REVIEW Applications of scanning optical …fraundorfp/lucio/sirm_rev.pdfApplications of scanning optical microscopy in materials science to detect bulk microdefects in semiconductors

REVIEW

Applications of scanning optical microscopy in materialsscience to detect bulk microdefects in semiconductors

P. TOROK* & L. MULE’STAGNO†*Multi-Imaging Centre, University of Cambridge, Downing Street, Cambridge CB2 3DY, U.K.†MEMC Electronic Materials Inc., 501 Pearl Drive, St Peters, MO 63376, U.S.A.

Key words. Bulk defects, materials science applications, scanning infra-redmicroscopy.

Summary

We review the application of scanning optical microscopy tobulk microdefect detection in semiconductor materials.After an extensive literature review we summarize theore-tical aspects of the scanning infra-red microscope anddescribe the theory of contrast formation. We also showexperimental examples of scanning infra-red images takenby different modes of the microscope and give an experi-mental confirmation of the contrast theory.

1. Introduction and literature review

In this paper we review the state of the art of the scanninginfra-red microscope (SIRM) applied to image bulk inho-mogeneities in semiconductor materials. In what follows wepresent results of theoretical work most relevant to theimage formation of the SIRM and also some simplifiedtheoretical description of light scattering that occurs whenlight is scattered from bulk inhomogeneities. Experimentalimages are also presented for a wide variety of specimensand imaging modes. The effect of spherical aberration onimaging is examined in detail. Experimental confirmation ofcontrast theory is presented.

In the SIRM the light of an infra-red laser (solid state orsemiconductor) with a typical wavelength of 1.1–1.3 mm isfocused/imaged by a high-numerical-aperture lens (typi-cally 0.8–0.9) into the bulk semiconductor specimen, thusforming the probe. The relative positions of the specimenand the probe are varied such that raster scanning isperformed. The transmitted/scattered light is detected by anappropriately placed detector or a combination of pinhole

and detector. Detector signal, corresponding to individualscan positions, is collected, amplified and stored in acomputer memory. The image is built up on the computerscreen.

It is not the objective of the present work to present acomplete review of the literature of confocal microscopy. Forthis the reader is referred to the exhaustive work of Wilson& Sheppard (1984) and Wilson (1990). In the following wereview the literature of applications of confocal microscopyto semiconductor materials and, in general, to materialsscience.

Wilson et al. (1980) and Hamilton & Wilson (1987a)used a scanning optical microscope in the OBIC mode toexamine a GaP light-emitting diode. When a laser ofwavelength 1.15 mm was used to inject the electricalcarriers, subsurface defects were imaged because of thelarge penetration depth of the infra-red light. Hamilton &Wilson (1987b) used a reflection confocal scanning opticalmicroscope with infra-red light to examine a siliconmicrocircuit. By focusing from the front surface downthrough the silicon wafer they imaged the metal bonding atthe back surface.

Considerable work has been performed at the Universityof Oxford using transmission nonconfocal SIRM to investi-gate semiconductor specimens. Kidd et al. (1987a,b) exam-ined As-rich precipitate particles in LEC GaAs wafers, Lacziket al. (1989a,b) examined oxide particles in Czochralskisilicon wafers and Te-rich particles in CdTe wafers, and Jinet al. (1993) examined In-rich particles in InP wafers. Someof this work was reviewed (Booker et al., 1992), mainly fromthe materials science point of view. For light of wavelength1.3 mm and a lens of NA = 0.6, lateral and depth resolutionsof typically 2 mm and 30 mm were obtained. Particle numberdensities and distributions were determined. Individualdislocations were observed either because they were

Journal of Microscopy, Vol. 188, Pt 1, October 1997, pp. 1–16.Received 6 January 1997; accepted 7 April 1997

1q 1997 The Royal Microscopical Society

Correspondence to: P. Torok, University of Oxford, Department of Engineering

Science, Parks Road, Oxford OX1 3PJ, U.K.

decorated with precipitate particles, or on using polarizedlight because of their strain fields.

The development of the last generation of the SIRM hasbeen reported in a number of articles. Laczik et al. (1991)described, for the first time, a transmission confocal SIRMand a polarized mode transmission SIRM. With the latter itwas possible to image and measure the direction of Burgersvectors for end-on dislocations in LEC GaAs. The axial andlateral resolutions of the confocal transmission SIRM weremeasured to be 7 and 1 mm, respectively. Torok et al. (1993)reported on new imaging modes of the SIRM. Theseincluded transmission confocal phase contrast, confocaldouble-pass, confocal double-pass phase contrast andreflection confocal and reflection phase contrast modes.They pointed out that phase contrast imaging modes arebeneficial in the SIRM because some particles did not giveamplitude contrast and therefore would not be shown byamplitude contrast imaging. Also, in the reflection confocalmode, a phase contrast arrangement results in partial or fullrejection of specular surface reflection.

The imaging modes available to construct SIRM weresummarized by Torok (1994). This work examined in detailall possible imaging modes and gave experimental examplesfor each imaging mode. The effect of spherical aberrationwas studied both theoretically and experimentally. It wasrevealed that overcorrection of spherical aberrationadversely affects resolution whilst undercorrection has lesseffect on the imaging properties of the microscope.

Torok et al. (1995a) presented a combined study of SIRMand transmission electron microscopy (TEM) examinationsin silicon specimens. They found that SIRM and TEMtechniques provide complementary information concerningthe oxide precipitation process. Laczik et al. (1995) pre-sented dark-field reflection confocal SIRM images. With thisimaging mode it is possible to eliminate specular reflectionfrom the surface of the specimen. A series of later studies byTorok et al. (1996a,b,c) analysed the theoretical aspects ofthe half-stop dark-field reflection confocal SIRM. Theyfound, by applying the paraxial theory, that the resolutionof this microscope mode is maintained as long as the half-stop does not cover more than exactly half of the lensentrance pupil. There was, however, significant light losspredicted when the half-stop is applied. Laczik et al. (1995)also studied the effect of spherical aberration, mainly byrepeating the experiment performed earlier by Torok(1994), on the role of over- and undercompensation ofspherical aberration in confocal reflection SIRM.

Mule’Stagno (1996) studied the limitations of a confocalreflection SIRM in detecting precipitates in silicon. It wasfound that the intensity of the scattered signal essentiallyobeys Rayleigh scattering laws and that the maximumdensity of precipitates that can be measured is limited by thephysical size of the probe within the sample. Using Poissonstatistics Mule’Stagno (1996) explained the inability of the

instrument to measure beyond a certain defect densitydetermined by the probe dimensions. Khanh et al. (1995)used the SIRM to study nondestructively microvoids at theinterface of direct bonded silicon wafers. By using the SIRMthey were able to study void formation in wafers bonded bydifferent techniques, and the effect of different bondingtemperatures on the void distribution and size.

Confocal scanning optical microscopes (CSOMs) in gen-eral have been put to a wide variety of other uses in thematerials sciences. Kino & Corle (1989) used a CSOM toimage different layers of stacked transparent materials.Thomason & Knoester (1990) used a CSOM to study thefibre reinforcement of polymer composites. Jang et al. (1992)applied a CSOM to the study of wood pulp fibres. They wereable to obtain the transverse dimensions of these fibres bymeans of image analysis of the digitally captured images.These instruments prove to be especially valuable indetecting surface roughness or anomalous features. Theywere used in this way by Lange et al. (1993).

