Aspects of quantitative secondary ion mass spectrometry

NUCLEAR

INSTRUMENTS

AND M E T H O D S

168 (1980) 3 4 3 - 3 5 6 ;

(~) N O R T H - H O L L A N D

PUBLISHING

CO.

ASPECTS OF QUANTITATIVE SECONDARY ION MASS SPECTROMETRY KLAUS WITTMAACI~

Gesellschafi fiir Strahlen- und Umweltforschung mbH, Physikalisch-Technische Abteilung, D-8042 Neuherberg, Germany

The present state of quantitative secondary ion mass spectrometry (SIMS) is analysed critically. Because of the strong gain in sensitivity obtained by loading the instantaneous sample surface with either oxygen or cesium, chemically enhanced secondary ion emission is discussed almost exclusively. The implications brought about by a fixed experimental geometry and by the mass dependence of instrumental factors are discussed in some detail. Normal beam incidence is to be prefered because of the high steady state concentration of oxygen attainable. Positive secondary ion yields of elements emitted from a common matrix under conditions of complete saturation with oxygen are proportional to exp(-flEi), where E i is the respective ionization potential and/3 a parameter of unknown origin. Interpretation of/3 in terms of equilibrium thermodynamics (i.e. /3- I = kT) is shown to be unjustified and misleading. Enhanced positive ion emission in the presence of oxygen is likely to result from disintegration of metal oxygen complexes occurring at the final stage of sputter emission (bond breaking model). Similar processes may determine negative ion emission in the presence of cesium. However, a simple relation between negative ion yields and electron affinity does not seem to exist. Presently, the most accurate quantitative analyses are obtained by the use of experimentally determined relative sensitivity factors.

1. Introduction Due to its unparalleled sensitivity for many elements, there has been a steadily growing interest in secondary ion mass spectrometry (SIMS) as an analytical tool. SIMS has been applied successfully to a large variety of problems, ranging from ion microscopy ~'2) to surface analysis 3-5) and depth profiling6-9). In many cases the desired information could be derived without a calibration of the SIMS signals. The only assumption made was that the measured secondary ion intensity is proportional to the respective (impurity) concentration. Quantitative SIMS analyses have been hampered by the difficulty of relating secondary ion signals to elemental concentrations. Secondary ion yields have been found to vary by orders of magnitude throughout the periodic table of elementsS'~°-12). These yield variations are mainly due to differences in atomic properties such as the ionization potential or the electron affinity. In addition it has been realized that ion yields can vary by orders of magnitude, depending upon the environment of the respective element (matrix composition) and the sampling conditions13-17). Last but not least, instrumental factors have been shown to affect elemental sensitivities considerably 16,17). These facts illustrate the problems encountered in trying to arrive at a practical quantitation approach which, necessarily, must reduce variables to a minimum and be adaptable to any SIMS instrument. In this review we describe the physical phenom-

ena and chemical effects of importance in quantitative SIMS. The relevance of instrumental features and experimental parameters will be illustrated. The different models and procedures which have been proposed and used for the conversion of secondary ion intensities to elemental concentrations will be discussed with reference to the underlying assumptions.

2. Secondary ion production The basic features of SIMS are rather simple: The sample is bombarded by a probing beam of primary ions with energies ranging from several 100 eV to =20 keV. The primary ions cause sputter erosion of the sample. Thereby atoms as well as clusters are emitted from the upper atomic layers. Most of the sputtered species leave as neutral atoms or molecules, but a small fraction is ejected as positive or negative ions. These secondary ions are extracted into a mass spectrometer for mass-to-charge separation to provide an analysis of that part of the sample which is exposed to the primary ion beam. Due to the application of mass spectrometric techniques, isotopic analysis of all elements including hydrogen can be achieved. Secondary ion emission is a rather complex phenomenon. Fig. 1 schematically illustrates the relevant processes introduced by the impact of an energetic primary ion on a solid surface. In the energy regime of interest here, the primary ion energy is dissipated almost exclusively among sevV. S P U T T E R P R O F I L I N G AND SIMS

344

K. W I T T M A A C K Primary Spuftered neutrals and (secondary) ions

Adsorbed gas

.

,

Colhsion [

(

cascade..~f'~f '

\

~ ~

Implanted projectile

Sample

Fig. 1. Schematic illustration of SIMS-relevant effects introduced by impact of an energetic heavy ion on a solid.

eral generations of recoiling target atoms set in motion by a series of quasielastic collisions~S). This "collison cascade" (fig. 1) is mostly responsible for sputter erosion in SIMS analysis. [Other mechanisms become effective with very light projectiles such as H and Helg).] Near-surface atoms of the solid sample as well as adsorbed species are emitted into vacuum if recoiled atoms end up at the solid vacuum interface with an outward directed momentum and an energy large enough to overcome the surface potential barrier. Since the energy spectrum of recoil atoms peaks at low energies~8), sputtered particles originate mostly from the topmost layer at the surface 5'1s). It is of considerable importance to realize that the cascade structures produced by successive impact of primary ions exhibit pronounced fluctuations in space and time2°'21), which in turn result in correspondingly strong fluctuations of the sputtering yield2°'2~). The calculated standard deviation of the sputtering yield is quite large and may exceed the average sputtering yield2~). Accordingly the measured average sputtering yield (including all~emitted particles), provides only very limited insight in the details of the sputtering process. As to secondary ion emission, one would expect that fluctuations in cascade structure will be even more important than for the emission of neutrals. It is tempting, for example, to relate the projectileenergy dependence of secondary ion emission from clean metals 22'23) to the probability for the production of a heavily perturbed surface. Similarly, one might expect emission of homonuclear clusters to occur only if certain cascade structures are produced24). Secondary ion emission from clean samples, however, is of little interest in quantitative analyses, not only because the samples to be investigated

are usually not " c l e a n " but also because the degree of ionization, a~-+, of particles emitted from a clean surface is usually very 1OW4'16). In order to achieve the desired high sensitivity in SIMS analyses it is necessary to perform the measurements in a way that ~-+ becomes as large as possible. It has been known for some time that the presence of electronegative elements such as oxygen at the surface of the bombarded sample enhances the degree of ionization of positive secondary ions by up to three orders of magnitude, compared to emission from an oxygen-free sample under noble gas ion bombardment4's'13-17'2s-27). A comparable effect is observed in the negative secondary ion emission mode if the sample is (partly) covered with an electropositive element, e.g. cesium~l'~2'28). Details will be discussed in sect. 4. Here we consider one aspect of yield fluctuations which seems to have been overlooked in the past. Under conditions of saturation with oxygen, the (positive) secondary ion yield of many elements, in particular those with a low ionization potential, can be of the order of 1 4,16). In that case there is a certain probability for the emission of more than one secondary ion per cascade. Individual atoms and ions emitted from the same cascade will leave the sample within a time interval no longer than the cascade lifetime. The latter has been estimated to be ---2x10-~Ss2~). This is several orders of magnitude smaller than the pulse width observed at the exit of electron multipliers used for signal amplification in SIMS analysis. If standard pulse counting techniques are applied, arrival at the detector of more than one secondary ion from the same collision cascade will result in only one count. This discrimination effect has not been encountered with presently available SIMS instruments for reason of low spectrometer transmission. Future improvements in instrumentation, however, might lead to a situation where the above effect becomes important.

