Quantitative trace metal analysis of silicon surfaces by ToF-SIMS

SURFACE AND INTERFACE ANALYSISSurf. Interface Anal. 26, 984È994 (1998)

Quantitative Trace Metal Analysis of SiliconSurfaces by ToF-SIMS

M. A. Douglas* and P. J. ChenMaterials Characterization, Kilby Analysis Laboratory, Texas Instruments, Inc., PO Box 650311, MS 3704, Dallas, TX 75265,USA

Volumetric relative sensitivity factors (RSFs) are determined for 52Cr, 56Fe and 58Ni in an siliconO2‘-formed

oxide using a 12 keV Ga‘ primary ion beam, and the inÑuence of matrix oxygen content on these RSF values isevaluated. A multivariate expression for RSF values as a function of oxygen content is developed.Si

2‘-referenced

This expression indicates that 12 keV Ga‘ ion beam RSF values for 52Cr, 56Fe and 58Ni in oxide atO2‘-formed

1.0 nm depth are in excellent agreement with well-established 8 keV RSF values in a silicon matrix. BecauseO2‘

calculated RSF values for oxide at 1.0 nm depth and native silicon oxide are almost equivalent,O2‘-formed

time-of-Ñight (ToF) SIMS metal RSF values and detection limits in native oxide for a Ga‘ liquid metal ion sourceare predicted, using the well-established 8 keV RSF values for metals in a silicon matrix. Time-of-ÑightO

2‘

SIMS silicon surface detection limits of 5 Â 106 to 5 Â 108 atoms cm—2 0.5 nm are predicted for most metals=

of interest to the semiconductor community. 1998 John Wiley & Sons, Ltd.(

KEYWORDS: ToF-SIMS; SIMS; metal ; contamination ; Si

INTRODUCTION

The deleterious inÑuence of metallic contamination attrace surface concentrations on complementary metal-oxide semiconductors (CMOS) and bipolar integratedcircuit performance, yield and reliability is well-established.1h12 Surface concentration levels at whichmetal contamination is of concern decrease with eachnew generation of integration density. Recent forecastsindicate that the 180 nm technology node requires ana-lytical methods with detection limits \5 ] 108 atomscm~2 for Na, Fe, Ni and Cu.13 Similar detection limitsare required for metals associated with alternative,high-k capacitor dielectrics and fer-(BaSrTiO3 , Ta2O5)roelectric materials under(PbZrTiO3 , SrBiTaO3)evaluation for use in non-volatile memory components.Unfortunately, analytical techniques currently used todetect trace concentrations of metals on a substratesurface exhibit serious deÐciencies at the 180 nm tech-nology node.

For about 10 years, total reÑection x-ray Ñuorescence(TRXRF) spectroscopy has been used by the semicon-ductor community to characterize trace concentrationsof metals on highly-polished, featureless, silicon sub-strate surfaces.14 However, TRXRF exhibits several sig-niÐcant deÐciencies at the 180 nm technology node :(1) Li, Be, Na, Mg and Al metals cannot be detected ;(2) experimental detection limits for 3d transition

metals range between 5] 1010 and 5 ] 1011 atomscm~2 using a W anode ;

* Correspondence to : M. A. Douglas, Texas Instruments, Inc., POBox 650311, MS 3704, Dallas, TX 75265, USA.

(3) the best experimental detection limits for 4d and 5dtransition metals are D1 ] 1011 atoms cm~2 usinga Mo anode.

In addition to these detecton limit deÐciencies, theTRXRF sampling depth, corresponding to the arealdensity concentration value (in units of atoms cm~2), isnot deÐned for each assay and exhibits large variationsfrom 10 nm to over 100 nm,14 causing substantial metalareal density concentration variations and inaccuraciesif metallic contamination is not conÐned to the samplesurface (\5 nm). A well-deÐned sampling depth mustbe reported with any surface areal density concentrationvalue for complete and accurate characterization of asurface metal concentration that can be meaningfullycompared to other metal concentration measurements.But an experimental TRXRF sampling depth cannot bereported for each assay because sampling depth valuescannot be determined experimentally. Moreover,current and next-generation technology nodes requireanalytical methods capable of examining small spatialregimes of \100 ] 100 lm2] 1 nm in size, with preciseand accurate, lateral and depth spatial deÐnition of theanalytically sampled region and the position of analysis,to interrogate speciÐc spatial regimes in test structureson processed wafers at speciÐc points in the processÑow, while still achieving the above-speciÐed metaldetection sensitivities. Total reÑection XRF acquiresdata from a 1 cm2 surface region with ambiguous deÐ-nition of a large analytical sampling depth exceeding 10nm. Finally, trace metal analysis of non-silicon sub-strates is required by current and next-generation tech-nology nodes, but TRXRF trace metal analysis hasbeen conÐned to silicon substrates. Hence, TRXRFcannot adequately satisfy analytical requirements posedby the 180 nm technology node, due to insufficient

CCC 0142È2421/98/130984È11 $17.50 Received 27 April 1998( 1998 John Wiley & Sons, Ltd. Revised 14 July 1998

Accepted 30 July 1998

METAL CONTAMINATION OF Si SURFACES 985

metal sensitivities, large ([10 nm) and ill-deÐned ana-lytical sampling depths, inability to interrogate smalltest structures on patterned wafers and limitation tointerrogation of only silicon substrates.

Several analytical methodologies are under exami-nation in an e†ort to address TRXRF analytical deÐ-ciencies. Heavy ion backscattering spectroscopy (HIBS)o†ers 5 ] 108 atoms cm~2 detection limits for 4d and5d transition metals with standardless quantiÐcation ;however, detection limits for elements with Z\ 30 (Zn)are [5 ] 1010 atoms cm~2.14 Moreover, element peaksoverlap (e.g. Br overlaps Sr and Ru) and sampling depthresolution and deÐnition are sacriÐced to achieve highmetal sensitivity. Vapor phase decompositionÈdropletcollection (VPDÈDC) is a concentration technique thatessentially increases the analysis volume by the productof the wafer area and the surface oxide thickness toincrease metal detection limits. This is accomplished bydissolving the surface oxides with HF vapor, followedby scanning a metal collection droplet over the entirewafer surface. The droplet is then analyzed for metalcontent by Inductively Coupled Plasma-Mass Spec-trometry (ICP-MS) or Graphite Furnace AtomicAbsorption (GFAA). However, metal at the oxide/silicon interface or below is not collected, and metalcollection efficiencies vary14 and can be small for ele-ments with redox potentials of less than zero (Cu, Pt,Au, Ag, . . .). This concentration technique can also inad-vertently concentrate spurious contamination, such asparticulate matter, and spatially-selective analysis of alarge area for wafer mapping, or of a small feature in atest structure, is not possible.

