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SURFACE AND INTERFACE ANALYSIS, VOL. 21, 747-757 (1994)

The Infinite Velocity Method: a New Method for SIMS Quantification

P. A. W. van der Heide,* Min Zhang, G. R. Mount and N. S. McIntyre Surface Science Western, Western Science Centre, University of Western Ontario, London, Ontario, Canada, N6A 3K7

Twelve elements spanning a mass range of 197 atomic mass units from five standard reference materials and three implant materials were analysed to ascertain the validity of a new method, termed the infinite velocity method, for quantifying the negative monatomic secondary ion emissions resulting from Cs-bombarded surfaces. This method extracts quantitative data by extrapolating secondary ion yield versus kinetic energy data to the infinite velocity limit. Extrapolation to infinite velocity is done because matrix effects are theoretically predicted to be removed at this limit. Plotting the extrapolated data against known concentrations for the homogeneous standard reference materials yielded linear standardization curves for all elements analysed, indicating that the matrix effect is indeed removed, i.e. sensitivity factors were not required. Likewise, the resulting concentration profiles of the implant materials analysed agreed well with concentration profiles calculated via the integration method. Thus, samples can be quantified by this procedure without the requirement for matrix-matched calibration materials. Theoretical implications and the assumptions used in the calculations are also discussed.

INTRODUCTION

Secondary ion mass spectrometry (SIMS) has been shown to be capable of analysing surface, interfacial and bulk regions over a wider elemental range than any other surface microanalytical technique presently avail- able. Furthermore, most elements can be detected down to part per billion concentration levels. This technique, however, suffers from a strong secondary ion yield dependence on the chemical composition of the surface. This is commonly referred to as the 'matrix effect'. As the matrix effect is still not fully understood on a funda- mental level,'*' quantification of SIMS results has pro- ceeded largely via the careful calibration of secondary ion signals with matrix-matched reference materials containing known concentrations of the relevant ele- m e n t ~ . ~ This has therefore posed a limitation on the number of materials that can be quantified accurately by the SIMS technique.

Empirical4p9 and the~re t i ca l "~ '~ studies of the exit velocity of monatomic secondary ions from solid surfaces have shown that the ion yield (per secondary neutral) may be characterized by the following expression

where v is the emission velocity, 0 is the emission angle with respect to the sample normal and vo is a constant termed the characteristic velocity. This characteristic velocity is a constant used to describe the influence of the surface electronic environment on the ionization/ neutralization probability of escaping atom/ion. Thus, this constant contains those variables responsible for the SIMS matrix effect. Equation (1) also suggests that the influence of the characteristic velocity and hence the

CCC 0142-2421/94/110747-11 0 1994 by John Wiley & Sons, Ltd

matrix effect can be removed by increasing the secondary ion emission velocity value to infinity, because the vo/v fraction would tend to zero.

As demonstrated in previous values of the characteristic velocity (typically of the order of 1 x lo6 cm s-') can be determined from the slope of the linear trend exhibited by plots of secondary ion yield (natural log scale) versus inverse velocity (linear scale). A value directly proportional to the secondary ion yield (termed 'corrected intensity') is used in this work because absolute secondary ion yields are extremely difficult to measure. The corrected intensity is determined from secondary ion intensity data by correcting for the energy- dependent instrument transmission and then referencing to a well-established sputter yield relationship. The velocity component, on the other hand, is extracted directly from the secondary ion kinetic energy. An example of such a plot, along with the energy distribution from which this was calculated, is shown in Fig. 1.

Recently it has been observed that the linear trends resulting from the secondary ions from a number of different elements present within a particular substrate tended to merge as infinite velocity was appr~ached .~ This was found to occur only after concentrations were accounted for in the calculations of the corrected intensity, indicating that the infinite velocity intercept data are directly related to the elemental concentrations within the substrate analysed. On the basis of these results and the predicted removal of the matrix effect at infinite velocity, it was suggested that such an approach could be developed into a practical quantification procedure for the SIMS analysis of solid samples.' The procedure would encompass :

(1) Measurement of the secondary ion energy distributions (intensity versus kinetic energy) of the secondary ions for each element of interest.

(2) Correction of the recorded secondary ion intensity values for instrument transmission function and

Received 10 January 1994 Accepted 21 J u w 1994

748 P. A. W. v. d. HEIDE ET AL.

10'

1 o8

10'

1 O K

I I I

0 0 0 5 1 .0 1 5 2.0 2 5

' h ( X l 0 - 6 ~ cm- i )

Figure 1. Corrected intensity versus inverse velocity plot for the negative secondary ions of 46Ti emitted from the Ti1087 reference material. The respective energy distribution is shown in the inset. The data were collected under a 2.5 eV energy window.

then referencing this to the secondary neutral sputter yield.

