Spatially multidimensional secondary ion mass spectrometry analysis

ANALYTICA CHIMICA ACTA

ELSEVIER

Analytica Chimica Acta 297 (1994) 197-230

Review

Spatially multidimensional secondary ion mass spectrometry analysis F .G . Riidenauer Austrian Research Dr . Seibersdorf, A-2444 Seibersdorf, Austria

(Received 21st November 1993)

Abstract

This article gives a survey on recent technical developments in imaging secondary ion mass spectrometry (SIMS) analysis . In the first section, the three instrumental imaging principles (scanning ion microprobe, ion microscope, image dissector) are shortly described and their capabilities are compared . In the second section, data acquisition and data handling techniques are treated, with particular emphasis on 2-dimensional imaging and its natural extension to 3 spatial dimensions via image stacking . The potential of retrospective analytical evaluation of 3D image stacks is demonstrated . The third section concentrates on quantification techniques for mass spectra and ion images . The state of the art of image quantification is described and the limitations of the standard method, sensitivity factor correction, are demonstrated . In the fourth section the concept of "imaging" of an analytical sample is treated as a process of (imperfect) information transfer, transforming the spatially 3-dimensional elemental atomic density in the sample into an "ion image" stored in a computer . This view offers a natural mathematical concept of "resolution" and its dependence on instrumental as well as sample parameters . This concept can be naturally extended to statistically limited imaging where spatial resolution is not limited by instrumental parameters but rather by the number of atoms available for analysis . Keywords:

Mass spectrometry; Spatially multidimensional SIMS ; Technical developments in SIMS

1 . 2D-Imaging principles in SIMS "Imaging" in secondary ion mass spectrometry (SIMS) can be considered as the process of reconstruction of the spatially 2-dimensional ion emission density at the sample surface from the spatial or temporal distribution of secondary ions arriving at the mass spectrometer detector . Three different imaging principles have been technically

* Corresponding author .

realized (a) the scanning ion microprobe, (b) the ion microscope, (c) the image dissector ion microscope . 1 .1 . Scanning ion microprobe In the scanning ion microprobe the spatial information is impressed onto the primary ion beam : a focused beam with small diameter is scanned across the sample surface by applying certain time-dependent voltage patterns onto X/Y deflection plates. Secondary ions emitted in

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close vicinity of the impinging primary ions, are mass analyzed and detected time-sequentially at the mass spectrometer detector (Fig . 1) . The spatial information contained in the primary beam is used to decode the time series of detector pulses and reconstruct the spatial distribution of ion emission at the sample surface . An essential requirement in this process is, that secondary ions are emitted in close spatial and temporal vicinity of the impinging primary ions . Thus, physical properties of the emission process, i .e . the spatial and temporal extent of the collision cascade are essential to the 3-dimensional localization of the point of origin of emitted secondary ions . Computer simulations yield typical values of 10 - ' 2 s and 30 nm for lifetime and spatial extent respectively of a collision cascade released by a 50 keV Ga ion on Si [1,2]. Modern ion micropro es equipped with liquid met l prim ry ion source ctu lly re ppro ching this "c sc de" resolution limit.

The first commerci l sc nning ion micropro e w s developed y Lie l [3] . This instrument used Duopl sm tron prim ry ion source, two-st ge electrost tic prim ry lens system nd dou le focusing m ss spectrometer for n lysis of second ry ions . The sm llest resolv le dist nce w s of the order of 1-2 gm nd ll three convention l n lytic l SIMS modes : ulk n lysis, profile n lysis nd im ging n lysis were successfully performed . The instrument w s known s the IMMA (ion micropro e m ss n lyzer) nd m rketed y Applied Rese rch L s . t Sunl nd, CA. The next m jor step forw rd occurred when high rightness liquid met l prim ry ion sources were introduced [4-6]. Sm llest resolv le dist nces elow 0 .1 µm now ec me v il le in commerci l SIMS instruments . The new instrument gener tion w s equipped with n ultr high v cuum (UHV) s mple ch m er, utom ted t rget m nipul tion nd computerized e m sc n-

PROeMIc

deflection

Fig. 1 . Im ge form tion in sc nning ion micropro e (left) nd ion microscope (right), schem tic .



F. G. Ruden uer /An lytic Chimic Act 297 (1994) 197-230

ning nd digit l im ge stor ge c p ility. VG IONEX t Burgess Hill (formerly VG Instruments) w s pioneering the commerci l introduction of this instrument type . M ny rem rk le results were o t ined. A sc nning ion micropro e with very high sp ti l resolution w s designed nd uilt t the university of Chic go, in cooper tion with Hughes Res . L s . [7,8] (UC-HRL-ion pro e). A schem tic of this system is shown in Fig . 2. The prim ry ion gun consists of G liquid met l ion source (LMIS) simil r to th t descri ed y Seliger et l . [9] nd three-element symmetric electrost tic lens [10] forming n intermedi ry source crossover in the pl ne of differenti l pumping perture . A pre-o jective electrost tic du l octupole ssem ly is used for e m djustment nd sc nning . An electrost tic "einzel-lens" o jective produces the fin l e m spot with perpendicul r incidence t the t rget surf ce . Positive or neg tive second ry ions le ving the t rget in perpendicul r direction re cceler ted y volt ge of the order of ± 100

DISPLA OSCILLOSCOPE __

199

V, pplied to the t rget nd energy n lyzed y sm ll, 8 mm r dius cylindric l electrost tic deflector fitting into the sp ce etween t rget nd o jective lens (tot l height 1 .2 cm). The deflected second ry ions re focused y multielement tr nsport optics into qu drupole m ss n lyzer. M ss selected second ry ions re detected y ch nneltron multiplier oper ting in the pulse counting mode . Im ging inform tion c n e o t ined either from the qu drupole detector (SIMS mode) or second ch nneltron detecting either ion induced non-m ss filtered second ry ions ("ISI"-mode) or ion induced second ry electrons ("ISE"- or "SIM"-mode, "sc nning ion microscopy"), respectively. Be m positioning nd sc nning is controlled y digit l im ge cquisition nd processing system [11]. This system lso t kes over im ge stor ge, displ y nd processing t sks . T le 1 lists some of the ch r cteristic d t of the instrument . Sm llest resolv le dist nces down to 20 nm h ve een determined in SIMS im ges (Fig. 3) .

HIGH RESOLUTION RGB

MONITOR

II I I

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PROCESSOR

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ELECTRONICS

RESIDUAL GAS IONIZER C LINDRICAL' DECEL LENS EINZEL C L . LENS

ISI

TRANSPORT

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ISI SECTOR ELECTROSTATIC ENERG SPECTROMETER EINZEL C L . LENS QUADRUPOLE

Fig. 2. Schem tic of the UC/HRL su micron ion micropro e; courtesy R . Levi-Setti.

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T le 1 Typic l oper ting d t of the UC-HRL sc nning ion micropro e Prim ry ion energy Spot di meter Prim ry e m current Pixel num er Im ge recording time Second ry ion tr nsmission M ss resolution B se pressure in ch m er

20-60 keV prim ry 20-100 nm 2-50 1024 X 1024 256 s (typ .) = 0 .2% for A1+ M/AM=300 5 X 10 -10 Torr

This is close to the limit set up y the sp ti l extent of the sputtering c sc de [1]. With e m current of 2 pA into 20 nm prim ry spot counting r tes of the order of 10 5 counts/s re o t ined from oxygen ted surf ces for m ny ele-

ments. This tr nsl tes into useful yields (see 3 .1 .) etween 1 X 10 -4 (for Si') nd 0 .1 (for Li+) detected ions/sputtered tom [12] . For the lowm ss r nge this is of the s me order, for he vier m sses it seems to e lower th n wh t is chievle in high sensitivity dou le focusing m ss spectrometers [13] . The destructive n ture of SIMS however is setting up n interdependency etween sp ti l resolution (in three dimensions) nd detection limit [14,15] . Curves representing theoretic l estim te for this rel tion re shown in Fig. 4 together with some experiment lly determined v lues . O viously, t 20 nm resolution, detection limits re in the 10 t .% r nge . This is of the s me order of m gnitude th n estim ted for Auger micropro es in this resolution r nge . In SIMS however, n im ge of such sp ti l resolution c n e recorded in out 256 s, where s n

Fig. 3. High resolution A]+ ion im ge o t ined with the UC/HRI ion micropro e . Sc le

r 1 Am. Courtesy R . Levi-Setti .



F. G. Ruden uer /An lytic Chimic Act 297 (1994) 197-230

Auger pro e requires im ge recording times of the order of 30 min.

IMS 4F version, the microscope nd micropro e modes re incorpor ted in single instrument (Fig. 5) . Two ion sources (1) nd (2) c n e oper ted ltern tely. A m gnetic m ss selector (3) selects ions with the ppropri te m ss num er nd deflects them into 3-lens prim ry focusing gun. A sc nning system deflects the focused e m cross the s mple (5). Second ry ions from the s mple re focused y n immersion lens (4) nd n electrost tic tr nsfer system (7) so th t virtu l im ge of the s mple emission intensity distriution is gener ted inside the dou le focusing m ss spectrometer (8-14). A dyn mic emitt nce m tching system is incorpor ted in the tr nsfer optics which gu r ntees high ion tr nsmitt nce from l rge field of view in the sc nning pro e mode of oper tion. A projection lens system (15) projects the m ss selected virtu l s mple im ge onto multich nnel-pl te/ scintill tor com in tion where m gnified im ge of the element distri ution is displ yed . This im ge c n e viewed

1 .2. Ion microscope

In n ion microscope the s mple is om rded ("illumin ted") y ro d prim ry ion e m. (Fig . 1). Second ry ions re cceler ted y n electrost tic emission lens forming virtu l imge of the second ry ion emission density distriution y virtue of the im ging properties of homogeneous electrost tic cceler tion field [16]. This im ge then is tr nsported through stigm tic focusing m ss spectrometer nd projected in m gnified sc le on scintill tor screen or equiv lent detector equipment . The l ter l resolution of this im ging process is limited y the energy spre d of the second ry ions nd the chrom tic err tion of the emission lens . The commerci l st nd rd of n ion microscope instrument is the CAMECA IMS 3F [17] . In the

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Fig . 4. Connection etween detection limit nd l ter l resolv le dist nce in SIMS . 5 10, sputtering depth 10 nm ; 5 . , depth equ l to spot di meter (useful resolution). Assumptions : sputter yield = 5, -r„ = 10 -3 (curves 1,2); T„ = 1 (perfect postioniz tion nd tr nsmission, curves 3,4). M rks : experiment l points (lower limits) ccording to Ch l et l. [12] .