Scanning confocal microscopes are also useful in imagingparticles in colloidal solutions or transparent solids. Thistechnique was applied together with a variety of othertechniques by Van Blaaderen (1993), who studied concen-trated colloidal dispersions, and Pistillo (1996), who studiedmicronized additives in coatings. In the colloidal case thedispersion was the object of interest, while in the coatingscase the effect of these additives on the hardness of thecoating was investigated. This technique has also proved tobe useful in the imaging and measurement of the density ofdefects in semiconductors (e.g. Laczik et al., 1989a; Toroket al., 1995a; Mule’Stagno, 1996). Falster et al. (1992) usedthe same technique to study the gettering of (deliberatelyintroduced) metallic contamination onto SiO2 particles insilicon. In the latter cases, the laser had a wavelength of1320 nm. At this wavelength silicon is transparent (i.e. theimaginary part of the complex refractive index is zero) andthe light scatters off the precipitates which are generallywell under 1 mm in size. Mule’Stagno (1996) also correlatedthe signal scattered off these precipitates with the actual sizeof the precipitates as measured by TEM.

Another interesting use to which laser scanning confocalmicroscopes have been applied is the monitoring of in-situreactions. Two such studies were carried out by Chung &Alkire (1995) and Gu et al. (1992). In the first study, thelateral copper deposition from a liquid solution was studied,while the second study was concerned with the monitoringof the surface structure of an electrode during redoxreactions of metals. In both cases the scanning confocalmicroscope enabled the real-time monitoring of a dynamicchange occurring on a surface as a result of the reaction.

Other places where applications have been found forscanning confocal microscopes include geology andcosmology. Fredrich & Menendez (1995) studied porestructures of geological structures by impregnating the

2 P. TOROK AND L. MULE’STAGNO

q 1997 The Royal Microscopical Society, Journal of Microscopy, 188, 1–16

200-nm pores with an epoxy. The instrument was also usedto study the holes and other damage produced by cosmicdust on a spacecraft (Anderson, 1994).

Petford & Miller (1993) applied the confocal scanningmicroscope in the reflection mode to study microdefects andfission tracks in apatite. They obtained a three-dimensionaldistribution of these crystal defects in a manner similar tothe SIRM studies.

The above examples show that there is a wide range ofapplications of confocal microscopy in materials science. Inaddition to the most commonly used semiconductormaterial, silicon, it is certainly possible to use the SIRMwith other semiconductors, such as GaAs, InP, etc. In thiswork, however, we present only experimental results on Sibecause it is still by far the most important semiconductormaterial.

2. Theory

A theoretical description of the SIRM is of primaryimportance, mainly to gain a proper understanding of theimages taken by the microscope. In the following we discusstwo possible ways to approach the problem of theoreticaldescription. Firstly we summarize the relevant results of theparaxial theory as developed by Sheppard & Choudhury(1977) and Wilson & Sheppard (1984). We show that thistheory cannot possibly account for all of our experimentalresults. Subsequently we refine our approach and discussthe high-aperture theory applicable to the SIRM asdeveloped by Torok et al. (1995b,c,d, 1996d) and Torok &Wilson (1997). Inhomogeneities in the bulk semiconductorare also considered as light scatterers. Although there is noexact theory available to describe the imaging of the SIRMwhen inhomogeneities are scanned we present simplifiedtheories that can predict the SIRM contrast with goodaccuracy.

2.1. Paraxial theory of image formation

The paraxial theory of confocal microscopy has beendeveloped during the last 20 years. The fundamentalprinciples were established by Sheppard & Choudhury(1977), whose work was followed by a number of differentpublications on the subject. The sate of the art wassummarized by Wilson & Sheppard (1984) and Wilson(1990).

Without getting involved too deeply with the relevantmathematical techniques, in this section we summarize theprincipal results of the above workers. Before this, however,it is essential to define those conditions under which thistheory is applicable.

The paraxial theory is based on the paraxial approxima-tion of Kirchhoff ’s scalar diffraction integral. When thistheory is compared with experimental results and other,

more rigorous theories we find that the paraxial theory isapplicable to numerical apertures up to < 0.6 (numericalaperture is defined as the convergence semi-angle of the lensin the given optical medium, which essentially means theangle at which the lens is capable of collecting light). Inpractical confocal microscopy objective lenses with muchhigher NA are used. This means that results of the paraxialtheory should be treated as second-order approximations,the first order being the geometrical optics approach. Theparaxial theory cannot, by nature, take into account anypolarization-dependent effects of the optical system. It isshown below that polarization-dependent phenomena playan increasingly important role in the imaging properties ofthe SIRM.

The basis of the paraxial theory is to determine the point-spread function (PSF) of the microscope. This approach iswell known in the field of electronic engineering where theDirac-delta function is frequently chosen as the inputexcitation to analyse an electronic circuit. In optics thesame principle is employed and the physical meaning of thecalculation of the PSF is that of how the optical systemresponds when an infinitesimally small point object isimaged by the microscope. It is possible to show (see e.g.Wilson & Sheppard, 1984) that the overall confocal PSFhoverall(u,v) is given by multiplying the PSFs correspondingto the illumination hill(u,v) and the detection hdet(u,v) opticalpaths:

hoverallðu; vÞ ¼ hillðu; vÞhdetðu; vÞ ð1Þ

where u and v are the normalized optical co-ordinates givenby

u ¼ ð8p= lÞz sin2ða=2Þ

v ¼ ð2p= lÞr sin a ð2Þ

with r and z denoting the radial and axial co-ordinates andsina is the NA of the lens. In reflection confocal SIRM theillumination and the detection PFSs are identical and givenby

hillðu; vÞ ¼ hdetðu; vÞ ¼ hðu; vÞ

¼

�1

0PðrÞ exp

12

iur2� �

J0ðvrÞrdr ð3Þ

where P(r) is an arbitrary pupil function of the lens andJ0 (.) is the Bessel function zero kind, order zero. Equation(1) is only applicable when the imaging process is coherent.The term coherence here means that (i) the scattering frominhomogeneities is such that the scattered light is coherentwith respect to the illumination and (ii) the pinhole size isinfinitely small. Condition (i) is automatically satisfied forthe SIRM (see e.g. Born & Wolf, 1970, p. 633) whilstcondition (ii) is not satisfied in practical confocal microscopyas the size of the confocal pinhole can rarely be consideredas being infinitely small. For the latter case the imaging is


MATERIALS SCIENCE APPLICATIONS OF SCANNING OPTICAL MICROSCOPY 3

said to be partially coherent and this problem was addressedby Carlini (1988).

As stated above, Eq. (1) gives the overall PSF of theconfocal microscope which also means that this functiondescribes the response of the SIRM to a point object.Equations (1) and (3), in the special cases u = 0, v = 0 andP(r) = 1, yield for the detected intensity from a point object:

Iðu ¼ 0; vÞ ¼ ½2J1ðvÞ=vÿ4

and Iðu; v ¼ 0Þ ¼ ½sinðu=4Þ=ðu=4Þÿ4 ð4Þ

where J1 (.) is the Bessel function first kind, order zero.Figures 1(a) and (b) show the typical intensity distributionsalong the principal lateral and axial directions, respectively.

