A numerical study of resolution and contrast in soft X-ray ...xrm.phys.northwestern.edu/research/pdf_papers/1998/wang_jmic_1998.pdfA numerical study of resolution and contrast in soft

A numerical study of resolution and contrast in soft X-raycontact microscopy

Y. WANG & C. JACOBSENDepartment of Physics, State University of New York at Stony Brook, Stony Brook,NY 11794-3800, U.S.A.

Key words. Contrast, photoresists, resolution, soft X-ray microscopy.

Summary

We consider the case of soft X-ray contact microscopy usinga laser-produced plasma. We model the effects of sampleand resist absorption and diffraction as well as the processof isotropic development of the photoresist. Our resultsindicate that the micrograph resolution depends heavily onthe exposure and the sample-to-resist distance. In addition,the contrast of small features depends crucially on thedevelopment procedure to the point where information onsuch features may be destroyed by excessive development.These issues must be kept in mind when interpretingcontact microradiographs of high resolution, low contrastobjects such as biological structures.

1. Introduction

Soft X-ray microscopy offers a means to view biological andmaterials science specimens at a resolution superior to thatof confocal optical microscopes (Michette et al., 1992; Aristov& Erko, 1994). In particular, if X-rays with an energybetween 280 eV and 520 eV are used (corresponding to the Kedges of carbon and oxygen, respectively), wet, micrometre-thick biological specimens such as whole-cell preparationscan be studied with reduced radiation damage as comparedto electron microscopes (Sayre et al., 1977), even when phasecontrast and zero-loss energy filters are employed.

Many soft X-ray microscopes employ zone plate, multi-layer-coated mirror, or grazing incidence mirror optics withresolution in the 30–100 nm range (Kirz et al., 1995). Suchmicroscopes are usually operated at synchrotron radiationcentres, and involve image-recording times of seconds tominutes. An alternative approach is to illuminate thespecimen with an X-ray beam and use a high-resolutiondetector to record the intensity pattern which passesthrough the specimen. This contact microradiography orcontact microscopy technique offers experimental simpli-city, the ability to use nonmonochromatic flash X-raysources such as laser-produced plasma sources, and thepotential for very high image resolution.

In this paper we consider the nature of contact X-raymicrographs recorded on photoresists, and the limitationson image resolution imposed by photon statistics, diffrac-tion and by the process of developing the photoresist.Numerical simulations corresponding to typical experimen-tal conditions suggest that it is difficult to reliably interpretdetails below the 40 nm level by these techniques as theynow are frequently practised.

2. X-ray contact microradiography

There is a long history of research in which X-rayradiographs have been viewed with optical microscopes tostudy submillimetre structures (Gorby, 1913). A major stepforward was made in 1956 by Ladd et al. who replacedsilver halide film and optical microscope enlargement with‘grainless’ ammonium dichromate crystals. Upon X-rayexposure and immersion in methyl alcohol, these crystalstransferred the X-ray exposure into a surface relief pattern;Ladd et al. then viewed a polymer surface replica of thisrelief pattern using an electron microscope (Ladd et al.,1956). While others carried out further explorations ofnonsilver halide recording media and electron microscopeimage enlargement (Cosslett & Nixon, 1960), none of thetechniques appear to have caught on in contact micro-radiography at that time, largely because of the muchlonger exposure times required.

In the late 1960s, poly(methyl methacrylate) or PMMAwas developed as a reasonably fast and extremely highresolution resist for electron beam lithography (Haller et al.,1968; Hatzakis, 1969). Primary (10–100 keV) and inelas-tically scattered (especially 10–1000 eV) electrons causechain scission in the polymer chain, and the loweredmolecular weight near exposed areas leads to highdissolution rates when placed in developer. Recognizingthat 10–1000 eV electrons are also produced following X-ray absorption in solids, groups at IBM (Feder, 1970; Spiller,1993) and at MIT (Spears & Smith, 1972) began to usePMMA as a resist for studies of X-ray lithography for

Journal of Microscopy, Vol. 191, Pt 2, August 1998, pp. 159–169.Received 24 April 1997; accepted 12 September 1997

159q 1998 The Royal Microscopical Society

microelectronics fabrication. The IBM group then realizedthat they had a technique for generating high resolutionrecordings of sub-micrometre structures, and they produceda series of demonstrations of high resolution X-ray contactmicroscopy (Feder et al., 1976; Feder et al., 1977; Spiller et al.,1976) using both laboratory and synchrotron X-ray sourcesand scanning electron microscope (SEM) image enlargement.A large number of researchers have contributed variousimprovements to the technique. These include:1 The use of pulsed X-ray sources for flash imaging,including plasma pinch X-ray generators (Feder et al.,1985), laser-produced plasmas (Rosser et al., 1985; Tomieet al., 1991; Stead et al., 1993; Kinjo et al., 1994), and X-raylasers (Skinner et al., 1990).2 Improved methods for resist readout which include directTEM enlargement (Feder et al., 1981; Cheng et al., 1986;Howells et al., 1987), TEM enlargement of surface replicas(Shinohara et al., 1986; Cheng, 1987), and atomic forcemicroscopy (Tomie et al., 1991; Lindaas et al., 1992; Cottonet al., 1994; Howells et al., 1994).