(3) Plotting the corrected intensity values against the inverse of the emission velocity such that the resulting linear trends can be extrapolated to infinite velocity (the l /v = 0 intercept). The value of the intercept (once corrected for the detector sensitivity dependence to secondary ion mass) for each element, termed i,,,, , defines the relative concentration for each element studied.

Absolute concentrations can then be obtained for all elements within the sample analysed if the concentration of any one element is known, i.e. a matrix element, because this would relate the intercept values to an absolute concentration scale. Alternatively, if the secondary ions from all elements present at concentration levels greater than 0.1 at.% are analysed, a reference signal would not be required since the sum of the intercept values, i,,,, . can be normalized to 99.9 at.%. The concentration of a particular element would then be proportional to the (icorr/x i,,,,) fraction.

The present work was carried out with the aim of ascertaining the validity of this quantification method for negative monatomic secondary ions resulting from Cs + primary ion bombardment. This was accomplished by testing the method on a wide variety of elements and samples (five standard reference materials and three implant materials), and examining the relationship between the resulting intercept data and actual concentrations for these elements. In the case of the implant materials, the concentrationdepth profiles collected were compared with those calculated via the integration method.

EXPERIMENTAL

The instrument used in data collection was a Cameca IMS-3f SIMS instrument. This instrument has under-

gone electrical (lens supply) and computer interface modifications (with the addition of in-house developed software), which allow for greater freedom in both data collection and manipulation.

Energy distribution analysis

Energy distribution analysis was initially carried out on a number of homogeneous standard reference materials in order to ascertain the validity of the trends predicted by Eqn. (1). These were carried out by altering the extraction potential by 1 V increments between secondary ion kinetic energies of - 50 to 250 eV (1 V equates to 1 eV for singly charged ions). Zero emission energy was defined as being at the 50% intensity level of the steep low-energy shoulder. All ion intensities, over the energy range used in extracting the linear trends out of the corrected intensity versus inverse velocity plots, were kept below 5 x lo5 counts s - l to ensure that the relevant data were not affected by the intrinsic dead time of the electron multiplier. An ETP AF15OH electron multiplier was used.

The samples analysed under energy distribution conditions consisted of five NIST titanium standard reference materials (Ti352b, Ti1087, Ti1088, Ti648 and Ti649' 5 ) . These highly homogeneous reference materials, used for calibration purposes, contain several minor and trace elements whose concentrations have been determined previously by a range of other analytical techniques, as reported in Table 1. Only interference-free isotopes were analysed.

All Ti reference materials were analysed under a 100 nA Cs' primary beam (14.5 keV incident energy) scanned over a 500 pm x 500 pm raster pattern. This was made significantly larger than the field of view (60 pm) to ensure that crater edge effects were not included. The contrast aperture and imaged field were set to 400

Table 1. Quoted concentrations of relevant elements within the specified reference materials

Element Sample Concentration (wt) Uncenainty

Al Cr Zr Mo Sn B At Cr Sn V H 0 H 0 H 0 cu Ni As

648 648 648 648 648 648 649 649 649 649 352b 352b

1087 1087 1088 1088 500 500 500

a NL, not listed. NC, not certified.

5.1 3% 3.84% 1.84% 3.75% 1.98%

10 PPm 3.08% 2.96% 3.04%

46.9 ppm N La

57.5 ppm 840 ppm 88.5 ppm

1850 ppm 99.7%

140 ppm

15.1 Yo

603 ppm

0.05% 0.03% 0.04% 0.05% 0.02%

NCb 0.02% 0.02% 0.04% 0.1 Yo 0.8 ppm

NL" 2.5 ppm

NCb 2.5 ppm

NCb 0.025/"

10 ppm 12 PPm

THE INFINITE VELOCITY METHOD 749

pm and 150 pm, respectively. However, different secondary ion energy windows were used: 40 eV for the Ti648 and Ti649 reference materials; 2.5 eV for the Ti352b, Ti1087 and Ti1088 reference materials. These different settings affect only the energy resolution and intensity of the resulting data, as has been demonstrated in a previous study.' Data were collected only after steady-state sputtering conditions were established.

In the case of the Ti352b, Ti1087 and Ti1088 reference materials, where the measurement of trace hydro- gen concentrations was desired, the background H - level was minimized by prepumping the samples (placed side by side) in the analysis chamber for 48 h prior to analysis, and utilizing the cryo-shroud during analysis. The pressure in the analytical chamber during analysis remained around the 1 x lo-' Pa level; this was suffi- cient for the detection of H - down to 1 ppm by weight concentrations (- 5 x 10l6 atoms cmP3).l6

Depth profile analysis

Depth profile analysis was then carried out on the Ti648 standard reference material and several implant materials in order to ascertain the effectiveness that a truncated data collection procedure (fewer data points used in the infinite velocity calculations) would have on the accuracy and scatter of the concentration data, and to ascertain the applicability of this method to samples in which the concentrations of particular elements vary with depth. The implant materials analysed consisted of single-crystal silicon ( 100) substrates implanted with "B, 75As and 1 9 7 A ~ at doses of 1 x 1014, 1 x 1015 and 1 x 1014 atoms ~ m - ~ , re~pective1y.l~ This has been confirmed by Rutherford backscattering (RBS) analysis.' Implant energies ranged from 150 keV (' B) to 200 keV (75As and 197A~) .