The other typical way to characterize the SIRM is bymeans of the coherent transfer function (CTF). The physicalmeaning of this function is that it reveals the capability ofthe optical system to transmit optical frequencies. It is wellknown from the theory of electronic circuits that Fourieranalysis of an electronic system shows how accurately itresponds to, for example, a unit step function. If the systemis capable of transmitting high spatial frequencies then thereproduction of the unit step function will be more accuratecompared with a system that is only capable of transmittinglow spatial frequencies. This analogy also applies to opticalsystems. In this case, however, we have introduced the termoptical frequencies. This can be best understood from Abbe’stheory of image formation (see Born & Wolf, 1970, p. 418):the image is constructed as an interference of individualplane waves propagating through the optical system. Theseplane waves emerge from the object and propagate withdifferent direction cosines. The CTF characterizes the opticalsystem in the sense that it reveals what direction cosines thesystem is capable of transmitting. It can also be shown thatwhen a confocal microscope images a plane reflector then,according to the paraxial theory, the axial distribution of theCTF gives the response of the confocal system:

IðuÞ ¼ f½sinðu=2Þÿ=ðu=2Þg2 ð5Þ

again, assuming a clear aperture and no aberrations.Equation (5) is shown in its functional form in Fig. 1(b).As this figure shows, a point object produces a lower depthresolution compared with a plane object. This, however,causes little concern from the SIRM point of view. The well-pronounced axial secondary side lobe for the distributioncorresponding to the plane object causes the real concern.This is because, as we show below, the signal differencebetween a scatterer and the surface of the specimen is suchthat even the relatively low secondary axial lobe of thedistribution from a plane reflector can hinder the detectionof a point scatterer.

In the following we consider a simple model of the SIRMimaging a slab of silicon. We model a particle that is situated

at depth d below the front surface and determine theminimum depth at which the particle is visible. This modelconstitutes the very essence of the reflection confocal SIRM,namely design principles of the microscope aim at thesuppression of the specular reflection from the front surfaceof the specimen and detection of small scatterers against thehigh background of surface reflection. In practice, thedetected signal from the front surface of the specimen is twoor three orders of magnitude higher than that from ascatterer. In our simple model we choose this ratio to be800. Figure 2 shows when the signal from a scatterer canbe detected against surface reflection, where the unit levelmeans that the signal from the scatterer is stronger than thedetected intensity of the specular reflection. This figureshows that a scatterer can only be detected within well-defined depth regions. When scatterers are situated atgreater than < 55 unit depth, which is equivalent to

Fig. 1. Normalized intensity response of a confocal microscope to apoint and plane object: (a) distribution along the principal lateraldirection; (b) distribution along the axial direction for a pointand plane object.



< 10 mm depth in air or 35 mm depth in silicon (calculatedfor l = 1.3 mm, NA = 0.9 and nSi = 3.5) the detection is nolonger hampered by surface reflection.

As the above example shows, the paraxial theory canbe useful in describing certain features and in under-standing experimental results of the SIRM. In fact, weshow below that the detection limit calculated from theparaxial theory is rather accurate when compared withexperimental data.

2.2. High-aperture theory

In case of the SIRM the light, usually of a semiconductoror solid-state laser, is focused by a high-NA lens intothe specimen. The measurement is required to be non-destructive and noncontaminating, hence the focusingoccurs from air directly into the semiconductor specimen.The refractive index of semiconductor materials is high(e.g. nSi = 3.5 for l = 1.3 mm) compared with that of the airand thus, owing to the large refractive index difference,spherical aberration will be introduced by the focusingprocess. It is also known that the transition of the focusedwaves through the air/semiconductor interface is apolarization-dependent effect (see Born & Wolf, 1970, p.36). It is therefore essential to consider the polarization ofthe waves incident upon the interface. The implications areas follows.1 Owing to the presence of spherical aberration theresolution of the SIRM will be aberration- rather thandiffraction-limited;2 in order to be able to incorporate polarization-dependent

phenomena into our theory we must use a full vectorialtreatment.

The need for a full vectorial theory also arises becauselight scattering is a polarization-dependent phenomenon.

The basis of the high-aperture theory is the integralformulae developed by Wolf (1959) and Richards & Wolf(1959). Their results are not directly applicable to ourproblem because it considers only a homogeneous mediumof propagation. The theory that is capable of incorporatingdielectric interfaces was developed later by Torok (1994),Torok et al. (1995b,c,d, 1996d) and Torok & Varga (1997).The basis of this solution is to consider convergent sphericalwaves, produced by the lens, as the superposition ofindividual plane waves. These plane waves were transmittedindividually via the interfaces and then summed usingthe principle of coherent superposition. We note thatthe same theory was used later to obtain high-aperture vectorial PSF for the fluorescence microscope forbiological application and for a single interface by Sheppard& Torok (1997) and for multiple interfaces by Torok et al.(1997).

Following Torok et al. (1995b), we write the Cartesiancomponents of the electric energy as:

Ex ¼ ¹iðI0 þ I2 cos 2vpÞ

Ey ¼ ¹iI2 sin 2vp

Ez ¼ ¹2I1 cos vp ð6Þ

where we ignored a constant multiplier and

In ¼

�a

0AnðJ1;J2Þ exp½ik0WðJ1;J2;¹dÞÿ

× Jn½ðv sin J1Þ= sin aÿ exp½ðiu cos J2Þ= sin2 aÿdJ1 ð7Þ

we note that the optical co-ordinates v and u are defined in amanner slightly different from those of Eq. (2). Now v = k1rp

sinJpsina and u = k2zsin2a. In Eq. (7)

A0 ¼ cos1=2 J1 sin J1ðts þ tp cos J2Þ

A1 ¼ cos1=2 J1 sin J1tp sin J2

A2 ¼ cos1=2 J1 sin J1ðts ¹ tp cos J2Þ ð8Þ

and

WðJ1;J2;¹dÞ ¼ ¹dðn1 cos J1 ¹ n2 cos J2Þ ð9Þ

is called the aberration function. In the above equationssubscripts 1 and 2 denote quantities in the medium inwhich the lens is embedded and that of the semiconductorspecimen, respectively; furthermore, tp and ts denote theFresnel coefficients, Jn is the angle of incidence andrefraction, cp is the polar angle of the observation point,a is the solid semiangle of the lens and d denotes the depthat which the particle is located (focusing depth).

With the help of the above equations a number ofparameters can be studied that are characteristic of the


Fig. 2. The depth below the surface at which a particle is detectable(unity response) for a reflection confocal SIRM. Surface reflectionsuppresses particle detection close to the front surface.


electric field. Such quantities are the lateral and axial fullwidth at half-maxima (FWHM) of the electric energy densitydistributions and peak value and axial location with respectto the Gaussian focus (the location where axial geometricrays intersect with the axis).

In order to study the effect of spherical aberration of theimage formation in the SIRM we first plotted the axialdistribution of the electric energy density as a function offocusing depth for a lens numerical aperture of 0.85,n1 = 1.0, n2 = 3.5 and l = 1.3 mm. These parameters, apartfrom the numerical aperture, are used in all of our followingnumerical computations in this section. The resulting plot isshown in Fig. 3. This figure reveals that as the depth d andthus the spherical aberration increase the peak electricenergy decreases dramatically and its axial distributionwidens considerably. The distribution of the electric energyexhibits a strong negative axial lobe that becomes higher inenergy at < 70 mm than the original main peak. Thisprocess repeats at < 150 mm depth. As a conclusion we canstate that the original peak of the electric energy decreasesrapidly with increasing focusing depth, but this peak is soonto be overtaken by one of the original axial secondary lobes.If the original peak was not overtaken by the axialsecondary lobe the SIRM would not be able to detectscatterers at depths greater than < 70 mm as a result ofexcessive light loss due to spherical aberration. When thestrength of the main peak (Strehl intensity) is computedagainst the numerical aperture and the probe depth and theresult is plotted on an axonometric plot the result is shownin Fig. 4. It is clearly shown that this curve exhibits anirregular behaviour that is the result of the higher orderlobe overtaking the primary peak. This figure alreadysuggests that it will be rather difficult to interpret the imagestaken by the SIRM unless spherical aberration correction is

employed. We can also compute and plot the focus shift in amanner similar to that of Fig. 4 and the result is shown inFig. 5. Not surprisingly, this curve also exhibits the irregularbehaviour previously observed in Fig. 4. Finally, we havecomputed and plotted the axial FWHM of the electric energydensity in Fig. 6. This plot shows three regions of the curve,A, B and C which are interpreted as follows: region A isreferred to as a linear region where, owing to a low NA (upto 0.6), the focusing depth does not cause nonlinearbehaviour. Region B is referred to as the nonlinear region,where the combined effect of high numerical aperture andfocusing depth causes a nonlinear behaviour. Finally, regionC is referred to as the irregular region, where the combinedeffect of high numerical aperture and focusing depth causesan irregular behaviour. It is clear that the most favourableregion is A, where images are readily interpreted. It isinteresting to note that sometimes application of a low-NAlens can be more beneficial as far as the resolution of themicroscope is concerned.