With these advancements, a soft X-ray contact micro-scopy laboratory can be built at reasonable cost by using alaser-produced plasma X-ray source, PMMA photoresists,and an atomic force microscope for resist readout (Cottonet al., 1994; Kado et al., 1994). Such an approach offersreasonable experimental simplicity, and the possibility torecord <100 nm resolution flash images on a nanosecondtimescale. Such an advantageous timescale is believed to befaster than that of thermal expansion of the specimen at therequired resolution level (Solem, 1986; London et al.,1992), and faster than the timescale of the larger-size-scaleconsequences of radiation damage (Shinohara & Ito, 1991).

In practice the major limiting factors to the resolution ofthis technique are as follows (Spiller & Feder, 1977; Cottonet al., 1993): secondary electron exposure of the resist at alocation distant from where the X-ray photon was absorbed,Fresnel diffraction over the distance from the sample to therecording media, shot noise caused by photon statistics, andsidecutting during the wet etch processing of the exposedphotoresist. The secondary electrons have mean free path ofaround 10 nm (Spiller & Feder, 1977; Early et al., 1990);this is less than the resolution limit set by other factors withtypical current laboratory setups (as we shall demonstrate).Therefore, we will only concern ourselves with exposureand development strategies to obtain the optimum contactmicrograph.

3. Method of simulation

There are no commercial contact microradiography systemsat present, so methods and conditions vary amongpractitioners. We will assume that a typical experiment iscarried out as follows:1 The specimen is placed on a photoresist-coated substrate.

An aluminium-coated silicon nitride window is placed ontop of the specimen to trap a micrometre-thick water layerto keep the sample hydrated. (The aluminium coating alsoblocks UV light.) The specimen/resist package is thenmounted in the vacuum chamber of the laser-producedplasma X-ray source.2 A laser pulse is used to generate X-rays from hot plasma,exposing the resist through the silicon nitride window,water layer and specimen.3 The specimen is washed off the resist, and the resist is‘developed’ by immersion in a solvent that transfers theX-ray exposure pattern into a surface relief pattern.4 The resist surface is examined with an atomic forcemicroscope, giving an image related to the X-ray absorptionpattern of the specimen.

We will represent this process by the following sequence,the steps of which are described in further detail in thesections indicated:Section 3.1. The laser-produced plasma emits an X-rayspectrum which is well approximated by a kT ¼ 100 eVblackbody spectrum.Section 3.2. This spectrum is modified by transmissionthrough a 100 nm thick Si3N4 window coated with 100 nmof Al2O3. We then assume that the X-rays must also travelthrough 1 mm of water to reach the specimen (such a waterthickness is nearly unavoidable due to surface tension).Section 3.3. As the X-rays travel through the specimen ofthickness t, they are attenuated and phase shifted. To modelthis, we break the spectrum up into a series of closely spacedwavelengths, and treat the passage of each monochromaticX-ray wavefield through the specimen using a multislicemethod (Cowley & Moodie, 1957; Hare & Morrison, 1994).We then propagate the resulting wavefield to the photoresistplane.Section 3.4. At each wavelength, the number of photonsincident on a given area of photoresist is calculated.Statistical fluctuations (shot noise) are incorporated intothis number.Section 3.5. Photoresists respond according to absorbedradiation dose. At each X-ray wavelength, the absorbed doseis calculated from the areal photon density as calculatedabove, and the absorption cross-section of the photoresist.The total dose to the surface layer of the photoresist is thenobtained by summation of the fractional dose at each of theX-ray wavelengths.Section 3.6. The etching rate R at the photoresist surface isassumed to vary with absorbed dose D according to

R ¼ R0ðD=D0Þg ð1Þ

where the parameters R0, D0 and g are determinedexperimentally. The etching process at each point of theresist surface is assumed to take place along the surfacenormal direction. The evolution of the resist surface is thencalculated over a sequence of time steps.

160 Y. WANG AND C. JACOBSEN

q 1998 The Royal Microscopical Society, Journal of Microscopy, 191, 159–169

We will assume that the developed resist surface isaccurately mapped by the atomic force microscope at theresolution scale of interest to us. The X-ray exposure portionof the sequence outlined above is shown schematically inFig. 1. These steps will be modelled on a grid with transversespacing Dx,y.

The sequence of steps described above is similar to thatwhich exists in proximity X-ray lithography (indeed,advances in contact microscopy in the 1970s grew outof the development of X-ray lithography as noted above).Model calculations of many of the above steps have beenperformed in the context of X-ray lithography at 0·5–1 nmwavelengths, involving transmission through metal a fewtenths of a nanometre thick mask patterns located atgaps of typically 2–30 mm from a resist surface (Schatten-burg et al., 1991), and involving simulations of shot noiseand resist development (Rosenfield, 1981; Turner et al.,1991). Indeed, in some cases most or all of these stepshave been combined to model the complete process(Khan et al., 1994). Therefore the general method ofmodelling we have used is not unique; however, theparameters used in soft X-ray microscopy of biologicalspecimens are considerably different from those used inX-ray lithography. For that reason, we have modelled thespecific case of soft X-ray contact microscopy ofbiological specimens.