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y microscope or TV-c mer . TV im ges c n e digitized nd stored in n im ge processing system. Altern tely, the m ss selected second ry ions c n e deflected electrost tic lly (9) onto F r d y detector/ multiplier com in tion (21),

(22) where they c n e detected in DC or ion counting mode . The sign l from the multiplier is used in the ion micropro e mode to gener te sc nning ion im ges with high sensitivity . The m ss spectrometer c n e oper ted in high

n

Fig . 5 . Schem tic of IMS 3f ion microscope [17) .

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F. G . Riiden uer /An lytic Chimic Act 297 (1994) 197-230

m ss resolution mode (M/AM > 12 000) for sepr tion of iso ric m sses . 1.3. The im ge dissector ion microscope The im ge dissector ion microscope is hy rid etween ion microscope nd sc nning pro e . Simil r s in the ion microscope, the s mple is illumin ted y ro d prim ry ion e m (see Fig. 6) . An emission lens produces virtu l im ge of the ion emission density t the s mple surf ce . A m gnified re l im ge of this first virtu l im ge is projected onto n perture pl ne . A p ir of X/ -deflection pl tes is sc nning the whole imge cross sm ll centr l perture in this pl ne so th t only th t p rt of the ion im ge corresponding to the centr l resolution element c n p ss through the m ss spectrometer . Detection nd decoding of the im ge inform tion from the time series of detector currents is identic l to the sc nning pro e . As in the ion microscope, the sp ti l resolution nd the second ry ion tr nsmission in the dissector is determined y the properties of the emission lens . The first im ge dissector ion microscope w s uilt y McHugh ( s reported in [14]) who comined n immersion lens system with deflector nd m gnetic m ss spectrometer . Another imge dissector microscope h s een uilt t Kiev, Ukr ini n Repu lic y Cherepin [19] (see Fig . 6) . The prim ry e m is gener ted in cold c thode duopl sm tron (19), sh ped y two condenser lenses (20,21) nd is hitting the t rget (1) . An immersion lens (2) cceler tes nd focuses the second ry ions into n unfiltered intermedi ry im ge of the surf ce, much s in the ion microscope . The contr st di phr gm (3) limits l ter l energy spre d of tr nsmitted ions nd therefore determines sp ti l resolution. The unfiltered intermedi ry im ge is projected in v ri le m gnific tion to the surf ce electrode of n ion/ electron im ge converter (7-9) with the help of the tr nsfer lens (5) . Second ry electrons from the converter electrode re cceler ted ck into the direction of the incoming ion e m nd focused y the immersion lens (9-7) onto the scintill tor screen (18) where m gnified electron im ge (c . 200 X) corresponding to the tot l ion emission

T Fig. 6 . Schem tic of Kiev monopole im ge dissector ion micropro e; further expl n tions see text ; courtesy V .T. Cherepin.

density in the s mple pl ne c n e o served . A sm ll perm nent m gnet (6) is used to deflect the electron im ge ,out of the xis of the second ry ion e m . This o serv tion system for the unfiltered im ge is simil r to th t used in e rly ion microscopes [16] . Ions p ssing the hole in the converter electrode (9) re deceler ted y the



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F. G. Riiden uer /An lytic Chimic Act 297 (1994) 197-230

immersion lens system (9-11) into the qu drupole m ss n lyzer (12). M ss-filtered ions hit the conversion dynode of the electron multiplier (13) producing ion pulses which re mplified (14) nd recorded in the centr l processing unit. The unfiltered im ge o served on the scintill tor screen is m inly used to pl ce the re of interest into the dissector perture in (9) . By v rying the optic l power of the immersion/ tr nsfer lens system (2,5) nd y feeding ppropri te volt ges to the deflection system (4) it is possi le to v ry size nd loc tion of the re of interest from which m ss spectr or depth profiles re to e o t ined . If the crossover of the tr nsfer lens (5) is pl ced into the dissecting perture, the second ry ion e m p sses completely nd n ver ge n lysis of the full illumin ted s mple re is o t ined. By setting the qu drupole to cert in m ss num er nd sc nning the unfiltered im ge cross the dissecting di phr gm, using the deflection system (4), "sc nning" element l distri ution im ge of the selected element c n e o t ined .

of pixels in the micropro e nd little inform tion from l rge num er of pixels in the microscope. Therefore, the im ge recording time gener lly is lower in the microscope since ll pixels within the field of view re processed in p r llel . On the sis of equ l tot l count num ers/ im ge the r tio of im ge recording times for the sc nning micropro e (SP) nd the microscope (MS) mode c n e c lcul ted y multiplying the pixel recording times t Pix y the num er of pixels in n im ge of di meter df [µ] [20] :



1 .4. Comp rison

Sp ti l resolution is ctu lly limited y physic l properties of the second ry ion emission process in ll three im ging modes . Where s in the sc nning pro e the limit is set up y the sp ti l extent of the collision c sc de, the essenti l f ctor in the microscope nd the im ge dissector is the energy distri ution of the second ry ions . Where s the c sc de width contri ution is fund ment l in the micropro e, the resolution in the microscopic mode c n, in principle t le st, e improved y n rrowing down the ccept nce windows for emission energy nd e m divergence t the cost of sign l intensity . Note lso, th t in the microscope the l ter l extent of the collision c sc de is not f ctor limiting l ter l resolution . Inform tion flow, s expressed e.g . y the tot l num er of detected ions/s, irrespective of the point of origin, t high sp ti l resolution is higher in the microscope th n in the micropro e since it is spot limited in the former nd ccept nce limited in the l tter c se . In given time interv l we o t in high inform tion from sm ll num er

timsP

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2

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TMS

d

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TSP

( 5f )

', Ms

= 7 X 10-' .

JsP

S[µ]23 .

6

( d )2

sf

(1)

Here, TMs , T5 re the tr nsmissions nd JMS , JsP the loc l prim ry current densities for microscope nd micropro e respectively ; Tsp = 1 h s een ssumed nd S[µ] is the l ter l resolution me sured in micrometers . Assuming st nd rd v lues JsP = 1 A/ cm2 (chrom tic lly limited liquid met l prim ry source), J MS = 5 mA/ cm 2 , E = 10 ° V/cm, e = 1OV, d f/S = 256 we o t in tim,sP -

4 .

S[µ]23

(l )

t im,MS

i .e . pprox. 50 times f ster im ge recording in the microscope t 1 µm sp ti l resolution nd comp r le im ge recording times t hypothetic l 3 .2 nm resolution . A slightly different rel tion h s een derived for spheric lly limited prim ry ion e ms [14] . The useful yield (see Section 3 .1 .) ctu lly determines the mount of inform tion (detected ions) which c n e o t ined from given s mple volume . It therefore is the essenti l p r meter determining detection efficiency in the reconstruction of 3-dimension l element distri utions .



F.G . Ruden uer/An lytic Chimic Act 297 (1994) 197-230

The r tio of useful yields for micropro e microscope c n e c lcul ted s [20]: TsP T MS

TsP -

=

2-5/3

(CIE)

nd

2f3

52/3

TMs

)2I3

1 .46 x

102-

(CIE,

(2) cS[A ]z/3

For the s me numeric l ssumptions s we estim te 1 .46 5 [ g] 213 T Ms !

ove

T sP

(2 )

i .e. definite dv nt ge for the micropro e t resolv le dist nces elow 1 µm . The r tio of useful yields lso determines the r tio of sputter depths A required to cquire im ges with the s me tot l pixelcount num ers in the microscope nd the micropro e [19] : A ms A SP

T sP

,T MS

1 .46 B [ µ ]2/3

(3)

Ag in, slightly different expression holds for spheric lly limited prim ry e msA comp r tive ssessment of the two im ging principles which tod y re employed in commerci l instruments must consider the following f cts: (i) ll pixels re processed p r llel in the microscope. (ii) instrument tr nsmission is lower in the microscope . (iii) gener lly im ge recording time is shorter in the microscope. g is higher in the microscope . (v) useful yield is higher in the sc nning pro e . Note th t the terms "ion pro e" nd "ion microscope" refer to p rticul r prim ry e m illumin tion modes [21] of the s mple nd not necess rily to physic lly different instruments. In f ct, the CAMECA 4F-instrument (see Section 1 .2 .) incorpor tes oth the prim ry e m sc nning ion micropro e nd the direct im ging ion microscope modes.

205

2. 3D-Im ging nd im ge processing Ion micropro e m ss spectrometry, y virtue wellof its ion optic l im ging c p ility, is known method for investig tion of 2-dimension l element distri utions t solid surf ces . This property c n e com ined with the continuous sputter-remov l of tomic surf ce l yers, inherent to ll ion e m methods, to perform sp ti lly 3-dimension l micro n lysis of solids. The technique c n e implemented on sc nning ion micropro es nd ion microscopes . A microcomputer is required to control cquisition of second ry ion intensity d t which re stored s pixel intensities st ck of 2-dimension l ion im ges o t ined from the s me l terl field of view during continued e m sputtering (22] . This im ge st ck cont ins the sp ti lly 3-dimension l element distri ution in the n lyzed microvolume of the solid (Fig. 7). From this 3D-d t set ll convention l n lytic l modes (loc l n lysis, line sc n n lysis, depth profile n lysis, im ge n lysis) of ion pro e n lysis c n e reconstructed retrospectively using numeric l methods [15,23] . Addition l displ y modes, e.g . nim ted im ge series, surf ce reconstruction of inclusions or gr in ound ries c n e implemented y suit le selection nd re rr ngement of 3D im ge elements ("voxels"). Sp ti l resolution limits of the technique in the l ter l dimension re determined y ion optic l properties of the micropro e used, depth resolution is limited y physic l properties of the sputtering process . St te-of-the- rt v lues re < 20 nm nd < 0 .3 nm respectively under f vour le s mple conditions [6,7,14] . A superseding resolution limit m y e set up y the destructive n ture of SIMS [15] : since sputtered microvolume (voxel volume) cont ins limited num er of toms, of which gener lly sm ll ionized fr ction is recorded t the detector, the detected ion count depends on voxel volume, instrument tr nsmission nd element concentr voxel count with desired st tistic l . For gnific nce, the voxel volume therefore must exceed minimum size (Fig . 4). Retrospective point n lysis now is performed y selecting single correl ted voxels in e ch element l 3D-st ck nd displ ying voxel intensity in



