Secondary electron energy analyzers for electron-beam testing

142

Nuclear Instruments and Methods in Physics Research A298 (1990) 142-155 North-Holland

Secondary electron energy analyzers for electron-beam testing Erich Plies

Forschungslahoratorien, Siemens AG, Otto-Hahn-Ring 6, D-8000 München 83, FRG

Existing post-lens and through-lens analyzers for electron-beam testing are reviewed . A novel through-lens analyzer is proposed which can be operated m two modes: m the conventional retarding-field mode with a feedback technique or in a dispersive multichannel mode with an open-loop technique. In addition, an improved and fast ray-tracing method for the secondary electron trajectories is introduced, which uses Lenz's model field and series expansions for calculating the spatial magnetic field. 1. Introduction Electron-beam (e-beam) testing is a high-performance test method for design and chip verification as well as for failure analysis of integrated circuits (ICs). The electron probe allows waveform measurements at internal nodes and imaging of the logic operation of entire parts inside the IC . With decreasing interconnection line width, e-beam testing has become increasingly common and has replaced test techniques using a mechanical tip [8]. The major advantages of e-beam testing are the fine diameter of the electron probe, which may be quickly positioned on submicron interconnection lines, and its nonloading and nondestructive application at low primary electron energies .

Up to the middle of the eighties, modified scanning electron microscopes (SEMs) were used for e-beam testing of ICs. The electron-optical modifications of the SEM usually comprised a beam-blanking system between the anode and the first magnetic condenser lens and a simple retarding-field spectrometer between the magnetic objective lens and the IC . Today, dedicated e-beam testers (EBTs) are available. The electron-optical column of such an EBT must be optimized with respect to primary-electron (PE) probe forming (small diameter of 0.1-0.3 P.m and high current of > 1 nA for low beam voltage of < 1 kV) and PE pulse generation (10 ps for GaAs devices and = 200 ps for MOS ICs) . Additionally, the collection of the secondary electrons (SEs) must be optimized to achieve precise voltage

UE

I -- UPE

Fig. 1 . (a) Schematic representation of the electron-optical column of a dedicated EBT (ICT 9010) . (b) Distributions of the axial (cathode related) potential O(z) and the axial magnetic flux density B(z) along the optical z-axis . UEx = extraction voltage for the primary electrons m the triode gun, Ur.E = lens voltage of the immersion condenser lens, UE = extraction voltage for the secondary electrons and Up. = final beam voltage of the primary electrons. (c) Light-optical counterpart of the electron-optical column and primary-electron ray path. Equivalent lenses of magnetic origin are m light print, whereas equivalents of electrostatic origin (concave and convex lenses and plane parallel plates) are shown dark . 0168-9002/90/$03 .50 © 1990 - Elsevier Science Publishers B.V . (North-Holland)

E. Phes / Secondary electron energy analyzers

Table 1 Comparison of the primary-electron optical performance of two electron-beam testers - a modified SEM [99] (based on a Cambridge Instruments S150) and a dedicated EBT [10,11,6570] (ICT 9010).

Electron optics optinuzed for Cathode Condenser system Final PE-energy [keV] Brightness for final PE-energy [A CM-2 sr-1] Normalized brightness [A CM-2 sr - ' V - '1 Minimum PE-pulse width [ns] Objective lens Working distance [ Spherical aberration constant [mm] Axial chromatic aberration constant [-1 Final aperture [rad] PE-probe diameter [y.m] PE-probe current [nA]

Modified SEM

Dedicated EBT

2.5-30 keV W purely magnetic

0.5-1 .5 keV LaB6 immersion lens

2.5

1 .0

1.2x104

3.2x104

4.8x10 3

3.2x104

1 purely magnetic

0.15

combined electrostaticmagnetic

11

2

70

10

20 0.02 0.4 5

4 0.02 0.12 2.5

measurements and a negligible influence of the local fields of the IC . The low energy of the PEs is necessary to avoid damage, charging and loading of the IC . Optimized low-voltage optics are also of interest for other applications, such as wafer inspection, surface science and biochemistry . Fig. 1 illustrates the electron-optical column of a dedicated EBT [10,68-70]. Part (a) shows a schematic cross section through the column. The column consists - in principle like every dedicated EBT - of the follow-