3.1. Laser-plasma X-ray generation

While monochromatic synchrotron sources are some-times used (Spiller et al., 1976) for contact micro-radiography, the more common approach is to usebroadband X-ray illumination from laser-producedplasmas. We assume that X-rays are generated from a

laser-produced plasma with a blackbody spectrum char-acterized by kT ¼ 100 eV (Tomie et al., 1991) as is shownin Fig. 2. In order to match the total exposure levels usedin practice, we have assigned a value of 0·21 J cm¹2 to bethe spectrally integrated irradiance incident on theentrance window of the specimen chamber. This gives us0·032 J cm¹2 at the resist surface. While relay optics aresometimes used to reduce debris on the exposure area(Rosser et al., 1985), we assume that the effects on thespectrum are small because reflectivity from high-Zsurfaces is quite spectrally uniform at grazing incidenceangles well below the critical angle (Henke, 1981).

Along with the blackbody spectrum, spectral linesare often present. The strongest of these lines typicallycontain less than 1% of the total power emitted, so wehave chosen not to include their presence in our model.The use of polychromatic light will reduce diffractionfringe artefacts in the image, for fringe maxima producedat one wavelength may well lie on top of fringe minimareduced at another wavelength. Therefore by leavingout spectral line emission, one is likely to obtain a morefavourable result for contact microscopy from thesesimulations.

3.2. X-ray refractive index

At photon energies large compared to the "qp energycorresponding to the plasma frequency qp, the refractiveindices of materials become complex so that wavefields areboth absorbed and phase-shifted. Soft X-ray refractiveindices are well characterized (except for within < 10 eVof X-ray absorption edges) by tabulated values for the


Fig. 2. Irradiance spectra for the 100 eV blackbody source (solidline) and the source as filtered by transmission through 100 nmof Si3N4, 100 nm of Al2O3 and 1 mm of water (dashed line). Thespectrally integrated irradiance is assumed to be 0·21 J cm¹2 beforeentering the sample holder, resulting in an irradiance of0·032 J cm¹2 after transmission through the window and water.

Fig. 1. Example geometry used for recording contact micrographsof hydrated specimen using a laser produced plasma X-ray source.

SOFT X-R AY CONTACT MICROSCOPY 161

complex number of electrons per atom f1 þ if2 (Henke,1981). The intensity attenuation per thickness t can thenbe calculated as

IðtÞ ¼ Ið0Þe¹2kbt ð2Þ

and the phase advance per thickness t is given by

eikdt ð3Þ

where k ¼ 2p/l

d ¼ 1=ð2pÞrel2na f1 ð4Þ

b ¼ 1=ð2pÞr2l2na f2 ð5Þ

re ¼ 2·812 × 10¹15 m is the classical radius of the electron,and na is the volume density of atoms. For collections ofatoms which are amorphous on a scale of the soft X-raywavelength l, the refractive indices can be calculated from asum weighted by the volume density of each type of atompresent:

nað f1 þ if2Þ →X

z

na;ið f1;i þ if2;iÞ ð6Þ

We use here the tabulation of (f1 þ if2) of Henke et al. (1993).The relationship for attenuation of Eq. (2) can then be used tocalculate the spectrum reaching the specimen region follow-ing transmission through a 100-nm thick Si3N4 window(r¼ 3·44 g cm¹3) coated with 100 nm of Al2O3 (r¼

3·96 g cm¹3), followed by 1 mm of water. The resulting modi-fication to the source blackbody spectrum is shown in Fig. 2.

3.3. Multislice propagation

We now model the transmission of the X-ray wavefieldthrough the specimen region. Since this region is notuniform, we must consider diffraction effects using amultislice calculation (see, e.g. (Cowley & Moodie, 1957;Hare & Morrison, 1994). This calculation will be carried outseparately for each of many wavelengths throughout theillumination spectrum, where X-ray optical constants aretabulated at a multiplicative spacing in energy E withEiþ1 ¼ 1·016 Ei.

We can model the diffraction effects assuming spatiallycoherent radiation at each wavelength. Because theultimate resolution limit of contact microradiography is atleast an order of magnitude larger than the wavelength,most of the signal from a feature will be contained within anarrow angular range. Given that the specimen must beplaced in close proximity to the photoresist, all interferenceeffects will be confined within a small transverse distance.For example, with d ¼ 10 nm structures at l¼ 3 nm andwith a z ¼ 1 mm sample-to-resist gap, far-field diffractionfringes have a spacing of lz/d ¼ 30 nm and Fresnel knife-edge diffraction fringes have a spacing characterized by√

(lz) ¼ 50 nm. As a result, one needs to consider mutualcoherence over submicrometre transverse distances.