3. SIMS instrumentation and quantitation The essential features of a secondary ion mass spectrometer may be discussed with reference to fig. 2. The primary ion beam, delivered by an appropriate ion gun, hits the sample at an angle of incidence, O, with respect to the surface normal. In order to avoid implantation of source-borne impurities, the primary ion beam should be massanalysed. The secondary ions sputtered from the sample exhibit a characteristic angular and energy

345

SECONDARY ION MASS SPECTROMETRY

,A

Ii~=~YAci~ijzlgifzlEf o

Mass Pmmary ton b e a m

Mass analyser I, \ Jl

=

ff-(E)AE

E'E"

&l

"~'

,

Energy Fig. 2. Schematic presentation of a secondary ion mass spectrometer.

distribution n+-(~g,E, 0 .... ) which depends upon a variety of experimental parameters such as, for instance, the angle of beam incidence. Secondary ions emitted into the solid angle .Q pass through the entrance aperture of the mass spectrometer and are subject to energy analysis as well as mass (or momentum) analysis. Mass-energy analysed ions end up in a suitable detector followed by signal amplification and data processing. As illustrated in fig. 2, the solid angle ,(2 accepted by the spectrometer is rather small unless additional ion optical means is used to optimize secondary ion transport. The effective solid angle may be enlarged by acceleration of the secondary ions to energies typically of the order of 1 keV and by introducing electrostatic lenses. If quadrupole filters are used for mass analysis, a retarding lens has to be placed between energy analyser and mass filter because the transmission of quadrupoles peaks at low energies

(= 10 eV). The performance of a secondary ion mass spectrometer can be described by three characteristic quantities: mass resolution, energy resolution and transmission. These quantities are interdependent in the sense that transmission can be improved only at the expense of mass and energy resolution. In the present context it is of importance that mass analysis is usually performed at a fixed setting of the energy analyser. The signal height I~)~ recorded at a certain mass number reflects the respective secondary ion intensity emitted into the (effective) solid angle .Q and the energy interval E . . . E + z J E

(cf. fig. 2),

(1)

4,=

ana,yser

n-+(~E,3,...}

x ni(E,~k, 9 .... ) dEdI2, where

\,"l /~, S2 t-necgy Sample ~

cz/:I:(E' ~'°q . . . . ) ×

flux density of primary ions (ions/m 2 s), Y = (total) sputtering yield (atoms/ion), A = area viewed by the spectrometer, i.e. the effective field of view (m2), concentration of element i in the sample, Ci ~= abundance of the isotope j of element i, 2-i __~ transmission factor for element i, detector efficiency for element i, ~i- ----- positive or negative degree of ionization of element i, normalized energy and angular distribution H i of sputtered particles, where ~---

÷

f n,(E, tp .... )dEdf2 = 1. For the sake of simplicity we have assumed that mass interference does not occur. In order to reduce the complexity of eq. (1), the assumption has usually been made that z~, e~ and n~(E, ¢J) are the same for all elements in a given sample, so that eq. (1) becomes

Ii~ = ciT,j Y (~/~> G~b,

(la)

where G is an instrumental factor. As we will see below, the above assumption is not valid in general. Therefore, we rewrite eq. (la) by introducing an element specific "instrumental" parameter G , ,

I,~ = c,)'ij Y <~?> G? ¢,.

(lb)

The unknown concentration c~ may thus be determined by measuring/,if, G~ and 4, and by evaluating (~x#) either experimentally or theoretically.

4. Secondary ion yield enhancement It has already been pointed out in sect. 2 that in materials analysis by means of SIMS (or by any other technique) high sensitivity is a major demand. With a given instrument, sensitivity in SIMS analyses can be improved by orders of magnitude by intentionally introducing a high surface concentration of either electronegative elements (in the analysis of positive secondary ions) or electropositive elements (in the analysis of negative secondary ions). Yield enhancing species most frequently used in SIMS are oxygen and cesium, respectively. The V. SPUTTER P R O F I L I N G AND SIMS

346

K. W I T T M A A C K

methods used to enrich the sample surface in the respective element are illustrated in figs. 3-6. Fig. 3a shows the response of various secondary ions emitted from argon-bombarded 301 stainless steel to oxygen exposure at room temperature2S). The total bombardment fluence applied in recording the data depicted in fig. 4a was fairly low so that the effect of ion impact on the progress of oxygen adsorption may be neglected [low fluence or "static" SIMS4'5)]. Adsorption and incorporation of oxygen in metals is currently investigated by a large number of groups using SIMS. The state of the art of SIMS as a means of surface analysis has been reviewed very recently by the present authorS). Most of the previous work has been devoted to adsorption on pure metals. The alloy study of Schubert 25) shown in fig. 3a is one of the few exceptions. Prior to oxygen exposure the stainless steel sample was cleaned by heating to 1000°C. Both the metal ions, Fe + and Cr +, as well as the metal oxide ions, FeO ÷ and CrO ÷ , first increase rather rapidly with increasing 02 exposure, then pass through a maximum and apparently achieve a steady state at high exposure. The observation of a maximum in the exposure curves suggests that oxygen uptake into bulk of the sample has taken place. Since oxygen incorporation usually causes a significant reduction in the sputtering yield, Ym, of

partial

uq

~o 3

4:3

10 2

-~@// /

~

10 :. d J., I

I r ,Itlllt

I

I I

I 1v11111

I

I IIHII

1

,

,

I

I

Illllvq

I

r÷fFe/cr; 10

a

fb )

~ - - " )

r.,ooj 10

,,I ........ I ,/, ...... r ........ I ........ f 10 i 1 10 10 2 10 3 O x y g e n e x p o s u r e (L)

Fig. 3. (a) Intensity of various ions emitted from stainless steel 301 vs oxygen exposure25). Low fluence (" static") SIMS mode. (b) Intensity ratios determined from (a).

substrate atoms3°), the secondary ion yield Y+ --- ~+Ym will decrease even though the degree of ionization, 7+, remains high or may keep increasing. In the present context the most important result of fig. 3a is that, although oxygen exposure has the positive effect of enhancing the degree of ionization of both Fe and Cr, the intensity ration, l(Fe+)/ I(Cr+), varies almost as much as either signal. This is illustrated in fig. 3b. Clearly, any model proposed for quantitative SIMS analyses of samples containing oxygen must either include the (local) oxygen concentration as a free parameter or specify conditions under which the SIMS measurements should be performed (e.g. in the oxygen saturation regime). Also shown in fig. 3b are the metal oxide-tometal intensity ratios. M), for iron and chromium. These ratios vary comparatively little with increasing oxygen exposure, at least in the regime where the oxide ions were detectable. With an oxygen-free sample, should be zero before introducing oxygen. Therefore, one would expect to drop towards lower exposure in a manner indicated by the dashed (extrapolated) curves in fig. 3b. Analysis of published O2 adsorption studies has shown that is in fact sensitive to the oxygen coverage at the early stage of exposureS). Due to the low fluence applied in recording the data of fig. 3, sample erosion can be neglected. The information obtained stems from the depth of origin of sputtered species, i.e. mostly from the topmost surface layer. Surface analysis, however, constitutes only one aspect of sample characterization. Moreover, the application of low fluences restricts the analysis to an investigation of the major constituents or high yield species whereas trace elements will not appear with sufficient intensity. In order to improve trace sensitivity and to provide bulk or in-depth analysis, reasonably high primary beam currents as well as high (average) current densities are necessary. In that case surface oxides or layers of adsorbed oxygen are sputtered off rather rapidly and the original secondary ion yield enhancement disappears unless the lost oxygen is continuously replaced during sputter erosion of the sample. This can be achieved by simultaneous exposure of the sample to the primary (noble gas) ion beam and a suitably high flux density of oxygen gas. Fig. 4 illustrates the effect of oxygen on the

