A Numerical Study of Resolution and Contrast in Soft X-Ray Contact Microscopy
Journal of Microscopy, Vol. 191, Pt 2, August 1998, pp. 159–169. Received 24 April 1997; accepted 12 September 1997
A numerical study of resolution and contrast in soft X-ray contact microscopy
Y.WANG&C.JACOBSEN Department 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 In this paper we consider the nature of contact X-ray micrographs recorded on photoresists, and the limitations We consider the case of soft X-ray contact microscopy using on image resolution imposed by photon statistics, diffrac- a laser-produced plasma. We model the effects of sample tion and by the process of developing the photoresist. and resist absorption and diffraction as well as the process Numerical simulations corresponding to typical experimen- of isotropic development of the photoresist. Our results tal conditions suggest that it is difficult to reliably interpret indicate that the micrograph resolution depends heavily on details below the 40 nm level by these techniques as they the exposure and the sample-to-resist distance. In addition, now are frequently practised. the contrast of small features depends crucially on the development procedure to the point where information on such features may be destroyed by excessive development. 2. X-ray contact microradiography These issues must be kept in mind when interpreting contact microradiographs of high resolution, low contrast There is a long history of research in which X-ray objects such as biological structures. radiographs have been viewed with optical microscopes to study submillimetre structures (Gorby, 1913). A major step 1. Introduction forward was made in 1956 by Ladd et al. who replaced silver halide film and optical microscope enlargement with Soft X-ray microscopy offers a means to view biological and ‘grainless’ ammonium dichromate crystals. Upon X-ray materials science specimens at a resolution superior to that exposure and immersion in methyl alcohol, these crystals of confocal optical microscopes (Michette et al., 1992; Aristov transferred the X-ray exposure into a surface relief pattern; & Erko, 1994). In particular, if X-rays with an energy Ladd et al. then viewed a polymer surface replica of this between 280 eV and 520 eV are used (corresponding to the K relief pattern using an electron microscope (Ladd et al., edges of carbon and oxygen, respectively), wet, micrometre- 1956). While others carried out further explorations of thick biological specimens such as whole-cell preparations nonsilver halide recording media and electron microscope can be studied with reduced radiation damage as compared image enlargement (Cosslett & Nixon, 1960), none of the to electron microscopes (Sayre et al., 1977), even when phase techniques appear to have caught on in contact micro- contrast and zero-loss energy filters are employed. radiography at that time, largely because of the much Many soft X-ray microscopes employ zone plate, multi- longer exposure times required. layer-coated mirror, or grazing incidence mirror optics with In the late 1960s, poly(methyl methacrylate) or PMMA resolution in the 30–100 nm range (Kirz et al., 1995). Such was developed as a reasonably fast and extremely high microscopes are usually operated at synchrotron radiation resolution resist for electron beam lithography (Haller et al., centres, and involve image-recording times of seconds to 1968; Hatzakis, 1969). Primary (10–100 keV) and inelas- minutes. An alternative approach is to illuminate the tically scattered (especially 10–1000 eV) electrons cause specimen with an X-ray beam and use a high-resolution chain scission in the polymer chain, and the lowered detector to record the intensity pattern which passes molecular weight near exposed areas leads to high through the specimen. This contact microradiography or dissolution rates when placed in developer. Recognizing contact microscopy technique offers experimental simpli- that 10–1000 eV electrons are also produced following X- city, the ability to use nonmonochromatic flash X-ray ray absorption in solids, groups at IBM (Feder, 1970; Spiller, sources such as laser-produced plasma sources, and the 1993) and at MIT (Spears & Smith, 1972) began to use potential for very high image resolution. PMMA as a resist for studies of X-ray lithography for