Assuming a spatially incoherent source (the laser-producedplasma) of 100 mm diameter, the Van Cittert-Zernike theoremtells us that we obtain good mutual spatial coherence withm12 ¼ 0·88 over angular separations of up to

vcoh # l=d ð7Þ

or a transverse distance of 2 mm when the resist is located20 cm from the laser-produced plasma. Therefore, theassumption of spatial coherence is justified.

Under this assumption, the changes of the wavefield as itpasses through the specimen can be calculated using amultislice method. In reality, the wavefield is attenuated andphase shifted according to the refractive index d(x, y, z) þ ib(x,y, z) at each point (x, y, z) through the volume of the object,and diffraction governs the propagation of the wavefield fromz to z þ dz. In the multislice method, we imagine slicing theobject into a number of discrete slabs of finite thickness Dz(see Fig. 3). If we represent the wavefield entering one slab aswi(x, y), the exiting wavefield is then multiplied by the totalattenuation and phase shift which would be imposed upon aray travelling through the Dz thickness of the slab at the point(x, y), giving a modulated wavefield wi

0(x, y) of

w01ðx; yÞ ¼ wiðx; yÞ exp½¹kbðx; yÞDzÞ exp½ikdðx; yÞDzÿ: ð8Þ

This wavefield is then assumed to propagate a distance Dzthrough free space before it enters the next slab. Thispropagation operation can be calculated by convolution ofthe wavefield wi with a propagator function, which can beimplemented as (Collier et al., 1971):

wi þ 1ðx; yÞ ¼ FT ¹1fFTfw0iðx; yÞg exp½¹iliDzð1 ¹ f 2

x ¹ f 2y Þÿg

ð9Þ

where FT indicates a Fourier transform, FT¹1 is an inverseFourier transform, and fx and fy are spatial frequencies.

3.4. Photon statistics

We now have an estimate of the wavefield w enteringthe resist at each of the discrete wavelengths li which

Fig. 3. Schematic representation of the multislice method used topropagate the wavefield through the sample.



represent the illumination spectrum; the intensity is thengiven by I(x, y) ¼S|w|2. We must next confront the factthat the irradiance distribution which reaches the photo-resist involves a finite number of photons. For a numericalcalculation, the irradiance distribution has already beenspatially discretized. Therefore, at a wavelength li and aposition Dx,y(i, j), we can calculate the integer number ofphotons hNi which are present. This number was calculatedas if there are no statistical fluctuations in the signal, so wemust also include Poisson fluctuations. For hNi$ 25, thiscan be well approximated by a Gaussian distribution with avariance s2 of s ¼

√hNi. Given a computer routine which

generates pseudo-random numbers n on a Gaussiandistribution with a mean of zero and a variance of 1, theshot-noise-included signal N is

N ¼ hNi þ n��hNi

p: ð10Þ

We also impose the constraint N $ 0 for those rare caseswhen the Gaussian approximation to the Poisson distribu-tion would give N<0·

3.5. Resist exposure

We now have the shot-noise-included number of photons Nat each wavelength li and pixel Dx,y(i, j). We must nextcalculate the effect of this exposure on the photoresist. Thefraction of photons absorbed in a thickness dt of resist is –d(I/I0)/dt ¼ 2kb. X-ray photoresists respond to absorbed dose D,which in our case is given at a depth z into the resist by

DðzÞ ¼ Nhcl

� �2kb

1D2

x;yrre¹2kb;z

; ð11Þ

where hc/l is the photon energy, k ¼ 2p/l is the wavenumber, b is the absorptive part of the refractive index of thephotoresist as given by Eq. (5), Dx,y is the calculation pixelsize, and rr is the density of the resist.

When an X-ray photon is absorbed in the photoresistPMMA, an Auger electron is usually generated which willthen produce a number of low energy (10–1000 eV)electrons by collisions. Many of these electrons will breakthe polymer chain of the photoresist, thereby loweringthe effective molecular weight in that region. When placedin a solvent, the resist will be dissolved according to thelocal molecular weight. The net result is that thedissolution rate R(D) is dose dependent, and it can beapproximated by

RðDÞ ¼ R0ðD=D0Þg: ð12Þ

Various measurements of R0 and D0 can be found in theliterature (Hawryluk et al., 1975; Spiller & Feder, 1977;Shinozaki, 1988). In X-ray holography experiments, it hasbeen found that the highest resolution photoresist imagesare obtained when low concentration developer is used (1:5methyl isobutyl ketone in isopropyl alcohol), in which casevalues of R0 ¼ 2·3 × 10¹4 nm s¹1, D0 ¼ 104 Gy, and g¼ 2·2can be estimated from the literature (Jacobsen, 1988).

3.6. Resist development

Having computed the exposure and therefore the dis-solution rate of the resist volume, we must now simulatethe development of the resist. A common model for thisprocess is to assume that development proceeds into theresist along the direction of the local surface normal. In the


Fig. 4. Illustration of the resist development model. (a) For each point on the resist surface, the normal vector is first calculated. The depthof etching (and therefore the length of the vector) is calculated according to the etching rate at the grid point and the time step. (b) The endsof the normal vectors define a deformed surface. The height of this new surface is linearly interpolated onto the regular grid points and usedas the representation of the surface profile for the subsequent etching step.


case of a computer calculation on a discrete grid ofpoints, the surface normal direction is calculated at eachgrid point, and a ‘ray’ is drawn with a length given byproduct of R (D) and the time step Dt. The ends of these‘rays’ generate a new surface and the height of thissurface on regular grid points is interpolated to producethe surface profile for the next iteration in thecalculation cycle (Fig. 4). The end result is that theshape of the resist surface is simulated as a function ofdevelopment time.