The Ti648 and implant reference materials were analysed with 2000 and 250 nA Cs' (14.5 keV incident energy) primary ion beams, respectively. Depth profiles were collected by setting the instrument to a particular mass, collecting the secondary ion intensity values a t several differing emission energy values (by altering the sample potential) and then switching to the next mass of interest. In the case of the Ti648 standard reference material, boron was analysed at emission energy values centred at 50, 75, 100 and 125 eV, while Al, Ti, Zr and Mo were analysed at emission energy values centred around 50, 100, 150 and 200 eV. In the case of the "B- implanted Si material, the "B signal was analysed at emission energy values of 25, 50, 75, 100 and 125 eV, while 28Si and 30Si were analysed at secondary ion emission energies of 100, 125, 150, 175 and 200 eV. The As- and Au-implanted Si materials were analysed in an identical manner. The I5As and 1 9 7 A ~ were analysed over emission energy ranges centred around 50, 75, 100, 125 and 150 eV (a 40 eV energy window was used), while 30Si was analysed at emission energies of 100, 125, 150, 175 and 200 eV. The energy window was fixed at 40 eV throughout, while all other instrument variables remained the same as under the energy distribution analysis.

In order to reduce hydride interference problems (29SiH on 30Si), depth profiles were collected under liquid nitrogen cryo-shroud conditions after the inten-

sities of the 29Si and 30Si isotopes fell within 5% of their listed isotopic abundance levels.

Calculations

Corrected intensity values were calculated from the resulting secondary ion intensity data by dividing the recorded intensity data by the previously determined instrument transmission function, then referencing this data to the secondary neutral sputter yield and dividing all this by the isotopic abundance of the isotopes studied, i.e.

where Z-(E , 0) is the recorded secondary ion current, T(E) is the instrument transmission factor, S(E, 0) is the sputter yield and R , is the isotopic abundance, E and 9 refer to the emission energy and angle with respect to the sample normal of the secondary ions analysed.

The recorded secondary ion intensities were divided by the instrument transmission function to correct for the increasing degree of discrimination that the instrument imposes on those secondary ions with greater emission energies. For secondary ions with emission energies greater than 6-7 eV, the transmission function for the Cameca IMS-3f to -6f series of instruments takes the form"

T(E) = (1 - /-) (3)

where h is the contrast aperture diameter (600 pm); D is the sample to extraction plate distance (4500 pm), g is the crossover magnification (0.28), q is the secondary ion charge (l), V is the extraction potential (variable) and E is the secondary ion emission energy (variable).

To extract relative secondary ion yield values, the transmission-corrected secondary ion intensities were then divided by the secondary neutral sputter yield. This was assumed to follow the well-established Sigmund-Thompson relation"-20

(4)

where Eh is the binding energy. Values of 2.3 and 6.1 eV were used for the Cu and Ti reference materials, respectively, while a value of 3.8 eV was used for the Si implant materials.27 This relation has been verified empirically for numerous elemental matrices, including A1,2' Ti,22 V,23 Cr,22*24 CuZ3 and Zr,22*25 and in addition has been fitted to the neutral emissions from several non-elemental matrices.2 1,24*26

Calculations of absolute secondary ion fractions (the secondary ion yield) were not undertaken because the primary ion current measured by the instrument is only a relative value: absolute values are required in such calculations. However, because the samples analysed consisted of homogeneous matrices, the sputter yield will remain constant for all elements within a given matrix (assumming that steady-state sputtering conditions have been realized). Furthermore, the quantification method described relies on referencing the


1000 L7-- -- 1-- -7

0 50 100 150 200 250

Mass(amu)

Figure 2. Electron multiplier (ETP 150H) sensitivity (arbitrary units) to secondary ion mass. EM/FA = Electron rnultiplier/Faraday cup.

extrapolated intercept data to each other. Thus, the cal- culation of absolute values that require additional assumptions (for example, see Ref. 4) would not be of any additional use, although this would ensure the dimensional correctness of Eqn. (2). Finally, image field potentials were not included in the calculations because the trends exhibited by the secondary ion populations used in the quantification procedure (those with emission energies greater than 40 eV) were not found to be influenced by such effects.

Corrected intensity versus inverse velocity plots were then constructed on a log-linear scale for all elements analysed. The inverse velocity was calculated directly from the secondary ion emission energy (from E = +muz), with the addition of binding energy. Linear regressions were placed through the linear portion of all corrected intensity versus inverse velocity plots in order to ascertain values for the y-intercept, i, and goodness of fit, r . Values of v o were determined from the slope of the linear regressions placed through the linear portion of the natural log of the corrected intensity versus inverse velocity plots. Positive deviations from this linear trend at high l / v values (those corresponding to emission energies less than 40 eV) noted for some elements have previously been attributed to the introduction of a stimulated desorption process.