143

ing electron-optical components : electron gun, beamblanking system, condenser lenses and a compound spectrometer objective lens which acts as an objective for the PEs and a spectrometer for the SEs . Part (b) shows the axial distribution of the potential O(z) = 0(0, 0, z) referred to the cathode and the magnetic flux density B(z) = BJ0, 0, z), which are among the factors affecting the electron-optical performance data (cardinal elements, image aberrations) . The kinetic energy of the axial primary electrons is eO(z) . The stage is, of course, grounded, and the cathode has a potential - UPE with respect to this ground connection, where UPE is the beam voltage of the primary electrons at the IC . Part (c) of fig. 1 shows the light-optical analog of the column and the principle of primary-electron (PE) focusing, with the equivalent elements of electrostatic origin (concave and convex lenses and plane-parallel plates) shown dark and the equivalent lenses for the magnetic lens fields shown bright . The primary and secondary electron-optical performance data of this dedicated EBT is summarized in tables 1 and 2 respectively, together with the performance of a modified SEM [99] . The clearly superior performance data of the dedicated EBT were attained by improving the individual electron-optical components and the customized low-voltage column concept. In the following, we will first briefly touch upon objective lenses and present a concise review of individual existing analyzers for e-beam testing. We will then discuss an improved and fast ray-tracing method and propose a new analyzer which may be operated in dispersive multichannel mode and open-loop technique. In the detailed reviews [5,6] of e-beam testing, analyzers for this technique are also discussed, as in ref. [7], where all electron-optical components of an EBT are reviewed . 2. Objective lenses In a compound spectrometer objective lens, such as shown in fig. 2, the spectrometer part in principle also acts on the primary electrons and the objective lens on

Table 2 Comparison of the secondary-electron optical performance of two types of electron beam testers - a modified SEM and a dedicated EBT. Type of spectrometer Location of spectrometer Detector Spectrometer constant Cross-talk between 1.5 ~Lm interconnection lines

Modified SEM

planar retarding field post-lens one Everhart-Thornley 5 x 10 -s V A s

Dedicated EBT hemispherical retarding field through-the-lens two Everhart-Thornley 5 x 10 -9 V A s

< 400

< 3%

111. SPECTROMETERS/ANALYZERS

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E. Phes / Secondary electron energy analyzers a)

Primary electron beam

ts

L

IV4

0, '00

Grid electrode 1 Accelerating grid

FAI

11

ii

UR 's_ " * UL U E -2kV

Magnetic lens

I

Deflection coils Stigmator Grid electrode 3 U E -2 kV Integrated circuit, UL Suppressorgrid Deflection grid

v o ô

i

SE-detector Retarding grid U R x-6V t U l_ Grid electrode 2 U E - 2 kV

Magnetic lens Extractiongrid UE -2kV Integrated circuit, Fig. 2. Schematic of the compound spectrometer objective lens . The primary electron beam is focused on the specimen by superimposed electric and magnetic fields (a). The emitted secondary electrons are simultaneously extracted and focused into the center of a hemispherical retarding-field spectrometer (b). UR = retarding voltage, UE = extraction voltage for the SEs and UL = line voltage to be measured

the secondary electrons (SEs). We will therefore briefly touch upon objective lenses. The objective lenses of all modified SEMs and of most dedicated EBTs are purely magnetic . The design of purely magnetic lenses is at the state of the art and their properties, including those of single pole-piece lenses [14], are known [3,12,13,15] . The commercial EBT from Sentry Schlumberger [87,88] and the laboratory setup by Dubbeldam and Kruit [89-93] (see fig. 3) use a variable-axis immersion lens (VAIL) which has already been successfully used for a number of years in electron beam lithography [16-18] and represents a clever superposition of the magnetic lens and deflection field. In the compound spectrometer objective lens of the dedicated EBT shown schematically in figs . 1 and 2, the

electrostatic spectrometer fields (ô0/8z =# 0 in fig. 1b) must be taken into account when calculating the PE focusing and the aberrations [24] . Fig. lc shows the light-optical counterpart of the spectrometer objective lens . In order to largely eliminate the upper lens group, which is generated by the spectrometer itself, with respect to the PE focusing, we place the intermediate image in or just before this group. The lower lens group represents a retarding combined electrostatic-magnetic lens system distinguished by small image aberrations [11,24,103] . If a magnetic deflection element is added in the objective lens, as in fig. 2a, we obtain a combined focusing and deflection system with spatially superimposed fields which is no longer quite so simple to calculate. However, existing theories and programs [1924] allow the numerical calculation of compound sys-

E. Phes / Secondary electron energy analyzers

Predeflectors

Scintillator discs & light pipes

145

Up to 1984, exclusive use was made of post-lens analyzers . Starting with the first in-lens analyzer by Menzel [59], a series of in-lens and through-lens analyzers were still proposed and constructed. In the meantime, all dedicated EBTs are equipped with analyzers of this kind, as these allow both superior PE and SE performance data to be attained (see tables 1 and 2) . However, this double performance gain was traded off against a more complex electron optical system in every dedicated EBT . Besides the spatial resolution (PE probe diameter) and the time resolution (PE pulse width), the voltage resolution is another figure of merit of an EBT . According to Gopinath [9] the minimum detectable voltage change DU is mainly determined by the shot noise in the SE current and can be expressed by Gopinath's formula : AU= nC CV/0f/'PE ,