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F. G. Riiden uer/An lytic

the form of "m ss spectrum" . 1-Dimension l line n lysis c n e performed y selecting voxels long n r itr ry line in the st ck nd displ ying voxel intensity s "line sc n" . Depth profiling is re lized y summing voxel intensities over identic l r itr ry su re s in surf ce-p r llel st ckpl nes nd displ ying the voxel sum versus depth from the origin l surf ce . Convention l 2D im ge n lysis is performed y selecting n r itr ry surf ce-p r llel st ck-pl ne nd displ ying voxel intensity distri ution in the form of n intensity modul ted "ion im ge" . These im ges re usu lly ddressed s "co xi l" im ges since the direction of o serv tion is co xi l with the sputtering direction . Digit l stor ge nd processing of 3D d t sets llows to gener lize nd extend these "convention l" modes nd lso to cre te qu lit tively new n lytic l modes. In line sc n n lysis, for ex mple, the line long which voxel intensities re displ yed c n e r itr rily oriented in 3D sp ce,

Chimic Act 297 (1994) 197-230

nd m y even e n r itr ry 3D-curve . In ddition, sp ti l ver ging c n e performed long the line in order to improve st tistics of d t . In im ge n lysis, the 3D st ck c n e intersected y r itr rily oriented pl nes nd the voxel intensities in the intersection pl ne c n e displ yed s 2D im ge . A speci l c se here re "tr ns xi l" im ges o t ined for intersection pl nes oriented perpendicul rly to the origin l m croscopic s mple surf ce. Simil r to CT (computer tomogr phic) im ge, tr ns xi l im ge offers view into the interior of the s mple . Contr ry to tomogr phic im ging however, tr ns xi l im ges c n e o t ined in SIMS, in principle t le st, y simple re rr ngement of r w voxel d t so th t complic ted im ge reconstruction lgorithms re not required [22,24] . A qu lit tively new n lytic l mode is the reconstruction of 3D fe ture sh pes in the form of 2D surf ces in 3D sp ce [18] which turns out to e p rticul rly useful for morphologic n lysis of microstructures such s

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x

1

F.C. Ruden uer/An lytic Chimic Act 297 (1994) 197-230

207

gr in ound ries, precipit tes or lithogr phic structures . Ex mples for pr ctic l pplic tion of these techniques will e descri ed elow . 2.1 . Displ y of 3D-distri utions Series of co xi l im ges

The simplest w y to visu lize 3D element l distri ution is to simult neously displ y num er of co xi l im ges, directly cquired nd stored during 3D n lysis session, on the screen of the im ge stor ge unit . Rough comp rison of im ge fe tures t different sputtering depth is possi le in this w y. Fig . 8 shows such "st tic" im ge series o t ined during sputtering through lithogr phic lly produced Al-microdot of 50 µm dimeter nd 0 .2 Am height on Si-su str te (Fig. 9) . A series of 64 Al-im ges with 256 x 256 pixels e ch w s o t ined in this w y . St rting from the im ge o t ined immedi tely t the microdot surf ce (upper left), im ge sh pe nd intensity seem to rem in pproxim tely const nt through rows 1-4 ; this is to e expected due to the cylindric l sh pe of the microdot . St rting from row 5, however, the im ge ppe rs to shrink gr du lly until lmost no Al sign l is present fter im ge no. 62. The im ges lso seem to move off centre some-

Fig. 8 . Series of co xi l Al' im ges o t ined during sputtering of microdot shown in Fig . 17. Origin l in pseudocolours .

Fig . 9 . S mple geometry of lithogr phic lly produced Al microdot.

wh t in the lower rows, the degree of this shift c nnot however e e sily determined in such displ y mode . Anim ted im ge series

Another possi ility of presenting the complete 3-dimension l distri ution of one or more elements to the o server is to repl y, in n ccelerted timesc le, the surf ce distri ution s it ch nges in the course of the origin l d t -t king sputtering process . The o serving n lyst then c n stop the repl y t ny desired time nd ev lu te in det il the "frozen" im ge corresponding to the l ter l distri ution t cert in depth elow the origin l surf ce. In our terminology such n nim tion sequence would consist of time-sequenti l displ y of consecutive co xi l element l distri ution im ges . The pro lem to overcome here is the frequently sm ll num er of individu l element l fr mes cquired during sputtering through the s mple ; even if f st stor ge c p city for s y 50 fr mes per element is v ille, repl y of these d t , t the usu l TVst nd rd would t ke only out 2 s . V rious methods re v il le to extend this to timesc le more d pted to hum n perception c p ilities, e .g . fr me-jump, line r interpol tion [20] nd r ndom upd ting [25] .



F G. Ruden uer /An lytic Chimic Act 297 (1994) 197-230

208

Co xi l

nd tr ns xi l sections

An ex mple illustr ting the c p ilities of tr ns xi l sectioning is given in Fig. 10 . The s mple is structured impl nt of oron in Si consisting of 4 µm wide impl nted stripes nd 6 µm wide sp ces . The depth of the impl nted regions is out 0 .6 Am. The s mple w s sputtered in n ion microscope until the full impl nted depth w s sputtered through . Co xi l im ges were t ken continuously during sputtering using re ctive node encoder (RAE) in the im ge pl ne of the microscope (see Fig . 5) . The resulting co xi l im ge st ck w s sectioned long line perpendicul r to the impl nt stripes, giving the tr ns xi l 2D-im ge shown in Fig. 10 . In this "cross section" through the s mple it c n e seen th t the B-intensity in the impl nted stripes pe ks t depth lying somewh t elow the surf ce . This is known property of the impl nt-r nge distri ution . Wh t

IMPLANTATION

M

M166

SILICON

ME

PHOTORESIST (Removed After Impl nt tion)

SUBSTRATE PROCESSED

6\ \\1

l\ 3

1 1OB IMPLANTS

0 .60 x m

SILICON SUBSTRATE

<---25 MICROMETERS ---- >

RESISTIVE ANODE ENCODER CROSS-SECTION IMAGE 10B

IMPLANT

\RAE\ B7x ytes-. 2 Log se 2

Fig. 10. Upper h lf: production steps for structured oron-impl nt in Si . Lower h lf: tr ns xi l im ge of t° B + . Origin l colour coded. Courtesy C .A. Ev ns nd Associ tes .

is however peculi r is the f ct th t B lso c n e detected in the "unimpl nted" regions. This m y e either n instrument l rtif ct or n incomplete shielding y the photoresist m sk used in the f ric tion of the p tterned impl nt (see Fig . 10) . Another ex mple for tr ns xi l sectioning is shown in Fig. 11 . This is retrospective vertic l slice from st ck of im ges cquired during sputtering through AIG As/ G As multiqu ntum-well of 70 A repe t l yers . The im ge demonstr tes the excellent depth resolution c p ility of the method . Since the microvolume, sputtered during 3D n lysis usu lly does not extend to more th n few µm in depth ut covers few tens of µm l ter lly, the displ y depth sc le usu lly is extended in order to utilize the full displ y re . Pie sections

A very inform tive method for displ y of 3Ddistri utions is "Pie"-sectioning . From the 3D d t set piece, defined y two tr ns xi l sectioning pl nes, is "cut out" like piece is cut out from pie. The cut out piece (or the rem ining piece, ccording to visi ility) of the 3D d t set is dr wn in perspective onto the displ y screen . The distri ution of selected element on the surf ces of the cut out piece is displ yed using st nd rd 2D-displ y techniques (intensity modul tion, colour coding or iso-intensity contours) . The visile surf ce consists of sp ti lly connected p rts from one co x section nd from two tr ns x sections through the 3D d t set . Thus, the chemic l structure of the interior of the s mple c n e o served nd sp ti lly correl ted to the structure t the surf ce [26,27]. The usefulness of the Pie-sectioning technique oron-dou le is demonstr ted in the n lysis of impl nt (50 kV, 2 x 10 16 /em 2 ) in Si . The first impl nt zone is in the sh pe of vertic l (with respect to the field of view of the instrument) strip of 200 µm width . It h s een nne led for 2 h t 1000°C. The second impl nt (horizont l strip of s me dimension) is not nne led (Fig . 12) . An lysis w s performed in the intersection re of the impl nts y sputtering to depth of pproxim tely 2 projected r nges nd recording st ck of 18 co xi l im ges during this process .



F. G. Ruden uer /An lytic Chimic Act 297 (1994) 197-2301

Intersecting this d t volume with two perpendicul r tr ns xi l pl nes p r llel to the impl nted stripes would o viously show tr ns x distri ution im ges through the diffused nd the undiffused stripes in the front nd right view of the cutout Pie piece respectively nd n ddition l co x distri ution in the top view . Fig. 13 shows n ctu lly me sured Pie-section through the n lytic l volume. The top pl ne of this section is the co xi l im ge directly t the s mple surf ce . The dimensions of the im ged volume re 350 x 350 µm l ter lly nd 0 .6 Am in depth . The different distri utions of oron in the diffused (vertic l) nd the undiffused stripe re cle rly visi le : ( ) B h s diffused to the surf ce so th t the vertic l stripe is cle rly visi le in the top pl ne, where s lmost no intensity is visi le in the horizont l

209

stripe; ( ) B h s lso diffused l ter lly s visi le from the widths of the intersections through the l nted zones; (c) the depth positions nd intensities of the concentr tion m xim in the two stripes re lmost identic l; diffusion m inly h s occurred in the low-concentr tion regions of the profile . A more qu ntit tive comp rison of the B diffusion in the un nne led nd the nne led stripes is possi le y constructing retrospective loc l depth profiles nd loc l lines sc ns, indic ted schem tic lly in Fig . 12. 2.2. Loc l depth profiles

Once 3D im ge st ck h s een stored in the computer, depth profiling c n e performed ret-

Fig. 11. Tr ns xi l im ge (A12) of AIG As/G As multi-qu ntum-well device with 70 Hill, UK .

A repe t l yers. Courtesy VG Ionex, Burgess

210

F. G. Ruden uer/An lytic Chimic Act 297 (1994) 197-230

impl nt tion direction for oth impl nts undiffused Impl nt tion

i

N

z

depth profile

linesc n impl nt . pcx

Fig. 12. Possi ilities for retrospective qu ntit tive 3D ev lu tion of dou le impl nt; further expl n tions, see text .

Fig . 13 . Pie section through structured dou le impl nt of 11 B descri ed in Fig . 12. Diffusion of nne led vertic l stripe is cle rly visi le. Origin l colour coded .

rospectively t ny loc tion inside the r stered s mple re (see Fig . 7) y selecting, in e ch co x im ge from the st ck, the pixels with the s me X/ -coordin tes nd displ ying the content (ion function of fr me count) of these pixels s num er (fr me num er c n e e sily coded in sputtered depth) . Inste d of displ ying the intensity of single pixel in e ch fr me, the sum of pixel intensities within cert in region, centred round the selected pixel, c n e c lcul ted nd displ yed s depth profile . This procedure reduces st tistic l noise in the depth distri ution, pproxim tely proportion l to the di meter of the ver ging surrounding . Fig. 14 shows oron-profile, computed from the 3D d t set of the structured impl nt lre dy shown in Fig . 10. The ver ging zone w s 4 X 4 gm re centred in one of the impl nted stripes . Also shown in Fig . 14 is second oron profile, computed from



F. G. Riiden uer/An fytic

file . The incre sed ckground in the l tter c se is due to worse counting st tistics, since less ions contri ute to the selected- re profile th n to the full-field profile.

the full field of view shown in Fig . 10 (25 µm di m .) . It c n e seen th t oth profiles re lmost identic l, with exception of the higher " ckground" level for the 4 x 4 µm loc l pro-

n IM _ANT INT .

i ATTE ,Nr_L

lint

0

21 1

Chimic Act 297 (1994) 197-230

IMA5E

i)tr-T,

H

i

,3

TOTAL IMPLANTED REGION

4 X 4 MICROMETER REGION

z 0 F d L1!--

Z

010 ~ .