2.3. Light scattering

The high-aperture theory of focusing reveals that the focalregion is a complicated mixture of differently polarizedplane waves and so the resulting field will possess a complexpolarization structure. Equation (6) shows that for anon-axis illumination the polarization will always be linear.In the SIRM lenses are used with numerical apertures up to

Fig. 3. The effect of spherical aberration. Electric energy density isplotted (grey scale), as predicted by the high-aperture theory, as afunction of axial position and focusing depth.

Fig. 4. Main peak of electric energy density as a function offocusing depth and numerical aperture as predicted by the high-aperture theory.



0.85; therefore, the question arises as to how much thepolarization of the incident electric field will affect thescattering. The maximum numerical aperture (0.85) inside,for example, silicon will be reduced dramatically by thelarge difference in refractive index of air and silicon. In fact,the convergence angle, corresponding to NAAir = 0.85, in

air is < 588 but in silicon this is only < 148 (NASi = 0.24). Ithas been shown by Torok et al. (1995c) that the finaldistribution is influenced mainly by the paraxial rays. Itseems reasonable therefore to consider light scatteringwhereas the illumination occurs by a single plane polarizedplanewave with the polarization direction coinciding withthe axial polarization of the illuminating electric field.

Here we follow Torok (1994) to obtain the contrastcurves that are expected when the SIRM images smallspherical scatterers. The theory presented below is based onMie’s theory of light scattering that applies only to sphericalscatterers. It is well known that inhomogeneities insemiconductors possess shapes different from spherical.For low- and medium-temperature heat treatment plateparticles are formed whilst for high-temperature heattreatment polyhedral, typically octahedral, particles areformed (Laczik & Booker, 1996). We show, however, that aslong as the particle size remains small the scatteredintensity dependence on the equivalent size of the particlesis unaffected by the particle shape. When the size ofscatterers becomes large the particle shape and orientationplay a significant role.

The classical theory of light scattering (Mie theory) isused to compute the angle-dependent distribution of lightscattered from a spherical particle (see Born & Wolf, 1970,p. 634) and the results are plotted on a normalized scale inFig. 7. These and the following computations wereperformed for nSi = 3.5 (refractive index of silicon),npt = 1.5 (refractive index of silicon dioxide particles) andl = 1.3 mm (wavelength of illumination in air). For a particleradius (q) of 25 nm the distribution is symmetrical withrespect to the 908 direction, which indicates that Rayleigh


Fig. 5. Focus shift as a function of focusing depth and numericalaperture as predicted by the high-aperture theory.

Fig. 6. FWHM of the main peak of the electric energy density as afunction of focusing depth and numerical aperture as predicted bythe high-aperture theory. Numbered regions correspond to A lin-ear, B nonlinear, regular and C irregular regions.

Fig. 7. Angular distribution of scattered light from a spherical SiO2

particle embedded in Si as predicted by the classical theory of lightscattering. Particle radii, from top to bottom: 25, 50, 75, 100, 125,150, 175, 250 nm.


scattering occurs. When the particle radius increases to50 nm the distribution loses its symmetry. The asymmetry isthe most pronounced for the highest particle radiuscomputed (250 nm). It is also apparent from the figurethat the 1808 scattered intensity for a particle radius of250 nm is two orders of magnitude lower than that in the 08

direction, which might be regarded as disadvantageous forreflection SIRM measurements where the detection occursfrom the 1808 direction.

It is also possible to compute from these data the detectorsignal of the SIRM. As stated above a microscope objectivelens with a numerical aperture of 0.85 collects light insilicon within an a = 148 solid angle. When the scatteredlight is integrated within this solid angle the angle-dependent scattering coefficient Qsca(a, q) is obtained. Thisfunction is plotted on a log–log scale in Fig. 8, where wealso give fittings for different sections of the curve. It isshown by this figure that particles exhibit q6 dependence upto < 50 nm radius. When the particle radius becomesextremely large 250 nm) a q1.2 dependence is found, aprediction that is likely to be not as accurate whencompared with experimental data.

As the result of the classical theory of light scattering it isclear that for small sizes the shape of the particles is notsignificant. We examine now for an arbitrary particle size,by following Booker et al. (1995) and Laczik & Booker(1996), how the shape of the particle affects its scatteringproperties. The work of the above authors applies thediscrete dipole approximation (DDA) to determine thescattered field. According to this method a scatterer isreplaced by an array of electric dipoles and, on a plane wave

illumination, their response irradiation is coherently super-imposed, thus obtaining the scattered field (Laczik, 1995).Booker et al. (1995) compared the results given by the DDAmethod for spherical particles with those given by therigorous Mie theory and found an excellent agreement. Inthe following we define the normalized particle size x, wherex = 2pqnSi/l.

Oxide particles in silicon are amorphous in structure andcan be regarded as SiO2 in composition (Torok et al., 1995a;Laczik & Booker, 1996). Particles formed by low- andmedium-temperature heat treatment are platelets on {100}planes with edges along h011i directions. Their width/thickness aspect ratio is < 10:1. Particles formed by high-temperature heat treatments are polyhedral in shape withfacets on {111} planes and with edges along h110i

directions and are frequently octahedral with {100} baseplanes. Particle sizes occur, depending on the heat treat-ment, in the range 5–500 nm (Laczik & Booker, 1996).

The numerical work of the above authors considers anillumination wave vector k and polarization vector p to beparallel to the h100i and/or h110i crystallographic direc-tions in silicon. The resulting three-dimensional distribu-tions are plotted in Fig. 9 for an octahedral particle (firstcolumn), a face-on plate particle (second column) and anedge-on plate particle (third column). The three rowscorrespond to normalized particle sizes of x = 0.1, 1 and 5

Fig. 8. Detected intensity Qsca(a, q) as a function of spherical par-ticle radius q (computed for nSi = 3.5, npt = 1.5, l = 1.3 mm anda = 148) as predicted by the classical theory of light scattering.

Fig. 9. Three-dimensional distribution of scattered light from anoctahedral particle (first column), a face-on plate particle (secondcolumn) and an edge-on plate particle (third column) as predictedby the DDA method. The parameter is the normalized particle size.Reprinted with permission from Laczik & Booker (1996). Copyright1996 American Institute of Physics.



that are equivalent to q = 6, 60 and 300 nm, respectively.Each three-dimensional plot has been normalized to theintensity maximum. For particles with x = 0.1 the distribu-tion reveals Rayleigh scattering. When the particle sizereaches x = 1 the distributions are asymmetrical, showingthat Rayleigh scattering no longer occurs. It is interestingthat whilst the scattered intensity distribution for the octahe-dral and the edge-on particles are asymmetrical with respect tothe [011] direction the face-on plate produces a closelysymmetrical response revealing a strong scattering in thedirection [100] (that is, the detection direction of the reflectionSIRM).