We have tested the resist development simulation bymodelling the development of a step-shaped exposure.

When two regions of the photoresist have different etchingrates R1 and R2, the developed resist profile will have aslope with an angle ∠ A < tan–1(R1/R2), if R1qR2 (seeFig. 5). Our two-dimensional resist development simulationroutine gives results that are in agreement with this simpleone-dimensional model (see Fig. 6). To check this in thesimulation, we used R1 ¼ 20 nm s–1, and R2 ¼ 5 nm s–1

with 256 × 256 pixels size of 2 nm.

Fig. 5. Estimate of the resist wall slope resulting from developmentof a step exposure. As the resist is etched, a step on the surface isproduced. In the next etching time interval, the step is etcheddownward by a distance R1Dt and rightward by a distance R2Dt.In the limit of a large number of short time intervals, this modelpredicts a wall slope angle of ∠ A < tan¹1 (R1/R2).

Fig. 6. Simulated development of two 2-D rect functions.The dissolution rate is assumed to be either 5 or20 nm s¹1 (a). The calculated resist profiles after 5, 15and 30 s of development are shown in (b), (c) and (d),respectively. The square shaped surface profile emergesin (b), and with further development the side-cuttingeffect of wet etching is evident in (c), until in (d) thefinal resist shape becomes triangular dueto the sideways development. The ∠ A measured fromthe slightly curved side walls in (d) is < 75, in agree-ment with the expected tan¹1 (20/5) < 76.

Fig. 7. Spectra of calculated dose in Gray deposited in the photore-sist at the minimum (solid line) sphere-to-resist gap of 20 nm, andat the maximum (dashed line) sphere-to-resist gap of 1000 nm.



4. Model calculations

The model described above has been used to consider threemain factors which affect resolution in contact microscopy:Fresnel diffraction, shot noise and development (wetetching). These effects will be considered in turn.

4.1. Effect of Fresnel diffraction during exposure

It is important to know the extent to which Fresneldiffraction degrades the image during exposure. To studythis effect, we used the multislice method described earlier.The sample was assumed to consist of three spheres of


Fig. 8. The spectrally integrated dosage deposited on photoresist as a function of the sample-resist gap and the linear distance along the line ofthe protein spheres (from the 2-D calculation). For the five different sized objects shown here at different scales, many general characteristicsof the gap-dependent exposure pattern scale from one exposure to another though there are detailed differences. The image alteration due toFresnel diffraction is evident in all the graphs and becomes more pronounced for smaller feature sizes. As the gap becomes larger than thescale of the sphere-to-sphere distance, the exposure pattern appears to show not three spheres, but more complex and narrower structures.


protein of diameter s (s ¼ 10–50 nm) separated by adistance s and the X-ray exposure spectrum was assumedto be as in Fig. 2. The spectra of X-ray reaching thephotoresist for the cases of 20 and 1000 nm sample-to-resistgap are shown in Fig. 7. The resulting exposure-vs.-gapimages are shown in Fig. 8. The remarkable point of thisfigure is how three simple structures appear to produce a widevariety of images at even submicrometre gap d2. In a sense,one is seeing more complex manifestations of the well-knownArago’s spot behind an opaque absorber. These figures clearlyillustrate that knowledge of the specimen-to-resist distance iscrucial for interpreting high-resolution images in contact

microscopy. To reliably produce images representing thesample, the sample to resist distance should ideally be on thesame scale as the desired feature resolution.

4.2. Effect of shot noise and wet etching

The simulation method described above was also used tostudy the effect of shot noise and wet etching on theobserved ‘images’. In this case, the specimen was assumedto consist of protein spheres and cylinders with diametersranging from 30 to 50 nm as indicated.

Figure 9(a) and (b) shows a set of test objects with size of

Fig. 9. Simulation of exposure and develop-ment of protein spheres and rods of dia-meter s, separated by a distance s withs ¼ 38, 40, 42 and 44 nm, from left toright in (a). The exposure pattern shownin (b) reflects the effect of shot noise,while the images (c) through (f) show theresist surface calculated following thedevelopment time indicated. Comparedwith image (c), the resist surface in (f) issmoother, but some high-resolution fea-tures are lost during the additional 48 s ofdevelopment. We have used the followingparameters in the calculation: dosage¼ 2·06 MGray, sample–resist gap ¼ 1 mm,g¼ 2·2, and pixel size ¼ 2 nm.



38, 40, 42 and 44 nm, and the resulting exposure pattern.Figure 9(c–f) shows the resist profile at four developmenttimes. In this calculation, the parameters used were:dosage ¼ 2·06 MGrey, g¼ 2·2, sample-resist gap ¼ 1 mm,and pixel size ¼ 2 nm.