B i 1 1 l 2 - t i l f 1 1 I ' s t 1 I I i I I I t t

2000

4000

6000

8000

DEPTH

Fig . 14. Loc l depth profiles of i0 B in device shown

10000

12000

: I t I I I I

14000

16000

( ngstroms)

Fig . 10 reconstructed from 3D im ge st ck. Lower curve, reconstructed from full field of view (25 H m di m ); upper curve, reconstructed from 4 X 4 µm su field, centred in one of the impl nted stripes . Courtesy C .A. Ev ns nd Associ tes. Sputter time : 697 s.

212

F. G. Ruden. uer /An lytic Chimic Act 297 (1994) 197-230

2 .3 . Surf ce reconstructions Another n lytic l question often is to reconstruct the morphologic l sh pe of more or less homogeneous chemic l structure (e .g. gr in ound ry or n rtifici lly f ric ted structure) . Ag in, this n lytic l mode m y e performed posteriori y numeric l oper tions on 3D st ck of im ges o t ined during SIMS n lysis . Fig . 15 shows, in 2 different views, the n lytic l reconstruction of sm ll luminum microdot structure, lre dy descri ed in Fig . 9 . The n lysis w s performed y sputtering completely through the microdot nd simult neous recording of 36 co xi l Al-im ges. These co x im ges re line rly interpol ted for etter visi ility to st ck of 64 co x im ges (see Fig. 8). The surf ce of the 3D-structure w s defined s th t surf ce in 3Dsp ce consisting of ll voxels with 90% of m ximum voxel intensity. For given direction of o serv tion this surf ce w s loc ted nd sh ded y r y-tr cing lgorithm for e ch pixel of the displ y screen . There y, pl stic impression of the topogr phy of the microdot structure is o t ined . It c n e seen th t the reconstructed surf ce is not cylindric l s expected, ut h s n symmetric protrusion in the xi l direction. This indic tes f ult in one of the processing steps during m nuf cture of the microdot . Reconstruction of the surf ce from different viewing ngles llows to set up im ge series which c n e repl yed s nim ted im ge sequences (displ ying

e .g. rot tion of the microdot round its xis) . Thus, convenient quick survey of the complete sh pe of the structure is possi le nd interpret tion c p ility of 3D d t is consider ly improved .

3. Qu ntific tion 3.1 . The line r postul te or "fund ment l" SIMS formul The physic l phenomen le ding to emission of second ry ions from n ion om rded solid, re not fully understood yet . Presently discussed physic l models of the ion emission process t est llow semiqu ntit tive c lcul tion of element concentr tions from first principles nd me sured ion intensities [14] . In pr ctic l n lysis therefore, phenomenologic l lgorithms re pplied lmost exclusively . SIMS qu ntific tion usully is sed on the line r "fund ment l" SIMS equ tion (FSE) rel ting the detected ion current N+'(X) (ions/s) of the n lytic l tomic ion species X to the fr ction l tomic concentr tion c(X) of th t species in the s mple [14] :

N+'(X) =NP • tot -c(X) • +(X) • T(X)

(4)

Here, Np is the prim ry ion current, + (X) is the degree of ioniz tion (num er of emitted X + ions/ num er of tot l emitted X toms), nd T(X) is the tr nsmission of the m ss spectrometer for element X. Eq. 4 h s een written down for

Fig . 15 . Reconstruction of 3D surf ce of microdot (schem tic lly shown in Fig . 9) from 3D im ge st ck shown in Fig. 8. Two views from different directions shown .



F. G. Ruden uer/An lytic Chimic Act 297 (1994) 197-230

singly ch rged positive tomic ions; n logous equ tions c n e formul ted for molecul r n lytic l species of different ch rge st te . At first sight the formul seems to e self-evident, ec use, on the right h nd side, the first two terms Np • tot design te the tot l num er of sputtered toms/s ; the first three terms, including c(X), design te the tot l num er of toms of kind X +(X), emitted/s ; the first 4 terms, including represent the tot l num er of ionized toms of kind X emitted/s ; nd the full right h nd side, including T(X) represent the tot l num er of detected ions/s of kind X . The following deriv tion of Eq. 4 m y shed different light on the ctu l me ning of the "fund ment l" formul . The deriv tion st rts from n identity nd is repe tedly exp nded y v rious f ctors identic lly equ l to unity. Regrouping nd ren ming of these f ctors gives the desired equ tion . N+ (X)

1V + ' (X) = N + '(X) .

N+ (X)

N(X) Ntot . IV (X) . Ntot

4 NP

(4 ) The following v ri les nd revi tions h ve een introduced in this equ lity : N + (X) tot l emitted num er of X+ ions/s N(X) tot l num er of X toms (irrespective of ch rge st te) emitted/s tot l num er of t rget toms (irrespecNtot tive of element nd ch rge st te) emitted/s Ntot

ytot =

C(X)

tot l sputtering yield

Np = N( X) Ntot

N+ X) + ( X) = N(X)

fr ction l tomic concentr tion of X toms in s mple degree of (positive) ioniz tion of sputtered X toms

_ N+'(X) T(X) N tr nsmission for X+ ions + (X) O viously, in deriv tion like Eq . 4 virtu lly ny v ri le (pressure, temper ture, etc .) might

21 3

h ve een introduced without form lly f lsifying the equ tion . We therefore must come to the conclusion, th t "fund ment l" equ tion such s Eq . 4 m y h ve, in minim l interpret tion, very limited physic l content . In m ximum interpret tion the FSE tells us the following f cts: ( ) detected second ry ion current depends on the 5 physic l nd instrument l p r meters cont ined in Eq . 4; ( ) it does not depend on ny other p r meters ; (c) the dependence on the listed p r meters is line r ; (d) the listed p r meters re mutu lly independent. Only st tement ( ) h s een demonstr ted experiment lly ; st tements ( -d) on the contr ry h ve een shown wrong in one or the other inst nce . In p rticul r, the interdependence of tot , + (X) on c(X), known s the "m trix effect" h s een demonstr ted in m ny inst nces . An interdependence of p r meters however gre tly reduces the pr ctic l usefulness of the "fund ment l" Eq . 4 . In the SIMS liter ture, it ppe rs s self-evident postul te without ny ttempt of theoretic l found tion. It h s een shown however, th t the essenti l fe ture of the FSE, the proportion lity etween element l concentr tion nd n lytic l sign l ( t le st in the sm ll-concentr tion pproxim tion) c n e put on sound theoretic l found tion [28] . It is cknowledged th t it is gener lly impossile to predict or c lcul te the other f ctors ppe ring in Eq. 4 with n ccur cy sufficient for ccur te prediction of the n lytic l sign l from element l concentr tion c(X) or vice vers . Therefore, those f ctors which re known experiment lly, re explicitly ret ined in ddition to the element l concentr tion c(X), nd the rem ining f ctors re com ined into f ctors of proportionlity which h ve to e determined experiment lly . These f ctors gener lly depend on properties of the s mple nd the n lytic l instrument. According to the p rticul r n lytic l situ tion, v rious f ctors m y e explicitly ret ined so th t Eq. 4 m y e ltern tively written s : N + ' = S (X) c(X) N + ' = S p (X) c(X) . Ip N + ' _ TUN c(X) Ip - tot

(5)



F. G. Ruden uer /An lytic Chimic Act 297 (1994) 197-230

214

The f ctors of proportion lity S (X), S P (X), T„(X) c n e considered "sensitivities" since for given element l concentr tion the n lytic l sign ls incre se with incre sing numeric l v lue of these f ctors . They re n med " solute sensitivity", "pr ctic l sensitivity" nd "useful sensitivity" respectively. Since these f ctors lso incre se with instrument tr nsmission T, they c n e considered figures of merit for p rticul r SIMS instrument . The sensitivities in Eq . 5 h ve to e determined under controlled experiment l conditions from s mples of known concentr tions ( nd known sputtering yield) . Inversion of Eq . 5 forms the sis for phenomenologic l interpret tion s well s the experiment l determin tion of sensitivities : S (X)

N+'(X)

detected X ions s - '

c(X)

concentr tion

from st nd rd s mples with known concentr tion r tio for elements X nd . Eq. 8 is the sis for two simil r qu ntific tion lgorithms y which rel tive concentr tion figures of n unknown element X, c(X), c n e computed from me sured ;) second ry ion intensities of elements E ;, AE cont ined in the s mple : ( ) intern l st nd rd v il

le

If n intern l st nd rd, i .e . n element ( ) with known fr ction l concentr tion c( ) is v ille in the s mple, the concentr tion of the unknown c n e c lcul ted from Eq. 8 . 1 C(X)

Sr(X)

I(X) I( ) C( )

O viously, single r tio of two second ry ion intensities, (from the unknown nd from the intern l st nd rd) h s to e me sured during n lysis . ( ) no intern l st nd rd v il

S P (X) N+' (X)

detected X ions s -'

NP • c(X)

prim ry ions • concentr tion

Tu(X) tor .