The resulting intercept values, i , were then multiplied by a (mass)'.5 factor in order to a.ccount for the empirically observed mass-dependent sensitivity of the electron multiplier to the secondary ion mass. The product is termed i,,,, . This sensitivity was noted on comparing the relative secondary ion intensities recorded by both the electron multiplier (ETP 150H) and the Faraday cup under identical conditions (the Faraday cup signal was used as the reference, because this unit detects the absolute secondary ion current). All secondary ion species shown (with the exception of Ga and As) were collected from the pure elemental matrices. The G a and As signals were collected from a GaAs matrix. Identical instrumental conditions were used, with the exception of the primary ion current setting, to those described above. The primary beam current was altered such that

the secondary ion currents fell within the linear range of both detectors. A more in-depth discussion with additional results can be found in a separate report." The results are shown in Fig. 2. The line passing through the data points represents the l/(mass)'.' function. The observed relationship agrees with previous reports in which both electron multipliers and channeltrons have been found to exhibit similar mass-dependent detection e f f i~ i enc ie s .~~~~ ' This dependence is ascribed to the kinetic emission process of secondary electrons on ion impact with the first dynode."

Finally, it should be emphasized that with today's computers (a 486 PC) and the correct algorithm, minimal time restraints exist in calculating the corrected intensity versus inverse velocity plots, i.e. such plots can be calculated within minutes of obtaining the raw data.

RESULTS

Energy distribution analysis

Energy distributions collected from the negative secondary emissions of H, 0 and Ti, emitted from the Ti1087 reference material, yielded the corrected intensity versus inverse velocity plots shown in Fig. 3(a). As the energy window used in the data collection procedure spanned 2.5 eV, the corrected intensity versus inverse velocity plots could be extended to cover an energy range as wide as 6-250 eV (plus E J . Regressions placed through the linear sections of these plots, and those for the Ti352b and Ti1088 reference materials, yielded the characteristic velocity, y-intercept and goodness of fit values listed in Table 2.

Following this, the energy distributions collected from the negative secondary ions of 27Al, 52Cr, 90Zr, '''MO, "'Sn and lz4Sn within the Ti648 reference

Table 2. Characteristic velocity, intercept and goodness of fit values for the secondary ions emitted from the Ti reference materials

Sample

648 648 648 648 648 648 649 649 649 649 352 352 352 1087 1087 1087 1088 1088 1088 500 500 500

yo( x lo6 cm s- ' ) I

8.31 9.0 x 1 0'' 6.49 3.2 x 10" 4.51 2.8 x 109

3.89 5.6 x 109 0.88 3.6 x 109 0.87 3.7 x 109

8.1 1 7.5 x 10" 3.71 7.5 x 1O'O

6.39 1.5 x 10" 0.25 3.9 x 109 2.1 3 5.0 x 10'

8.1 0 6.1 x 109

8.1 4 8.2 x 109 2.1 7 1.3 x 109 1.57 1.9 x 109

4.51 2.1 x 109

- -

2.1 5 2.8 x lo* 1.58 8.5 x 10'

8.09 1.4 x 10''

6.37 2.6 x 1 0j2 2.02 3.1 x lo*

r

0.9981 0.9969 0.9927 0.81 39 0.8228 0.81 82 0.9971 0.9964 0.9924 0.7342 0.8792

0.9869 0.8776 0.91 99 0.9905 0.8902 0.9254 0.9903 0.9400 0.9995 0.8763

-

THE INFINITE VELOCITY METHOD 75 1

' O ' O 1 10'

h 4

III - 4 5 lo8 c V 9) 4

.-

E 10' 0 u

1 o6

1 o5

118 -

0.00 0 50 1 .oo 1 50

1 /v (X I 0-6s cm-1)

1 /v (XI 0-6s cm-1)

0.00 0.50 1 .oo 1.50

1 /v (X I 06s crn-1)

1 o8

i / v ( x i 0-6s cm-1)

Figure 3. Corrected intensity versus inverse velocity plots for: (a) 'H-, l60- and 46Ti- secondary ions emitted from the Ti1087 reference material; (b) 90Zr-, 'ooMo- and '"Sn- secondary ions emitted from the Ti648 reference material; (c) 27AI- and 52Cr- secondary ions emitted from the Ti648 reference material; (d) 27AI-, 51V- and '24Sn- secondary ions emitted from the Ti649 reference material.

