shows the SNMS signal as a function of the delay t for fixed values of tp and vice versa. The solid lines have been calcu-lated according to Equations (34), (36) and (37) using values of r = 1 mm and vb = 1.6 × 105 cm s–1. The dots, on the other hand, depict experimental data which have been measured for neutral silver atoms sputtered from a clean, poly crystalline silver surface by 5-keV Ar+ ions. Post-ionisation was performed by non-resonant two-photon ionisation using a focused laser beam (wavelength l = 364 nm) located at a distance of 1 mm above the surface. The data have been normalised to the signal detected under cw primary ion bombardment.

Figure 13. Dependence of laser SNMS signal on primary ion pulse width tp and delay time t between primary ion and ionising laser pulse. The data have been normalised to the signal measured under cw primary ion bombardment. Solid lines: calculated data; dots: experimental data.


Several important conclusions can be drawn from the data presented in Figure 13. In the limit of short primary pulses, the measured signal passes through a maximum with increasing delay time t. The reason is that under these conditions t (in connection with r) acts as a velocity filter for the detected sputtered neutral particles. By scanning t with a fixed value of r (and sufficiently small Dr), it is therefore possible to measure the emission velocity distribution of the sputtered neutral particles.32,33 Since this distribution generally varies between different sputtered particles (and may, moreover, depend on the composition of the investigated surface!), the optimum delay time will vary from species to species, a condition which is of course detrimental to quantitative surface analysis. Moreover, as seen in Figure 13(b), the signal increases with increasing tp irrespective of the delay t. In SNMS, one will therefore usually work with much longer primary ion pulses than used in SIMS. However, the figure also shows that the SNMS signal saturates at primary ion pulse lengths of typically a few microseconds. It is seen that the signal measured under these conditions decreases with increasing delay time. At zero delay, the same signal is detected as would be measured under cw ion bombardment (corresponding to infinitely long primary ion pulses). Variation of r and vb shows that the optimum primary pulse length at which the signal reaches about 90% of its satura-tion value scales as

trvb

90 2 3% .@ . (40)

Using much longer values of tp will therefore not increase the measured signal but only waste sputtered material, the reason being that neutral particles which are sputtered long before the laser pulse will already have passed and left the ionisation volume by the time the ionisation laser is fired. In order to optimise the detection sensitivity, it is therefore advisable to use primary ion pulses with a duration of several micro-seconds in connection with the shortest possible delay which can be experimentally realised.

As already mentioned, different sputtered species will, in general, exhibit different emission velocity distri-butions. Even under conditions where the post-ionisation process is saturated, this will lead to variations in the detection sensitivity for different species. In order to estimate the magnitude of this effect, we calculate the geometry factor h0

X entering Equation (35) as a function of the characteristic emission velocity vb. The same approximations as employed in the calculation of h0

X|max in Section 8.5.4 have been used in order to arrive at quantitative values. The results are displayed in Figure 14. In order to indicate the relevant range, the vb-values calculated from the sublimation energies of all elements (which are taken to be representative of the respec-tive surface binding energies) have been included at the bottom of the figure.i For long primary ion pulses in connection with short delay times, the displayed values correspond to h0

X|max which shows the expected inverse proportionality to vb (solid line in Figure 14). This behaviour naturally discriminates against fast particles possessing high average kinetic emission energy and/or small mass. It is seen that this effect is enhanced for longer delay times [Figure 14(a)]. Decreasing tp at zero delay, on the other hand, is shown to discriminate against slow particles [Figure 14(b)]. The smallest overall variation across the relevant range of vb and, hence, the least discrimination with respect to the emission velocity distribution of sputtered neutral particles, can be obtained with zero delay in connection with a primary pulse duration corresponding to

tr

p ≅ ⋅ −2 5 105 1. cm s (41)

(400 ns in the example of Figure 14).

i Note that data representative for cluster ion bombardment will be located at the left boundary of Figure 14.