When a detector placed in the [100] direction thedetected intensity can be computed in a manner similar tothat presented above for Mie scattering and for a lensnumerical aperture of 0.85, thus obtaining the angle-dependent scattering coefficient Qsca(a, q). When this func-tion is plotted on a log–log scale for a spherical, octahedron,face-on plate and edge-on plate (Fig. 10) particle the graphshows that Qsca(a, q) depend strongly upon the particleshape, size and orientation but the detector signal for smallparticles is expected to be q6.

Theoretical results are utilized in the SIRM measurementsin many separate ways. As the examples described with theparaxial theory show, it is easy to understand why the SIRMis not capable of imaging particles situated close to the frontsurface of the specimen. From the results of the high-aperture theory we learn to interpret the SIRM images.Results of the high-aperture theory will result in numerical

algorithms that can be programmed and used to obtainirregularity free images (e.g. by means of deconvolution).Scattering theories can provide a simple way to estimate thesize of the scattering precipitate particles by measuring therelative peak intensity of individual scatterers.

3. Imaging modes of SIRM

Imaging modes of the SIRM have been extensively discussedby Torok (1994). Here we give a brief account of the imagingmodes that have been realized already for SIRM. We should,however, emphasize that in principle any imaging mode of ascanning optical microscope can be realized.

First we address the question of surface reflection fromthe design point of view. When the SIRM is operated in thereflection mode surface reflection inevitably plays animportant role in the image formation of the microscope.The ‘confocality’ of any reflection mode SIRM is essentialbecause the surface reflection would not allow the imagingof depth structures. When the SIRM is operated in thetransmission mode it is not crucial to employ confocaldetection. When, however, it is applied, the depth resolutionof the microscope increases by a factor of < 5–10×. Thereare two basic differences between the transmission andreflection modes of the SIRM. Firstly, the contrast that anin-focus inhomogeneity causes in the transmission SIRM ismeasured as the dark level (extinction) against a brightbackground, whilst for the reflection SIRM this is measuredas the bright level (scattering) against a dark background.Secondly, the transmission SIRM, when operated in theconfocal mode, is sensitive to nonuniformity in specimenthickness and the perpendicular alignment of the specimenwith respect to the optical axis. The reflection SIRM is notsensitive to any of the above problems with the specimen.

Design principles of the SIRM, when operated in thereflection confocal mode, are aimed primarily at thesuppression of surface reflection and secondly at a possibleincrease in sensitivity. For the transmission confocal SIRMsurface reflection does not affect imaging and thusincreasing the sensitivity is of the utmost importance.

3.1. Transmission nonconfocal

A configuration of the SIRM is shown in Fig. 11(A), whichembodies the simplest example for a transmission nonconfo-cal scanning microscope. Light emerges from the laser (a).Light is incident on the input aperture of the lens (b) whichimages/focuses the light inside the specimen (c). Lighttraverses the specimen and is collected by either detector (d)or detector (e). The specimen is scanned with respect to theoptical beam and the image is built up in the memory of acomputer where position data and an amplified signal of thedetector are stored. As the magnified area of the specimen inFig. 11(A) shows, if a particle is situated in the focus region


Fig. 10. Detected intensity Qsca(a, q) as a function of normalizedparticle size for various particle shapes as predicted by the DDAmethod. Data abstracted with permission from Laczik & Booker(1996). Copyright 1996 American Institute of Physics.


then light is scattered from this particle. We consider first theeffect of a detector (e) displaced from the optical axis.

As a particle approaches the focus, light is scattered bythe particle. The strength of the scattered light depends onthe distance between the particle and the diffraction focus.It is advantageous to detect the scattered light close to theoptical axis, as it gives the strongest scattered intensity. Ifthe detector is displaced from the optical axis and detects nolight propagating within the solid angle determined bygeometrical optics, then the detection is said to be dark-field.There are some advantages to detecting scattered light inthis way. Dark field images of large oxide particles in asilicon specimen were successfully obtained using adisplaced detector and the transmission nonconfocal SIRM.

In the usual transmission nonconfocal set-up, the detector(d) is placed on the optical axis close to the specimen. In such aset-up the detection is said to be bright-field. The particlecontrast mechanism in this case is substantially different fromthat of dark-field as here the scattering is not responsibleprimarily for the contrast but the blocking effect, at least forthe particle size range of present interest.

The advantages of this method are as follows. This set-upis the simplest and easiest to align. It does not require high-precision fine mechanics or optics. Disadvantages are thatthe lateral and depth resolutions are essentially similar tothose of a conventional microscope. It follows that theparticle number density range that can be examined islimited, typically 105–108 cm¹3. Furthermore, the speci-men must be polished on both sides. The size of the detectoris a dominant parameter since either it must be placed closeto the specimen to collect sufficient light or must possess alarge area. This SIRM mode is sensitive to background lightor heat radiation.

3.2. Transmission confocal

With some modification the transmission nonconfocal SIRMcan achieve better lateral and depth resolution. When a lensis placed in front of the detector to collect the transmittedlight and image the probe to the detector through a pinhole,the optical arrangement is called the transmission confocal

SIRM. This mode is a bright-field microscope and its blockdiagram is shown in Fig. 11(B). Light emerging from thelaser (a) is imaged into the specimen (c) by the probe-forming lens (b). Light traversing the specimen is collectedby the collector lens (d) and imaged to the detector througha pinhole (e). The specimen is raster scanned in a mannersimilar to that described above for the reflection confocalSIRM. For the box schematically shown and denoted as (a)the same considerations apply as for the reflection confocalSIRM. When the collector lens is corrected for infinite tubelength then an additional lens should be applied to focus thelight beam collimated by the collector lens to the detector.The application of the transmission confocal microscope forvisible and ultraviolet light is well known, mainly forbiological specimens. The transmission confocal SIRM canbe applied in materials science to detect precipitates insemiconductors, especially when the power of the illuminationlaser is not high enough to use it in reflection confocal mode.

This set-up, however, possesses a big disadvantage in thatchanges in the position and/or thickness of the specimenmodify the lateral position of the imaged probe on thepinhole (e). In particular, when the specimen surface is notaligned perpendicular to the optical axis and is moved in thelateral direction (e.g. scanned), then the direction of eachray pencil traversing the specimen will be differentdepending on the focusing depth. The above process resultsin a laterally misplaced image at the detector (e). Aspecimen of nonuniform thickness gives the same result.

The main advantages of this imaging mode are as follows.The surface reflection does not affect the imaging andtherefore investigations can be performed for particles closeto the surfaces. The lateral and axial resolutions are high,which makes it possible to examine specimens in theparticle number density range 106–1010 cm¹3. The maindisadvantage is misalignment arising from the specimenthickness variations.

3.3. Transmission DPC confocal

When the differential contrast principle is applied in thetransmission mode then the microscope is called a

Fig. 11. Schematic diagrams of the optical system and experimen-tal images. Individual figures correspond to the following cases: (A)transmission nonconfocal SIRM;

Fig. 11. (B) transmission confocal SIRM;



transmission confocal differential phase contrast SIRM. Itsschematic diagram is shown in Fig. 11(C). Light emergingfrom the laser (a) is incident on the probe forming lens (b)which images the exit aperture of the laser into thespecimen (c) so forming the probe. Transmitted light iscollected by the collector lens (d) which images the probethrough a beam splitter (e) onto two detectors (g). In front ofeach detector a pinhole is placed. The half-stops (f) arearranged so that when the probe is not blocked or scattered,both detectors give the same intensity of light. For this set-up the use of a half mirror and/or two closely placed (orsplit) detectors behind a single pinhole can also besuccessful. By the usual classification this imaging modeembodies a bright-field microscope.