material resulted in the corrected intensity versus inverse velocity plots shown in Figs 3(b) and 3(c). Like- wise, the corrected intensity versus inverse velocity plots of the negative secondary ions of 27Al, "V and '24Sn emitted from the Ti649 reference material are shown in Fig. 3(d). These corrected intensity versus inverse velocity plots extend over the 25-250 eV (plus Eb) emission energy range. Lower energies were not plotted because the use of a 40 eV secondary ion energy window smeared out the low-energy peak due to the resulting loss of energy resolution. Again, strong linear trends were noted in all plots. Values of the characteristic velocity, the y-intercept and the goodness of fit of the regressions placed through the linear portion of these plots are also listed in Table 2 for both samples. Varia-

tions ( f 2.5 eV) of the value of E , used in the Sigmund- Thompson relation yielded variations in these values of

If the infinite velocity method is valid, all i values should be proportional to the actual concentration of the element analysed and unaffected by the problems associated with the matrix effect. To determine whether the i values are proportional to known concentrations, the i data for the secondary ions of H emitted from the Ti352b, Ti1087 and Ti1088 reference materials were referenced against the matrix Ti intercept data and then plotted against the reported concentration values of H within these materials. The H i values were referenced to the matrix Ti i values in order to remove any instrument collection efficiency variations that may have been

< 2.5%.


introduced in the analysis of different samples. As can be seen in Fig. 4, the resulting H/Ti i ratios could be well correlated with the reported H concentrations on a linear scale. This indicates that the proportionality between secondary ion intensities and concentration is indeed carried through to the infinite velocity limit in the extrapolation procedure. The background H level could also be defined from the y-intercept of this plot as being equal to 42 ppm by weight.

The second requirement can be illustrated by plotting the i,,,, values for a group of elements within a particular reference material against reported concentration values. The argument is that, if the problems associated with the matrix effect are removed, then sensitivity factors will not be required in generating plots in which a clear relationship between the reported concentrations and i,,,, for a number of elements of differing electron affinity could be seen. Conventional SIMS quantification procedures require sensitivity factors to construct such standardization curves in order to circumvent the matrix effect.'-3 Values of i,,,, were used, as opposed to i values, to account for the electron multiplier sensitivity to secondary ion mass.

The i,,,, data obtained from the secondary ions emitted from Ti648 and Ti649 were then plotted against known concentrations (once atomic densities were accounted for) as can be seen in Figs 5(a) and 5(b), respectively. A plot was also constructed from the i,,,, data collected from the negative secondary ions of 60Ni, 65Cu and 75As emitted from the Cu500 reference material analysed in a previous study (relevant data listed in Tables 1 and 2).' The results for the Cu500 reference material are shown in Fig. 5(c). This figure was plotted on a log-log scale because the data covered three to four orders of magnitude on both axes.

As can be seen in Figs 5(a) and 5(b), linear trends (or standardization curves) could be fitted through all plots. This could also be said for the data presented in Fig. 5(c), because this plot exhibited a slope of 0.988. Although some degree of scatter is evident in the plot

-

Sample

35213 -

v 1087 7 1088

0 000 0 025 0.050 0 075 0 100

I H / iTi

Figure 4. Standardization curve for H- emitted from the Ti352b. Ti1 087 and Ti1 088 reference materials.

illustrated in Fig. 5(a), it should be emphasized that all i,,,, values yielded data within 2 wt.% of the listed values, and likewise for the data illustrated in Fig. 5(b). This is rather significant, considering that these secondary ions exhibit sensitivity factors that span over two orders of magnitude. The secondary ions plotted in Fig. 5(c) also exhibit sensitivity factors that cover two orders of magnitude.

In all cases, the same result was obtained by incorp- orating the factor into Eqn. (2). The route used, however, allowed this factor to be considered as a separate 'instrument calibration factor'.

Depth profile analysis

Ti648 reference material. The depth profile analysis of the B, AI, Ti, Zr and Mo secondary ions emitted from the Ti648 standard reference material resulted in the plot shown in Fig. 6. These intensities were then used to construct inverse velocity plots (inverse of the velocity against the corrected secondary ion intensity) for each element analysed over each cycle of the depth profile. An example of such a plot for a particular cycle is shown in Fig. 7. From these plots, i values were extracted and mass corrected to yield i,,,, values for each element over each cycle of the depth profile.

The corrected intensity versus inverse velocity plots over the entire depth profile exhibited linear plots that yielded i values (and hence the i,,,, values) that deviated by less than 1% (with respect to the mean Ti values). This indicates that the use of the truncated procedure under depth profile analysis works equally well in the construction of inverse velocity plots. Furthermore, as i values can be extracted for each element during each cycle of the depth profile, instrumental variants such as fluctuating primary ion beam current should be reduced. Hence, performing this type of quantitative analysis under depth profile conditions should yield data that are as accurate, if not more accurate, as those obtained under energy distribution conditions.

The mean of the resulting i,,,, data were then plotted against the quoted concentration for each element analysed, as can be seen in Fig. 8. From this plot a clear linear relationship with listed concentrations was noted, i.e. a slope of 1.03 resulted. Error bars represent one standard deviation. Actual concentrations were then ascertained by collecting i,,,, data for all the elements present at above 1 ppt concentration levels and then multiplying the i , , , , / ~ i,,,, fraction of the element of interest by the atomic density of the material. The resulting values, listed in Table 3, were found to agree to within 10% of the quoted values (see Table 1).