᭧ 1998 The Royal Microscopical Society 159 160 Y. WANG AND C. JACOBSEN microelectronics fabrication. The IBM group then realized An aluminium-coated silicon nitride window is placed on that they had a technique for generating high resolution top of the specimen to trap a micrometre-thick water layer recordings of sub-micrometre structures, and they produced to keep the sample hydrated. (The aluminium coating also a series of demonstrations of high resolution X-ray contact blocks UV light.) The specimen/resist package is then microscopy (Feder et al., 1976; Feder et al., 1977; Spiller et al., mounted in the vacuum chamber of the laser-produced 1976) using both laboratory and synchrotron X-ray sources plasma X-ray source. and scanning electron microscope (SEM) image enlargement. 2 A laser pulse is used to generate X-rays from hot plasma, A large number of researchers have contributed various exposing the resist through the silicon nitride window, improvements to the technique. These include: water layer and specimen. 1 The use of pulsed X-ray sources for flash imaging, 3 The specimen is washed off the resist, and the resist is including plasma pinch X-ray generators (Feder et al., ‘developed’ by immersion in a solvent that transfers the 1985), laser-produced plasmas (Rosser et al., 1985; Tomie X-ray exposure pattern into a surface relief pattern. et al., 1991; Stead et al., 1993; Kinjo et al., 1994), and X-ray 4 The resist surface is examined with an atomic force lasers (Skinner et al., 1990). microscope, giving an image related to the X-ray absorption 2 Improved methods for resist readout which include direct pattern of the specimen. TEM enlargement (Feder et al., 1981; Cheng et al., 1986; We will represent this process by the following sequence, Howells et al., 1987), TEM enlargement of surface replicas the steps of which are described in further detail in the (Shinohara et al., 1986; Cheng, 1987), and atomic force sections indicated: microscopy (Tomie et al., 1991; Lindaas et al., 1992; Cotton Section 3.1. The laser-produced plasma emits an X-ray et al., 1994; Howells et al., 1994). spectrum which is well approximated by a kT ¼ 100 eV With these advancements, a soft X-ray contact micro- blackbody spectrum. scopy laboratory can be built at reasonable cost by using a Section 3.2. This spectrum is modified by transmission laser-produced plasma X-ray source, PMMA photoresists, through a 100 nm thick Si3N4 window coated with 100 nm and an atomic force microscope for resist readout (Cotton of Al2O3. We then assume that the X-rays must also travel et al., 1994; Kado et al., 1994). Such an approach offers through 1 mm of water to reach the specimen (such a water reasonable experimental simplicity, and the possibility to thickness is nearly unavoidable due to surface tension). record < 100 nm resolution flash images on a nanosecond Section 3.3. As the X-rays travel through the specimen of timescale. Such an advantageous timescale is believed to be thickness t, they are attenuated and phase shifted. To model faster than that of thermal expansion of the specimen at the this, we break the spectrum up into a series of closely spaced required resolution level (Solem, 1986; London et al., wavelengths, and treat the passage of each monochromatic 1992), and faster than the timescale of the larger-size-scale X-ray wavefield through the specimen using a multislice consequences of radiation damage (Shinohara & Ito, 1991). method (Cowley & Moodie, 1957; Hare & Morrison, 1994). In practice the major limiting factors to the resolution of We then propagate the resulting wavefield to the photoresist this technique are as follows (Spiller & Feder, 1977; Cotton plane. et al., 1993): secondary electron exposure of the resist at a Section 3.4. At each wavelength, the number of photons location distant from where the X-ray photon was absorbed, incident on a given area of photoresist is calculated. Fresnel diffraction over the distance from the sample to the Statistical fluctuations (shot noise) are incorporated into recording media, shot noise caused by photon statistics, and this number. sidecutting during the wet etch processing of the exposed Section 3.5. Photoresists respond according to absorbed photoresist. The secondary electrons have mean free path of radiation dose. At each X-ray wavelength, the absorbed dose around 10 nm (Spiller & Feder, 1977; Early et al., 1990); is calculated from the areal photon density as calculated this is less than the resolution limit set by other factors with above, and the absorption cross-section of the photoresist. typical current laboratory setups (as we shall demonstrate). The total dose to the surface layer of the photoresist is then Therefore, we will only concern ourselves with exposure obtained by summation of the fractional dose at each of the and development strategies to obtain the optimum contact X-ray wavelengths. micrograph. Section 3.6. The etching rate R at the photoresist surface is assumed to vary with absorbed dose D according to g 3. Method of simulation R ¼ R0ðD=D0Þ ð1Þ
There are no commercial contact microradiography systems where the parameters R0, D0 and g are determined at present, so methods and conditions vary among experimentally. The etching process at each point of the practitioners. We will assume that a typical experiment is resist surface is assumed to take place along the surface carried out as follows: normal direction. The evolution of the resist surface is then 1 The specimen is placed on a photoresist-coated substrate. calculated over a sequence of time steps.