In the transmission mode the specular reflection from thesurface of the specimen does not play any role. Therefore thesignificance of the application of the transmission confocalDPC SIRM is different from that of the reflection confocalDPC SIRM. As discussed above, the contrast mechanism of atransmission microscope is different from that of thereflection SIRM. This difference is caused by the blockingeffect of the particles as they block or absorb some of theincident light. There are, however, other features inthe semiconductor specimens that affect the propagationof the light. These mainly are strain fields surroundingparticles. By scanning through a small particle surroundedby a strain field, the effect of both imperfections changes thedirection of propagation of light close to the focus. Thisdirection changing results in a laterally displaced image ofthe probe on the pinholes and therefore in some change inthe difference signal. It can be shown experimentally thatsome particles can be revealed by the transmission confocalDPC SIRM which are invisible for conventional transmissionconfocal SIRM.

The advantages of the above imaging mode are as follows.It is simple to align, especially when using two closelyspaced detectors or a split detector. It provides additionalinformation with respect to the previous imaging modes asit images some particles which would not have beenrevealed. The disadvantages of this method are the sameas those of a conventional transmission confocal SIRM.

In Fig. 11(D) experimental images of the same specimen

taken by transmission confocal and transmission DPCconfocal SIRM are compared. As the arrows indicate, twoparticles are identified by the transmission DPC confocalSIRM which were not revealed by the transmission confocalSIRM examination. Images were taken at a depth of 35 mmbelow the front surface. The scale bar corresponds to 40 mm.

3.4. Reflection DPC confocal

Differential phase contrast (DPC) microscopy makes itpossible to suppress the effect of specular reflection fromthe surface of the specimen in the reflection mode. Thisimaging mode by the usual classification is a dark-fieldmicroscope. The schematic diagram of the reflection modeDPC SIRM is shown in Fig. 11(E). The light of the laser (a) isincident on a collimator lens (b) and traverses a beamsplitter (c). Light is focused by the probe forming lens (d)into the specimen (e). Reflected/scattered light is collected


Fig. 11. (C) transmission differential phase contrast (DPC) SIRM;

Fig. 11. (D) experimental images of SIRM set-ups for (B) and (C),respectively;

Fig. 11. (E) reflection confocal DPC SIRM;


by the probe forming lens and split by the beam splitter (c).In the detector path another beam splitter halves the lightbeam in such a way that one half is split towards onedetector lens (h) and the other half after traversing thebeam splitter is incident on the other detector lens (h).Before the light reaches the detectors through the pinholes(g), two half-stops are placed into the detector path in sucha way that each of them stops a different half of the incidentbeam. The alignment of this system is difficult; moreover,the light loss due to the half-stops can be significant. Toovercome this problem in practice, instead of using thesecond beam splitter, a half mirror can be placed so that ittransmits one half of the light and reflects the other halftowards the other detector. It is also possible to use twoclosely spaced detectors placed behind a pinhole. This latterarrangement provides the best solution against misalign-ment in the system.

The operation principle of this mode is as follows. Whenthe specimen surface is in focus, both detectors give thesame intensity. If the signals of the two detectors are added,the resulting signal is identical to that of a reflectionconfocal microscope. If, however, the signals are electricallysubtracted, then no signal is detected. If a lateral scan isperformed then no signal is detected as long as the surfaceof the specimen is evenly smooth. When a line scan occursthrough an imperfection on the surface, the light isscattered, resulting in a direction change in the collimatedbeam in the detector path. This causes the image of theprobe at the detector plane to be laterally displaced withrespect to the optical axis. It follows that one detector hasan increased signal whilst the other has a decreased signaland the difference is no longer zero. The same principleapplies when the probe is scanned through a particle in thebulk specimen, the only difference being the absence ofspecularly reflected light on the detectors. It is foundexperimentally that for oxide particles in silicon, thedifference signal gives a bright/dark image with both halvesequally pronounced when the particle is in focus.

The advantages of the reflection confocal DPC SIRM are

as follows. It suppresses the effect of specularly reflectedlight from the surface of the specimen. Based on experi-mental data it is found that this imaging mode offers thepossibility of distinguishing between in-focus and out-of-focus particles from a single measurement. By utilizing twoclosely spaced detectors, e.g. a single chip detector dividedinto two halves, the alignment of the system should besimilar to that of the reflection confocal microscope. Themain disadvantage of the method is that when no splitdetector is available, the alignment is difficult and thesystem rarely gives optimum performance.

3.5. Reflection confocal

A schematic view of the SIRM is shown in Fig. 11(F). Itutilizes the principle of reflection scanning confocalmicroscopy to image inhomogeneities in the bulk of thespecimen (Torok et al., 1993). A beam of infra-red light(1320 nm wavelength) from a laser is expanded and thenfocused into the specimen thus forming a probe withapproximate dimensions of 1 mm wide by 7 mm long. Onlyprecipitates scatter light whose refractive index is differentfrom that of the bulk. Light scattered from the specimen iscollected by the probe forming lens and reaches the detector.A pinhole is placed in front of the detector that closes outlight not originating from the probe; hence depth sectioningoccurs.

The specimen is placed on a table driven by three piezocrystals and a stepper motor. The stepper motor provideslarge movement while the piezo crystals are used to rasterthe specimen in any orthogonal axis. While the specimen israstered a grey-level image is formed of the signal acquiredat each raster point.

In Fig. 11(G) images taken from the same specimen bythe reflection confocal and reflection confocal DPC SIRM arecompared. Images were taken at 35 mm below the frontsurface. Particle A corresponds to an in-focus particle, whileparticle B corresponds to a slightly out-of-focus particle.Scale bar corresponds to 20 mm.

Fig. 11. (F) reflection confocal SIRM;Fig. 11. (G) experimental images of SIRM set-ups for (E) and (F),respectively. Further notation can be found in the text.



4. Experimental

The SIRM is useful for imaging oxide precipitates in the bulkof silicon wafers formed during heat treatments. Theseparticles are created for two main reasons:1 to nucleate the interstitial oxygen;2 to create heterogeneous nucleation sites for metalcontaminants that are introduced during the devicemanufacturing process.

The density of these defects is often critical to the successof eventual process steps.

Since the defects are typically 5–50 nm in size, andtherefore much smaller than the wavelength of theilluminating laser light (l = 1.3 mm), Rayleigh scattering isexpected to be the dominant contrast mechanism. If this isthe case, the intensity is expected to be a function of the radiusof the scatterer to the sixth power (Jackson, 1975) as isdiscussed in Section 2.3. It is also clear (especially consideringthis dependence on r6) that there will be some lower limit ofprecipitate size below which the instrument cannot detect.

In the following we present results of calibrationmeasurements that were performed to evaluate the SIRM,and compare these results with other, more establishedtechniques (e.g. TEM and cleave-and-etch).

As far as the density is concerned, ideally the SIRMshould measure exactly the same density of defects as moretested techniques. Owing to the fact that the SIRM uses afocused beam as the probe there must also be somemaximum defect density above which the instrumentbecomes saturated (the probability of finding one or more

defects in each probe becomes large). The following twoexperiments were designed to answer these questions andtest these hypotheses.

The SIRM was used in the reflection mode to measuredefect density and output signal intensity in a set ofcommercial quality VLSI silicon wafers which were all giventhe same low-temperature, oxygen-nucleation heat treat-ment but different precipitation (growth) anneals. Thepretreatment is used to dissolve the oxygen clusters inexistence in the as-grown wafer formed during crystalcooling which can give rise to anomalous precipitationbehaviour. The low-temperature anneal nucleates thedesired density of defects which are then grown to a stablesize at 800 8C and grown further by the 1000 8C anneal.These last two anneals are not believed to create furthernuclei. The wafers were first pretreated for 15 min at1000 8C, followed by a ramped anneal between 450 8C and650 8C, and 4 h at 800 8C (Table 1). This heat treatment wasdesigned to create a set of samples with the same defectdensity but different defect sizes. The size distribution inthe precipitates was measured by means of TEM, while thedensity of defects was measured both by TEM and thecleave-and-etch techniques.