Time-of-Ñight secondary ion mass spectrometry(ToF-SIMS) has the potential to satisfy most of the ana-lytical challenges posed by 180 nm and smaller inte-grated density technology nodes for accurate,quantitative surface analysis of metals at trace concen-trations. Typically, ToF-SIMS is used to characterizequalitatively the organic molecular contamination onsilicon substrates exposed to semiconductor processingand storage ambients.15h20 Ultrasensitive character-ization of organic contamination on semiconductor sur-faces is of keen interest, owing to the broad scope ofdetrimental e†ects that organic contamination has ondevice yield and performance.21 Previous studies22,23indicate that ToF-SIMS achieves 3d transition metaldetection limits of \5 ] 108 atoms cm~2 in a siliconoxide matrix, using a Cs primary ion beam, for a well-deÐned sampling area of \100 ] 100 lm2 and a well-deÐned, ultrashallow sampling depth of 2È3 nm.However, accurate, quantitative trace metal analysis byToF-SIMS cannot be performed because volumetricrelative sensitivity factors (RSFs) for metals in a siliconoxide matrix, using a Ga primary ion beam, are notknown. Moreover, the e†ect of oxygen content withinvarious types of silicon oxide matrices on RSF values isnot understood.

This studyÏs objective is to evaluate accurate, volu-metric relative sensitivity factor (RSF) values for select3d transition metals in a silicon oxide matrix using a Gaprimary ion beam and to evaluate the e†ect of oxygencontent in silicon oxide matrices on these RSF values.Volumetric RSF values are determined by measuringmetal ion and reference ion peak intensities with ToF-SIMS in craters generated at several depths in a metal-

implanted silicon standard by an ion source, usingO2`dynamic SIMS to evaluate an accurate metal impurityconcentration at each crater depth. The e†ect of siliconoxideÏs oxygen content on the RSF value can be exam-ined by measuring metal ion and reference ion peakintensities with ToF-SIMS at various depths within theD10È12 nm thick oxygen-rich surface layer created atthe bottom of each crater by bombardment,24O2`assuming that each craterÏs measured metal impuritydensity does not change signiÐcantly through thisoxygen-rich surface oxide layer.

EXPERIMENTAL

The standard used for this study was prepared byimplanting isotopically-selected 52Cr, 56Fe and 58Niions at energies of 100, 70 and 40 keV, respectively, intoa Czochralski p-type silicon (by IICO Corp., SantaClara, CA), all with a nominal ion Ñuence of 5] 1013cm~2. A 7¡ o†-normal angle was adopted during theimplant to minimize ion channeling e†ects. The accu-racy of the quoted ion Ñuence is typical (10%) of thoseo†ered by modern medium-current ion implant instru-ments.

All metal concentration measurements and sputtercrater generation into the silicon metal-implanted stan-dard were conducted with a Cameca IMS-6f magneticsector dynamic SIMS instrument using a 12.5 keV O2`beam and a sample bias of ]4500 V. These instrumentconditions result in an net impact energy of 8 keVO2`and D39¡ angle of incidence from the sample normal.The following instrument parameter values wereemployed while determining metal concentrations andgenerating sputter craters : 100È120 nA; 500 ] 500 lm2raster size ; 60 lm diameter analysis region ; and massresolving power (M/*M) D3500 (90È10% deÐnition).

The impurity concentration values for 52Cr, 56Fe and58Ni at the 12 nm thick oxygen-rich surface of eachcrater bottom were determined by : evaluating experi-mental RSF values for each metal in the metal-implanted silicon standard by dynamic SIMS with an

ion beam, using each metalÏs ion implant ÑuenceO2`value (atoms cm~2) ;25 measuring the ratio valueIr/Imat each crater depth for each metal ; and applying theexperimental RSF values to calculate metal impurityconcentration values (atoms cm~3), according to thefollowing relationship25

MRSFm(i)[Ii Am/Im]\ ci (1)

where M denotes the matrix, RSF denotes the elementalrelative sensitivity factor, m denotes the referencematrix ion corresponding to matrix M, i denotes theimpurity metal ion, I denotes the integrated ion peakintensity (counts), denotes the fractional isotopeAmabundance of the matrix ion m and denotes the impu-cirity metal concentration (atoms cm~3).

For each sputter crater, all ion inten-O2`-generatedsity data at all depths within the 12 nm thick oxidelayer at the crater bottom are collected using a PhysicalElectronics (PHI) TRIFT I ToF-SIMS instrumentequipped with an FEI Ga liquid metal ion source(LMIS). During ion acquisition, the instrument wasoperated under the following conditions : 2 nA Gaprimary ion beam current ; 15 kV primary ion beam

( 1998 John Wiley & Sons, Ltd. Surf. Interface Anal. 26, 984È994 (1998)

986 M. A. DOUGLAS AND P. J. CHEN

potential (12 keV Ga` impact energy) ; 3 kV samplepotential ; 25 kHz primary ion beam pulse rate ; 12 nsion beam pulse width, compressed to a 0.7 ns pulsewidth ; 40] 40 lm2 raster ; D35¡ angle of incidencewith respect to sample normal. Sputtering within the 12nm thick oxygen-rich surface layer at the bottom ofeach crater, created by the ion source, was per-O2`formed with the Ga LMIS using a 160 ] 160 lm2 rasterand a continuous 2 nA ion beam current. All secondaryion acquisitions were performed with the 40 ] 40 lm2raster concentrically nested within the 160] 160 lm2Ga` sputter crater. A 6 s continuous 2 nA presputter,removing the equivalent of 0.25 nm of thermal oxide,was performed prior to every surface analysis to reduceorganic contamination.

The RSF values, at various depths (and at corre-spondingly various silicon oxide oxygen concentrations)within the 12 nm thick oxygen-rich layer at the bottomof each crater, were calculated using theO2`-generatedrelationship

MRSFm(i)\ [Im/Ii]ci (2)

working under the assumption that the measured metalimpurity density within each craterci O2`-generateddoes not signiÐcantly change throughout the oxygen-rich surface layer. The oxygen content of this oxidelayer is less than that of and decreases withSiO2increasing depth if the beam does not exhibitO2`normal incidence with respect to the silicon surface.24Further oxygen depletion of the surface silicon oxidewith sputter depth is caused by preferential sputteringof oxygen relative to silicon by Ga` bombardment.Both 30Si` and are used in this study as referenceSi2`matrix ions, m, to highlight di†erent ion yield trends.