Implant materials. The negative secondary ion intensities of B and Si initiated by Cs primary ion bombardment of the "B-implanted Si material resulted in the depth profile illustrated in Fig. 9. A selection of inverse velocity plots calculated from these data are shown in Fig. 10 for the sputter times indicated. Concentration values of "B in Si as a function of depth were then determined by multiplying the icorr(1'B)/ico,,(30Si) fraction by the atomic density of the matrix element. The resulting concentration values for each cycle were then plotted against depth (determined by a Dektak IIA


A l - 27

15 0 10 20 30 1.5

i x mass (x10l2)

1 0 1 1 1012 1013 1014 1015 io16 1.5

i x mass Figure 5. Standardization curves for the elements analysed from: (a) the Ti648 reference material; (b) The Ti649 reference material; (c) the Cu500 reference material.'

profilometer), as represented in Fig. 11 by solid circles. Also plotted in this figure is the concentration profile determined from the "B and 28Si pair (inverted triangles) and that determined by the integration method (hollow circles).

Table 3. Measured concentrations of the analysed elements within the Ti648 reference material

Element Measured values Error

Ti 84.2 wt.% 0.1 wt.% Al 5.09 wt.% 0.03 wt.%t Mo 3.38 wt.% 0.07 wt.% Zr 2.04 wt.% 0.03 wt.% 0 NC" NC"

a NC, not calculated.

The integration method values were determined by multiplying the secondary ion intensity values by a constant termed the RSF:. The RSF in turn was determined by summing all the I lB secondary ion counts (integrating the area under "B implant curve) referenced to the 30Si secondary ion signal and then making this value equal to the quoted dose multiplied by the volume analysed. The surface-enhanced ' B and depleted 30Si secondary ion intensities seen in Fig. 4 were artificially removed during the integration method calculations.

All methods were found to yield typical implant concentration profiles with a "B concentration peaking at a sampling depth of 0.28 pm. This is consistent with the Charles Evans and ,4ssociates specification sheet value of 0.273 pm." The agreement between the infinite velocity peak concentration value (3.8 x 10" atoms ~ m - ~ ) and that determined by RSF measurements

P. A. W. v. d. HEIDE ET AL. 754

I I I 1 107

1 0 300 600 900 1200

Time (s)

Figure 6. Negative secondary ion depth profile of "B, 27AI, 46Ti, 90Zr and ' o o M ~ within the NBS Ti648 reference material (the Deriodic variation in the boron intensity is believed to result from minor segregation).

7 Legend

0 "B (208 s) A 2'AI(217s)

V q i ( 2 2 6 s )

0 @%(236s)

0 'OOMO (245s)

." 0.00 0.25 0.50 0.75 1.00 1.25

l / v (xiO-6s cm-1)

Figure 7. Corrected intensity versus inverse velocity plots for the "B, 27Al, 48Ti, "Zr and looMo secondary ion data relayed in Fig. 6. Times in legend refer to depth profile cycle times (see x-axis in Fig. 6).

1010 ioii 1012 1073 1014 1015 1016

Intercept x mass1

Figure 8. Mass-corrected intercept values versus the quoted concentrations for the Ti648 reference material.

107 Legend

106 "B(50V) . "B(75V) * "B(100 V) ' "B(125V)

"B f150W

105

0 "Sl(1OOV) O "Si (125 V)

3 104 - "SI (I50 V) "Sl (175V) - "SI (200V)

$ 103 P -

102

10

0 1 ~ " " " " ' " ' ' " ' ' ~ " ' ~ ~ 0 500 1000 1500 2000 2500

Time (s)

Figure 9. Negative secondary ion depth profile of ' l B and "Si within the boron implant reference material

e 1012

l o lo 10s I 1Ds

i 07

106

Legend

0 "Si (507s) 0 "Si (609s)

0 llB (498 s) A "B (522s)

V "B(547s) 0 l iB (571 s)

0.0 0 2 0.4 0 6

l/v (x10-6s cm-1)

Figure 10. Corrected intensity versus inverse velocin/ plots for the "B and "Si secondary ion intensity data relayed in Fig. 9. Times in legend refer to depth profile cycle times (see x-axis in Fig. 9).

i 0 lntegrabon method "SI reference

* z8Si reference 1020

0.0 0.2 0.4 0.6 0.8

Depth (mm) Figure 11. Concentration versus depth profiles for the "6 implant reference material. Solid symbols represent the infinite velocity data referenced to the 30Si (circles) or the 28Si (inverted triangles) matrix signal, while hollow symbols represent the integration method data.