Several observations can be made concerning Fig. 9. InFig. 9(b), the cylinders can be distinguished from shot noiseeven for the smallest, 38 nm diameter. However, in all casesthe spherical structures are difficult to discern. With theonset of wet etching, the largest cylinders and spheres becomerecognizable owing to the g¼ 2·2 nonlinear response of thePMMA. As the exposure time is increased, the presence of thelargest cylinders becomes even more pronounced, althoughthe separation between them becomes less distinct.

For the smallest (38 nm) features, the simulationsindicate that they are observable after 6 s of development,but progressively less visible after longer times. At 54 s, it isnot possible to tell that the object consisted of two smallcylinders. Similarly, cylinders of other sizes show goodcontrast at 6 and 18 s and reduced contrast with furtherdevelopment. This effect, which is included in the model ofresist development described above, can be explained by the

following argument (see Fig. 10): when low contrast peaksof poorly resolved features emerge, they expose a largersurface contact area to the developer than the nearby valley,leading to higher effective local etching rate; they aretherefore etched preferentially. This process will continueuntil the effective dissolution rate of the peaks is equal tothat of the valley. At this time, either the peaks are nolonger peaks (the feature is lost) or the final contrast isreduced to a degree determined by the size of the peak andthe contrast in dissolution rate. After such time, furtherdevelopment will not alter the contrast.

This behaviour is summarized in Fig. 11, where weplotted the normalized contrast (height difference betweenthe peak and valley) as a function of feature size anddevelopment time. The contrast of small features will reachits maximum value after a short development time and willbe reduced by further development. This indicates that thereis an optimum development time for a certain feature size,when the feature is resolved with maximum contrast. Suchoptimum time was determined from data in Fig. 11 and isplotted as a function of the feature size in Fig. 12. Thisgraph is approximately linear and its intercept on thefeature size axis can be loosely defined as the resolution limit(< 30 nm in this case) of the contact print under thisparticular exposure condition.

The calculation results of Fig. 9 show that small and lowcontrast features (i.e. biological structures) offer challenges


Fig. 11. The contrast (normalized for each feature size) as a func-tion of the feature size and development time. Fig. 12. Optimum time of development as a function of feature size.

Fig. 10. Etching of poorly resolved lines. The effective etching rate is higher at the peak than the valley because of higher contact area withthe developer, resulting in the reduction of the peaks and hence the contrast.


for contact microscopy. The best results can be expectedusing high exposure dosage and short development time, asthe adverse influence from both the shot noise and the wet-etching is minimized this way. Figure 13 shows the contrastof 40 nm size features exposed by three different dosagesand developed for different time durations. The higherexposure dosages with shorter development times lead tohigher feature contrast.

5. Conclusion

Our simulations have indicated that the resolution of acontact micrograph depends heavily on the sample-to-resistdistance. Furthermore, because of the nonlinear etchingprocess, features that show low contrast in exposure can belost during subsequent development. The net effect is tolimit the attainable resolution in contact microscopy. Toobtain the best possible resolution, one must place thespecimen in immediate contact with strongly absorptiveresists, and use heavy exposure and light development.Alternatively, dry etching techniques may provide a meansto avoid sidecutting during development.

Acknowledgment

We thank the NSF for the support of this work throughgrant RCD 92–53618.

References

Aristov, V.V. & Erko, I. (eds) (1994) X.-ray Microscopy IV.Chernogolovka, Russia Bogorodskii Pechatnik. Proc. 4th Int.

Conf., Chernogolovka, Russia, September 20–24 1993.Cheng, P.C. (1987) Recent advances in contact imaging of

biological materials. X-Ray Microscopy: Instrumentation andBiological Applications (ed. by P. C. Cheng and G. J. Jan), pp.65–104. Springer-Verlag, Berlin.

Cheng, P.C., Feder, R., Shinozaki, D.M., Tan, K.H., Eason, R.W.,Michette, A. & Rosser, R.J. (1986) Soft x-ray contact microscopy.Nucl. Instrum. Methods Phys. Rev. A246, 668–674.

Collier, R.J., Burckhardt, C.B. & Lin, L.H. (1971) Optical Holography.Academic Press, New York.

Cosslett, V.E. & Nixon, W.C. (1960) X-ray Microscopy. CambridgeUniversity Press, London.

Cotton, R.A., Dooley, M.D., Fletcher, J.H., Stead, A.D. & Ford, T.W.(1992) Atomic force microscopy employed as the final imagingstage for soft x-ray microscopy. Soft X-ray Microscopy, Vol. 1741,pp. 204–212. Bellingham, Washington. Society of Photo-OpticalInstrumentation Engineers (SPIE).

Cotton, R.A., Tomie, T., Shimizu, H., Jajima, T., Miura, E., Stead,A.D. & Ford, T.W. (1994) A study of the factors affecting theresolution in soft x-ray microscopy. X-ray Microscopy IV, pp.450–454. Chernogolovka, Russia Bogorodskii Pechatnik. Proc.4th Int. Conf., Chernogolovka, Russia, 20–24 September 1993.