An important aspect of any mass spectrometric surface analysis technique is related to the efficiency by which the sputtered material is used. This is particularly important in imaging applications where two- or three-dimensional microanalysis of the investigated surface is required. The quantity of interest in this context is the useful yield t, which is defined as that fraction of sputtered neutral particles which is actually detected as photoions. Following the concepts developed in Section 8.5, the number of neutral particles X sputtered during the primary ion pulse is given by IpYXtp, and the useful yield can therefore be written as

τα η

=⋅ ⋅

=⋅S

I Y t tX

p X p

X X

p

0 0

. (42)

Figure 14. Variation of the geometry and transmission factor h0X as a function of the characteristic emission

velocity vb for different values of the primary ion pulse width tp and the delay time t. The absolute values have been calculated from Equation (34) using DV / r 2 = 1 mm, cos(q) = 1 and T = 0.1.


In principle, two limiting cases can be identified. For very short values of tp, the velocity integral in h0

X can be replaced by the integrand, thus yielding h0X µ tp. As a consequence, the useful yield becomes

independent of tp in this limit. For large values of tp, on the other hand, h0X saturates and the useful yield

therefore falls inversely proportional to tp. In order to illustrate the behaviour for intermediate cases, Figure 15 shows data which have been calculated by means of Equation (42) using DV / r 2 = 1 mm, r = 1 mm, a0

X = 1, cos(q) = 1, T = 0.1 and vb = 1.6 × 105 cm s–1. As a rule of thumb, it is seen that, for a given delay t, the maximum useful yield is roughly achieved for a primary ion pulse length satisfying the condition

t trvp

b

+ ≈ . (43)

The optimum value of t is then obtained with delay times slightly below the maximum value for which Equation (43) can still be satisfied. From the data presented in Figure 13, it is obvious that these conditions do not yield maximum signal. Under circumstances where most efficient use of sputtered material is required, one will therefore have to sacrifice detection sensitivity by as much as a factor of five.

8.6.2 Primary ion sourceIn contrast to secondary ions, the sputter emission of secondary neutral particles is relatively inde-pendent of the chemical state of the investigated surface. In SNMS, it is therefore generally neither necessary nor desirable to use chemically reactive primary ions. The projectiles of choice would be either rare gas ions or, for the sake of lateral resolution in microanalysis applications, liquid metal

Figure 15. Variation of the useful yield t as a function of the primary ion pulse width tp for various values of the delay time t. The data have been calculated using DV = 1 mm3, r = 1 mm, a0

X = 1, cos(q) = 1, T = 0.1 and vb = 1.6 · 105 cm s–1.


ions. Recently, cluster ion sources have been introduced for routine ToF-SIMS analysis, in particular for molecular depth profiling applications. Due to the high sputter yields achievable with such projectiles, these beams can also be used in post-ionisation experiments with essentially the same advantages regarding detection sensitivity and ion-induced chemical damage reduction, provided the implications regarding the emission velocity distribution are kept in mind with respect to the timing scheme. As seen from Equation (35), the primary ion current should be as large as possible in order to achieve maximum detection sensitivity, unless static analysis conditions are required. In contrast to ToF-SIMS, the primary beam may be operated either in cw or in pulsed mode, the influence of the pulse length has been discussed in Section 8.6.1. Moreover, in SNMS, it is not advantageous to bunch the primary ion pulse.

A few words are in order regarding the focusing conditions of the primary beam. In analytical applica-tions where lateral resolution is not required, one may, in principle, use loosely focused or even defocused ion beams in order to ensure static conditions. If the dimension of the bombarded spot becomes compa-rable to the distance r between the surface and the ionisation volume, however, this will lead to a decrease of the measured signal. In order to illustrate this fact, Figure 16 shows the dependence of the geometry factor h0

X on the diameter of the ion bombarded spot on the investigated surface. The data have been calcu-lated from Equation (34) using DV / r 2 = 1 mm, cos(q) = 1, T = 0.1 in connection with different values of the primary ion pulse width tp and delay time t. Moreover, it has been assumed that the current density profile is rectangular and that the total ion current Ip remains constant, i.e. the x-axis values of Figure 16 corre-spond to different primary ion current densities. It is seen that the largest signal is always detected under tightly focused conditions where the ion bombarded spot can be regarded as a point source of sputtered neutral particles. Depending on the timing parameters, the signal loss upon defocusing to about 2 mm spot diameter may reach factors of two to five.