X–Y scans were then made with the SIRM at variouspoints along the radius of each wafer. From the data in theimages the defect densities and mean scattering signals werecalculated. A plot of the densities as measured by the threetechniques is shown in Fig. 12. The fall-off in the SIRM-measured density is attributed to the loss of sensitivity as theparticles became smaller, since all the samples were known


Table 1. Wafer data for samples used in the experiment.

Initial Oi Ramp 1000 8C Residual Oi D OiWafer no. ( ×1017 cm¹3) Pre-treat anneal 800 8C, 4 h growth ( ×1017 cm¹3) ( ×1017 cm¹3)

1S 7.461 no no no no 7.461 0.0001D 7.743 no no no no 7.742 0.0012S 7.461 yes yes yes no 7.455 0.0062D 7.743 yes yes yes no 7.736 0.0073S 7.474 yes yes yes 1 h 7.436 0.0383D 7.781 yes yes yes 1 h 7.781 0.0004S 7.474 yes yes yes 2 h 7.371 0.1034D 7.781 yes yes yes 2 h 7.766 0.0155S 7.518 yes yes yes 4 h 7.250 0.2685D 7.885 yes yes yes 4 h 7.675 0.2106S 7.518 yes yes yes 8 h 6.775 0.7436D 7.885 yes yes yes 8 h 7.057 0.8287S 7.500 yes yes yes 16 h 5.057 2.4437D 7.734 yes yes yes 16 h 5.414 2.3208S 7.500 yes yes yes 32 h 3.138 4.3628D 7.734 yes yes yes 32 h 3.271 4.463

Oi = interstitial oxygen in solution.


to have the same density from the TEM measurements.From this and the sizes of precipitates, given by the TEMexaminations, it is estimated that the SIRM is unable todetect particles smaller than 50–60 nm in diameter. It isalso found, as shown in Fig. 12, that the densities measuredby all the techniques essentially agreed.

By comparing the mean scattered intensity with the meandefect size for each sample, it is also found that the intensityvaries approximately as a function of the radius of thescatterers to the sixth power, hence proving that Rayleighscattering is responsible for the contrast mechanism.

In the second experiment a set of wafers with a range ofdifferent defect densities was prepared. The wafers were,however, all given the same growth thermal cycle of 16 h at1000 8C. As a result these samples all had the same sizeprecipitates but different particle number densities. Thisdensity was measured by the cleave-and-etch technique(Table 2) and then by the SIRM.

The densities measured by the SIRM are plotted againstthe cleave-and-etch densities in Fig. 13. It is clearly seenthat the two techniques measure approximately the samedensity up to about 5 × 1010 cm¹3 but above this the densitymeasured by the SIRM decreases. This effect was explainedby Mule’Stagno (1996) in terms of counting statistics. Itshows that the instrument is able to measure accuratelydefect densities below < 5 × 1010 cm¹3. From this densityMule’Stagno calculated that the volume of the probe had tobe about 13 mm3, which agreed well with theoreticalcalculations.

We have measured a particle close to the front surface inorder to confirm results of paraxial calculations that havebeen presented in Fig. 2. We found that the first particleeasily visible occurs at < 35 6 3 mm from the front surface.Particles closer to the front surface can also be measuredwhen sufficient offset is applied. This example shows thatresults of paraxial theory can, occasionally, yield accurateestimates on basic imaging properties of the SIRM.

Summary

In this paper we have presented a review of the scanninginfra-red microscope (SIRM) and its applications to detectbulk microdefects in semiconductor materials. Following an

Fig. 12. Defect densities as measured by the different techniques.

Table 2. Bulk defect density of the samples used in the secondexperiment as measured by the cleave-and-etch technique.

Cleave-and-etch densityWafer i.d. (× 109 cm¹3)

MD1A1 1.019_10 3.0ME5A1 7.2TXC136 7.7MH5A1 8.5MG1A1 10.0SRM7D 12.3SRM8D 16.8HF1A1 20.0TXCOE6 24.1HL1A1 38.0HG1A1 77.0TXCOH6 77.1TXCOF6 211.0TXCOK6 261.0

Fig. 13. The SIRM vs. the cleave-and-etch technique measureddensities for 15 specimens. The one-to-one correlation breaksdown above a density of about 5 × 1010 defects cm¹3 where satura-tion effects occur.



exhaustive literature review we have summarized therelevant results of paraxial and high-aperture theory.Theoretical aspects of contrast theory have been describedand we have found that they gave an excellent agreementwhen compared with experimental results. We have alsopresented experimental schematic diagrams for the variouspossible SIRM imaging modes as well as experimentalimages taken by the microscope.

Acknowledgments

The original research on the SIRM was initiated at theUniversity of Oxford, Department of Materials, by Dr G. R.Booker. One of the authors (P.T.) was supervised, during thefour years of his DPhil project, by him. This paper would nothave been written but for the foresight of Dr Booker. We arealso indebted to Dr R. Falster for his continuous advice andsupport during the last seven years. We gratefully acknowl-edge Drs G. R. Booker and Z. Laczik for their kind permissionto reproduce Figs. 9 and 10.

References

Anderson, S.G. (1994) Confocal laser microscopes see a wider fieldof application. Laser Focus World, 30, 83–87.

Booker, G.R., Laczik, Z. & Kidd, P. (1992) The scanning infraredmicroscope (SIRM) and its application to bulk GaAs and Si: areview. Semicond. Sci. Technol. 7, A110–A121.

Booker, G.R., Laczik, Z. & Torok, P. (1995) Applications of scanninginfra-red microscopy to bulk semiconductors. Inst. Phys. Conf.Ser. 146, 681–692.

Born, M. & Wolf, E. (1970) Principles of Optics. Pergamon Press,London.

Carlini, A.R. (1988) Imaging modes of confocal scanning microscopy.DPhil thesis, University of Oxford.

Chung, D.S. & Alkire, R.C. (1995) In-situ monitoring of depositedmorphology and adsorption of organic additives using laserscanning confocal microscopy. Interface, 4, 131–132.

Falster, R., Laczik, Z., Booker, G.R., Bhatti, A.R. & Torok, P. (1992)Gettering and gettering stability of metals at oxide particles insilicon. Mat. Res. Soc. Symp. Proc. 262, 945–956.

Fredrich, J.T. & Menendez, B. (1995) Imaging the pore structure ofgeomaterials Science, 268, 276–279.

Gu, Z.H., Fahidy, T.Z. & Dixon, A.E. (1992) In-situ monitoring ofelectrode surface modification via confocal scanning beam lasermicroscopy. J. Electrochem. Soc. 141, L153–L155.

Hamilton, D.K. & Wilson, T. (1987a) Infrared sub-band-gapphotocurrent imaging in the scanning optical microscope ofdefects in semiconductor devices. Micron Microsc. Acta, 18, 77–80.

Hamilton, D.K. & Wilson, T. (1987b) Optical sectioning in infra-redscanning microscopy. Proc. IEE, 134, 85–86.

Jackson, J.D. (1975) Classical Electrodynamics. John Wiley & Sons,New York.

Jang, H.F., Robertson, A.G. & Seth, R.S. (1992) Transverse

dimensions of wood pulp fibers by confocal laser scanningmicroscopy and image-analysis. J. Mater. Sci. 27, 6391–6400.