I(MO+)/I(M+)--r+(MO/

r+(MO/M)

r+(MO/M)

r+(MO/M)

S E C O N D A R Y I O N MASS S P E C T R O M E T R Y i

T

,r

I iillll

r

I

s, Go/

Ar'~

]

rr~llf

I

I

1 Iltltl

10a

2 •

z

,,

10

I I

~¢'# ff

o

r

i

-

"

8

8

I

/-

~ :o °

/

/

-:

7"--'! -

.'f-'c.r,' 'z~. . . . . . .

t ' 105 E

" ......

v

/<

= ,

10-7

,k,,,,,I

........

I

........

I

........

I

,

,

10-6 lo-S lO-Z 10-9 Oxygen parttol pressure {Po)

Fig. 4. Intensity of 28Si+ emitted from argon bombarded silicon versus oxygen partial pressure in the target chamber27). High fluence ("dynamic") SIMS mode. Parameters are the primary ion energy and the current density.

intensity of Si + emitted from a clean, argonbombarded silicon sample under so-called " d y namic" conditions27). The variation in oxygen partial pressure was achieved by bleeding oxygen undirectionally into the target chamber. As one might have expected the onset of noticeable yield enhancement as well as the pressure required for saturation of the Si ÷ intensity depend upon the primary ion current density. It should be pointed out that the secondary ion signal usually does not follow changes in oxygen pressure instantaneously. Instead the intensity passes through a transient regime, the new steady state being established only after exposure to a certain bombardment fluence16al). This indicates that saturation in yield enhancement requires oxygen incorporation into the sample (rather than mere adsorption)31). The depth sputtered while producing the respective bombardment-induced compositional changes can be estimated to be of the order of 1 nm or less16"31). The occurrence of transients is not specific to silicon but has been observed also with metals, e. g. monocrystalline nickel26). Note, however, that in order to identify a transient it is necessary to use low to moderate current densities because otherwise the transient time becomes shorter than the time required to attain a new steady state flux density of oxygen to the sample surface (after the respective change of the gas flow through the leak). The technique of enhancing secondary ion yields by operating at elevated oxygen partial pressure introduces several complications.

347

1) In cases where high primary ion current densities (>0.1 m A / c m 2) are used in order to achieve sufficiently high erosion rates, the oxygen pressure required for yield saturation may be in the upper 10 -2 Pa rangen). Under such conditions the mean free path for elastic collisions and/or charge transfer will be of the order of 10 cm, i. e. these processes are no longer negligible in the respective SIMS analysis. Moreover, the performance of electron multipliers, in particular channeltrons, degrades at elevated oxygen pressure (notably in the presence of an ion beam) and complete destruction of the device has been experienced. These problems may be circumvented to some extent by applying a directional flow of oxygen (oxygen " j e t " ) so that the increase in oxygen pressure in the remainder of the target chamber and the spectrometer is reduced considerably33-35): 2) Sputtering in the presence of an oxygen ambient results in a reduction in matrix erosion rate by up to a factor of five13'27'3°'36). This unwanted side effect can be understood qualitatively by realizing that, under conditions of continuous incorporation and reemission of oxygen, the metal component is eroded only according to its partial sputtering yield in the altered layer3°). 3) The ability to adsorb and incorporate oxygen differs from sample to sample. A comparison of Si and GaAs, e. g., shows that in the latter case the oxygen pressure required to observe an indication for a yield enhancement is about a factor of 200 larger than in the former case37). Therefore, oxygen exposure as a means of (positive) secondary ion yield enhancement is practical only with a limited number of matrices. In view of these complications bombardment with an oxygen beam may be considered an ultimate remedy to these problems of quantitative SIMS. In fact, it has been demonstrated frequently 15'|6'32'38) that oxygen implantation produces the desired effect of enhancing the positive secondary ion yield. [The enhancement of negative ion yields depends strongly upon the electron affinity of the respective elementS).] Fig. 5 shows the build-up of the Si + and O ÷ signals observed while bombarding a silicon sample with a mass-analysed beam of 8 keV 02-. The sample was chemically etched before being introduced into the target chamber so that the signals due to the thin "surface oxide" are quite small and disappear rapidly. With reference to analytical applications the most important result of fig. 5 is that a steady state V. S P U T T E R P R O F I L I N G AND SIMS

348

K. W l T T M A A C K I I

I

I

I

I

~

6

/60÷

(3 U

//

105

prO2 ) ~ IO-zPo

b -t'"

~ _ 0

2 02

t I I__ I 4 6 8 10 f l u e n ce (ld61ons/cm 2)

12

Fig. 5. Evolution of the O + and Si + signals during bombardment of an etched silicon sample with a focussed, raster scanned oxygen beam at normal incidence. Edge effects were avoided by electronic gating (K. Wittmaack, unpublished results).

secondary ion intensity is established only after exposure to a fluence of = 6 x 1 0 1 7 O b / c m 2. This causes sputter erosion of the sample to a depth of =10 nm. Accordingly, a subsurface layer of this thickness cannot be analysed quantitatively. The thickness can be reduced by lowering the ion energy38). In practical situations, however, the low energy limit is set by current density requirements. Now we turn to negative secondary ion yield enhancement. The effects are qualitatively the same as those discussed above except for the fact that oxygen is replaced by cesium. Fig. 6 shows the I

I

I

I

I

1

10 ~ i

~Mo-

~ 1o~

?_

£ 10 I0

_-/ 1

I

0

1

I

I

I

2 4 Cs d e p s i h o n hme

I

6

I

8

[min)

Fig. 6. Intensity of M o - sputtered from neon-bombarded molybdenum as a function of the duration of cesium deposition on to the sample surface28).