Figure 16. Variation of the geometry and transmission factor h0X as a function of the diameter of the ion

bombarded spot for different values of the primary ion pulse width tp and delay time t. The absolute values have been calculated from Equation (34) using DV / r 2 = 1 mm, cos(q) = 1 and T = 0.1.


8.6.3 Ionisation laserAs outlined in Section 8.4, the generalised photoionisation cross sections of different species may vary over many orders of magnitude. In principle, the ionisation laser should therefore be operated at the maximum achievable intensity in order to achieve, or at least approach, saturation ionisation. With a given laser pulse energy EL the laser intensity can be roughly approximated by

IE

h tLL≅⋅ν ∆

, (44)

where Dt denotes the effective laser pulse duration calculated by Equation (11). In principle, IL can therefore be enhanced by decreasing Dt. However, it should be kept in mind that—at least in the MPI regime—the important parameter which must be maximised in order to achieve the highest post-ionisation probability is EL

n / Dt(n – 1) [see Equations (10) and (21)]. In order to optimise, for instance, a non-resonant two-photon process, it may therefore be favourable to use an excimer laser delivering 100 mJ/pulse into a pulse width of 10 ns instead of using a (much more complicated) ultrashort pulse laser system of the same wavelength delivering 0.1 mJ into say 100 fs. In this context, it should be emphasised again that if a pulsed extraction field is employed and the laser is fired prior to switching this field on, the laser pulse duration has no influence on the achievable mass resolution. On the other hand, modern ultrashort pulse laser systems deliver pulse energies of up to 10 mJ and <100 fs duration at kHz repetition rates. With these systems, field ionisation can be exploited and saturation ionisation can be reached for many species. In particular, for molecules, it has been demonstrated that fragmentation appears to decrease both with increasing laser intensity and wavelength. For efficient post-ionisation of such species, it may therefore be favourable to use as high a peak power density in connection with as long a wavelength as possible. At the other extreme, single photon ionisation at moderate power density using tuneable VUV radiation may also be a suitable route for soft, efficient post-ionisation of sputtered molecular species.34,35

8.6.4 ToF spectrometerIn contrast to ToF-SIMS, the post-ionised neutral particles are not created at a constant electrostatic starting potential (the surface potential in ToF-SIMS). Instead, the starting coordinate along the extrac-tion axis exhibits a distribution, the width of which largely corresponds to that of the ionising laser beam. As a consequence, the time refocusing conditions of the ToF spectrometer must, in a laser SNMS experiment, be optimised with respect to both the starting position within the extraction field and to the initial kinetic energy of the sputtered neutral particles. Since, in principle, it is not possible to achieve flight time focusing with respect to both conditions simultaneously, a reasonable compromise must be found. In many cases, the first requirement is much more stringent than the latter one. In practice, the spectrometer will therefore be largely operated under either first or second order space focusing condi-tions (cf. Figure 12).

Due to the fact that ToF-SNMS spectra are generally recorded by direct digitisation of the detector output (cf. Section 8.2), care must be taken not to saturate the detector with high-intensity peaks which may contain many ions of the same mass. At peak output currents exceeding a few mA, it is therefore advisable to reduce the detector gain. For the analysis of small impurities, on the other hand, the detector must be operated under maximum gain and single ion counting registration techniques must be employed. It is important to realise that, in this case, the detector must be blanked during the flight time intervals corresponding to the high intensity matrix peaks.

8.7 Determination of secondary ion formation probabilities 27

8.7 Determination of secondary ion formation probabilities

An important application of post-ionisation with respect to ToF-SIMS is related to the determination of the secondary ion formation probability a±

X of a sputtered particle, i.e. the probability that the particle leaves the surface in a positively or negatively charged state. In this context, the laser post-ionisation tech-nique offers the unique possibility to determine the absolute value of a±

X without any prior knowledge of the photoionisation cross-section.36 In principle, this is achieved as follows.