Additional coils for parallelizer Device

Fig . 3 . Through-lens analyzer with two energy channels after Dubbeldam [93] . VAIL = variable axis immersion lens .

tems from any superposed electrostatic and magnetic lens and deflection fields to be made . 3 . Existing analyzers The SE energy analyzer is the key electron-optical component of any EBT. All previously used analyzers are retarding-field energy devices, which integrate over the SE spectrum or parts of it . Under ideal conditions, the detected SE current depends only on the potential difference between the measuring point in the IC and the retarding-field grid . To linearize the quantitative voltage measurement, the energy analyzer is usually operated in a feedback loop . The following electronoptical requirements are made on today's analyzers : - the SEs must be detected, as far as possible, independently of their angle of emission, - the detection must, as far as possible, be independent of existing microfields (local fields) of the IC or the analyzer must reduce these microfields as far as possible, - the analyzer must not have a negative effect on the performance of the primary electron probe, e.g . give rise to unwanted deflection or astigmatism, - beyond this, the analyzer must be designed and configured so that it does not, in principle, limit the performance of the PE probe .

where n is the signal-to-noise ratio, 0 f is the bandwidth of the detection system, IPE is the primary electron probe current, ano C is the spectrometer constant in which all spectrometer parameters are summarized . Specifying DU = 10 mV, setting n = 1 and using I PE and C of the dedicated EBT in tables 1 and 2, eq. (1) yields a bandwidth 0f = 10 kHz. In the following, let us initially present an overview of the various post-lens analyzers and then discuss the various in-lens and through-lens models . In view of the ongoing increase of component integration with ever smaller interconnection dimensions and thus increasing field strength of the microfields at the surface of the ICs, in section 5 .1 we will also discuss the question of whether retarding-field analyzers do in fact represent the best solution for electron-beam measurement technology. 3.1 . Post-lens analyzers Retarding-field analyzers have already been used in other sectors prior to e-beam testing of ICs and are still used in other applications today (see refs . [25-38]) . Application sectors were or are SE emission studies [26,36], Auger electron spectroscopy [27], electron spectroscopy for chemical analysis [28,31] and M6ssbauer spectroscopy [38] . Compared with dispersive energy analyzers, retarding-field devices have a high luminosity but a low energy resolution. The latter results from the width of the cut-off curve of the retarding-field analyzer [25,49], which has a high-pass characteristic . This smeared cut-off characteristic of the retarding-field analyzer produces an effect on the form of the detected integral SE spectrum (S-curve) . The slope of the S-curve decreases with increasing field strength of the retarding field, and with growing mesh width of the retarding-field grid ; also, the S-curve is flatter for a planar retarding III . SPECTROMETERS/ANALYZERS

146

E. Plies / Secondary electron energy analyzers Deflection coils

H 1cm

Fig 4. Post-lens analyzer after Feuerbaum [45] integrated m a modified scanning electron microscope [99] .

field than for a spherical one [25,29,30,49] . In electronbeam measurement technology, a flatter S-curve means a worse voltage resolution (greater spectrometer constant) [49] . The retarding-field analyzers used by Gopinath et al . [39-41] for e-beam testing had hemispherical grids and were constructed similarly to the analyzers used for the SE emission studies (see e.g . ref . [26]) . They suffered from a weak extraction field, which was increased by Goto et al . [42] by means of an additional control grid. Hannah [43] and Balk et al . [44] used cylindrical deflector analyzers which have a band-pass characteristic and suffer from a long working distance (65 mm and 22 mm, respectively) . The analyzer designed by Feuerbaum [45] (see fig. 4) was optimized with respect to height and extraction field strength and is still widely used . The retarding field spectrometer of Plows [46] was the first commercially available system (Lintech Instruments Ltd .) . It is attractive due to its rotational symmetry and was evaluated in refs . [47,48] . All previously mentioned post-lens analyzers [39-46] were compared in detail in ref. [49] and/or ref . [50] . Plies [51] invented an analyzer in which a plane extraction field and a hemispherical retarding field are combined so that the virtual source of the SEs coincides with the center of the hemispherical retarding field . An analyzer of this type was first constructed by Nakamae et al . [52-54] . Due to its high extraction in conjunction with an angle-independent detection of the SEs, according to refs. [52-55] thus analyzer provides a steeper S-curve, an improved spectrometer constant and a smaller local field effect [56] than the Feuerbaum

analyzer with a plane retarding field. In the local field effect (LFE), Nakamae et al . [56] make a distinction between two effects or types . LFE I is characterized as the effect by which slow SEs cannot overcome a retarding local microfield above the interconnection. However, the trajectories of SEs which are not reflected from the microfield can nevertheless still be affected by it, which also leads to an error in the quantitative voltage measurement . This effect is designated as LFE II . By changing the retarding field of Feuerbaum's post-lens analyzer from a planar to a hemispherical one, the spectrometer constant was improved [55] from 5 X 10 -s V Ai/2 si / 2 to 1 .7 X 10 -8 V At/2 s1 /2. 3.2 . Through-lens analyzers