effect of cesium vapour deposition on the yield of Mo- emitted from neon bombarded molybdenum28). At low Cs coverage the M o - intensity increases exponentially with increasing coverage, then turns over to pass through a maximum and finally decreases. The drop in intensity most likely resembles the reduction in the sputtering rate of molybdenum which should become noticeable as soon as the coverage exceeds about half a monolayer. Similar to fig. 3, the data of fig. 6 were recorded by low fluence SIMS28). To preserve the enhanced degree of ionization under high fluence ("dynamic") conditions, continuous replacement of sputtered cesium is required. This is not as simple as in the case of oxygen. Although a successful attempt using continuous cesium vapour deposition has been reported39), this approach has not received further attention. Instead cesium bombardment is currently used in SIMS analysis to produce high negative secondary ion yields in particular of those elements which are characterized by a low degree of ionization in the positive spectrum ~1'12'4°). As far as analysis of the first 5-20 nm below the surface is concerned, build-up effects similar to those of fig. 5 must be taken into account also in using cesium primary ions. The problems involved have been discussed in some detail by Storms et a1.12). 5. Relative secondary ion yields of elements The first systematic measurement of secondary ion yields was performed by Beske 1°) who noticed a correlation between the positive ion yields of the elements and the respective ionization potentials. Beske's data relate to argon bombardment under ordinary vacuum conditions. Here we concentrate on secondary ion yields observed under oxygen and cesium bombardment, respectively. Relative yields recently reported by Storms et al. ~2) are compiled in figs. 7 and 8. The full circles to ion emission from the respective elements whereas the open circles reflect yields measured with suitable compounds. Where necessary, the yields have been corrected for isotopic abundance and sample composition. Figs. 7 and 8 reveal a very pronounced variation of the secondary ion yields with atomic number Z2. Neighbouring elements may exhibit ion yields that differ by orders of magnitude. Striking examples are B + and C ÷, N - and O - , A u - and Hg-. It should be noticed, however, that the data of figs. 7 and 8 do not reflect the degree of ionization directly. This is due to the fact that (1) the sputtering yields also

S E C O N D A R Y ION MASS S P E C T R O M E T R Y

"~ 1

0

t~ 10z

~

Positivesecondory ions • elements

II 10

7

~Au

~N 0

20

40 60 Atomic number

80

100

Fig. 7. Relative positive secondary ion yields of various elements from either elemental or compound targets under oxygen bombardmentS2). Stars mark "oxide elements" with r+(MO/ M)>0.3. The indicated intensities represent the sum I + (M)+ I + (MO).

exhibit a strong Z2 dependence ~8) and (2) the steady state surface concentration of oxygen and cesium, respectively, will vary from matrix to matrix. Whereas gold, e.g., hardly incorporates oxygen26'32), easy-to-oxidize elements such as silicon

,o7! i

i

p

i

T

r

1

I

to l S

, keV Cs+. ,--O°

/SI|

Negahvesecondary Ions of ~ • elements

/ T/

///

t

° c°mP° 'n 'SAu

I..11

O

~

v

foe

Te

0,_41

-~

3

E no t4n-I/

;-

,

20

II ,

/ l/ j

_,

~0 60 Atomic number

,

80

1

100

Fig, 8. Relative negative secondary ion yields of various elements from either elemental or compound targets under cesium bombardmentl2). Bracketed elements were barely detectable.

349

retain implanted oxygen to the extent that an oxide (SiO2) layer can be produced35). A very important finding in this context is that the degree of implantation-induced oxidation depends on the angle of incidence of the oxygen beam. Whereas normal impact of 15 keV 0 2 on silicon results in more than 95% SiO2 at the surface (as seen by Auger electron spectroscopy), the steady state SiO2 contents under 45 ° bombardment amounts to only = 10%35). In the latter case almost complete surface oxidation can be achieved by additionally bleeding in oxygen35). We have attributed the low SiO2 contents produced under O3 impact at 45 ° to enhanced preferential sputtering of oxygen35). In view of these complications, relative degrees of ionization of the elements relating to the same chemical yield enhancement can be obtained only if (1) the (sub)surface concentration of the yield enhancing species is very well controlled or (2) ions of different (trace)elements are emitted from the same homogeneously doped matrix. Metal alloys are not well suited for basic studies of this kind because spatial heterogeneity of elemental distributions is not unusual, e. g. in stee14t'42). Glasses 43) and semiconductors 9'44'45) are much preferable in this respect. A severe problem encountered in trying to evaluate relative degrees of ionization of the elements emitted from doped matrices is due to the fact that quite often the respective concentration is not known accurately enough. A reliable, although time consuming method has been used recently by Deline et a1.44'45). Standards have been produced by ion implantation. Relative secondary ion yields were determined by depth profiling through each implantation distribution and by integrating the respective intensity-versus-time curve9'44). From a knowledge of the number of dopant atoms contained within the analysed area " u s e f u l " secondary ion yields were determined. With reference to eq. (lb) we notice that these yields correspond to .(~z,)F,, i.e. the measured numbers reflect both Tl{e mean degree of ionization (or,-+> and the instrumental parameter GF. The latter has been assumed to be the same for all elements investigated44). Positive and negative ion yields compiled from the data reported in refs. 44 and 45 are plotted in figs. 9 and 10 as a function of the ionization potential and the electron affinity, respectively. Ions emitted from a common matrix are indicated by the same symbol. Matrix ions are edged. V. S P U T T E R P R O F I L I N G AND SIMS

350

K. W I T T M A A C K

10-3

'

I

'

I

'

O- bombardment

I

According to fig. 9 the positive ion yields observed under oxygen bombardment depend upon both the substrata material and the ionization potential of the element. Ions sputtered from silicon exhibit a degree of ionization which, under the conditions of rats. 44 and 45, is nearly three orders of magnitude larger than in the case of a tin matrix. This difference most likely reflects differences in the steady state surface concentration of oxygen. [The simplified semi-quantitative explanation put forward by Deliria et al. 44'45) neglects important physical processes such as matrix dependent preferential oxygen sputtering and is thus misleading. A detailed criticism has been given elsewhere46)] For a given matrix the positive ion yields scatter around a straight line in the semilog plot of fig. 9 which suggests a relation of the form

i

,~=30 °

;

N~ Si+

10-~

& m Q

lO-S

.~ 10-s

.s~.ni'L \ , ~TA+

Matrix:

oGe • GoAs

X

X~

~ o\

.Sn

lO-a 4

t

t

I

I

I

II

(c~+) --- K exp ( - flEi),

I

6 8 10 Ionization potential (ell)

12

Fig. 9. Positive secondary ion yields, i.e. the number of ions detected for each atom sputtered, of B, P, As and Sb implanted in Si, Ge, GaAs and Sn, respectively, vs the ionization potential. Compiled from rats. 44 and 45; cf. ref. 46. As expected under conditions of oxygen-induced yield enhancement, the matrix ion yields (edged) exhibit the same trend as the yields of implanted species. The scatter around the straight lines increases with decreasing oxygen surface concentration from Si to Sn.

(3

.£

b

8

0

1

2

Electron affinity

3

/,

(eV)

Fig. 10. Negative secondary ion yields of B, C, F, P, As and Sb implanted in Si, Ge, GaAs and Sn, respectively, vs electron affinity. Cesium bombardment. The lines are drawn to guide the eye. Compiled from rats. 44 and 45; cf. ref. 46.