NP • c(X)

S ( )

SP( )

Sr (X) =

(X) c(E)

i=1

sputtered X toms

The r tio of sensitivities for two elements X nd from the s me s mple is c lled the rel tive sensitivity f ctor S 1 (X) of element X with respect to reference element : SP(X)

c(X) - N

detected X ions s -'

3.2 . Rel tive sensitivity f ctor qu ntific tion

S (X)

le

In this c se, RSF qu ntific tion st rts from the identity (6)

N+, (X)

(9)

c(X)

T u (X)

r.( )

where N is the tot l num er of elements cont ined in the s mple . In this equ tion, c(X) nd c(E) re c lcul ted from Eq . 9 for ll elements X nd E ; nd su stituted in the right side of the l st equ tion . O viously, intensity nd concentr tion c n e elimin ted, of the reference element fin lly giving

(7)

=N(X)/Sr(X)



(10)

E I(Ej)/Sr(Ej) i=1

From the phenomenologic l interpret tion of sensitivities follows phenomenologic l interpret tion of the rel tive sensitivity f ctor (RSF): S,(X) _

I(X)/c(X)

(8)

j( )/c( ) Since n RSF is r tio of two empiric l const nts, it m y itself e determined empiric lly

In this c se, ion currents of ll elements cont ined in the s mple h ve to e me sured nd rel tive sensitivity f ctors of ll these elements h ve to e known for qu ntific tion of single element X . Algorithm ( ) requires less n lytic l nd comput tion time th n lgorithm ( ). In ddition, the concentr tion of n intern l st nd rd



F. G . Ruden uer /An lytic Chimic Act 297 (1994) 197-230

element nd the RSF of the unknown with respect to the st nd rd h ve to e known priori . Algorithm ( ) requires more n lytic l time nd the knowledge of more RSFs ; no intern l st ndrd however is required . Which of these lgorithms is to e preferred, depends on the p rticul r n lytic l situ tion . In qu ntific tion of impl nt profiles, lgorithm ( ) is frequently used . The unknown X here is the impl nted species, the reference element frequently is the m trix species nd the RSF usu lly is o t ined from knowledge of the tot l impl nted dose [14] . Note th t rel tive sensitivity f ctors re purely empiric l const nts. RSF qu ntific tion lgorithms therefore c n only give ccur te nd correct results ( ) if RSFs re determined from c li r tion s mples with simil r composition s the unknown s mple, nd ( ) if experiment l conditions re simil r during determin tion of RSFs nd n lysis of the unknown s mple . According to condition ( ), tr nsfer of RSFs etween different SIMS instruments gener lly is not n llowed procedure . Only under very speci l st nd rdised instrument tuning conditions ("cross c li r tion" [281) is it possi le to chieve semiqu ntit tive n lytic l results (error f ctor < 2) using "tr nsferred" rel tive sensitivity f ctors . 3.3. Im ge qu ntific tion One of the m in go ls of multidimension l SIMS n lysis is the determin tion of the sp ti l distri ution of element concentr tions (element l m ps) inside solid . Two-dimension l ion im ges (ion microgr phs), s cquired during SIMS n lysis, ctu lly show the sp ti l distri ution of loc l second ry ion emission intensities . The tr nsfer from ion microgr phs to qu ntit tive element l m ps gener lly is known s "im ge qu ntific tion". This, y no me ns, is str ightforw rd process nd presently c n e performed rigorously for very limited cl ss of s mples only. It should however e pointed out th t in m ny n lytic l situ tions useful inform tion c n lso e extr cted from unprocessed ion microgr phs .

2 15

Im ge rtif cts It is known [14] th t in SIMS the proportion lity etween concentr tion nd ion count is not lw ys gu r nteed . In the gener l c se therefore, num er of rtif cts re cont ined in n ion im ge s cquired directly from the instrument [14]. "Artif cts" in 3D n lysis of solids c n e understood s effects which c use devi tion of the me sured concentr tion c m(x,y,z) m t me sured s mple loc tion (x,y,z) m from the ctu l concentr tion co(x,y,z) which w s present t loc tion (x,y,z) efore the n lysis w s performed. It is possi le th t the loc tion (x,y,z) of the n lytic l pixel is correctly determined lthough the me sured concentr tion v lue cm (x, y, z) is incorrect . In this c se, one is o serving " rtif ct contr st " : C m(x,y,Z)

*co(x,y,Z)

This type of rtif ct m y e .g . e c used y m trix effects nd cryst llogr phic, topogr phic or chrom tic contr st [14] . It c n lso h ppen, th t concentr tion is correctly determined, ut the corresponding voxel is incorrectly pl ced in sp ce ; in this c se, one is spe king of "misregistr tion" : (x,y,Z )m #

(x , y , Z )o

This type of rtif ct c n e c used y e .g. differenti l sputtering effects, c using loc lly v rile sputtering speed . A third cl ss of rtif ct is tomic reloc tion, in the sense th t sp ti l element l distri ution t the time of n lysis differs from th t prior to n lysis . This phenomenon c n e c used y tomic mixing [29], r di tion enh nced diffusion nd redeposition [26] nd ppe rs in p rticul r t high sp ti l resolution n lysis of nonpl n r s mples [30,31] . There re, however, l rge num er of pplic tion re s, where rtif cts c n e neglected, e .g . ion impl nt tion (see Fig . 12) or topogr phic reconstruction of homogeneous structures (Fig . 15). In ddition, selected rtif cts m y e removed from the imges y pixelwise pplic tion of correction lgorithms [32,33] . pl n r surf ce ion tr nsmission is pOn proxim tely const nt cross the full field of view



2 16

F.G. Ruden uer/An lytic

Chimic Act 297 (1994) 197-230

iii

f F

x concentr tion contr st

topogr phic contr st

chrom tic contr st

Fig . 16 . Artif ct contr st on nonpl n r surf ces comp red to ide l concentr tion contr st (left) . Bottom row : SIMS m trix sign l long s mple sections shown in upper h lf.

element A

element

S llsnn nnS

ion microgr phs

r r#AAAA~#1~~~RlAA∎ rr∎r∎ OWS. mono! r##rrRA~ i ~:MNS ∎∎rr#RA~i~ w ~~AARARi rRAGARAAAAA~~E~~i#tRAAAr RAGA#~#i~~i~iAlRARARARAi RAE#>~s€€~RAAAAARARARAAA∎ RARA#<~;r:~~RARAAA#rrr∎ RR#~r~RARAr##rr∎ ∎RAAArr>~RA r rrr# r AARAWOMErrrr∎N

B

element

nownunons n o rr ~~~ trr∎rrn ∎r rnrr∎r# • nrrrrrr w t n#rrrr r~~~~~r~trrrr ∎r#rrr#iR ∎r/ rr#rrrr~~~tn#r

#nnnnnnn ∎

&rrrr#∎ r

∎~~:~r~rr~ :~~nr

rr~#rrrrr~~r~rr mnnm#∎r#r#rr rrrrrnrrrrrr~ rrrrrrrrrr#rrr ∎rrrrrnrrU.MI. r#rr*nn ∎ni #rrnrrrnrrrr rrnnrrn ni

qu ntific tion lsorithn

H

rrt~t~nniR#~~~~ rr txnr~tt~r~ ~~ ::: rr$tfrr~tt rm> f

priori inforn tion

n , nomm mew AA&MCRE#GAl ii#€i e ff e fg lmw #EtAId .NomE wwwwwwwi

enrr

(qu ntit tive) element l m ps

~ frr rru • ∎##nn###r r∎ rrr###rrr# rrr r rr®rnrr®rrf rrr##rr∎#®rr#~ r rrr#®rrr®~ r r#r#∎rrrrr∎i r ~rn nsrrrrr ∎r ~ ~ ~ ~ rr®rrrr . ; : :rrrrrrr rt : i

r

°fir#rrr/#r~ r rr n

Fig . 17. Im ge qu ntific tion in SIMS, schem tic. "R w" ion microgr phs qu ntit tive element l m ps .

re corrected pixelwise

nd thus tr nsformed into



F. G. Ruden uer /An lytic Chimic Act 297 (1994) 197-230

with possi le tr nsmission decre se t the field edges ("vignetting") . The sp ti l dependence of the m trix sign l from s mple with homogeneous m trix cont ining few inclusions (Fig . 16, left) will therefore reflect the loc l concentr tion of the m trix element . On rough surf ce the sign l from homogeneous m trix will show modul tion ccording to the loc l topogr phic structure . When the second ry ion extr ction field is sm ll, the m in contr st effect will e due to the different solid ngles of ions re ching the extr ction optics from deep crevices nd high ridges respectively (Fig . 16, centre): we h ve "topogr phic contr st" . In this c se the intensity distri ution in the ion microgr ph reflects the topogr phic structure of the surf ce nd not the concentr tion distri ution of the m trix element. When the extr ction field is stronger, the electrost tic field distri ution ne r topogr phic microstructures introduces tr nsmission discrimin tion etween ion species with different me n emission energies (Fig . 16, right). Since f ster ions (M f ) re less deflected y n electrost tic field th n slow ions (M S ), the topogr phic lly introduced sign l modul tion will e stronger for f st nd less pronounced for slow ions "chrom tic contr st " . Im ge correction nd qu ntific tion lgorithms An ion im ge (microgr ph) with N l lines nd NC columns consists of N i X N, pixels with pixel intensities which must e considered to e independent from e ch other. Qu ntific tion of n ion im ge then is equiv lent to performing N1 X N. independent pixel qu ntific tions . Qu ntific tion lgorithms which re v il le for single point qu ntific tion c n, in principle t le st, lso e pplied for qu ntific tion of im ges. Fig. 17 shows the schem tic procedure . The input d t here re the r w element l ion microgr phs from corresponding n lytic l volumes in the s mple . From e ch of these microgr phs the pixel intensities in corresponding loc tions (X„ ;) re used s input to qu ntific tion lgorithm. Most qu ntific tion lgorithms need ddition l priori knowledge for comput tion of element l concentr tions (see Section 3 .2.) . This inform tion m y consist of set of ppropri te rel tive sensitivity

217

f ctors nd/or n intern l st nd rd . In the c se of im ge qu ntific tion of course this st nd rd must e v il le in e ch pixel, thus constituting "st nd rd im ge" . Using ll this input, the qu ntific tion lgorithm computes concentr tion figures for ll input elements . This procedure is repe ted for ll input pixels (X ;/ ;), thus uilding up set of qu ntified element l m ps for ll input elements . The re liz tion of this scheme is difficult due to the following f cts : ( ) the ccur cy of qu ntific tion lgorithms in SIMS is not very high ( ) for the most precise lgorithm, the RSF qu ntific tion, it is difficult to o t in proper RSFs which, in the most gener l c se, must e considered s loc lly dependent . (c) it is difficult to o t in loc l intern l st nd rds for e ch pixel in the im ge . As consequence, ccept le solutions h ve een found so f r only for speci l c ses . In one c se [34] "homogeneous" intern l st nd rd (i .e . n element for which there w s re son to ssume homogeneous distri ution in the s mple) h s een used s sis for loc lly d ptive im ge qu ntific tion sed on the LTE lgorithm [14] . In nother c se reported loc lly inv ri nt RSFs were used for qu ntific tion of the distri ution of n ion impl nt [33] . In other c ses, the use of sp ti lly inv ri nt RSFs seems to e less ppropri te due to the loc lly v ri le m trix composition . Contr ry to full im ge qu ntific tion, remov l of selected rtif ct contr st effects, h s een tried with good success . Topogr phic contr st in p rticul r c n e p rti lly removed y r tioing of ion intensities in e ch pixel . This procedure is suggested y the consider tion th t loc l surf ce structure influences the ccepted solid ngle of e ch ionic species in the s me w y. R tioing of ion intensities (or referencing specific element l intensity to the sum of element l intensities) in e ch pixel therefore produces im ges which re not fully corrected, ut which t le st cont in less influence of loc l or glo l topogr phy . Such p rti l correction h s een done in h rdw re [35] nd softw re. An ex mple for n n lytic l pro lem which requires rtif ct correction is the n lysis of conliquid t min tion elements on the surf ce of met l ion emitter . The emitter consists of st in-