(5.2 x lo'* atoms cmP3) is considered to be good. The scatter of the infinite velocity data results from the use of secondary ions emitted at higher emission energies, because these have lower intensities and hence suffer increased statistical scatter. This is especially evident for the data referenced to the 28Si isotope, because analysis of 28Si under electron multiplier conditions resulted in significant reduction in the "B secondary ion intensities.

Following this, analysis of the implant reference materials containing 75As in Si and I9'Au in Si resulted in the concentration profiles illustrated in Fig. 12. As in Fig. 11, the solid symbols represent the concentrations relayed by the infinite velocity method, while the hollow symbols represent the data relayed by the integration method. All peak concentrations and peak concentration depths were found to be consistent with those listed in the specifications sheet.17 The discrepancy in the shapes of the implant distributions seen over the 25-125 nm range is believed to result from the increased concentration gradients present over these regions, 'since

i

Integrationmethod %ireference

0 0 0.1 0.2 0.3 0.4

Depth (rm)

Figure 12. Concentration versus depth profiles for: (a) the "As implant reference material; (b) the 19'Au implant reference material. Solid symbols represent the infinite velocity data referenced to the 30Si matrix signal, while hollow symbols represent the integration method data.

any significant variation in the concentration of the element analysed within a particular depth profile cycle would result in the introduction of errors into the calculated concentration values.

DISCUSSION

The fact that the empirical data (secondary ion intensities corrected for instrument transmission, and sputter yield extrapolated to infinite velocity) could be correlated linearly with the reported concentrations without the use of RSFs for a large number of secondary ions not only provides strong evidence for the validity of the infinite velocity method but also indicates that the matrix effect is removed at the infinite velocity limit. (Note : the secondary ions analysed exhibit sensitivity factors that span up to three orders of magnitude.) This removal of the matrix effect is also supported by several empirical s t ~ d i e s ~ ~ , ~ ~ and theoretical prediction^.'^-'^ For example, a previous in which the negative secondary ion emissions of Zr across a metal/oxide interface were studied as a function of emission velocity revealed that the corresponding matrix effect decreased in an exponential-like manner with increasing emission velocity. Extrapolating this trend to infinite velocity resulted in the complete removal of this matrix effect. Additionally, other have found the matrix effect to decrease with increasing emission energy.

Theoretical models used to describe the secondary ion emission process as resulting from the electronic interaction of the sputtered atom/ion with the s ~ r f a c e ' ~ - ' ~ also predict this removal of the matrix effect at infinite emission velocity. For example, the quantum mechanical arguments derived by Norskov and Lundqvist" for the probability of negative ion for- mation, P - , take the form

2 P - = - exp [.-nC,(@ - A)/hyv cos 01

n

x exp (- nC,/hyv cos 0) (5) where A is the electron affinity of the escaping atom/ ion, @ is the work function of the surface, C , and C , are constants accounting for the variation of the respective atom/ion and substrate electronic levels as the atom/ion moves away from the surface, y is a constant termed the characteristic distance and v is the emission velocity. The predicted removal of the matrix effect can be seen when increasing v in this equation to infinity, because this reduces the influence of all the remaining exponential parameters, to zero. As the matrix effect results from the variation of these parameters, this too will tend to zero. In Eqn. (l), vo represents all the exponential parameters, with the exception of v, present in Eqn. (5 ) and thus yields a similar trend.

The major attraction of this quantification method lies in the fact that all samples displaying conductive surfaces will be quantifiable without recourse to RSFs and no instrumental effects such as site dependence will result; all data are extracted from the same site during the same analysis.

At this stage it is worthwhile discussing the assumptions used in the derivation of the corrected intensity data. These assumptions were that the Sigmund-

756 P. A. W. v. d. HElDE ET AL.

Thompson relation correctly models the secondary neutral populations, that the emission velocity can be defined on a macroscopic rather than a microscopic (atomic) level, that the final results remain relatively insensitive to the energy value used (average or weighted over the energy window employed in the data collection procedure) and that the electron multiplier sensitivity to mass follows the l/(mass)'.5 trend for all the elements analysed.

The question surrounding the Sigmund-Thompson relation is probably the most important because all the data are divided by this expression in Eqn. (2). This expression [Eqn. (4)] was derived from extensive empirical analyses of the secondary neutral populations from amorphous elemental matrices,' 1-25 and in addition has been fitted to the secondary neutral emissions from a number of alloy and oxide surface^.^^,'^^^^ Th e majority of these empirical studies, however, were limited to secondary neutral emission energies of < 100 eV. Thus, the question of whether the E-' trend predicted by Eqn. (4) continues to higher emission energies (up to 250 eV) arises. Deviations from the Sigmund- Thompson relation from surface crystallinity effects34 and off-normal primary ion impact angles23925 have also been reported.