(2)

where K and fl unknown functions (or factors) and Ei is the ionization potential of the element i. Within experimental accuracy the slope of the straight lines in fig. 9 is the same for all four matrices, /J -1 =0.8eV. Notice that the implantation fluences applied in ref. 44 were rather high, q b = 5 x l 0 ~s ions/cm 2, so that at the energies used, E = 60 keV9), the peak concentrations were of the order of 10% for heavy dopants in heavy substrates (As, Sb in Sn). Precipitation effects may thus be responsible in part for the relatively large scatter of the data for the tin matrix. An exponential law as susggested by the results of fig. 9 is not evident in case of negative ion emission under cesium bombardment (fig. 10). Similar to positive ion emission, the degrees of ionization are high with silicon substrates and low if tin serves as a matrix. The most important parameter, however, is the electron affinity EA. This quantity affects the degree of negative ionization in particular in the regime EA < 2 eV, whereas for high electron affinity elements such as fluorine ( ~ - ) becomes relatively insensitive to the (assumed) variations in cesium concentration. A functional dependence ( o ~ - ) = f ( E A ) is not evident from fig. 10.

6. Empirical formulas for the degree of ionization Many approaches to quantify secondary ion emission are based on the assumption that the processes which govern the degree of ionization are thermal in character. Consequently it has been pro-

SECONDARY ION MASS SPECTROMETRY posed 47'48) t h a t

(~+) = K~+ exp ( - Ei/kT),

(3a)

and ( ~ - ) = K7 exp (EA,/kT),

(3b)

351

surface always enhances the positive ion yields, the work function may either increase (Cu, W) remain constant (A1) or decrease (Mg) with increasing surface concentration of oxygen. This is clearly in contradiction to Andersen and Hinthorne's interpretation of positive ion yield enhancement. Under the assumption of a local thermal equilibrium the ionization process has been described 4s) as a dissociation reaction between neutral atoms M °, singly charged positive ions M + and electrons e - , M° ~ M + + e-, (4)

where k is the Boltzmann constant and T the relevant temperature. The functions K,+ and K,.+ depend on the details of the assumed ionization mechanism. Either the non-equilibrium Dobretsov equation 47) or the Saha-Eggert equation 48) have been applied. In either case K ? and T have been treated as adjustable parameters. Interpretation of with the dissociation constant (5) the physical significance of " T " (which comes out O + = N + N e / N ° . to be in the 103-104K range) or of " k T " has N ÷, N O and Ne are the densities of ions, atoms and prompted repeated discussions16' 17'28'33'43'47-56). electrons, respectively, in the assumed plasma. D ÷ Whereas Jurela 47) has merely shown that the calcu- has been calculated from the Saha-Eggert equation lated "temperatures" do not exceed critical temper- which involves a Boltzmann factor, atures (for argon bombarded elemental and comD ÷ oc e x p ( - E / k T ) , (6) pound targets), Andersen and Hinthorne 48) have derived the composition of various classes of sam- where E is the dissociation energy. Combining eqs. ples from relative secondary ion intensities under (5) and (6) one finds the relative concentration of ions N + / N ° which, for N + ,~N °, equals the degree oxygen bombardment. One of the most surprising facts with respect to of ionization the thermal approaches is that a clear physical ~+ ~_ N+/N ° oc N~ 1 e x p ( - E / k T ) . (7) picture of the ionization mechanism has not been presented. Without any experimental evidence, An- According to eq. (7) ~z÷ should be inversely propordersen and Hinthorne have postulated that the tional to the electron density Ne. This relation has sputtering region resembles a dense plasma in local not been verified experimentally. On the contrary, thermal equilibrium (LTE)48). The spatial location of it has been found, e. g., that the total number of this LTE plasma remained obscure. Recent at- electrons emitted from an argon bombarded, oxidtempts to interpret the LTE model have concen- ized silicon surface is a factor 4 - 6 times larger than trated on the space above the irradiated sur- for a clean surfaceS8). Energy analysis revealed that face54.s5). electron emission is enhanced in the low energy Rather than adding to previous criticism concern- part of the distribution ( < 2 eV)59). ing, e. g., the non-thermal character of secondary We have performed an experiment similar to that ion energy distributions 16'17'5°) we like to discuss of fig. 5, the difference being that variations in the experimental findings that led to the proposal of secondary electron emission during 8 keV O~- iman LTE plasma. Andersen and Hinthorne 48) stated: plantation were monitored6°). This was done rather The emission o f positive ions is enhanced and stabil- rigorously by recording the indicated target current ized by the increased electronic work function created with and without secondary electron suppression. It by bombardment with an electronegative gas such as was found that the steady state secondary electron oxygen, while the emission of negative ions is yield under oxygen impact is - 4 times larger than enhanced and stabilized by the decreased work functhe yield minimum observed after sputter erosion tion created by bombardment with an electropositive of the surface oxide6°). This result and the results gas such as cesium. These experimental results can be of refs. 58 and 59 clearly indicate that secondary understood in terms o f a simple thermoionic emission ions and electrons do not interact in the manner model. As a matter of fact, the effect of (reactive) suggested by eq. (4). An experimentally supported ion bombardment on the work function has never basis for the L TE model does not exist. been measured by the authors of ref. 48. Blaise and In view of these findings it is not surprising that Slodzian57), on the other hand, have shown that in many applications of the LTE model a samplewhile the presence of oxygen at the bombarded specific, self-consistent pair of Ne, T-values could V. SPUTTER P R O F I L I N G AND SIMS

352

K. W I T T M A A C K

not be derived. T-variations by more than a factor of t w o 52'53) and N~-variations by four orders of magnitude 53) have been observed, depending on the internal standards chosen. This is hardly what one would expect if the local thermal equilibrium were attained53). Nevertheless, surprisingly accurate analyses have been obtained sometimes by use of the LTE model48). As we shall see in the next section this success is mostly due to the Boltzmann factor inherent in all thermodynamic models. As an alternative explanation for the yield enhancement in the presence of oxygen, a bond breaking model has been proposed by French groups57'61'62). This model is based on the idea that the ionic character of the metal-oxygen bonds promotes direct emission of ions. Blaise 62) has recently specified the model by considering the potential energy diagram of the M--O system as a function of the internuclear distance. He showed that when a metal and an oxygen atom become separated during sputtering, crossing of the potential energy curves will occur, whereby a large variety of exit channels become available for dissociation into the fundamental state M + O as well as into excited states M * + O . The lowest lying ionized state is M + + O - , in which case the energy required for ionization of the metal atom amounts to only E j - E A ( O ) = E i - 1 . 4 6 eV. Accordingly, the effect of oxygen might be attributed in part to a lowering of the effective ionization energy. Notice that by substracting EA from E~ the general form of eqs. (2) and (3a) remains uneffected because the factors exp(/3EA) or exp(EA/kT) will be the same for all metal elements and will thus not affect the relative degree of ionization. The bond breaking model has been criticized recently by Williams and Evans 32) who proposed a surface polarization model to "rationalize" the well-known f a c t 5'16) that certain elements exhibit not only strong positive but also moderate negative ion yield enhancement due to the presence of oxygen. The proposed model is only qualitative in nature and mainly stresses the accepted fact that a heavily bombarded, oxygenated surface is likely to be microscopically heterogeneous. We have pointed out elsewhere 5) that adequate tests of the model 32) require low fluence (" static") SIMS studies rather than high fluence experiments as reported in ref. 32. It should be pointed out that Williams and Evans 32) argued against the bond breaking model on the basis of rather inadequate experimental data.