Jin, N.Y., Booker, G.R. & Grant, I.R. (1993) Scanning IR microscopyand transmission electron microscopy studies of inhomogeneitiesin LEC S-doped InP. Mater. Sci. Eng. B20, 94–99.

Khanh, N.Q., Hamori, A., Fried, M., Ducso, Cs. & Gyulai, J. (1995)Nondestructive detection of microvoids at the interface of direct-bounded silicon wafers. J. Electrochem. Soc. 142, 2425–2429.

Kidd, P., Booker, G.R. & Stirland, D.J. (1987a) Infrared-laserscanning microscopy in transmission – a new high resolutiontechnique for the study of inhomogeneities in bulk GaAs. Appl.Phys. Lett. 51, 1331–1333.

Kidd, P., Booker, G.R. & Stirland, D.J. (1987b) 3-D distribution ofinhomogeneities in Lec GaAs using infrared-laser scanningmicroscopy. Inst. Phys. Conf. Ser. 87, 275–280.

Kino, G.S. & Corle, T.R. (1989) Confocal scanning opticalmicroscopy. Physics Today, 42, 55–62.

Laczik, Z. (1996) Discrete dipole approximation based lightscattering calculations for particles with real refractive indexsmaller than unity. Appl. Opt. 35, 3736.

Laczik, Z. & Booker, G.R. (1996) Computed light scattering crosssections of oxide particles in silicon. App. Phys. Lett. 68, 3239–3241.

Laczik, Z., Booker, G.R., Bergholz, W. & Falster, R. (1989a)Investigation of oxide particles in Czochralski silicon heat treatedfor intrinsic gettering using scanning infrared microscopy. Appl.Phys. Lett. 55, 2625–2627.

Laczik, Z., Booker, G.R., Falster, R. & Shaw, N. (1989b) Investiga-tion of precipitate particles in Si and CdTe ingot material usingthe scanning infrared microscope (SIRM). Inst. Phys. Conf. Ser.100, 807–812.

Laczik, Z., Torok, P. & Booker, G.R. (1995) The effect of sphericalaberration and surface reflection on the scanning infra-redmicroscope imaging of oxide particles in silicon. Inst. Phys. Conf.Ser. 146, 767–770.

Laczik, Z., Torok, P., Booker, G.R. & Falster, R. (1991) Newapplications of the scanning infra-red microscope (SIRM) toinhomogeneities in bulk GaAs and Si. Inst. Phys. Conf. Ser. 117,785–788.

Lange, D.A., Jennings, H.M. & Shah, S.P. (1993) Analysis ofsurface-roughness using confocal microscopy. J. Mater. Sci. 28,3879–3884.

Mule’Stagno, L. (1996) Quantitative non-destructive study of sub-micron defects in VLSI silicon using transmitted and reflectedscanning infra-red microscopy. PhD thesis, University of Missouri– Rolla.

Petford, N. & Miller, J.A. (1993) The study of fission track and othercrystalline defects using confocal scanning laser microscopy. J.Microsc. 170, 201–212.

Pistillo, W.R. (1996) The role of surface modifiers in high-solidscoatings. Paint and Coating Industry, 12, 56–59.

Richards, B. & Wolf, E. (1959) Electromagnetic diffraction inoptical systems II. Structure of the image field in an aplanaticsystem. Proc. R. Soc. London A, 253, 358–379.

Sheppard, C.J.R. & Choudhury, A. (1977) Image formation in thescanning microscope. Opt. Acta, 24, 1051–1073.

Sheppard, C.J.R. & Torok, P. (1997) Effects of specimen refractiveindex on confocal imaging. J. Microsc. 185, 366–374.



Thomason, J.L. & Knoester, A. (1990) Application of confocalscanning optical microscopy to the study of fiber-reinforcedpolymer composites. J. Mater. Sci. Lett. 9, 258–262.

Torok, P. (1994) Development, theory and application of the reflectionconfocal scanning infra-red microscope. DPhil thesis, University ofOxford.

Torok, P., Booker, G.R., Laczik, Z. & Falster, R. (1993) A newconfocal SIRM incorporating reflection, transmission anddouble-pass modes either with or without differential phasecontrast imaging. Inst. Phys. Conf. Ser. 134, 771–774.

Torok, P., Hewlett, S.J. & Varga, P. (1996e) The role of specimeninduced spherical aberration in confocal microscopy. J. Microsc.in press.

Torok, P., Laczik, Z. & Sheppard, C.J.R. (1996c) Effect of half-stoplateral misalignment on imaging of dark-field and stereoscopicconfocal microscopes. Appl. Opt. 35, 6732.

Torok, P., Laczik, Z. & Skepper, J.N. (1996a) Simple modification ofa commercial scanning laser microscope to incorporate dark-field imaging. J. Microsc. 181, 260–268.

Torok, P., Pecz, B., Laczik, Z., Booker, G.R., Radnoczy, G. & Falster,R. (1995a) Imaging of oxide particles in Czochralski siliconwafers using high-performance reflection confocal scanninginfra-red microscopy and transmission electron microscopy. Inst.Phys. Conf. Ser. 146, 771–774.

Torok, P., Sheppard, C.J.R. & Laczik, Z. (1996b) Dark-field anddifferential phase contrast imaging modes in confocal micro-scopy using a half-aperture stop. Optik, 103, 101–106.

Torok, P. & Varga, P. (1996) Electromagnetic diffraction of lightfocused through a stratified medium. Appl. Opt. 36, 2305–2312.

Torok, P., Varga, P. & Booker, G.R. (1995c) Electromagneticdiffraction of light focused through a planar interface between

materials of mismatched refractive indices: structure of theelectromagnetic field I. J. Opt. Soc. Am. A, 12, 2136–2144.

Torok, P., Varga, P., Konkol, A. & Booker, G.R. (1996d) Electro-magnetic diffraction of light focused through a planar interfacebetween materials of mismatched refractive indices: structure ofthe electromagnetic field I. J. Opt. Soc. Am. A, 13, 2232.

Torok, P., Varga, P., Laczik, Z. & Booker, G.R. (1995b) Electro-magnetic diffraction of light focused through a planar interfacebetween materials of mismatched refractive indices: an integralrepresentation. J. Opt. Soc. Am. A, 12, 325–332.

Torok, P., Varga, P. & Nemeth, G. (1995d) Analytical solution of thediffraction integrals and interpretation of wave-front distortionwhen light is focused through a planar interface betweenmaterials of mismatched refractive indices. J. Opt. Soc. Am. A, 12,2660–2671.

Torok, P. & Wilson, T. (1997) Rigorous theory for axial resolutionin confocal microscopes. Opt. Commun. 137, 127–135.

Van Blaaderen, A. (1993) Imaging individual particles inconcentrated colloidal dispersions by scanning lightmicroscopy. Adv. Mater. 5, 1, 52.

Wilson, T. (ed.) (1990) Confocal Microscopy. Academic Press,London.

Wilson, T., Gannaway, J.N. & Johnson, P. (1980) A scanning opticalmicroscope for the inspection of semiconductor materials anddevices. J. Microsc. 118, 309–314.

Wilson, T. & Sheppard, C.J.R. (1984) Theory and Practice of ScanningOptical Microscopy. Academic Press, London.

Wolf, E. (1959) Electromagnetic diffraction in optical systems I. Anintegral representation of the image field. Proc. Roy. Soc. LondonA, 253, 249–357.



REVIEW Applications of scanning optical …fraundorfp/lucio/sirm_rev.pdfApplications of scanning optical microscopy in materials science to detect bulk microdefects in semiconductors

Documents