The great disadvantage of a post-lens analyzer is the large working distance between the objective lens and the IC (see fig. 4) . This necessarily makes the axial aberrations of the objective lens relatively high (see table 1), and an electron probe with small diameter and high current cannot be generated . This drawback can be avoided by means of in-lens and through-lens analyzers . In the following, we intend largely to use the designation through-lens analyzer quite differently from the original term used by the inventors for their analyzer . For m most cases, the detector itself is positioned above the objective lens . The first analyzer of this type was invented by Menzel [59,60] . It is attractive because of its simplicity, but has not become popular because it is sensitive to LFE II .

E. Plies / Secondary electron energy analyzers 3.2 .1 . Through-lens analyzers with hemispherical retarding fields The commercial dedicated EBTs from Hitachi [6264], ICT [65-70] and Cambridge Instruments [71] make

a)

c)

147

use of through-lens analyzers with hemispherical grids. According to ref. [51], in the case of ICT's through-lens analyzer, the principle of the post-lens analyzer with a reduced LFE described in section 3.1 was modified so

b)

d)

Fig. 5. Radius r of the SE trajectories versus distance z along the optical axis for spherical grids ((a) and (b)), and planar grids ((c) and (d)) . In (a) and (c) the emission angle as = 60' is fixed, as is the starting energy Es = 6.3 eV m (b) and (d). O(z) = axial electrostatic potential, B(z) = axial magnetic flux density, NI = lens excitation and UPe = acceleration voltage of the PEs. The retarding voltage is UR = - 6 V and the whole device under test is grounded (UL = 0) . 111. SPECTROMETERS/ANALYZERS

148

E. Plies / Secondary electron energy analyzers

that the center of the spherical retarding field now coincides with an SE image of the measuring point [65] (see fig. 2b). The behavior of the SEs in the compound spectrometer objective was simulated by ray-tracing . The methods of field calculation and numerical integration of the equation of motion are described in ref. [67] . Figs . 5a and 5b show results of the ray-tracing in the radial section. All SE-trajectories of fig. 5a start with a fixed emission angle (as = 60 ° ) but varied starting energies Es, whereas all SE-trajectories of fig. 5b have the same starting energy (Es = 6.3 eV) and the starting angle as is varied . For both plots, the retarding voltage (between the IC and the second spherical grid) was UR = -6 V. In fig. 5a, all SEs with ES > 6.1 eV pass the retarding field, which corresponds almost exactly to the retarding voltage of 6 V. Fig. 5b portrays the angle-independent detection of the through-the-lens spectrometer. For comparison, we replaced the two spherical grids of the spectrometer by two planar grids situated at the vertex of the spherical grids. When using the same values for the parameters ES and as , the ray-tracing yielded the trajectories of figs . 5c and 5d . The better performance of the spherical grids is clear from the results. In figs. 5a and 5b, the center of the spherical retarding field and the SE-focus are correctly matched to the lens excitation necessary for focusing primary electrons of 700 eV . If the retarding field section of the spectrometer is kept fixed for higher PE-energies, then the performance of the spectrometer will be slightly worse, which can be seen from figs . 6a and 6b . It is nevertheless clear that the spherical grids are still much better than the planar grids.

Hitachi appeared to use the same principle (matching of SE image and center of spherical retarding field), although no direct reference was made to thus in refs . [62-64], and these three papers also specify various numbers of grids and different voltage values at the grids. The main difference between the two analyzers lies in their PE focusing . Hitachi uses a double lens as the objective, so that the PE beam is telecentric at the point of the hemispherical grids. This gives rise to a somewhat larger center hole in the spherical grids, so that it may happen that a higher proportion of the paraxially emitted SEs cannot be detected correctly or even at all. In the case of the ICT analyzer, a high extraction field as well as a relatively high retarding field is used . To eliminate lens effects of the axial retarding-field grid mesh with respect to the PE beam from the outset before that, an intermediate PE image was placed in the hemispherical retarding field (see figs . l c and 2a). The high extraction field (1 kV/mm) in the ICT analyzer greatly reduces LFE I but makes the voltage measurements on passivated or buried interconnections difficult to perform, due to charging. Deviating from the first design [65,68], Frosien [70] therefore introduced an additional electrode directly above the IC, which weakens the extraction field there and permits good measurements on passivated ICs [70] . This additional electrode ensures that the focusing principle of the SEs is not changed. No further details are known about the through-lens analyzer from Cambridge Instruments [71], apart from the fact that it is, including the scintillator, entirely symmetrical about the PE beam . In contrast, the systems from Hitachi and ICT each have two detectors arranged opposite to each other. Tang et al . [61] specify