Computer simulations of the sputtering event indicate that the E-' trend does extend to higher emission ener- g i e ~ , ~ ~ . ~ ' i.e. those studied in this work. They also indicate that the cos 8 function changes to a cos O2 function with increasing emission energy. Replacing the cos 8 function with a COS' .~ 8 or cos' 8 function in Eqn. (4), however, only resulted in a slight variation of the intercept data,' i.e. < 5%. This, and the observation that the intercept data varied by <2.5% on altering the value of E , over a 5 eV energy range (and 10 eV in a previous study3'), implies that the intercept is relatively insensitive to such variations.

On studying the transmission function characteristics of the Cameca IMS-3f to -5f series of instrument^,^^ it can be seen that this relative insensitivity results from the strong energy and angular filtering imposed by the contrast aperture. For example, the acceptance solid cone of the instrument for 100 eV secondary ions is limited to less than 15" from the sample normal. Divid- ing the resulting intensities by a cos 8 or cos2 6, function therefore only results in a deviation of 4-7% from unity, respectively. As this deviation decreases with increasing secondary ion emission energy, the final i values will deviate by a smaller amount. Likewise, the effect of E , on the final result becomes less significant with increasing secondary ion energy, as can be seen in Eqn. (4).

To reduce the possible deviations from the Sigmund- Thompson relation for off-normal primary idn impact angles, a 10 keV Cs' primary ion beam was used; such a beam will be deflected toward the sample normal by the 4.5 keV extraction field, i.e. the impact angle is reduced from 30" to 2O.2".' This secondary ion extraction field also acts to reduce any angular deviations of the secondary beam, i.e. deflects the secondary ion beam toward the sample normal. Surface crystallinity effects are expected to be minimized in Cameca-type instruments by the high extraction field, because this will smear out any angular effects that may be present. Additionally, it has been shown that primary ions of greater mass yield secondary neutral populations that

adhere more closely to the Sigmund-Thompson relation than lower mass primary ions.25

The question of whether the emission velocity can be referenced to a macroscopic surface rather than the microscopic (atomic) surface is important because the electron transfer leading to the ionizationfneutralization of the escaping atom/ion occurs over microscopic dis- tances (< 1 nm). From a practical perspective a macroscopic definition was used, because the high primary ion current density used would continually alter the microscopic surface topography in an unknown fashion. The fact that at least 100 secondary ions are counted per second per data point does, however, have an averaging effect on the range of possible microscopic angles. Thus, the summed average would approach that of the macroscopic value used.

Next, should a centred or weighted value be used for the energy of the secondary ions when using relatively large-energy windows (40 eV). This is difficult to ascertain at present because Eqn. (2) is not in integral form: a form that is required if the secondary ion intensities are to be integrated over a relatively large-energy span, as is done in the data collection procedure. However, if the energy dependences of T(E) and S(E, 8) in Eqn. (2) are assumed to be E-' and E-', respectively, then the error introduced by using an E 3 multiplication factor, with E defined as being at the centre of the energy window rather than an energy of velocity-averaged value, was found to be of the order of 1-1.5 times the energy window width divided by twice the emission energy, all squared. For emission energy and energy window width values of 100 and 40 eV, respectively, the resulting variation in the final values amounted to <4-6%. Fur- thermore, as data for all elements will vary in a system- atic manner, the degree of error resulting from the definition of the secondary ion emission energy is expected to be even smaller.

The observation that a l / (ma~s) ' .~ function could be fitted through the data points of the elements analysed in Fig. 2 (which includes most of the elements used in testing the validity of the infinite velocity method) sup- ports the assumption that such a function holds for all negative monoatomic secondary ions. Further work, however, is required and is presently being undertaken to prove this assumption and to determine whether any variations with time and/or operating conditions occur. For this reason this mass factor was not included in Eqn. (2), rather it was considered as a separate 'instrument calibration factor'.

Finally, the clear linear correlations between the empirically derived data and the reported concentration values from several differing ion-substrate systems in this and in previous also support the validity of these assumptions. The further work presently being carried out on the influence of these assumptions should, therefore, result in an improved understanding and refinement of this new quantification method.

CONCLUSION

In this work, the validity of the infinite velocity method for quantifying SIMS results was demonstrated for the negative secondary ion emissions emanating from five Ti-based reference materials and one Cu-based refer-


ence material. This was done by showing that the data extracted from the infinite velocity limit for a particular element correlated linearly with listed concentrations and also by showing that these data are not affected by the problems associated with the matrix effect. This point was illustrated by constructing linear standardization curves out of data relayed by the negative secondary ions from a number of different elements present within a particular reference material, and without the use of sensitivity factors.

The practicality of this method was then illustrated by analysing, in a depth profile manner, three Si-based implant materials. The resulting concentration-depth profiles compared well with profiles calculated by the

more traditional integration method. Thus, combining these results with the fact that the negative secondary ions analysed yielded. trends consistent with theory (secondary ion emission resulting from the non- adiabatic transfer of electrons through the surface region), it is predicted that all monatomic negative secondary ions resulting from such a process should be quantifiable by this method.

Acknowledgement

The authors wish to thank Peer Zalm for useful discussions regarding the error analysis of this procedure.

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