218

F_ G. Riiden uer /An lytic

less steel reservoir (4 mm di m.) nd tungsten needle (200 µm di m .), wetted with indium met l . During oper tion of the emitter sputtered m teri l from the st inless steel extr ction electrode is deposited on the liquid indium surf ce . The peculi r situ tion here is the m croscopic, rot tion lly symmetric s mple, with surf ce of loc lly v rile inclin tion nd therefore loc lly v ri le extr ction efficiency. Fig . 18 shows, in the left column, the ion microgr phs of In nd Cr o t ined on our sc nning ion micropro e . The field of view here is 1 .5 mm! The im ges o viously re strongly influenced y topogr phic contr st. The

Chimic Act 297 (1994) 197-230

distri ution of In, e.g ., should e roughly homogeneous long the needle nd the meniscus . Loc l referencing the In nd Cr im ges to the sum of element l intensities (In, Cr, Fe, Ni were me sured) gives the im ges displ yed in the right column of Fig. 18. The In-intensity here is much more homogeneous long needle nd meniscus, in the Cr-im ge the structure of the emitter ecomes more cle rly visi le . Note th t Cr seems to e lmost homogeneously distri uted on the meniscus with decre sing intensity long the needle in the tip direction . This is interpreted s "self cle ning" effect on the In-surf ce of the

Fig . 18. An lysis of cont min tion on liquid met l In ion emitter . Left column : ion microgr phs of In column : topogr phic contr st removed y loc l r tioing lgorithm . Origin ls colour coded.

nd Cr (cont min tion) . Right



F. G. Riiden uer/An lytic Chimic Act 297 (1994) 197-230

needle which is moving f ster during oper tion th n the st gn nt meniscus re . The loc l referencing process descri ed ove w s performed on f st pipeline processor . Tot l running time w s < 10 s. 4. Concepts nd limits of sp ti l resolution 4.1 . Im ge form tion process

s

n inform tion tr nsfer

The situ tion in im ging SIMS n lysis of "fl t" s mples c n e schem tic lly descri ed s shown in Fig . 19 : we h ve n o ject (s mple), ch r cterized y the distri ution of element E, n E(X, ) in the coordin te system {X, }, referred to s the o ject pl ne (= s mple surf ce). The SIMS instrument is considered s n im ge form tion system which cts upon the s mple (vi the prim ry e m), stimul tes emission of p rticle r di tion (vi the sputtering process), intercepts p rt of this r di tion, tr nsports it through sp ce nd tr nsforms it in such m nner th t in the coordin te system {X', '}, referred to s the

219

im ge pl ne, n im ge NE (X', ') is formed, n E(X, ) m y e given s the (loc lly ver ged) num er of E toms/ cm' in the s mple nd NE(X', ') s the num er of ion counts collected t position (X', ') of the fin l im ge . SIMS im ges c n e considered s represent tions of o jects (s mples) th t re sensed y direct interction of the im ge form tion system with the o ject. These consider tions re e sily gener lized to 3-dimension l o jects nd o ject represent tions . Neigh ourhood processes The im ge form tion system cre tes the im ge point (X', ') y cting upon nd tr nsporting the p rticles sputtered from the o ject . However, due to imperfections in the system, the im ge point (X', ') m y receive ions not only from the o ject point (X, ) ut from ll other points (x,y) of the o ject or their respective im ge points (x',y') . It c n e expected th t, s the dist nce from the o ject point (X, ) to other points in the o ject pl ne incre ses, the p rticle contri utions from these other points to the me sured intensity distort . pcx

s mple nE(X,

t/cm?] ) [

(distorted ) s mple im ge N E (X',

')

[cts/pixell

X' Fig. 19. Sym olic description of im ging micro n lysis s imperfect inform tion ch nnel etween element l distri ution in s mple nd distri ution im ge .



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F. G . Ruden uer /An lytic Chimic At 297 (1994) 197-230

NE (X', ') in the im ge point will decre se . B sic lly however, we must recognize the im ge form tion process s neigh ourhood process, i.e . (in the SIMS c se) the ion count in n im ge point m y depend on the tomic density in the o ject point nd on points in (possi ly infinite) neigh ourhood surrounding the o ject point . For the different physic l processes c using neighourhood effects in ion micropro es nd ion microscopes (see lso Section 1). In effect, these neigh ourhood processes re lurring ction in the fin l im ge . This c using lurring ction is ch r cterized y the point spre d function (PSF) h(x',y' ; X', ') which is the output im ge for unit-intensity o ject p t (X, ) (see Fig . 19). M them tic lly, the lurred im ge NE (X', ') is the convolution of the un lurred im ge N(X', ') with the point spre d function h(x',y' ; X', ') [20,36] . In other words, the o ject is " lurred" y the PSF to give the im ge : NE (X', ' ) 00

= Jf h(x' , ' ;X', ') .N(x',y') - dx'dy' on

-00

(11) The convolution interpret tion is v lid only for line r systems with "sp ce inv ri nt" point spre d function [20] . In Fourier sp ce, the convolution c n e expressed s multiplic tion (U,V) =h(U,V) - n(U,V)

( 12 )

where the underlined functions re the Fourier tr nsforms of the corresponding sp ti l functions nd (U,V) the sp ti l frequencies (in cm -1 ) in the X', ' directions of im ge sp ce. This shows, th t e ch sp ti l frequency in the o ject ppe rs in the im ge, modul ted y h(U,V ), the tr nsform of the PSF . h(U,V) therefore is c lled the optic l tr nsfer function (OTF) of the im ging system. In non-opticl pplic tions the OTF is frequently c lled the tr nsfer function of the system. In the c se of SIMS, o ject nd im ge functions re re l v lued, positive definite functions. The Fourier tr nsforms of o ject, im ge nd PSF gener lly re complex functions . The tr nsfer

function 12 c n e written s the product of re l mplitude nd complex ph se f ctor : (13) =MTF(U,V) •e ' .P '[-(1,V) MTF(U, V) nd PTF(U, V) re c lled the modul tion tr nsfer function nd the ph se tr nsfer function (PTF) respectively [36,37]. According to Eqs . 12 nd 13 therefore, e ch sp ti l frequency component in the o ject is d mped y the MTF nd shifted in ph se y the PTF to give the corresponding frequency component in the imge . G ussi n point spre d functions

In ion nd electron optics i is frequently ssumed th t the PSF is sp ce-inv ri nt nd h s the function l form of 2-dimension l G ussi n PSF(x', ') =

. e-(X

2+y12)/(2Q2)

( 14 ) 2ircr where, without loss of gener lity, X' = ' = 0, 2 is the v ri nce of the G ussi n nd N is its integr l . In SIMS, N c n e considered the tot l num er of detected ion counts cont ined in the im ge of qu si-point source . In ion micropro e im ging such G ussi n PSF might e the result prim ry ion e m with G ussi n current of density distri ution, in ion microscope im ging of g ussi n current density distri ution in the virtu l im ge spot produced y the emission lens [38] . Further properties of the g ussi n PSF re [20] : ( ) it h s rot tion l symmetry nd decre ses to fr ction of 0 .607 of its centr l m ximum t centr l dist nce equ l to ; ( ) homogeneous PSF ("top h t" cross section) with equ l centr l height nd tot l intensity h s r dius of vcr ; (c) 0 of the tot l intensity of the g ussi n re cont ined within circle of r dius 1 .18x, 90% within circle of r dius 2.15u. O viously, the sp ti l extent of the lurring ction of the PSF is connected to the notion of "sp ti l resolution" (for more ccur te definition see elow). The lurring ction of g ussi n PSF c n e expressed y single p r meter, viz. its st nd rd devi tion - . This f ct m kes it well suited for simple modelling of resolution eh viour in im ging systems . N



F. G. Riiden uer /An lytic

4.2. B sic pro lems in im ging n lysis Re lizing th t ny SIMS im ge cont ins distortions with respect to the true element l distriution, the centr l pro lem in sp ti lly resolved SIMS n lysis is the reconstruction of the true element l distri ution from me sured SIMS im ge ("restor tion pro lem"). It is o vious th t for this purpose the distorting properties of the im ge form tion system (SIMS instrument) must e known (Fig . 20c) ; the c se th t distortions m y lso depend on the o ject itself is not considered t the moment . The distortion properties of the im ge form tion system itself m y e determined posteriori y comp rison of suit le o ject with known distri ution (resolution test s mple) with its im ge s produced t the output of the im ge form tion system ("determin tion pro lem", see Fig. 20 ) . It is o vious th t we c nnot determine resolution in n im ge without ddition l priori inform tion ec use we h ve defined "resolution" s me sure of distortion which the true im ge sign l is suffering in the process of n lysis

221

Chimic Act 297 (1994) 197-230

nd im ge recording . A low contr st im ge m y represent perfectly tr nsmitted, close to homohe vily geneous, true o ject distri ution or lurred true distri ution with strong loc l concentr tion v ri tions . We therefore must cle rly sep r te etween the property of n im ge which c n e expressed s contr st, cut nce [3 ], etc. nd the property of the im ging nd recording process, expressed s distortion, resolution, resolving power, etc. The expected qu lity of the im ges representing suit ly given "true" o ject distri ution m y lso e estim ted priori (without ctu lly performing SIMS n lysis) . In this c se the distort(usu lly iming properties re estim ted from perfect) knowledge of the experiment l conditions nd physic l principles involved in SIMS n lysis ; m them tic l simul tion of the ction of the distortions on the known o ject distri ution llows to predict the im ge distri ution (" priori prediction pro lem", see Fig . 20 ). A priori prediction is typic lly pplied when the sic solvility of n n lytic l pro lem requiring high

SAMPLE

SPECTROMETER

I

SPECTROMETER

SPECTROMETER

'I

V

----- ----------IMAGE

-------------------IMAGE

( )

PREDICTION

IMAGE

(c) RESTORATION

( ) DETERMINATION Fig . 20 . Three fund ment l pro lems in im ging

n lysis .