a =60° 90-

e V-

\~w y\

ES 5-

'~/

deg 60 -

s

~~~

ES=6 3eV

spherical

(X

S 300

ZSE ZSE Fig. 6. Performance of spherical and planar retarding fields . A comparison resulting from SE ray-tracing. The center of the spherical retarding field and the SE image are correctly matched to an acceleration voltage UPr = 700 V of the PEs. as = emission angle, Es = starting energy of the SEs and zse = distance of the SE image from the device under test. The retarding voltage is UR= -6 V and the whole device under test is grounded (UL = 0) .

14 9

E. Plies / Secondary electron energy analyzers a through-lens analyzer which is very similar to the ICT device, but can work effectively with plane grids . This is made possible by its configuration, since the PEs have a high beam voltage of 10 kV . The associated high lens excitation means that the SEs (extraction voltage 820 V) are initially focused and then collimated.

3.2 .2. Magnetic-collimating analyzers

It is known from plasma physics that a "magnetic mirror" or "magnetic bottle' can confine charged particles [78,79] . This principle was first used, in an inverse sense, with the specimen in the "neck" of the bottle, by Kruit and Read [801 to build a magnetic field parallelizer for a photoelectron spectrometer . Garth et al . [81] were the first to build an analyzer for e-beam testing which magnetically collimates the SEs in this manner. For this purpose, they initially [81-83] fitted a single pole-piece lens according to Mulvey [14] under the IC. In a later paper [84], Garth made a critical study of the purely magnetic extraction of the SEs . He mentions the high LFE I as a significant disadvantage . An additional electrostatic extraction to reduce the LFE I would prevent the adiabatic SE motion, which is precisely what allows this procedure to record a low LFE II . Garth therefore suggests a virtual immersion lens spectrometer [85,86] (in which the single pole piece under the IC is obviated) in his paper [84] for the first time . In this elegant technique, the SEs are initially extracted electrostatically and then retarded again in the field maximum of a modified pin-hole lens. Finally, the SEs are collimated in the adiabatically declining magnetic field of the second lens half. In the analyzer of the commercial EBT from Sentry Schlumberger [87,88] the SEs are also magnetically collimated . For this purpose, a VAIL [16-18] is used and the analyzer possesses a plane retarding field . Kruit and Dubbeldam have suggested and implemented a combination of a VAIL and trochoidal analyzer with two energy channels [89,90,93] . Unfortunately this promising suggestion has not entirely fulfilled the expectations, as according to ref . [921 it has hitherto proved impossible to achieve good performance data for the PE and SE optics simultaneously. A small chromatic aberration of the VAIL is coupled with a relatively high energy error (0 .5 eV) of the trochoidal analyzer, whereas a small energy error gives rise to a relatively high aberration coefficient (10 mm) of the axial chromatic aberration. Nevertheless, the multichannel procedure proposed by Dubbeldam and Kruit [90] with a dispersive analyzer could be a step in the right direction . S-curves or spectrometer constants can be used for comparing the various through-lens analyzers. (Dubbeldam [93] gives a collection of spectrometer constants .) However, a much more rigorous comparative test is the measurement of known signals, which are injected into a test chip or a passive IC with interconnections of

maximum fineness. It can then be seen how well the level is measured and how high the sensitivity is with respect to local fields . Since the author was involved in the development of the electron-optical column of a commercial EBT, he intends to make no comparative evaluation at this point, but merely to refer to the LFE measurements in refs . [62,63,68,70,82,86-88,102,104] . In his own comparison, the reader should take into consideration the additional conditions of these LFE measurements such as interconnection width, spacing to the next interconnection and the degree of interference the signals have on the neighboring interconnections . Signals present on neighboring interconnections can give rise to crosstalk by means of LFE II .

3.3 . The detector unit When the SEs have traversed the retarding-field grid, they must still - for certain types of analyzers (with a planar or spherical retarding field grid normal to the optical axis) - be guided to one or two Everhart-Thornley detectors . Beam guidance systems designed specially for this purpose which deserve mention are the modified double stigmator by Garth et al. [83,85], the zeroth-order Wien filter by Otaka et al . [95] and the first-order Wien filter (crossed quadrupole fields) by Zach and Rose [96] . The latter was constructed and tested by Schmid and Brunner [97,98] . We also wish to draw the reader's attention to the simple but fascinating coaxial tube system by Tamura [94], in which the PE beam is totally shielded from the scintillator field . Systems with a coaxially arranged multichannel plate (e.g . ref. [54]) bypass the beam guidance problem mentioned above . In the analyzer designed by Plows [46], which is totally rotationally symmetrical - as far as the scintillator - the topological conversion problem is shifted to the optical waveguide system. The same is true for the analyzer by Dinnis [72-75], which uses a non-rotating final lens and whose radial magnetic field extraction is impressive from an electron-optical standpoint .