I

I

l

I III1

I

I

I

I

I Ilil

O- ---," Si {focussed beam]

I

/ j*"

10 7

surface oxide

.~ >~/

ul

i

"steady

106

."'~ I f S , * ) 10 5

I

o,

IfO-}

I I llllll

tO s

1

I I lltltl

tO 6

O- intens#y Fig. 11. Plot of the Si + evolution of the respective of a silicon sample covered from fig. 6 of ref. 32. The iour.

vs the signals with a dashed

10 z

&ounts/s) O - intensity, reflecting the during oxygen bombardment thin natural oxide. Compiled line indicates a linear behav-

In ref. 32 a non-analyzed ion beam was used which is known to provide qualitative build-up curves only and which prevents, e.g., the rapid establishment of plateaus as in fig. 5. Also, with the magnetic mass spectrometer used, the evaluation of positive and negative ion intensities during Obombardment had to be measured in separate runs. Fig. 9 of ref. 32 seems to reveal a non-linearity between the Si + and O - signals. However, analysis of fig. 6 of ref. 32, shows (fig. 11) that, if the data recorded while sputtering through the surface oxide are included, the proportionality is as good as one might expect in view of the poor experimental conditions of ref. 32. We conclude that Williams and Evans 32) have not provided any evidence against the bond breaking model.

7. Practical analyses In this section we briefly discuss some results of quantitative analyses by means of SIMS. To convert measured SIMS intensities to elemental concentrations, empirical ionization models as well as experimentally determined relative sensitivity factors have been used. As to the application of ionization models we concentrate on studies which are based on simple Boltzmann-type relations rather than on the LTE model. Some interesting results in this

353

SECONDARY ION MASS SPECTROMETRY

respect have been reported by Morgan and WernIn conjunction with the analysis of low alloy steels they have shown that for a Boltzmanntype relation to be obeyed it is necessary to increase the oxygen pressure to the point where the species least sensitive to oxygen attains its maximum intensity33). Fig. 12 shows, for an argon bombarded NBS 461 steel sample, the response of various ion signals to increasing oxygen pressure. Clearly, the relative sensitivities vary dramatically with increasing oxygen pressure. Note that the Fe+/Cr + inten: sity ratio exhibits qualitatively the same features as in fig. 3. However, the effect is much less pronounced in fig. 12. Also shown in fig. 12 is the Fe + intensity variation for 02 bombardment (dashed curve). As one might expect on the basis of the results discussed in sect. 5, O2 bombardment at base pressure and at an angle of incidence of 50 ° does not provide sample saturation with oxygen. Preferential oxygen sputtering seems to be effective also in this case. From a semilog plot of the saturated yields of fig. 12 versus the ionization potential, Morgan and Werner 3a) derived a "temperature" T = 6300 K for 0 - 2 0 e V ions. Combining eqs. (lb) and (3a) and inserting T one can calculate concentration ratio relative to the concentration of one constituent,

er33'43'63).

e.g, iron,

( c~_)

_ I+ (M 3 7j (Fe,

s,Ms

Ei-Ev,~

exp

I + (Fe) 7i(Mi)

k---~

(8)

These ratios may be compared with concentration ratios (C/CFe)t,,edetermined by conventional techniques. One can try to improve SIMS analysis by multiplying the ion intensities on the right hand side of eq. (8) with the respective ratios bj of the electronic partition functions33), b~ = B°(T)/B/-(73, (CIICFe)~IMS

(9)

= (cl/eFe)SlMS(bi/bF¢).

Ratios of measured-to-true concentrations 33) are plotted in fig. 13 as a function of the atomic number of the respective element. The average ratios deviate somewhat from one, a fact which might not be too surprising since all ratios have been weighed equally. Most ratios differ from the average by less than a factor of two. Inclusion of the partition functions, fig. 13a, does not improve the analytical accuracy significantly in comparison to the results of the simple Boltzmann-factor correction procedure depicted in fig. 13b. Before discussing peculiarities observed with elements which exhibit high MO ÷ intensities we like /0 -

1

1

1

I

'A B rerq

10-~"

n

u ruiou~

I

u

u uufprl

1

n

Ti+D'O Mn

5.5keV A P ~ NBS 461 0.1mA/cm 2 ~ . . r (×10-2) 3 ~-50 ° .

10-'~

~" f /

"Cr

~,

~02mA/cn

"~

(×10_3)

~/ ~

~

"

~1. ~Fe

+

r, *

5i P

+

,~ /

.

\

V+VO

Po overage

(A) Nb ÷ NbO (A) Mo÷MoO

t.,

AI +

,£

(oxygen soturoted J

co

~..7-" Fe+

55keV O~ . y /

(o) NBS 451 steel

u

f

I

I

I

i

I

I

I

Ti+TiO Mn

(b)

%

=_ B

~ 10-~6

"

-Co

.

Pb

-o co ~co

10-17 -

~

~lt]

I,,

10-5

Z

C] ,,,,,I

I

I IIIIlUl

I0-4 (02) pressure

i

I

~0 -1

• S i (~oe,..Cu Sn -~ C • / ~m • everege /Cr V÷VO (•) Nb+NbO AI • (•) Me ÷MoO __

10-3 (Po)

Fig. 12. Secondary ion intensities of various elements sputtered from an argon-bombarded NBS 461 low alloy steel sample as a function of the oxygen pressure in the target chamber. The oxygen flow was directed to the sample surface by a capillary. The Fe + intensity observed under oxygen bombardment is shown for comparison. Compiled from ref. 33).

0

I

I

I

I

20

40

60

80

/00

Atomic number

Fig. 13. Ratios of measured-to-true concentrations of various elements in NBS 461 low alloy steel, (a) with, (b) without the use of electronic partition functions. Bracketed data were derived by using I + ( M ) + I + ( M O ) instead of I+(M). From ref. 33. V. SPUTTER P R O F I L I N G AND SIMS

354

K. W1TTMAACK

tO illustrate the problems introduced by the mass dependence of instrumental factors. In their analysis of low alloy, steels, Morgan and Werner 33) assumed a mass independent instrumental factor G ? [cf. eq. (10b)]. Rudat and Morrison64), however, have shown that the detection efficiency in the CAMECA IMS-300, used also by Morgan and Werner33), varies significantly with atomic number Z2, as shown in fig. 14. Comparison of figs. 13 and 14 indicates that part of the deviation from the expected unit (or average) concentration ratio must be attributed to the Z2-dependence of the detection efficiency. In their later work, Morgan and Werner 43'63) have adopted an M Tl correction which has been justified merely by stating 43) that this correction improves the closeness of tl~e Boltzmann-type fit. Clearly, such a procedure must be viewed with reservation unless a possible mass discrimination of the instrument is clearly established. Otherwise one might suspect that the M~-~ correction artificially forces a fit that does not exist in reality. This could also cause an unwanted loss in information about the ionization process. It has been noticed already by Andersen and Hinthorne 48's°) that elements which exhibit intensity ratios r+(MO/M)>~1 yield concentration values much below the expected value, if the M ÷ intensity is used for analysis only. This problem has been discussed in more detail by Morgan and Werner 33'43'63'65) and WittmaackS'66). It has been found that r+(MO/M) depends almost exponentially on the bond dissociation energy of the oxide i0n5'65). In case of a high bond dissociation energy and with enough oxygen available, emission into the oxide channel becomes highly probably, provided the ion energy is not too high. This is illustrated in fig. 15 which shows a comparison of energy spectra of secondary ions emitted from niobium with either a I