RESULTS AND DISCUSSION

Concentration non-uniformity can be caused by chemi-cal potential-driven segregation and electric Ðeld-drivendi†usion. For the metalÈmatrix combinations examinedin this study, the magnitude of these e†ects is negligible.The beam oxide is formed in the absence of anO2`oxygen background pressure and the beam angle is inexcess of 30¡ with respect to the wafer normal, loweringthe oxygen surface content and hence the chemicalpotential for impurity segregation.25 Charge-induceddi†usion is not signiÐcant for transition metals in asilicon matrix.

Relative sensitivity factor trends referenced to matrixatomic ion

Table 1 details 52Cr, 56Fe and 58Ni metal concentra-tions and crater depths, corresponding to two craterswithin the metal-implanted silicon standard, created bythe Cameca IMS-6f ion beam.O2`Figures 1 and 2 illustrate RSF(i) values for 52Cr, 56Feand 58Ni as a function of depth (silicon oxide oxygenconcentration) through the 12 nm thick oxygen-richlayer, corresponding to craters 1 and 2, respectively, ref-erenced to 30Si` matrix ion. Because the 12 nm siliconoxide layer at the crater bottom is formed by an O2`

Table 1. Metal atom density at twodepths in metal-implantedsilicon standard, measuredby 8 keV dynamicO

2‘

SIMS

Concentration Depth

Crater Metal (atoms cmÉ3) (nm)

1 Cr 3.5 Ã1018 61

1 Fe 6.5 Ã1018 61

1 Ni 5.3 Ã1018 61

2 Cr 2.1 Ã1018 38

2 Fe 5.5 Ã1018 38

2 Ni 9.3 Ã1018 38

beam, the oxygen content in the 12 nm layer decreaseswith depth.24 The oxygen concentration in Czochralskisilicon is D20 ppma and is negligible compared to theoxygen concentration contributed to bombard-O2`ment in the top 12 nm. The RSF(i) trends are quite dif-ferent among the three metals. In Fig. 2, 52Cr and 56Fe

Figure 1. Log RSF(i) vs . depth into silicon oxideO2

½-formedlayer at the bottom of crater 1, where i ¼52Cr, 56Fe and 58Ni.Matrix reference ion is 30Si½.


½-formedlayer at the bottom of crater 2, where i ¼52Cr, 56Fe and 58Ni.Matrix reference ion is 30Si½.

Surf. Interface Anal. 26, 984È994 (1998) ( 1998 John Wiley & Sons, Ltd.


RSF values decrease by D50% and D20% between 1nm and 6 nm, respectively, whereas 58Ni RSF valuesincrease by D20% between the same depths. Thus, theslopes of the 52Cr and 56Fe RSF trends decrease withdecreasing oxygenation of the matrix whereas the slopeof the 58Ni RSF trend increases with decreasing oxy-genation of the matrix, as estimated between the 1 nmand 6 nm depth range. A negative slope typically indi-cates higher sensitivity to the metal impurity for lowerlevels of oxygen, contrary to the yield-enhancing e†ectof oxygen. This trend indicates that the Si` yield ismore sensitive to oxygen content compared to 52Cr and56Fe ion yields, i.e. the decrease in matrix 30Si ion inten-sity is greater than the decrease in 52Cr and 58Fe ionintensities for equivalently decreasing oxygen content inthe silicon oxide matrix. On the other hand, thedecrease in matrix 30Si ion intensity is less than thedecrease in 58Ni ion intensity for equivalently decreas-ing oxygen content in the silicon oxide matrix, resultingin the observed positive RSF(58Ni) trend line slope.

Both 52Cr and 56Fe RSF(i) trends also exhibit S-shaped curvature, where RSF(i) values increase betweenthe surface and 1.0 nm, decline between 1.0 nm and 8.0nm and then slightly increase between 10 nm and 12nm. In contrast, the 58Ni RSF(i) trend does not exhibita strong increase between the surface and 1.0 nm and islinear between 6 and 12 nm. Approximately 40% and30% increases in RSF(i) values are observed for 52Crand 56Fe between the oxide surface and 1 nm, respec-tively. Using a sputter etch to remove the equivalent of0.25 nm of silicon oxide prior to the surface analysisensured that the e†ect of organic surface coverage isessentially eliminated. On face value, a lower RSF valuefor these metals at the oxide layerÏs surface suggests thatthe uppermost monolayer oxygen content is signiÐ-cantly greater compared to the next, underlying layer,discounting the e†ect of physical sputtering. However,the confounding e†ect of competing matrix ion andimpurity ion yields on the RSF value precludes a con-Ðdent interpretation.

Referencing the integrated metal ion peak intensityvalue to the integrated 30Si` matrix ion peak intensityvalue extracts the e†ect of instrument variations on themeasurements among all assays and diminishes thee†ect of oxygen concentration variation (matrix e†ect)on metal ion yield, because 30Si` yield from a siliconsubstrate is also inÑuenced by variation in oxygencontent. However, di†erences in the relative yields of the30Si` matrix ion and metal impurity ions as a functionof silicon oxide oxygen content give rise to unusualRSF(i) trends, preventing a clear understanding of thee†ect of oxygen content in silicon oxide on only theimpurity ion yield. Novak and Wilson26 observe thatthe relative sensitivity factors (RSFs) of elements withionization potentials similar to that of the matrix refer-ence ion do not change signiÐcantly with oxygencontent because their respective yield enhancements arecomparable to the matrix ion. By measuring variationsin relative sensitivity factor rather than ion yield,changes in metal ion yield relative to the matrix ion aremonitored. Hence, when measuring RSF trends, alter-native matrix ions that are insensitive to silicon oxideÏsvariable oxygen content must be considered in order tounderstand the direct relationship between the metalion yield and oxygen content in silicon oxide.