F. G. Ruden uer /An lytic Chimic Act 297 (1994) 197-23©

222

sp ti l resolution h s to e decided ; when the ultim te theoretic l resolution limits of the method h ve to e estim ted ; or in the pre-development nd development ph se of new n lytic l technique when design nd oper ting p r meters h ve to e optimized . Fig . 20 shows schem tic lly, th t the prediction pro lem, the determin tion pro lem nd the reconstruction pro lem c n e considered complement ry processes of inform tion flow . The determin tion pro lem

We h ve seen in Section 4.1. th t the lurring effect which the im ge form tion system introduces into the represent tion of n o ject c n e fully ch r cterized y the point spre d function h(x',y' ; .X'', '). The posteriori determin tion pro lem therefore c n e considered solved, when the PSF c n e determined from the me sured im ge nd the corresponding true o ject distri ution. In the c se of gener l o ject nd sp ce inv ri nt PSF, the pro lem c n e solved in Fourier sp ce using the convolution theorem 12 . The Fourier tr nsform of the PSF (i .e ., the OTF) is given y n(u,v) h(u,v)

(15)

periodic function, the When the o ject is im ge consequently is lso periodic function . In this c se, the modul tion function 15 is re l [20] nd c n e expressed y the r tio of the modul tions M of im ge nd o ject respectively : . MTF = M M` where the modul tions M re defined s simple functions of m ximum v lues I M nd minimum v lues I. in the im ges respectively 36 : M=

(17) IM+I M

When, in ddition, the o ject is in ry, i .e . it consists of periodic " l ck" nd "white" re s only, the o ject modul tion o viously is equ l to

unity nd the MTF then is equ l to the modul tion in the im ge MTF = Ml

(18)

The determin tion of the spre d function from n ion im ge is consider ly simplified when speci l "resolution test p tterns" re used . Frequently used test p tterns re in ry point, line, edge, slit nd r p tterns. The width of the PSF (which is connected to the concept of "sp ti l resolution", see elow) c n e determined from the modul tion in the im ge of p ttern of known dimensions . In sc nning pro e instruments n ltern tive method to o t in im ge resolution is to connect ll " l ck" nd "white" p ir of cont cts nd to p ttern sections to me sure the current flowing to these cont cts s the e m is sc nned cross the p ttern . The resulting current/ e m position curve is equiv lent to n im ge intensity profile long the s me sc nning line. In the sections elow we ssume G ussi n PSF. The p ttern sh pes discussed re essenti lly 1-dimension l nd therefore llow to determine projections of the PSF onto the sc n direction only. The 2D sh pe of the PSF m y e o t ined y rot tion of the p tterns. Point nd line test p tterns . Let us consider

test p ttern consisting of two "points" situ ted t x = +d/2 on the x- xis (Fig. 21, right). When such p ttern is im ged, oth point im ges will e lurred y the g ussi n PSF nd the im ge intensity etween the point im ges t x = 0 will rise to nonzero v lue. When the point sources move closer, the depth of the intensity dip t x = 0 will decre se until, t cert in critic l dist nce, the imod l distri ution ch nges into monomod l one. The dist nce etween the point sources, t which their im ges c n just e visu lly resolved is c lled the "sm llest resolv le dist nce" (SRD) . Of course the criterion for rep r l rge ility of the overl pping im ges is, to degree, r itr ry. Frequently, it is defined in n logy to the R yleigh-criterion s drop to 73 .46% of m ximum intensity etween the lurred point im ges . This condition, derived from optic l diffr ction theory, is fulfilled when the first diffr ction minimum of one source coincides with



F. G. Riiden uer/An lytic Chimic Act 297 (1994) 197-230

the centr l m ximum of the other source . In this c se the intensity r tio f = I1 1 2 /Io h lfw y etween the point im ges is given y the Airy function It/2/lo= 2 .178J1(0 .617r) = 0 .73463 39 , where J1 is the Bessel function of first order 40 . In ion optics, diffr ction effects usu lly pl y minor role so th t the intensity distri ution in sc nning e m or virtu l point source im ge gener lly is (e .g., in the g ussi n c se ove) different from the Airy-function 39 . The 74% criterion therefore c n only e sed on n n logy to optics . Other uthors h ve defined the SRD s th t dist nce etween the point sources, where the dip etween the im ges just dis ppe rs, i .e . where the curv ture t the medi n point dis ppe rs 41,42 . This of course would e less r itr ry criterion, however it m y seem somewh t overst ting the resolution c p ilities of n im ging system ec use t such SRD point sources ctu lly m y not e sep r ted visully.

223

The intensity distri ution N(X) long line through the centers of two lurred point im ges corresponding to the im ges of two point o jects, sep r ted y dist nce d, is given y the superposition of the two G ussi n PSFs of the two o ject points . This function h s een c lcul ted 20 nd is shown gr phic lly in Fig . 21 . R yleigh modul tion (f = 0.735 = 1 - 0 .27 or M = 0 .153, respectively) is o t ined when the points h ve dist nce SRDP SRD p - 2 .80

(19)

Simil rly, the sm llest resolv le dist nces for the line, slit nd periodic r test p tterns shown in Fig . 21 re given y SRD L = 2 .800 SRD s =0 .68 SRD B = 1 .56u

(19 )

The corresponding "modul tion curves" (M vs . c/d) re shown in Fig . 22 . The modul tion

RESOPFIT7

X

I

VAVA

r p ttern Fig . 21 . Widths with width .

d of point, slit nd

slit p ttern r test p tterns producing R yleigh modul tion

point p ttern (M = 0.153) when im ged y G ussi n PSF



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F. G. Riiden uer/An lytic Chimic Act 297 (1994) 197-230

09 -0.8

-

0 .7

4 J

02 0.1 -0 -0 t

E

0

1 SK2MA/d

Fig. 22 . Modul tion curves from point, slit nd r test p tterns im ged with G ussi n PSF . sigm , width of PSF ; d, ch r cteristic p ttern width; horizont l line, R yleigh modul tion (M= 0 .153) .

curves offer convenient method for determin tion of the width o- of the lurring PSF . A suit le test p ttern with known fe ture width d is chosen nd im ged y the instrument . In the im ge, the modul tion M is determined, following Eq . 17 . The corresponding v lue of v/d = r, is t ken from the ppropri te curve in Fig . 22 . The width of the PSF simply is c lcul ted ccording to =r •d (20) The periodic r p ttern shown in Fig. 21 h s the fund ment l sp ti l frequency 1 n = 2d (line p irs/ mm) (21) The p ttern is considered to e just resolved when the im ge modul tion is equ l to the R yleigh v lue . The sp ti l frequency u . of this critic l dimension test p ttern is c lled the sp ti l resolution R of the im ging system : 1 1 R = uc 2SRD (lp/ mm) (22) = 2d C

Sp ti l resolution nd sm llest resolv le dist nce o viously re indirectly proportion l . Terminology . The terminology expressing con-

cepts of "sp ti l resolution" is often used in confusing nd m iguous w y. The fund ment l desire o viously is to give figure on how well distinct fe tures or dist nces etween fe tures in n o ject c n e resolved y microscopic instrument . This le ds to the concept of "sm llest resolv le dist nce" which is often thought to e n un m iguous property of the instrument itself . O viously microscopic instrument is considered of etter qu lity, the sm ller this sm llest resolvle dist nce is . A figure of merit which ssumes higher numeric l v lue with " etter" qu lity of the instrument is "resolution" or "resolving power" s defined ove . Often, the terms "resolution" nd "sm llest resolv le dist nce" re used synonymously which of course is sloppy l ngu ge . From the discussions in the previous sections it should however e cle r th t ( ) "sm llest resolv le dist nce" is not property of n in-



225

F. G. Riiden uer/An lytic Chimic Act 297 (1994) 197-230

fe ture dimension in the s mple nd "resolution" figure of the instrument, t le st when fe ture size nd "resolution" of the instrument re of the s me order. The w y to proceed in this c se would e to numeric lly convolve ( lur) the known s mple structure with the known PSF of the instrument (see Eq . 11) nd to decide if in the " lurred" im ge the fe ture of interest is sep r ted well enough . Such procedure is however seldom pplied ec use the ctu l experiment m y decide the issue f ster nd more reli le . The situ tion is different, when speci l situ tions re expected to ppe r in ctu l n lysis, e .g when the im ge sign l is noisy due to low e m intensity or low concentr tion of the n lytic l

strument lone, ut com ined qu lity of instrument nd s mple . ( ) The only figure of merit rel ted to sp ti l resolving c p ility which is independent of the s mple under test nd only property of the instrument is the point spre d function (which m y e represented y one or more p r meters descri ing its sp ti l extent) . Prediction pro lem

The prediction pro lem comes into effect in SIMS, when it h s to e decided, if structure of given sh pe c n e sp ti lly resolved in SIMS instrument with known point spre d function . We h ve seen ove th t this pro lem c nnot e uniquely decided y knowledge of the sm llest

STATSLIT

d=19 pixel x=74 pixel y=96 pixel $1=0 .0527/pix . M2=0 .8146 N3--0 .00879 N4=0 .00148 S1= 4 .4 pix . S2= 8 .3 S3=10 .6 S4=26 .0

I

2

**

3 * *

4

*

*

•

* •

*

* * •

*

*

•

Fig . 23 . Degr d tion of slit im ge recorded with progressively fewer ver ge ion counts/ pixel . Ni, ion counts/ pixel ; Si, me n dist nce etween occupied pixels.



226

F. G. Riiden uer /An lytic

Chimic .Act 297 (1994) 197-230

element. Methods for estim tion of im ge resolution in these c ses re given in the sections elow. Consider tion of count r te st tistics. At sm ll

second ry ion counting r tes (e .g. for tr ce elements or for su -0 .1 µm prim ry e ms), new limit to sp ti l resolution ppe rs . Due to the st tistic l n ture of second ry ion emission, n im ge will consist sic lly of single-ion count pixels sep r ted y empty pixels . Structures in the im ge (such s the slit fe ture in Fig. 23) will ecome unrecogniz le if the ver ge dist nce etween occupied pixels is l rger th n the ch r cteristic dimension of the o ject. Levi-Setti 8 h s introduced the concept of digit lly "me n sign l dist nce", d8 , long sc nned im ge line, i.e . the me n line r dist nce etween occupied pixels: (23) where d x is the sc nning step-width (= pixel dist nce) nd N the ver ge ion count/ pixel . The sm llest resolv le dist nce d i which c n e expected in low-ion count im ge, recorded y digit lly sc nned ion micropro e, then is c lcul ted s convolution of pro e di meter dp , sc nning stepwidth d r , me n sign l dist nce ds nd the width of the sputtering c sc de, d, 1,2 : J

1

~2

(24) For very sm ll counting r tes, the me n sign l dist nce d. o viously ecomes the limiting resolution p r meter nd A different concept is the use of the s me delect ility criteri for im ge fe tures (modul tion limits) s in the l rge-sign l c se descri ed in Section 4 .2. ove. Im ge st tistics is t ken into ccount y ddition lly requiring cert in precision limits on ll modul tion me surements . Let us consider test p ttern consisting of slit of width 8 in n otherwise homogeneous s mple . The im ge is ssumed to e s mpled with step

width of 8, the ver ge count num er in e ch in (pixel) of width 8 is N. If N is sm ll, the st tistic l fluctu tions in the count num er/ in will c use gr ininess in the im ge which m y prevent detection of the slit p ttern . In order to reduce st tistic l fluctu tions, the im ge m y e low-p ss filtered ( ver ged) y filter of width A . Such filter however is sme ring out the im ge of the slit p ttern so th t the intensity in the slit centre m y not e sufficiently depressed for n un miguous identific tion of the slit . Let us consider the intensity Nmin in the centre of the ver ged slit im ge nd Nm ,x in l rge dist nce from the slit centre : N ( d) .