~

I

I

i

Cu-Be ion-to-electron converter (~sskvj pl~ ~c,~t,,otor ~2,kvj

Q

10-~1 0

I

50

I

I

150 MOSS number (u) 100

I

200

250

Fig. 14. Detection sensitivity in the Camera IMS-300 ion microprobe vs mass number64).

10s

I

I

r~. [~xx~.

Oll o~

,

I

2 h A 0"2++ ~ O8tlA Ac 2keV,

m

104

I

Nb

:oo

, %, % --.

~

N

"

It \%

Nb+ (corrected)

"?<.

\

-0.,-,%

b

g ~10 2

10

I 0

I

I

20

40

I 50 Secondclry ton energy

I 80 (eV)

100

Fig. 15. Energy distributions (uncorrected) of various ions emitted from niobium bombarded with either argon or oxygen. The hatched area illustrates the loss of Nb + occurring at high oxygen concentration as a result of intense Nb emission into NbO (+) and NbO~ +) channels66).

low or a high surface concentration of oxygen (dashed lines and full lines, respectively). The " l o s s " in Nb+ intensity at high oxygen concentration can be estimated 66) if we fit the low-oxygen Nb ÷ distribution to the high-oxygen Nb ÷ distribution at high energies, where NbO ÷ emission is sufficiently small. This procedure yields a "corrected" Nb ÷ distribution with a peak concentration which exceeds the uncorrected high-oxygen value by about a factor 6. Comparison with correction factors deduced by Morgan and Werner 33) shows that the procedure sketched in fig. 15 yields values which are much more adequate than a mere summation over all Mr-carrying ions33). Analysis of energy distributions is important not only in case of the oxide elements. This becomes evident if we consider the result reported by Morgan and Werner 33'43'63) that the derived "temperatures" increase with increasing energy of the secondary ions. This apparent increase in " T " merely reflects the well-known fact 66'67) that the high energy slope of the secondary ion energy distributions is usually the steeper the lower the ionization potential of the respective element. This observation is presently not well understood. It should be pointed out, however, that the secondary ion energy distributions of elements with r+(MO/

S E C O N D A R Y ION MASS S P E C T R O M E T R Y

M) <~ 1 are not affected significantly by the presence of oxygen66'68). This observation (which justifies the correction procedure illustrated in fig. 15) rules out a pronounced change of the neutralization probability with increasing oxygen pressure, in contrast to the conclusions of Martin et al.69). In view of the complications encountered in quantitative SIMS analyses based on ionization models, it is not surprising that alternative approaches have been tried. Compared to the LTE procedure, improved analytical accuracy has been obtained s3) by the use of empirical correction factors determined on standards of similar composition, e. g. glasses or iron alloys. The most important problem faced in the application of relative sensitivity factors is related to the pronounced variation in response of the different elements to oxygen (cf. fig. 12). It is necessary therefore, (1) to determine sensitivity factors as a function of the oxygen (surface) concentration of the standard and (2) to evaluate the " s t a t u s " of the sample to be analysed. Means to characterize the sample with respect to the oxygen content have been discussed by McHugh s) and Ganjei et al.42). The suggested procedure involves the use of matrix ion intensity ratios which are sensitive to the presence of oxygen. As shown in fig. 16, r+(SiO/Si) is rather insensitive to variations in oxygen content and not suited for sample characterization, r+(Si/Si2), on the other hand, allows a very precise characterization of the '

' t'""l

' '''"'I

'

Ar + ~ Si(+ 0 2 ) EfkeV) j (/aA/cm 2)

I0 3

o

'

102 _

• o

4

l

e

• ~

70

I

e

10

"~

] 4 0 / /

' '''"'I

,

, ,r,"n',

+ . r (SI/bl2>~d" / /

71/

5

~1~

1 -

10~

/ vf

I

P

I

I

r~SiO/SI) ( ~ ~ooj

i

105 106 107 S i t Intensity [counts/HC)

355

oxygen (surface) concentration, independent of the current density and only slightly dependent on the primary ion energy. Matrix ion ratios suited for surface characterization can be found for all types of samples. 8. Conclusions It is evident from the analysis presented in this paper that a quantitative understanding of secondary ion emission under conditions of "chemical" yield enhancement does not exist presently. The only statement one can make with some confidence is that the relative yields of positive secondary ions emitted from oxygen-saturated samples are proportional to exp(-/3E). The origin of the parameter/3 is not known. Most likely,/'3 reflects the non-equilibrium statistics of secondary ion formation. /3-1 is the larger the higher the secondary ion energies at which relative yields are determined. Interpretation of/3 (or/3-1) in terms of equilibrium thermodynamics or equilibrium statistics is not justified on the basis of available experimental data. The LTE approach, in particular, must be considered a curiosity rather than a model, a dead-end road in the field of SIMS which should be left the sooner the better. Clearly, improvements in the understanding of secondary ion emission require experiments other than mere yield measurements at some energy and at some concentration of oxygen or cesium. E.g., measurements of the secondary ion yield as a function of the oxygen concentration are highly desirable. Combination of SIMS with other surface analytical techniques can be considered one way of attacking the relevant problems. The consequences of the bond breaking model should be worked out in more detail in the sense that secondary ion emission from oxidized (or cesiated) surfaces is likely to resemble important features of reactive scattering. One can hope that with increasing sophistication of SIMS experiments the understanding of the relevant phenomena will proceed to the point where SIMS may be used successfully not only for "simple" tasks such as depth profiling but also for a reliable analysis of samples of unknown composition.

108

Fig. 16. Intensity ratios r+(Si/Si2) and r+(SiO/Si) vs l+(Si). Intensity variations were produced by increasing the oxygen concentration in the sample surface (cf. fig. 4). Parameters are the argon energy and current density. Compiled from ref. 27, 70.