4 . An improved ray-tracing method for secondary electrons To determine the secondary electron trajectories in the compound spectrometer objective by ray tracing, the spatial field must initia ly be calculated. The electrostatic field of he spectroy eter objective shown in fig . 2b can be calcalated anal ; tcally, but the magnetic lens field only numerically. We chose the finite element method (FEM) for this purpose. In fact, this discrete method yields the spatial magnetic field directly, but additional interpolations of field values are required to allow a sufficiently accurate ray tracing . 111 . SPECTROMETERS/ANALYZERS

150

E. Phes / Secondary electron energy analyzers

In ref. [67], we therefore replaced the axial FEM values by an asymmetrical Glaser's bell-shaped model field and then continued this axial field distribution analytically into the space. This spatial field calculation is very fast and naturally requires no additional interpolation either . Although the asymptotic decline of the Glaser bell field is too slow, as we know, we got round this problem in ref. [67] by setting the magnetic field to zero from a specific axis coordinate (see fig. 5) . Let us once more start from the axial FEM values, but fit them with the following asymmetrical model field according to Lenz [105,106]:

derivation of tanh z. If the derivatives of tanh z are again expressed by tanh z itself, the following algorithm is obtained :

The four fit parameters Pl to P4 can be obtained from the axial FEM values by the method of least squares. Due to its rotationial symmetry, the spatial magnetic field can in principle be calculated by using the following well-known series expansions according to powers of the radial coordinate r: \ °° 2m 1 (z), (3a) B(2m) (M!)2 2 m=0 2m-1 1 Y- m(-1) m r (m')2 B(2m-1)(z) . Br(r, z) (2) m=1

g (2M-1) _

g= tanh z, g' = dg/dz = 1/cosh2z = 1 - tanh2z, g" = 2( - tanh z + tanh3z ), g "' = 2(-1 + 4 tanh2z - 3 tanh1 z) , g(4) = 2(2 - 4 tanh z - 4 - 5 tanh3 z + 3 - 4 tanhsz) ;

(4a)

B(z) =P 1 {tanh[P2(2z+P4 ) ]- tanh[P3 (2z-P4 ) ]) .

(3b)

The problem remains to determine the mth derivative B(m)(z) of the axial field distribution B(z). Due to eq . (2), however, this problem is reduced to a repeated

g (2M) = 0

M

Y a 2m tanh2mz =known, yields

m=0 M

+ E [2ma 2m (2m - 2)a2 .-21 tanh2m- 'z m=1

- 2Ma2M tanh2M+1 z . g (2M)

M

(4b)

m +l z =known, yields = E b2m+1 tanh2 m=0

M

g(2 M +1 )=b + y [(2m+1)b2 .+l 1 m=1

-(2m-1)b2- -1] tanh2mz

-(2M+1)b 2M+l tanh2M+2 z .

(4c)

Fig. 7. Comparison of the SE trajectories r(z) for two methods of calculating the spatial magnetic field. In the case of Glaser's asymmetrical model field and analytical continuation, we have drawn solid curves for B(z) and r(z) ; in the case of Lenz's model field and series expansions, dashed curves were used for B(z) and r(z) .

E. Plies / Secondary electron energy analyzers

We did not find the above algorithm, i .e. eqs . (4b) and (4c), in the literature, but it must surely be known . Since the series of (3a) and (3b) are of alternating type, it is a simpler matter to estimate the remaining term . The specification of a degree of accuracy consequently allows the series summation to be suitably terminated for every spatial point . In fig . 7 we contrasted the secondary electron trajectories obtained with the two methods of calculating spatial magnetic fields described above, using the same predictor-corrector algorithm for the trajectory integration as given in ref . [67] . Although the trajectories calculated by the two methods do differ, the difference of the SE image position is not relevant, so that the starting energy and angle of the SEs, which pass the spherical retarding field at limit values, differ only slightly . A further improvement in the trajectory integration might be to use the highly accurate method of Kasper, known as HPCD [107-109] . As long as the magnetic yoke is unsaturated, the boundary element method recently specified by Kasper and Strder [110] could also be used for calculating the spatial magnetic fields . However, experience shows that all boundary element and charge density methods cost a great deal of computing time for ray tracing, so that we also used the methods described above (Lenz's model field plus series expansions) for calculating an electron gun with a superimposed magnetic lens field.