S N

(25)

We use the s me delect ility criterion for the im ge s in Section 4.2 ., n mely th t the intensity r tio R = Nmin/Nm x should e elow the R yleigh-limit ("modul tion criterion") : Nmin

<1 R

( 26)

Nm x

where crR = 0.27. In st tistic lly domin ted imge this condition is however not sufficient for un m iguous identific tion, ec use R m y exceed the upper limit Eq. 26, just due to st tistic l second condition is fluctu tions. Therefore, necess ry, limiting somehow the llowed extent of st tistic l fluctu tions of R . It seems re sonle to require th t, once R yleigh modul tion h s een determined from the im ge, the expected st tistic l uncert inty &R of this determin tion is sm ller th n crR (im ge modul tion lw ys < 1). This le ds to second delect ility requirement ("precision criterion") : (27) SR=o-R --0 .27 For low pixel count (N/6 « 13 .7/d) the two criteri (Eqs. 26 nd 27) le d to sm llest, s fely detect le width d of " l ck" slit in "white" nd pixel count N 20 pl ne t given pixel size 8 (28) d w 4 .70

N



F. G. Riiden uer/An lytic Chimic Act 297 (1994) 197-230

The minimum required integr tion interv l A (minimum st tistic l resolution) then follows from Eq. 25 s 8 17 .70

(28 )

N

Ex mple : for me n count r te of N = 1 count/ pixel, the minimum detect le slit width is out 5 pixel widths (see Eq . 28). In order to me sure under these circumst nces the intensity depression corresponding to the slit with sufficient precision, we h ve to integr te counts long dist nce A of out 18 pixels . For the more heuristic "me n sign l-dist nce"-concept slit would lre dy ppe r detect le t count r te of 1/pixel, if its width is l rger th n out 1 .4 pixel widths. Sm llest resolv le volume nd detection limit . Counting r te st tistics, s descri ed in the previous section, m y e .g. ecome domin nt when the concentr tion of the n lytic l element is low . This o viously me ns, th t element concentr tion, i .e . s mple property, is setting limit to

227

sp ti l resolution . In contr st to the previous section, where the st tistic l limit tions to 2Dresolution were tre ted, it is shown in this section, th t the element concentr tion ctu lly sets limit to the size of the microvolume which c n e uniquely discrimin ted from the neigh ouring microvolume . In other words, element concentr tion is setting limit to 3D-sp ti l resolution. Let us consider microvolume with l ter l extensions 3 x 5 nd depth extension 8z which is sputtered in the course of n n lysis . We w nt to know the sm llest concentr tion C m;n which we c n detect in this microvolume . O viously, this microvolume cont ins limited num er of toms, mong them some of the n lytic l species X . In the process of SIMS n lysis, these n lytic toms re removed from the s mple y the sputtering effect, some of them in ionized st te . A fr ction of these n lytic ions is collected y the m ss spectrometer, m ss n lyzed nd detected, usu lly in counting rr ngement . Since the sputtering process is destructive, these ion counts re the only opportunity to o t in inform tion on the composition of the selected microvolume . Counting

3os1APE



2 1 i

u =

depth profiling

X,

y,

~ =

e

cn3 l

p 2 1 (c 1 T 1 )

isotropic 3D - distri ution dye

~ ~/ =L/, /.. . . .~ ~ ~

/101

e

4

~.-6 x .X

ti ~~> ~~~ti tt3 ~ ~~~~ tip

Fig . 24. Optim l sh ping of n lytic l microvolume in different n lytic l modes .

`

$



228

F. G. Riiden uer/An lytic Chimic Act 297 (1994) 197-230

st tistics therefore dict tes, th t we must collect minimum num er of 10 4 N+'(X) = P 2 (ions)

(29)

ions of the n lytic species for our intensity me surement to e precise to within p (%) 16 . Assuming unit detector efficiency, the num er of X ions detected rel tes to the tot l num er Ntot of toms cont ined in the microvolume considered (see Section 3 .1 .) : N -'- '(X) - Ntot • c(X) •

' (X) • T

= n • 5V , c(X) •

+ (X) • T

(30)

+(X) • c(X) •T

2x10 -19 p

2

' c(X)

(31) • 7-U(X)

where in the l st pproxim te equ lity n ver ge tomic density of n = 5 10 22 h s een ssumed nd the useful sensitivity of element X, 7u (X) h s een introduced (see Section 3 .1 .) . The useful sensitivity therefore is the relev nt sensitivity p r meter in 3D- n lysis where we re de ling with s mpling volume of limited size . Note th t Eq. 31 determines the minimum size of the s mpling volume required for detection of given n lyte concentr tion, ut not its sh pe . The s mpling volume now might e sh ped ccording to the p rticul r n lytic l requirement (see Fig . 24) . In depth profiling we usu lly re interested in sm ll resolved depth interv l Sz nd might sk wh t limit tions on the n lyzed re re imposed y the minimum s mpling volume required for ccur te me surement of n element with concentr tion c(X) . From Eq. 31 we X

5x10 -10

Mx) • Tj (X) • Sz

(32)

In (l ter l) im ging n lysis the pro lem is to estim te the minimum sputter depth 8z required for im ging n element X with concentr tion c(X) with desired l ter l resolution S . The respective rel tion g in is derived from Eq . 31 s 5 x 10 -19 p2 . . . 2

3

C(X) 7-u(x)

104 n *P 2

. S(X) > p

5Z(X) >

The l st equ lity in Eq . 30 h s een o t ined y rel ting the microvolume, S V, to the num er cot of toms cont ined in it y Ntot = SV • n (n is the tot l num er of s mple toms/ cm'). Comining Eqs . 29 nd 30 yields rel tion for the minimum s mpling volume required for the detection of n element of concentr tion c(X) with precision of p (%) : SV>8 2 •S z=

c n c lcul te the required l ter l extension S of the n lyzed re :

(32 )

In 3D n lysis of isotropic s mples it might e useful to define resolution element of equ l extent S u in ll three sp ti l coordin te directions . In this c se the volume S V = S ;, nd Eq. 31 yields for the minimum l ter l extension S u of the isotropic resolution volume 6

X

10 -7 (32 )

5U(X) > p 2/3 . ( C(X) T ( X)) 1/3

Note th t these resolution me sures depend on the n lytic l element X . The element dependent f ctor in ll these equ tions is the product c(X) • T„(X). Therefore, in the s me s mple, the sp ti l resolution limit for m trix (or high yield) element is etter th n for tr ce (or low sensitivity) element. N tur lly, Eqs . 32-32 c n e reversed to give expressions for the lowest detect le concentr tion in sp ti l resolution element of given dimensions . Note th t in ll n lytic l modes the lowest detect le concentr tion c(X) of n element X in given n lytic l volume is indirectly proportion l to the useful yield . Note lso th t postionis tion of the sputtered p rticles effectively ch nges the numeric l v lue of the useful yield Tu . In the ultim te c se of technique with 100% ioniz tion efficiency, 100% overl p etween ioniz tion volume nd sputtering plume nd 100% spectrometer tr nsmission, the effective useful sensitivity is 1 . Eqs . 31-32 then c n e used to estim te the respective sp ti l resolution limits for this "ultim te" sputtering technique .



F. G. Ruden uer /An lytic Chimic Act 297 (1994) 197-230

229

Fig . 4 shows gr phic lly the rel tionship etween sp ti l resolution nd lowest detect le concentr tion, s given y Eqs . 32 nd 32 . The solid lines represent the "useful resolution" S u (equ l sp ti l resolution in ll directions); the roken lines give the estim ted dependence of detection limit on l ter l resolution for the c se where the sputtering depth is limited to 10 nm . The right p ir of lines re c lcul ted for T . = 10 -3 ( ver ge v lue for good SIMS instrument, the left p ir of lines represent the c se 'ru = 1 (perfect postioniz tion)) . O viously, in this c se the "sputtering limit" to sp ti l resolution is close to tomic dimension.

reconstructed PSF, reconstruction of the (linesc n) im ge w s performed . The sm llest resolvle dist nce in the origin l im ge (2 µm) w s improved to out 1 µm y this process .

Reconstruction pro lem

References

There h ve een very few ttempts to t ckle the pro lem of im ge reconstruction, i .e . the reconstruction of the sp ti lly true loc l element distri ution from the me sured ion microgr ph nd n ssumedly known point spre d function (see Section 4 .1 .). The re sons re th t rtif ct contr st, which is true pixel property, must e completely removed efore the geometric "delurring", which ffects loc l vicinity, c n e ttempted . Since rtif ct remov l is only p rti lly possi le in SIMS, new rtif cts m y e induced when de lurring is ttempted on n incompletely "precle ned" im ge . It is hoped, however, th t successful pplic tion of reconstruction lgorithms llows to incre se im ge resolution eyond th t v il le in the r w ion microgr ph . De lurring ctu lly m y e implemented in Fourier sp ce y c lcul ting the Fourier tr nsform of the de lurred im ge, n(U,V), from the tr nsforms of the lurred im ge nd the point spre d function respectively (see Eq . 12). This procedure does not lw ys le d to success since there m y e infinities nd neg tive v lues in the output . Other filtering routines re v il le 36,37 which gu rntee non-neg tive finite output function . In one c se reported in the liter ture 43 , 1-dimension l linesc ns o t ined on sc nning ion micropro e, were de lurred nd n pp rent resolution incre se y f ctor of 1 .5-2 w s o t ined . The point spre d function w s o t ined y im ging n edge structure of known sh pe nd reconstructing the PSF from this im ge . Using this

Acknowledgements This work w s performed with support from TSP-progr m of the Austri n Ministry of Science nd Rese rch nd the Austri n Society for Microelectronics (GME) . M ny fruitful discussions with W. Steiger nd M. Alff re cknowledged .

1 2 3 4 5

6

7

8 9 10 11

12 13 14

15 16

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Chimic Act 297 (1994) 197-230

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