Relative sensitivity factor trends referenced to matrixmolecular dimer ion

Proton transfer and cationization both play dominateroles in the production of secondary positively-chargedmolecular fragment ions from parent organic precursorson a substrate. Cationization of neutral organic molecu-lar fragments by Ag` is a particularly efficient process.Metal oxide surfaces favor the production of negativesecondary metal oxide molecular ions, owingMemO

n~,

to their large electron affinities, and Me` production issharply increased (by several orders of magnitude) in itsoxide due to matrix proximity and chemical bonding tohighly electronegative oxygen, as inferred by high O~secondary anion production. Because inorganicMe

mO

nmolecular fragments favor secondary ion emission fromthe surface as anions, and Me` production is profoundfrom a metal oxide surface, it is not unreasonable tospeculate that a signiÐcant contribution to Me

mO

ncation production from a metal oxide surface is by Me`cationization of neutral atoms and molecules. The Me`cationization would be particularly prevalent when theMe` peak intensity dominates the positive secondaryion mass spectrum, as observed in the mass spectrum ofsilicon oxide, where the Si` peak intensity is at leasttwo orders of magnitude more intense than all molecu-lar ion peaks. Accordingly, the concentration of speciesX in a silicon oxide matrix, MXN, is proportional to SiX`molecular ion intensity. If X corresponds to Si, thenMSiN in silicon oxide is proportional to whichI(Si2`),should be insensitive to variation in matrix oxygencontent. The dependencies of and I(30Si`) as aI(Si2`)function of oxygen content are compared in Fig. 3.I(30Si`) decreases by nearly 70-fold between the oxidesurface and 10 nm depth ; in contrast, is aboutI(Si2`)the same at the surface compared to the 10 nm depth,but the maximum intensity value, observed at D2.0 nm,is about four-fold higher than the surface intensity.Thus, variation with oxygen content is over anI(Si2`)order of magnitude less than I(30Si`) variation. Thisdiminished sensitivity to oxygen content cor-I(Si2`)roborates postulated reaction kinetics and indicates thatimpurity ion intensities referenced to matrix ionSi2`will largely and directly reÑect impurity ion yield ten-dencies.

Figure 3. The I(M½)/minÍI(M½)Ë ratio vs . depth into O2

½-formedsilicon oxide layer at the bottom of crater 1, where M½ ¼30Si½ andSi

2½.



The dependence of 52Cr, 56Fe and 58Ni RSF(i)values, referenced to matrix ion, on depth into theSi2`12 nm oxide layer (silicon oxide oxygen concentration)is illustrated in Figs 4 and 5, corresponding to craters 1and 2, respectively. Because is fairly insensitive toSi2òxygen content, matrix-induced ion yield variations arenot cancelled by the matrix reference ion, and theRSF(i) trends directly reÑect ion yield trends for eachmetal impurity. As a result, larger variation in RSF(i)values as a function of oxygen content is observed com-pared to referencing the RSF to 30Si`. For instance, inFig. 2, RSF(58Ni) increases by only 20% between 1.0and 6.0 nm, whereas in Fig. 5, RSF(58Ni) increases bynearly 400% over the same depth range. Qualitatively,52Cr, 56Fe and 58Ni RSF(i) values referenced to Si2èxhibit very similar trends compared to quite dissimilartrends for corresponding RSF(i) values referenced to30Si`. All three metal log RSF(i) trend lines are fairlylinear between 1.0 and 12.0 nm and exhibit similar posi-tive slopes, indicating that these metal ion yieldsdecrease with decreasing oxygen content in the 12 nmoxide layer. In Figs 4 and 5, 52Cr, 56Fe and 58Ni exhibitlower RSF values at the oxide layer surface comparedwith their respective 0.5 nm depths : approximately


½-formedlayer at the bottom of crater 1, where i ¼52Cr, 56Fe and 58Ni.Matrix reference ion is Si

2½.


½-formedlayer at the bottom of crater 2, where i ¼52Cr, 56Fe and 58Ni.Matrix reference ion is Si

2½.

60%, 60% and 50% reductions, respectively. As metalimpurity ion yields are directly revealed by using Si2às the reference matrix ion, this trend suggests that theoxygen content in the uppermost monolayer is signiÐ-cantly higher compared to immediately underlyinglayers. This surface yield enhancement might be relatedto atmospheric oxidation of the surface of the O2`-

oxide or, perhaps, preferential sputtering offormedoxygen with respect to silicon by Ga` bombardment ofa silicon oxide matrix, coming to a rapid equilibrium inD0.5 nm. Compared with 30Si` matrix referenceSi2`,ion efficiently reduces the e†ect of large changes inoxygen content in the silicon oxide matrix on RSF(i)values and, in most instances, should be used as thematrix reference ion to measure metal impurity concen-tration. However, the reference matrix ion is pre-Si2`ferred when establishing a direct relationship betweenmetal ion yield and variations in matrix oxygen content.

Matrix RSF expression with weak metal dependency

Because the 52Cr, 56Fe and 58Ni log RSF(i) slopes arenearly parallel in Figs 4 and 5, di†ering by upward ordownward shifts, it is reasonable to conceive a matrixfactor with weak metal dependency whose value is adirect measurement of the local oxygen content ofsilicon oxide. This matrix factor can be applied to con-stant metal impurity RSF(i) values to reduce error inpredicting RSF(i) values, speciÐc to local matrix oxygencontent, using speciÐc matrix ion intensities directlyfrom the spectrum of the unknown, thereby enhancingthe accuracy of metal concentration measurements.McHugh27 and Ganjei28 developed empirical expres-sions for matrix adjustment factors for metal substratesinterrogated by primary ions, to achieve accuraciesO2òf the order of 10% relative error, using various matrixion ratios. However, a unique matrix adjustment factorexpression is required for each metal.27 By evaluatingthe direct e†ect of oxygen content on only the impuritymetal ion yield, without the confounding e†ect of com-petition between metal impurity and matrix referenceion yields, a matrix factor expression with weak metaldependency is formulated

MstdRSFm(i)M1MF\ M1RSFm(i) (3)

where Mstd denotes a standard matrix condition towhich the RSF(i) values are referenced, M1 denotes amodiÐed matrix condition corresponding to matriceswith various oxygen concentrations and MF denotes amatrix factor that varies with silicon oxideÏs oxygencontent. This MF can be applied to a set of MstdRSFm(i)values to calculate, according to Eqn (3), a correspond-ing, modiÐed set of M1RSFm(i) values speciÐc to theoxygen content associated with matrix condition M1.