References 1) R. Castaing and G. Slodzian, J. Microsc. 1 (1962) 395. 2) G, H. Morrison and G. Slodzian, Anal. Chem. 47 (1975) 932A, V. S P U T T E R P R O F I L I N G AND SIMS

356

3) 4) 5) 6)

K. WITTMAACK

A. Benninghoven, Z. Phys. 230 (1970) 403. A. Benninghoven, Surface Sci. 53 (1975) 596. K. Wittmaack, Surface Sci., 89 (1979). j. Maul, F. Schulz and K. Wittmaack, Phys. Lett. A41 (1972) 177. 7) W.K. Hofker, H.W. Werner, D. P. Oosthoek and H. A. M. de Grefte, Rad. Effects 17 (1973) 83. 8) j. A. McHugh, in Methods and phenomena, Vol. 1 : Methods of surface analysis, ed. A.W. Czandema (Elsevier, Amsterdam, 1975)p. 223. 9) p. Williams, IEEE Trans. Nucl. Sci, NS-26 (1979) 1807. 10) H.E. Beske, Z. Naturforsch. 22a (1967) 459. 11) C.A. Andersen, Int. J. Mass Spectr. Ion Phys. 3 (1970) 413. 12) H.A. Storms, K. F. Brown and J. D. Stein, Anal. Chem. 49 (1977) 2023. 13) J.-F. Hennequin, C. R. Acad. Sci. (Paris) 264B (1967) 1127. 14) A. Benninghoven, Z. Naturforsch. 22a (1967) 841. 15) C.A. Andersen, Int. J. Mass Spectr. Ion Phys. 2 (1969) 61. 16) K. Wittmaack, in Inelastic ion-surface collisions, eds. N.H. Tolk, J.C. Tully, W. Heiland and C.W. White (Academic Press, New York, 1977) p, 153. 17) G. Blaise, in Materials characterization using ion beams, eds. J.P. Thomas and A. Cachard (Plenum Press, New York, 1978) p. 143. 18) p. Sigmund, Phys. Rev. 184 (1969) 383. 19) R. Behrisch, G. Maderlechner, B. M. U. Scherzer and M T. Robinson, Appl. Phys. 18 (1979) 391. 20) M.M. Jakas, Phys. Lett., 72A (1979) 423. 21) j.E. Westmoreland and P. Sigmund, Rad. Effects 6 (1970) 187. 22) K. Wittmaack, Surface Sci. 53 (1975) 626. 23) K. Witmaack, Surface Sci., 90 (1979). 24) K. Wittmaack, Phys. Lett. 69A (1979) 322. 25) R. Schubert, J. Vac. Sci. Technol. 11 (1974) 903. 26) G. Blaise and M. Bemheim, Surface Sci. 47 (1975) 324. 27) j. Maul and K. Wittmaack, Surface Sci. 47 (1975) 358. 28) M. L. Yu, Phys. Rev. Lett. 40 (1978) 574. 29) p. Sigmund, Appl. Phys. Lett. 25 (1974) 169. 30) W. Wach and K. Wittmaack, Nucl. Instr. and Meth. 149 (1978) 259. 31) K. Wittmaack, Surface Sci. 68 (1977) 118. 32) p. Williams and C.A. Evans, Jr., Surface Sci. 78 (1978) 324. 33) A.E. Morgan and H.W. Werner, Anal. Chem. 48 (1976) 699. 34) C.W. Magee, W. L. Harrington and R.E. Honig, Rev. Sci. Instr. 49 (1978) 477. 35) M. A. Frisch, W. Reuter and K. Wittmaack, Rev. Sci. Instr., to be published, 36) W.O. Hofer and J. P. Martin, Appl. Phys. 16 (1978) 271. 37) A.M. Huber, G. Morillot, N.T. Linh, J. L. Debrun and M. Valladon, Nucl. Instr. and Meth. 149 (1978) 543. 38) K. Wittmaack, Int. J. Mass Spectr. Ion Phys. 17 (1975) 39. 39) G. Hortig, P. Mokler and M. Mtiller, Z. Phys. 210 (1968)

312. 4O) p. Williams, R. K. Lewis, C. A. Evans, Jr. and P. R. Hanley, Anal. Chem. 49 (1977) 1399. 41) j. D. Fassett, J. R. Roth and G. H. Morrison, Anal. Chem. 49 (1977) 2322. 42) j. D. Ganjei, D. P. Leta and G. H. Morrison, Anal. Chem. 50 (1978) 285. 43) A.E. Morgan and H.W. Werner, Anal. Chem. 49 (1977) 927. 44) V.R. Deline, W. Katz, C.A. Evans, Jr. and P. Williams, Appl. Phys. Lett. 33 (1978) 832. 45) V. R. Deline, C. A. Evans, Jr. and P. Williams, Appl. Phys. Lett. 33 (1978) 578. 46) K. Wittmaack, J. Appl. Phys., to be published. 47) Z. Jurela, Rad. Effects 13 (1972) 167; Int. J. Mass Spectr. Ion Phys. 12 (1973) 33. 48) C. A. Andersen and J. R. Hinthorne, Anal. Chem. 45 (1973) 1421. 49) H.W. Werner, Vacuum 24 (1974) 493. 50) C.A. Andersen, in Secondary ion mass spectrometery, eds. K. F. J. Heinrich and D.E. Newbury (NBS Spec. Publ. 427, Washington, 1975) p. 79. 51) K. Tsunoyama, T. Suzuki and Y. Ohashi, Jap. J. Appl. Phys. 15 (1976) 513. 52) D. S. Simons, J. E. Baker and C. A. Evans, Jr., Anal. Chem. 48 (1976) 1341. 53) D.A. Smith and W.H. Christie, Int. J. Mass Spectr. Ion Phys. 26 (1978) 61. s4) j.N. Coles, Surface Sci. 79 (1979) 549. ss) K.J. Snowdon, Rad. Effects 40 (1979) 9. 56) G. Blaise and A. Nourtier, Suurface Sci, in press. 57) G. Blaise and G. Slodzian, Surface Sci. 40 (1973) 708. 58) p. Gaworzewski, K.H. Krebs and M. Mai, Int. J. Mass Spectr. Ion Phys. 10 (1972/73) 425. s9) p. Gaworzewski, K.H. Krebs and M. Mai, Int. J. Mass Spectr. Ion Phys. 13 (1974) 99. 60) K. Wittmaack, unpublished. 61) G. Slodzian and J.-F. Hennequin, C.R. Acad. Sci. (Paris) 263B (1966) 1246. 6~) G. Blaise, Surface Sci. 60 (1976) 65. 63) A.E. Morgan and H.W. Werner, Surface Sci. 65 (1977) 687. 64) M.A. Rudat and G.H. Morrison, Int. J. Mass Spectr. Ion Phys. 27 (1978) 249. 65) A. E. Morgan and H. W. Werner, J. Chem. Phys. 68 (1978) 3900. 66) K. Wittmaack, in First Int. Conf. on Secondary ion mass spectrometry and ion microprobes, MOnster (1977) unpublished. 67) p.H. Dawson, Surface Sci. 65 (1977) 41. 68) H. W. Werner and A. E. Morgan, in Advances in mass spectrometry, ed. N.R. Daly (Heyden and Son, London, 1978) Vol. 7A, p. 764. 69) p. j. Martin, A. R. Bayly, R. J. MacDonald, N. H. Tolk, G. J. Clark and J. C. Kelly, Surface Sci. 60 (1976) 349. 70) j. Maul, PhD Thesis, Technische Universit~it Mtinchen (1974).