5. Future trends Wolfgang et al . [102] have shown that e-beam testing can be performed on 0 .75 Wm interconnection lines using ICT's commercial e-beam tester . But the structural reduction in microelectronics has continued unabated, so that the influence of the local fields has increased. Wolf et al . [76] describe a compensation method for the LFE by combining a weak electrostatic extraction field with a suitable objective lens field, through which a part of the high-energy SEs can pass only under the influence of the local field . The compensation is unfortunately performed at the cost of measuring time . In addition, the model taken as a basis for the local field was not very realistic, as the authors themselves admit, so their calculations did not agree well with existing measurements on 1 j,m interconnections. Meanwhile Janzen [111] has improved the simulation of the local field using the charge density method of Schonecker et al . [112] . His calculation of the crosstalk error now agrees pretty well with existing measurements [68,70,104] on 1 wm interconnection lines using ICT's commercial EBT [10] . In view of the problems associated with the LFEs, the use of alternative analyzers, i .e. non-retarding-field

analyzers, should be given greater attention . An example of an alternative of this kind is the time-dispersive detector suggested by Khursheed and Dinnis [77] . The use of energy-dispersive multichannel analyzers, as suggested by Kruit and Dubbeldam [89,90], for example, should also be further pursued . The evaluation of energy-dispersive analyzers by Menzel and Kubalek [49] seems to contradict that in refs . [89,90] at first glance . We will therefore touch upon this comparison m the next subsection . 5 .1 . Retarding field analyzer analyzer

versus

energy-dispersive

In principle, more information is obtained by detecting the SE spectrum than by determining its integral alone, as the retarding-field spectrometer does . This also applies to the spectrum degraded by LFE I and LFE II . But let us first take a look at the results obtained by Dubbeldam/ Kruit and Menzel/Kubalek . Dubbeldam and Kruit [90,93] calculated the signalto-noise ratio, the minimum measurable voltage difference DU and the spectrometer constant C of a dispersion analyzer. They considered the cases of a multichannel analyzer after a retarding grid and a two-channel analyzer (of the entire SE spectrum) . Both methods yield better values than the conventional retarding-field analyzer . However, the authors have ignored the influence of the local fields . In section 3 .1 of ref. [49], Menzel and Kubalek calculated the effect of the LFE I on the SE spectrum . The curves for N1 (not degraded) and N2 (degraded, interconnection line voltage UL = 8 V) in fig. 8 are redrawn from their results . In fig . 8a the measurement error SU for measurements on the 8 V interconnection was also specified as a function of the operating point U,,,p of a retarding-field analyzer. Menzel and Kubalek specified the 3 V spacing between the two peaks of the spectra Nl and N2 as a measurement error of the dispersive analyzer . But if we correlate the two high-energy edges of both spectra according to PN,NZ (ES) =

f

00

Ni (Es)N2(Es+Es) d Es

(5a)

together with the supplementary conditions NI , N2 < Nh .c

and

dNl /dES , dN2/dEs < 0,

(5b)

then we obtain a measurement error SU < 3 V, as can be seen from fig. 8b . However, the measurement error SU of the dispersive analyzer is still greater than that of the retarding-field analyzer. To summarize, we found that without the influence of the local field a dispersive analyzer would yield a smaller minimum measurable voltage difference AU, but with inclusion of the local field it has a larger measurement error SU due to this effect . In my view, however, III . SPECTROMETERS/ANALYZERS

15 2

E. Plies / Secondary electron energy analyzers the fundamentally (may be not practically) best solution is the dispersive multichannel analyzer, which detects the entire degraded SE spectrum (i.e . no multichannel

analyzer after a retarding grid), for the retarding-field mode can still be realized by summation over the individual channels, as can the correlation techniques de-

scribed by eq . (5). Analyzers which could be used for this purpose after some modification are already known in principle [43,44,57,58,1011 . However, they have other Es /e --UR-

bu

drawbacks, and we will therefore propose a new disper-

>

sive analyzer for e-beam testing in the next subsection . 5.2 . Proposal of a new analyzer

Fig. 9 shows the new proposal which represents a

modification of the through-lens analyzer of fig. 2. A configuration of crossed homogeneous fields is located above the hemispherical retarding grid . The electrical

field strength E and the magnetic flux density B should be selected so that the E X B configuration behaves like

a Wien filter with respect to the PEs [113-1191, i.e . axial

PEs with a speed u = E/B are not deflected. Fig. 9 bu

merely shows a schematic representation of the secondary electron trajectories, which in the E X B config-

Es /e = -UR --1w

Fig. 8. Influence of the local field effect on the SE spectrum and the voltage measurement error 8U for a retarding-field analyzer (a), and for a dispersive analyzer (b). Es = starting energy of the SEs, UR = retarding voltage, NI (Es) = undegraded spectrum and N2(Es)=degraded spectrum for a line voltage of UL = + 8 V, two neighboring grounded lines, a line width of 4 [Lm, a spacing of 2 [m and an extraction field of 400 V/mm . The N, and NZ curves are redrawn from ref. [49] .