Cowley, J.M. & Moodie, A.F. (1957) Fourier images the out of focuspatterns. Proc. Phys. Soc., B, 70, 497–504.

Early, K., Schattenburg, M.L. & Smith, H.I. (1990) Absence ofresolution degradation in x-ray lithography for l from 4.5 nm to0.83 nm. Microelectron. Engng, 11, 317–321.

Feder, R. (1970) X-ray projection printing of electrical circuitpatterns. IBM Technical Report TR 22.1065, IBM ComponentsDivision, East Fishkill Facility, Hopewell Junction, NY.

Feder, R., Sayre, D., Spiller, E., Topalian, J. & Kirz, J. (1976)Specimen replication for electron microscopy using x rays and x-ray resist. J. Appl. Phys. 47, 1192–1193.

Feder, R., Spiller, E., Topalian, J., Broers, A.N., Gudat, W., Panessa,B.J., Zadunaisky, Z.A. & Sedat, J. (1977) High-resolution soft x-ray microscopy. Science, 197, 259–260.

Feder, R., Costa, J.L., Chaudhari, P. & Sayre, D. (1981) Improveddetail in biological soft x-ray microscopy: study of blood platelets.Science, 212, 1398–1400.

Feder, R., Banton, V., Sayer, D., Costa, J., Baldini, M. & Kim, B.K.(1985) Direct Imaging of live human platelets by flash x-raymicroscopy. Science, 227, 63–64.

Gorby, P. (1913) Une application nouvelle des rayons x: lamicroradiographie. C. R. Acad. Sci. Paris, 156, 686.

Haller, I., Hatzakis, M. & Srinivasan, R. (1968) High-resolution positiveresist for electron-beam exposure. IBM J. Res. Dev. 12, 251–256.

Hare, A.R. & Morrison, G.R. (1994) Near-field soft x-ray diffractionmodeled by the multislice method. J. Mod. Opt. 41, 31–48.

Hatzakis, M. (1969) Electron resists for microcircuit and maskproduction. J. Electrochem. Soc. 116, 1033–1037.

Hawryluk, R.J., Smith, H.I., Soares, A. & Hawryluk, A.M. (1975)Energy dissipation in a thin polymer film by electron scatteringexperiment. J. Appl. Phys. 46, 2528–2537.

Henke, B.L. (1981) Low energy x–ray interactions: photoionization,scattering, specular and Bragg reflection. Low Energy X-rayDiagnostics, Vol. 75, pp. 146–155. American Institute of Physics,Monterey, CA.

Henke, B.L., Gullikson, E.M. & Davis, J.C. (1993) X–ray

Fig. 13. Contrast of 40-nm cylindrical features exposed at variousdosages. The contrast is expressed in terms of nm of resist heightabove the background resist surface. The dosage for each curveis, from left to right: 9·19 Mgrey (5 × 10¹5 photons mm¹2 flux),2·06 Mgrey (1 × 10¹5 photons mm¹2 flux) and 0·53 Mgrey(0·2 × 10¹4 photons mm¹2 flux).



interactions: photoabsorption, scattering, transmission andreflection at E ¼ 50–30 000 eV, Z ¼ 1–92. At. Data Nucl. DataTables, 54, 181–342.

Howells, M., Jacobsen, C., Kirz, J., Feder, R., McQuiaid, K. &Rothman, S. (1987) X-ray holograms at improved resolution: astudy of zymogen granules. Science, 238, 514–517.

Howells, M.R., Jacobsen, C.J. & Lindaas, S. (1994) X-rayholographic microscopy using the atomic force microscope. X-ray Microscopy IV, pp. 413–427. Chernogolovka, RussiaBogorodskii Pechatnik. Proc. 4th Int. Conf., Chernogolovka,Russia, September 20–24.

Jacobsen, C. (1988) X-ray holographic microscopy of biologicalspecimens using an undulator. PhD thesis, State University ofNew York, Stony Brook.

Jacobsen, C. & Trebes, J. (eds) (1992) Soft X-ray Microscopy, Vol.1741. Bellingham, Washington. Society of Photo-Optical Instru-mentation Engineers (SPIE).

Kado, M., Richardson, M., Gabel, K. & Jin, F. (1994) Monochro-matic x-ray microscopy in the water window with a compactlaser system. Proc. 52nd Annual Meeting of the Microscopy Societyof America, pp. 60–61. San Francisco Press, San Francisco.

Khan, M., Mohammad, L., Xiao, J., Ocola, L. & Cerrina, F. (1994)Updated system model for x-ray lithography. J. Vac. Sci. Technol.12, 3930–3935.

Kinjo, Y., Shinohara, K., Ito, A., Nakano, H., Watanobe, M.,Horiike, Y., Kikuchi, Y., Richardson, M.C. & Tanaka, K.A. (1994)Direct Imaging in a water layer of human chromosome fibrescomposed of nucleusomes and their higher order structures bylaser plasma x-ray contact microscopy. J. Microsc. 176, 63–74.