The laser post-ionisation experiment is conducted with a timing sequence as described in Section 8.2, i.e. the ionising laser pulse is fired before the ion extraction field is switched on. In this case, the starting point of the flight time measurement is determined by the switching time of the extraction voltage and not by the laser firing time. At the same time, the ionisation laser is defocused so that the effective ionisation volume is entirely determined by the sensitive volume of the mass spectrometer (cf. Section 8.5.3). By using a single photon ionisation scheme and increasing the laser intensity to the saturation regime, it is in general possible to determine a saturated signal of post-ionised neutral particles X which is described by Equation (34) using a post-ionisation probability of a0

X = 1. Now the same experiment is repeated with the only difference being that the ionisation laser is not fired. In this case, the experiment will detect secondary ions that have been sputtered during the primary ion pulse (while the extraction field was switched off) and migrated into the ionisation volume. Since the extraction region above the surface is originally field free, these ions emerge from the surface in the same way as the sputtered neutral particles. Upon switching the extraction field on, those ions present in the ionisation volume are swept into the ToF spectrometer and detected in exactly the same way as the post-ionised neutrals. In order to illustrate this, Figure 17 shows a mass spectrum of neutral Ge atoms and Ge+ secondary ions sputtered from a clean single crystalline Ge(111) surface by 5 keV Ar+ ions. It is seen that the spectral characteristics, i.e. predominantly the peak shape and mass resolution, are virtually identical in both spectra, although the SIMS spectrum has been acquired under the same conditions as the SNMS spectrum, i.e. with a relatively long primary ion pulse of several microseconds width. It should be noted that this method of recording ToF-SIMS spectra is entirely different from the usual way in which such spectra are acquired (where extremely short primary ion pulses are used in order to ensure good flight time resolution). As can be shown from the measured laser intensity dependence, the SNMS spectrum displayed in the upper panel of Figure 17 has been obtained under satu-ration post-ionisation conditions. Since the ToF spectrometer cannot distinguish between secondary ions and photoions of the same species, which are present within the ionisation volume at the time the extrac-tion field is switched on, the secondary ion formation probability of sputtered Ge atoms can be determined by direct comparison of the two spectra displayed in Figure 17. In the same way, it is also possible to determine the secondary ion formation probability of sputtered molecules.37

8.8 ConclusionsThe major goal of this chapter is to provide the reader with a basic understanding of the physics behind laser post-ionisation ToF mass spectrometry. Due to limitations in available space, the description is natu-rally far from being exhaustive. In order to serve as a guide for the application of laser SNMS, particular emphasis has been put on the description of the detailed role of various experimentally selectable param-eters. In this context, the examples shown represent typical cases that have been selected to demonstrate the essential dependencies. No attempt has been made to provide examples of analytical applications that


demonstrate the capabilities or potentialities of the technique for the analysis of elemental and molecular surfaces, since these topics are treated elsewhere in this book. In view of the examples presented therein, it is obvious that the laser SNMS technique represents a very promising tool for quantitative surface analysis with many still unexplored potentialities. Probably the most important aspect in this context concerns the three-dimensional high resolution microanalysis of surfaces and thin films. If the spatial (i.e. lateral and depth) resolution is increased to the physical limits induced by the typical diameter of a collision cascade (~10 nm) and the typical depth of collision induced mixing (~1 nm), respectively, the number of particles available for mass spectrometric analysis contained in one voxel becomes exceedingly small (£103). Due to its high achievable useful yield, laser SNMS seems to be the only SNMS technique that is capable of providing useful mass spectrometric information on sputtered neutral particles under these conditions. In connection with the virtual absence of matrix effects which allows relatively straightforward quantitation, laser post-ionisation SNMS therefore may, especially in this context, prove to be very valuable complemen-tary tool to ToF-SIMS.

60 65 70 75 80 85 901

10

S IMS

mass (amu)

1

10

100

1000

= 157 nm

2 x 107 W/cm2

S NMS

sign

al (

a.u.

)

Figure 17. ToF mass spectrum of post-ionised neutral Ge atoms and secondary Ge+ ions sputtered from a single crystalline Ge(111) surface by 5 keV Ar+ ions.

8.9 References 29

8.9 References1. H. Oechsner, Int. J. Mass Spectrom. Ion Proc. 143, 271 (1995). doi: 10.1016/0168-1176(94)04122-N2. H. Oechsner and E. Stumpe, Appl. Phys. 14, 43 (1977). doi: 10.1007/BF008826323. F. Koetter and A. Benninghoven, in Secondary Ion Mass Spectrometry (SIMS X). John Wiley & Sons Ltd,

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8 Laser post-ionisation— fundamentals

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