The MF is a function of speciÐc matrix ion intensitiesthat vary with oxygen content. The I(SiO`)/I(Si2`)ratio should monitor oxygen content in silicon oxideand be insensitive to Si` yield variations. To attend tovery low matrix oxygen concentrations, the

matrix ion ratio is selected because theI(Si2`)/I(Si`)Si` yield dramatically decreases with decreasing oxygencontent at the oxide/silicon interface. The dependenciesof and ratios on oxygenI(SiO`)/I(Si2`) I(Si2`)/I(Si`)content are illustrated in Fig. 6. Indeed, the



and matrix ion ratiosFigure 6. I(SiO½)/I(Si2

½) I(Si2

½)/I(30Si½)vs . depth into silicon oxide layer at the bottom ofO

2½-formed

crater 1.

matrix ratio is a strong function ofI(SiO`)/I(Si2`)oxygen content, declining the most between the surfaceand 0.5 nm. An inÑection in the ratioI(Si2`)/I(Si`)trend line is observed at 6.0 nm, caused by a largedecline in Si` yield with decreasing oxygen content,indicating that this ratio is very sensitive to very lowoxygen content.

Because the logarithm of the measured relative sensi-tivity factors is linear with depth and hence oxygencontent, the following expressions for M1RSFm(i) can begenerated

ln(M1RSFm(i))\ a ] b[I(SiO`)/I(Si2`)]

] c[I(Si2`)/I(Si`)] (4)

Using Eqn (3), an expression for M1MF can be gener-ated that is weakly dependent upon the impurity metalion

ln(M1MF)\ [a [ ln(MstdRSFm(i))]] b[I(SiO`)/I(Si2`)]

] c[I(Si2`)/I(Si`)] (5)

ln(M1MF)\ a@] b[I(SiO`)/I(Si2`)]] c[I(Si2`)/I(Si`)]

(6)

provided that a “standardÏ oxygen content is selected toevaluate MstdRSFm(i) for all three metals. The ion inten-sity ratios observed at the surface of a thermal oxidesputtered by a Ga ion beam to a depth of 5 nm is selec-ted as the “standardÏ oxide condition for this study. Dueto preferential sputtering of oxygen over silicon from asilicon oxide matrix by Ga` bombardment, the surfaceoxygen content of thermal oxide decreases with increas-ing sputter depth. The oxygen content in thermal oxideat a 5 nm sputter depth is similar to the oxygen content

of oxide formed by bombardment of silicon, asO2`characterized by similar matrix ion ratios.(SiO`)/(Si2`)Coefficients a, b and c for each metal impurity (52Cr,

56Fe and 58Ni) were evaluated by partial latent struc-ture (PLS) multivariate regression,29 using experimentalvalues for and RSF(i)(SiO`)/(Si2`), (Si2`)/(Si`)acquired from both craters. The regression coefficientsand MstdRSFm(i) values for 52Cr, 56Fe and 58Ni andstandard oxide and ratios are(SiO`)/(Si2`) (Si2`)/(Si`)presented in Table 2 and 3. The b coefficients for 52Cr,56Fe and 58Ni are fairly similar in magnitude, which isconsistent with the parallel trend line slopes observed inlogarithmic plots of RSF(i) vs. crater depth in Figs 4and 5. These similar slope values ([0.26, [0.30 and[0.34) numerically corroborate the qualitative notionof a matrix factor that exhibits weak metal dependency,as discussed above. The negative sign of coefficient bhas the e†ect of reducing the RSF value for higheroxygen content in the silicon oxide, which is consistentwith observing higher ion yields at higher levels ofoxygen. As coefficient c is positive, the correspondingterm increases the RSF value for higher silicon contentin the silicon oxide ; however, the relative fractional per-centage contribution of the term in theb(SiO`)/(Si2`)expression is 80% at 2.0 nm, and the magnitudes of thetwo terms are equal at D4.5 nm into the oxide formedby O2`.

The MstdRSFm(i) values were determined for eachmetal using the metal-speciÐc regression coefficients andthe “standardÏ oxide ion ratios tabulated in Table 3.These MstdRSFm(i) values are then used to generate aseries of M1MF values, corresponding to each sputterdepth within the two craters, using Eqn (3). Values forthe coefficients in Eqn (6) were determined and aretabulated in Table 2. The sign of each coefficient is iden-tical to the sign of the metal-speciÐc regression coeffi-cients ; the magnitudes of these coefficients are also

Table 2. Regression coefficients for 52Cr, 56Feand 58Ni RSF values and for matrixfactor (MF) values, using the generalexpression : In (RSF or MF) = a+ b [ (SiO‘)/(Si

2‘) ] + c [ (Si

2‘)/(Si‘) ]

Regression coefficients

Metal a b c

Cr 45.6 É0.26 0.33

Fe 47.0 É0.30 0.59

Ni 47.9 É0.34 0.81

MF 1.42 É0.28 0.62

Table 3. Matrix ion ratios and matrix factor (MF) values for varioustypes of silicon oxide ratiosa

Type of oxide Depth (nm) I(SiO½)/I(Si2

½) I(Si2

½)/I(30Si½) Si2

½MF

Native oxide Surface 3.0 0.11 1.9

O2

½ Beam oxide Surface 7.5 0.06 0.5

O2

½ Beam oxide 0.5 4.2 0.10 1.4

O2

½ Beam oxide 1.0 3.2 0.12 1.8

O2

½ Beam oxide 1.5 2.4 0.19 2.4

Thermal oxide 5.0 5.2 0.12 1.0



quite similar to those coefficients obtained for themetal-speciÐc regressions.

The dependency of the M1MF value on the oxygencontent, which declines with depth into the surfacesilicon oxide of crater 1, is illustrated in Fig. 7. TwoinÑection points are observed at D2.0 nm and D6.0nm. From the above discussion, the term(SiO`)/(Si2`)dominates ([0.8 fractional contribution) the MFexpression between the surface and 2.0 nm, so the 2.0nm inÑection corresponds to increasing contributionfrom the term. At depths of [6.0 nm, the(Si2`)/(Si`)

dominates the MF expression. Because the(Si2`)/(Si`)term does not cancel the strong sensitivity(Si2`)/(Si`)

to the 30Si` yield to oxygen content, greater error isexpected as this termÏs contribution to the expressionincreases in magnitude.