Kirz, J., Jacobsen, C. & Howells, M. (1995) Soft x-ray microscopesand their biological applications. Q. Rev. Biophys. 28, 33–130.Also available as Lawrence Berkeley Laboratory report LBL–36371.

Ladd, W.A., Hess, W.M. & Ladd, M.W. (1956) High resolutionmicroradiography. Science, 123, 370–371.

Lindaas, S., Jacobsen, C.J., Howells, M.R. & Frank, K. (1992)Development of a linear scanning force microscope for x-rayGabor hologram readout. Soft X-ray Microscopy, Vol. 1741, pp.213–222. Bellingham, Washington. Society of Photo-OpticalInstrumentation Engineers (SPIE).

London, R.A., Trebes, J.E. & Jacobsen, C.J. (1992) Role of x-rayinduced damage in biological microimaging. Soft X-rayMicroscopy, Vol. 1741, pp. 333–340. Bellingham, Washington.Society of Photo-Optical Instrumentation Engineers (SPIE).

Michette, A.G., Morrison, G.R. & Buckley, C.J. (eds) (1992) X-rayMicroscopy III, Vol. 67, Springer Series in Optical Sciences,Springer-Verlag, Berlin.

Rosenfield, M.G. (1981) Simulation of developed resist profiles forelectron-beam lithography. Technical Report Memorandum no.

UCB/ERL M81/40, Electronics Research Laboratory, College ofEngineering, University of California at Berkley, Berkley, CA.

Rosser, R.J., Baldwin, K.G., Feder, R., Bassett, D., Coles, A. & Eason,R.W. (1985) Soft x-ray contact microscopy with nanosecondexposure times. J. Microsc. 138, 311–320.

Sayre, D., Kirz, J., Feder, R., Kim, D.M. & Spiller, E. (1977)Transmission microscopy of unmodified biological materials:comparative radiation dosage with electrons and ultrasoft x-rayphotons. Ultramicroscopy, 2, 337–341.

Shattenburg, M.L., Li, K., Shin, R.T., Kong, J.A., Olster, D.B. &Smith, H.I. (1991) Electromagnetic calculation of soft x-raydiffraction from 0.1 mm scale gold structures. J. Vac. Sci. Technol.B, 9, 3232–3236.

Shinohara, K. & Ito, A. (1991) Radiation damage in soft x-raymicroscopy of live mammalian cells. J. Microsc. 161, 463–472.

Shinohara, K., Aoki, S., Yanagihara, M., Yagishita, A., Iguchi, Y. &Tanaka, A. (1986) new, A, approach to the observation of theresist in x-ray contact microscopy. Photochem. Photobiol. 44,401–403.

Shinozaki, D.M. (1988) High resolution image storage in polymers.X-Ray Microscopy II, Vol. 56, Springer Series in Optical Sciences,(ed. by D. Sayre, M. R. Howells, J. Kirz and H. Rarback), pp. 118–123. Springer-Verlag, Berlin.

Skinner, C.H., DiCicco, D.S., Kim, D., Rosser, R.J., Suckewer, S.,Gupta, A.P. & Hirschberg, J.G. (1990) Contact microscopy withsoft x-ray laser. J. Microsc. 159, 51–60.

Solem, J.C. (1986) Imaging biological specimens with high-intensity soft x rays. J. Opt. Soc. Am., B, 3, 1551–1565.

Spears, D.L. & Smith, H.I. (1972) High-resolution patternreplication using soft x rays. Electron. Lett. 8, 102–104.

Spiller, E. (1993) Early history of x-ray lithography at IBM. IBM J.Res. Dev. 37, 291–297. May.

Spiller, E. & Feder, R. (1977) X-ray lithography. X-ray Optics (Topicsin Applied Physics 22) (ed by H. J. Queisser), pp. 35–92. Springer-Verlag, Berlin.

Spiller, E., Feder, R., Topalian, J., Eastman, D., Gudat, W. & Sayre, D.(1976) X-ray microscopy of biological objects with Carbon Ka

and with synchrotron radiation. Science, 191, 1172–1174.Stead, A.D., Cotton, R.A., Page, A.M., Goode, J.A., Duckett, J.G. &

Ford, T.W. (1993) The use of soft x-ray contact microscopy usinglaser-plasmas to study the ultrastructure of moss protonemalcells. X-ray Microscopy IV, pp. 290–296. Proc. 4th Int. Conf.,Chernogolovka, Russia, September 20–24.

Tomie, T., Shimizu, H., Majima, T., Yamada, M., Kanayama, T.,Kondo, H., Yano, M. & Ono, M. (1991) Three-dimensionalreadout of flash x-ray images of living sperm in water by atomic-force microscopy. Science, 252, 691–693.

Turner, S., Babcock, C. & Cerrina, F. (1991) Modeling of shot noisein x-ray photoresist exposure. J. Vac. Sci. Technol. B, 9, 3440–3446.



Documents

A numerical study of resolution and contrast in soft X-ray ...xrm.phys.northwestern.edu/research/pdf_papers/1998/wang_jmic_1998.pdfA numerical study of resolution and contrast in soft