uration are deflected by 90 ° to a multichannel detector. The retarding voltage was selected to be UR = 100 V, so

that the relative energy width of the secondary electrons is still small enough to allow an acceptable focusing after the E X B field to be made, but the dispersion (see below) is still high enough . The left detector is designed for the normal retarding-field analyzer mode with UR =

-6 V + UL, for example, the secondary electrons can

be deflected to this single detector by inverting the

Dispersive E X B SE-deflector (Wien filter for PEs : Multi-channel SE-detector for open-bop technique SE-detector for , feedback-loops" technique

w

Retarding grid U R z 100V Grid electrode UE = 2kV

Magnetic lens ~rr" jj= ~1~~~~rw~aw

Extraction grid U E = 2 k V Integrated circuit, UL

Fig. 9. A dispersive multichannel through-lens analyzer with crossed homogeneous fields which may also be operated m a retarding-field mode using the left single detector . Retarding voltage UR =100 V if operated dispersively in an open-loop technique and UR = - 6 V+ UL, for example, if operated in integrating mode in a feedback loop The SE trajectories are shown schematically for dispersive operation.

E. Plies / Secondary electron energy analyzers electric and the magnetic fields and maintaining the quotient E/B but modifying the individual values of E and B . This E X B configuration therefore allows dispersive operation in an open-loop technique (see ref . [100]) and an integrating retarding-field mode in a feedback loop . Let us initially turn to the optics of the SEs and then to the PEs in the E X B configuration . The electron trajectories in crossed homogeneous electric and magnetic fields are known to be cycloids . This means that the curved beam axis (see fig . 9) does not follow a circular trajectory. The theory of electronoptical systems with an arbitrary curved optical axis is described in refs . [120-128], for example . Since we are interested only in a 90' deflection of this axis, we initially looked more closely at its analytical solution and found that the following applies in the case of the 90 ° deflection for the lengths 11 and lZ marked in fig . 9: 11 = v/w, lz=

w

where

lu

(u+v)z-u2 - arccos( u +v) },

w = eB/m , u = E/B, v

= ~ m ((Es) + eUR )

(6a)

(6b) .

In eqs. (6b), e refers to the elementary charge, m to the the mass of the electron and (ES ) to the mean start energy of the SEs . With some approximations, we obtain the following first-order relation for the object and image distances a and b marked in fig . 9 : ab =- 1I1(u+v) wz V

2

and for the energy dispersion in the image plane D

_ Ox _ DES - {

u lz v2 u 1 1-(u+vJ +(u+v)Zwa}evB'

It should again be mentioned that formulas (6) to (8) apply only to the 90 ° deflection and that the E X B configuration focuses only in the median plane (drawing plane of fig. 9) and not normal to it . No stigmatic focusing is required either, but perhaps some vertical focusing, to keep the length of the astigmatic line foci short. This can be done with the aid of a quadrupole in the SE beam path, for example, but the image distance b is then increased . Starting from eqs . (6) to (8), we worked out an example and found an energy dispersion of D = 0.1 mm/eV =10 pm/0 .1 eV for 1 1 = 28 mm, 12=13 mm, a=45 nun and b=11 mm . If weusea linear CCD sensor (charge-coupled device) as a multi-

15 3

channel detector, for example, then a channel width of 0 .3 eV is possible with the standard structure of the CCD sensor and the dispersion mentioned above . The use of a Wien filter to deflect the SEs is not new (see refs . [95,129] for example), but the utilization of its focusing property and its dispersion is an obvious extended step . Unfortunately, however, all PEs with a speed other than u = E/B suffer a dispersion, which is the most disturbing aberration of the Wien filter in this case . An integral expression is given to calculate this dispersion in refs . [22,96] . From this it can be seen that the PE dispersion disappears when an intermediate image of the PE beam path is placed at the mid-point of the E X B configuration . A remaining problem is the implementation of the homogeneity of the crossed fields, which seems solvable to us .

6 . Conclusions In view of the ongoing structural reduction of integrated circuits, e-beam testing is becoming increasingly more difficult. The SE energy analyzer for quantitative voltage measurements inside the ICs thus plays a key role within the electron-optical column of the EBT. Existing analyzers were discussed and ways were shown to improve this device. Another important electronoptical problem is due to the Boersch effect [130-141], which must be taken even more strongly into account in the future in defining the overall beam path of the low-voltage column.

Acknowledgements The author wishes to thank Dr . M. Guntersdorfer and Dr . E . Wolfgang for their general support, Dr. D. Krahl for discussions on electron counting and Mr . R. Michell for the translation of the manuscript.

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III. SPECTROMETERS/ANALYZERS