Percentage deviation between experimental and cal-culated element RSF values for all three metals as afunction of depth is illustrated in Fig. 8. The percentagedeviation signiÐcantly increases at depths of [6 nm,consistent with the greater contribution of the

term. The average percentage deviations(Si2`)/Si`)between depths of 0È5 nm and 6È12 nm are D15% andD50%, respectively. The MF is most e†ective in theoxygen-rich regime between 0 and 6 nm, where the

term dominates or is a signiÐcant com-(SiO`)/(Si2`)ponent of the MF expression.

Figure 7. Matrix factor (MF) vs. depth into siliconO2

½-formedoxide layer at the bottom of crater 1.

Figure 8. Percentage relative deviation between experimentalRSF(i) values and calculated RSF(i) values (using multivariateregression) vs. depth into silicon oxide layer at theO

2½-formed

bottom of crater 1, where i ¼52Cr, 56Fe and 58Ni.

Matrix factors for several types of silicon oxide havebeen determined and are tabulated in Table 3. Thesurface of an oxide is oxygen-rich compared to theO2`thermal oxide standard at a 5.0 nm sputter depthbecause oxygen is preferentially sputtered, giving rise tolower oxygen content at deeper sputter depths. Thesurface of an oxide is also oxygen-rich comparedO2`to the surface of native silicon oxide ; however, thematrix factor of the oxide at a 1.0 nm sputterO2`depth is about equal to native oxide. Hence, nativesilicon oxide RSFs for 52Cr, 56Fe and 58Ni metals usinga Ga LMIS can be predicted from the oxide RSFs,O2`factors corresponding to a 1.0 nm sputter depth.

As discussed above, although is used as a refer-Si2ènce matrix ion to examine unconfounded metal ionyield trends, 30Si` should be used as a reference matrixion to reduce the magnitude of ion yield variation as afunction of matrix oxygen content, stabilizing the RSFvalue over a small range of oxygen content. Hence, afterthe matrix factor is employed to predict a reasonablyaccurate by adjustment to the matrixM1RSFSi2`(i),oxygen content of a matrix, it is fruitful to transformthis value to a value in orderM1RSFSi2`(i) M1RSF30Si`(i)to reduce the inÑuence of small variations in oxygencontent on the RSF value, further improving quantiÐca-tion accuracy. Accordingly, the following expression isused to determine an from anM1RSF30Si`(i) M1RSFSi2`(i)value

M1RSFSi2`(i)] [I(30Si`)/I(Si2`)]\M1RSF30Si`(i) (7)

Table 4 tabulates calculated and experimental, elemen-tal Si RSF(i) values for a Ga` primary ion beam at 12keV impact energy, corresponding to a silicon oxidematrix with an oxygen content equivalent to oxideO2àt a 1.0 nm depth. These RSF(i) values can be appliedto native silicon oxide, understanding that the e†ectiveoxygen content of oxide at a 1.0 nm depth is veryO2`similar to the e†ective oxygen content of native oxide atthe surface. Elemental Si RSF(i) values from Stevie,30using an primary ion beam at 8 keV impact energyO2`to interrogate silicon, are also tabulated. There is verygood agreement between the calculated and the experi-mental RSF(i) values for 52Cr, 56Fe and 58Ni. Of strik-ing interest is the excellent agreement between 8 keV

RSF(i) values for a silicon matrix and 12 keV GaÒ2`RSF(i) values for a silicon oxide matrix, correspondingto a 1.0 nm depth into an oxide. ThisO2`-formedexcellent correspondence indicates that a Ga` doseexceeding 5] 1014 ions cm~2 does not signiÐcantlyalter the work function of the formed oxide. This agree-ment also implies that well-established 8 keV O2`RSF(i) values for a silicon matrix30 can be used to gen-erate a reasonably accurate set of 12 keV Ga` RSF(i)values for a silicon oxide matrix, corresponding to theoxygen content of native silicon oxide.

Accordingly, Table 5 tabulates converted 8 keV O2`RSF(i) values from Stevie and Wilson30 for ToF-SIMSquantitative trace metal analysis of native oxide, using aGa` LMIS. To facilitate the use of these values, eachmetal RSF value is adjusted for natural isotopic abun-dance and referenced to the 30Si` matrix ion. Measure-ment of a metalÏs major isotope directly corresponds tomeasurement of the elemental (all isotopes), as opposedto the isotopic, metal surface concentration. Becausenative silicon oxide is grown under a variety of



Table 4. Experimental, calculated and published 52Cr, 56Fe and 58Ni relative sensitivity factors (RSF) for an O2‘-

silicon oxideformed

ToF-SIMSb ToF-SIMSb ToF-SIMSb ToF-SIMSb

Measurement Calc. Calc. Exp. Exp. ToF-SIMSb Dynamic-SIMSc

Crater 1 2 1 2 Exp. av. Publishedd

Primary ion/energy Ga½/12 keV Ga½/12 keV Ga½/12 keV Ga½/12 keV Ga½/12 keV O2

½/8 keV

Cr RSF (atoms cmÉ3) 8 Ã1021 7 Ã1021 8 Ã1021 6 Ã1021 7 Ã1021 7 Ã1021

Fe RSF (atoms cmÉ3) 3 Ã1022 2 Ã1022 2 Ã1022 2 Ã1022 2 Ã1022 2.7 Ã1022

Ni RSF (atoms cmÉ3) 6 Ã1022 4 Ã1022 4 Ã1022 4 Ã1022 4 Ã1022 4 Ã1022

a The RSF values are Si elemental and the silicon oxide is formed by bombardment.O2

½

b 1.0 nm depth into the silicon oxide.O2

½-formedc Surface of silicon oxide.O

2½-formed

d From Ref. 30.

ambients and conditions, small variations in oxygenconcentration in the native oxide matrix are expected ;oxygen content variations do not signiÐcantly a†ectRSF(i) values referenced to 30Si` matrix ion, accordingto Figs 1 and 2.

The MF expression is e†ective within the range ofoxygen content associated with the oxide.O2`-formedIn view of the impurity ion yield behavior at the surfaceof the oxide, further study is required theO2`-formedevaluate the MF expression at higher oxygen content.

Table 5. Time-of-Ñight SIMS metal relative sensitivity factors (RSF) for nativesilicon oxide, using a Ga liquid metal ion source, predicted from 8 keV

RSF values for metals in a silicon matrixaO2‘

Metal 30Si½ RSFb,d Metal 30Si½ RSFa,bisotope (atoms cmÉ2 at 0.5 nm) isotope (atoms cmÉ2 at 0.5 nm)

7Li 1 Ã1012 115In 2 Ã1012

9Be 5 Ã1013 120Sn 1 Ã1014

11B 1 Ã1014 121Sb 2 Ã1015

23Na 6 Ã1011 130Te 7 Ã1015

24Mg 5 Ã1012 133Cs 5 Ã1011

27Al 2 Ã1012 138Ba 3 Ã1012

30Si 3 Ã1015 139La 4 Ã1012

39K 7 Ã1011 140Ce 5 Ã1012

40Ca 2 Ã1012 141Prc 1 Ã1012

45Sc 2 Ã1012 142Nd 1 Ã1013

48Ti 8 Ã1012 152Sm 1 Ã1013

51V 6 Ã1012 153Eu 5 Ã1012

52Cr 1 Ã1013 158Gdc 2 Ã1013

55Mn 2 Ã1013 159Tb 4 Ã1012

56Fe 5 Ã1013 164Dy 1 Ã1013

59Co 8 Ã1013 165Ho 4 Ã1012

58Ni 9 Ã1013 166Er 2 Ã1013

63Cu 7 Ã1013 169Tm 2 Ã1012

64Zn 4 Ã1015 174Yb 1 Ã1013

71Ga 5 Ã1012 175Luc 1 Ã1012

74Ge 6 Ã1014 180Hf 7 Ã1013

75As 3 Ã1015 181Ta 9 Ã1013

80Se 2 Ã1016 184W 3 Ã1014

85Rb 2 Ã1012 187Rec 2 Ã1014

88Sr 2 Ã1012 192Osc 1 Ã1015

89Y 3 Ã1012 193Irc 2 Ã1015

90Zr 7 Ã1012 195Pt 5 Ã1015

93Nb 2 Ã1013 197Au 4 Ã1015

96Mo 2 Ã1014 202Hg 2 Ã1016

102Ruc 1 Ã1014 205Tl 9 Ã1012

103Rh 8 Ã1013 208Pb 2 Ã1014

106Pd 8 Ã1014 209Bi 2 Ã1014

107Ag 2 Ã1014 232Th 3 Ã1013

114Cd 4 Ã1015 238U 6 Ã1012

a Metal i concentration (atoms cmÉ2 0.5 nm) ¼RSF(I)ÍI(M½)/I(30Si½)Ë.=b RSF values adjusted for metal isotopic abundance and referenced to 30Si½ matrix ion.c Determined from log (RSF) versus ionization potential plot.d From ref. 30.



Hence, this MF expression should not be applied tosilicon oxide matrices with signiÐcantly higher oxygencontent than the formed oxide surface, e.g. the surface ofthermal oxide.

Time-of-Ñight SIMS metal detection limits and RSFvalues

Using experimental and predicted RSF values fromTable 5, ToF-SIMS detection limits for various metalgroups in a native oxide, using a Ga LMIS, are tabulat-ed in Table 6. Detection limit values adopt the follow-ing assumptions : a volume corresponding to 40 ] 40lm2 by 0.5 nm is sampled ; corresponding to thisvolume, a 30Si` peak integral of 1 ] 106 counts isachieved ; the ion-count detection limit for a metal ionpeak corresponds to 10 counts ; sufficient mass-resolvingpower to isolate metal impurity peaks from interferingisobaric ions ; low baseline background signal fromintense, isobaric ion peaks in close mass proximity tometal ion peaks ; and low time-uncorrelated back-ground signal. Relative sensitivity factors are computedwith respect to 30Si` matrix ion, adjusted for naturalisotopic abundance of each metal (so that measurementof the major isotope directly corresponds to measure-ment of the element) and evaluated for a 0.5 nm arealdensity depth.

Figure 9 illustrates four mass regions of a spectrumacquired from a single analysis of the native oxide of asilicon wafer under the analysis conditions describedabove. The four mass regions illustrate : an intense30Si` peak with a peak integral of [1 ] 106 countsand a mass resolution (M/*M FWHM) value of 7880 ; aweak 56Fe` peak (227 counts) baseline-resolved froman intense, potentially interfering peak (50,100Si2`counts) mass separated by 19 milliamu; zero countbaseline in the mass region surrounding 63Cu`, adja-cent to an intense 28Si35Cl` peak separated in masswith respect to 63Cu` by only 17 milliamu; and a weak

40Ca` peak (174 counts) baseline-resolved from anintense SiC` peak mass separated by 14 milliamu.These results illustrate that weak metal ion peaks (10counts) can be readily detected with certainty withrespect to background signal and noise, even when inclose mass proximity to very intense, isobaric molecularion peaks. Hence, the detection limits tabulated inTable 6 can be readily achieved with current ToF-SIMSinstrumentation.

To provide complete deÐnition of the surface concen-tration, this paper uses the areal density concentrationunit of atoms cm~2 at areal density depth d (in nm). Toavoid inaccuracies associated with inhomogeneousimpurity distributions, the areal density depth shouldcorrelate to the physically-based analytical samplingdepth, which is D0.5 nm. Hence, a 0.5 nm areal densitydepth is selected, giving rise to the following unit : atomscm~2 0.5 nm. As expected, the detection limit trends=closely track metal ionization potential and electronconÐguration, where the lowest detection limit valuesare associated with low ionization potential, open-shell,Group I metals, and the highest detection limit valuesare associated with high ionization potential, closed-shell Group IVa metals. Detection limits between5 ] 106 and 5 ] 108 atoms cm~2 0.5 nm are=observed for most metals of interest to the semicon-ductor industry. Because current-generation Ga ioncolumns o†er a tenfold higher primary ion current com-pared to the Ga LMIS used in this study, in principle,detection limits between 5] 105 and 5] 107 atomscm~2 0.5 nm may be realized for these metals with=current ToF-SIMS instrumentation (with a correspond-ing increase in sampling volume), provided that thelevels of background noise and baseline peak signalfrom highly energetic ions associated with proximitypeaks are similar to the 2 nA condition.

To calculate a metal surface concentration from theRSF values tabulated in Table 6, the following exampleis o†ered, measuring I(40Ca`) \ 25 counts and

Table 6. Time-of-Ñight SIMS metal detection limits in native silicon oxidecategorized by electron conÐguration, predicted from 8 keV O

2‘

RSF values for metals in a silicon matrixa

Metal Detection limit

group Metals (atoms cmÉ2 at 0.5 nm)

— 52Cr 1.3 Ã108

— 56Fe 4.6 Ã108

— 58Ni 9.1 Ã108

Ia Li, Na, K, Rb, Cs 5 Ã106 to 1 Ã107

IIa Be, Mg, Ca, Sr, Ba 1 Ã107 to 5 Ã108

IIb Zn, Cd, Hg 5 Ã1010 to 1 Ã1011

IIIa B, Al, Ga, In, Tl 2 Ã107 to 1 Ã109

IVa Ge, Sn, Pb 2 Ã109 to 2 Ã1010

Va As, Sb, Bi 2 Ã109 to 3 Ã1010

3d Transition Sc–Cu 2 Ã107 to 9 Ã108

4d Transition Y–Ag 3 Ã107 to 2 Ã109

5d Transition La–Au 4 Ã107 to 5 Ã1010

Lanthanides Ce–Lu 1 Ã107 to 2 Ã108

Actinides Th, U 6 Ã107 to 2 Ã108

a Volume corresponding to 40 Ã40 mm2 by 0.5 nm is sampled; 30Si½ peak inte-gral equals 1 Ã106 counts. Detection limit : 10 count metal ion peak integral.



Figure 9. Four expanded mass regions of a spectrum acquired from a single analysis of the native oxide of a silicon wafer, correspondingto: (a) an intense 30Si½ peak (M /DM ¼7880 FWHM); (b) a weak 56Fe½ peak baseline-resolved from an intense peak (DM ¼19Si

2½

mamu); (c) zero count baseline in the 63Cu½ mass region, adjacent to an intense SiCl½ peak (DM ¼17 mamu with respect to 63Cu½) ; (d) aweak 40Ca½ peak baseline-resolved from an intense SiC½ peak (DM ¼14 mamu).

I(30Si`)\ 1 ] 106 counts

[25/1] 106]] [2.1] 1012]\ 5.3] 107 Ca atoms cm~2

for a 0.5 nm sampling depth

To compare data among samples or among analyticaltechniques, the sampling depths must be known, equiv-alent and well-deÐned, unless the contamination is con-Ðned to a speciÐc spatial regime. For example, if a metalimpurity is uniformly distributed through a 10 nm gateoxide, the ToF-SIMS concentration in atoms cm~2 =0.5 nm is multiplied by 20 to generate an areal densityvalue for the oxide, speciÐed as atoms cm~2 10 nm,=which should be equivalent to a TRXRF measurement,assuming that the TRXRF sampling depth is at least10 nm.

Application of these volumetric RSF(i) values permitsreasonably accurate, quantitative analysis of trace levelsof metals on silicon surfaces by ToF-SIMS equippedwith a Ga` LMIS. Trace metal concentrations arereported in areal density units for a well-deÐned arealdensity depth. Accordingly, surface concentrations arereported in units of atoms cm~2 d, where d equals the=areal density depth in nm, e.g. atoms cm~2 0.5 nm.=Ion image maps generated with Ga` LMIS 0.2 lmprobe beam enable accurate and precise lateral spatialdeÐnition of the sampled region and position ofanalysis. Owing to quasi-simultaneous ion acquisitionover the elemental mass range, high material efficiencywith low material erosion rates is achieved, permittingnot only an ultrashallow sampling depth but alsoprecise and accurate depth deÐnition of the sampling

depth and analysis depth. These instrument and per-formance characteristics fulÐll many of the demandinganalytical challenges posed by technology nodes beyonda critical feature size of 180 nm.

CONCLUSIONS

Volumetric 52Cr, 56Fe and 58Ni RSF values for asilicon oxide matrix are determined using a 12 keV Ga`primary ion beam. The dependencies of these RSFvalues upon matrix oxygen content are examined using

and 30Si` as matrix reference ions. The 30Si`-Si2`referenced RSF trends are confounded, due to com-petition between metal impurity and matrix ion yields ;however, RSF trends highlight onlySi2`-referencedmetal ion yields, showing common behavior among thethree metals. Although RSF values areSi2`-referenceduseful to predict the e†ect of oxygen content, 30Si`-referenced RSF values are best to use in daily practice,being largely invariant to small changes in oxygencontent. A multivariate expression for Si2`-referencedRSF values as a function of oxygen content is devel-oped. A weakly metal-dependent matrix factor (MF) inthis expression is used to modify metal RSF values,standardized to a given oxygen content condition, toaccount for oxygen content variations in a silicon oxidematrix. The MF for native silicon oxide at the surface isalmost identical to the MF for oxide at aO2`-formed1.0 nm depth. The 12 keV Ga` RSF values for 52Cr,56Fe and 58Ni in oxide at 1.0 nm depth areO2`-formedin excellent agreement with 8 keV RSF values in aO2`



silicon matrix. This agreement implies that well-established 8 keV RSF(i) values for a siliconO2`matrix can be used to generate a reasonably accurateset of 12 keV Ga` RSF(i) values for a native siliconoxide matrix surface, suitable for use by ToF-SIMS forquantitative trace metal analysis. Experimental detec-tion limits for 52Cr, 56Fe and 58Ni and predicted detec-tion limits for metals from various groups are reported,using areal density units of atoms cm~2 d, where=d \ 0.5 nm, corresponding to 0.5 nm sampling andareal density depths. Time of-Ñight SIMS detectionlimits between 5] 106 and 5 ] 108 atoms cm~2 0.5=nm are predicted for most metals of interest to the semi-conductor industry. For metals detected by TRXRF,ToF-SIMS o†ers detection limits two to four orders ofmagnitude lower compared to TRXRF, required bysemiconductor metrology roadmaps through 2010.

Further study is needed to : extend the expression forRSF as a function of oxide to higher oxygen concentra-

tions, associated with thermal oxide ; conÐrm theexpressionÏs validity with metals spanning a largerrange of ionization potentials ; correlate surface concen-trations by ToF-SIMS with those determined by othersurface analysis methods ; and translate RSF values forsilicon oxide to other matrix materials of interest to thesemi-conductor community. The inÑuence of physicalsputtering, independent of workfunction alterations, ondepth-proÐle pre-equilibrium artifacts can be assessedby examining the inÑuence of oxygen content on RSFvalues at higher oxygen concentrations, associated withthermal oxide.

Acknowledgements

We gratefully acknowledge the contributions of Allen Templeton andTommy Gray for insightful discussions and acquiring most of thedata associated with this study.

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Quantitative trace metal analysis of silicon surfaces by ToF-SIMS

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