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laser-produced plasma with a blackbody spectrum char- acterized by kT ¼ 100 eV (Tomie et al., 1991) as is shown in Fig. 2. In order to match the total exposure levels used in practice, we have assigned a value of 0·21 J cm¹2 to be the spectrally integrated irradiance incident on the entrance window of the specimen chamber. This gives us 0·032 J cm¹2 at the resist surface. While relay optics are sometimes used to reduce debris on the exposure area (Rosser et al., 1985), we assume that the effects on the spectrum are small because reflectivity from high-Z surfaces is quite spectrally uniform at grazing incidence angles well below the critical angle (Henke, 1981). Along with the blackbody spectrum, spectral lines are often present. The strongest of these lines typically contain less than 1% of the total power emitted, so we have chosen not to include their presence in our model. Fig. 1. Example geometry used for recording contact micrographs The use of polychromatic light will reduce diffraction of hydrated specimen using a laser produced plasma X-ray source. fringe artefacts in the image, for fringe maxima produced at one wavelength may well lie on top of fringe minima reduced at another wavelength. Therefore by leaving We will assume that the developed resist surface is out spectral line emission, one is likely to obtain a more accurately mapped by the atomic force microscope at the favourable result for contact microscopy from these resolution scale of interest to us. The X-ray exposure portion simulations. of the sequence outlined above is shown schematically in Fig. 1. These steps will be modelled on a grid with transverse 3.2. X-ray refractive index spacing Dx,y. The sequence of steps described above is similar to that At photon energies large compared to the បqp energy which exists in proximity X-ray lithography (indeed, corresponding to the plasma frequency qp, the refractive advances in contact microscopy in the 1970s grew out indices of materials become complex so that wavefields are of the development of X-ray lithography as noted above). both absorbed and phase-shifted. Soft X-ray refractive Model calculations of many of the above steps have been indices are well characterized (except for within Ϸ 10 eV performed in the context of X-ray lithography at 0·5–1 nm of X-ray absorption edges) by tabulated values for the wavelengths, involving transmission through metal a few tenths of a nanometre thick mask patterns located at gaps of typically 2–30 mm from a resist surface (Schatten- burg et al., 1991), and involving simulations of shot noise and resist development (Rosenfield, 1981; Turner et al., 1991). Indeed, in some cases most or all of these steps have been combined to model the complete process (Khan et al., 1994). Therefore the general method of modelling we have used is not unique; however, the parameters used in soft X-ray microscopy of biological specimens are considerably different from those used in X-ray lithography. For that reason, we have modelled the specific case of soft X-ray contact microscopy of biological specimens.
3.1. Laser-plasma X-ray generation Fig. 2. Irradiance spectra for the 100 eV blackbody source (solid While monochromatic synchrotron sources are some- line) and the source as filtered by transmission through 100 nm times used (Spiller et al., 1976) for contact micro- of Si3N4, 100 nm of Al2O3 and 1 mm of water (dashed line). The radiography, the more common approach is to use spectrally integrated irradiance is assumed to be 0·21 J cm¹2 before broadband X-ray illumination from laser-produced entering the sample holder, resulting in an irradiance of plasmas. We assume that X-rays are generated from a 0·032 J cm¹2 after transmission through the window and water.
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complex number of electrons per atom f1 þ if2 (Henke, Assuming a spatially incoherent source (the laser-produced 1981). The intensity attenuation per thickness t can then plasma) of 100 mm diameter, the Van Cittert-Zernike theorem be calculated as tells us that we obtain good mutual spatial coherence with m ¼ 0·88 over angular separations of up to IðtÞ¼Ið0Þe¹2kbt ð2Þ 12 v Յ l=d ð7Þ and the phase advance per thickness t is given by coh ikdt or a transverse distance of 2 mm when the resist is located e ð3Þ 20 cm from the laser-produced plasma. Therefore, the where k ¼ 2p/l assumption of spatial coherence is justified. Under this assumption, the changes of the wavefield as it d ¼ 1=ð2pÞr l2n f ð4Þ e a 1 passes through the specimen can be calculated using a 2 b ¼ 1=ð2pÞr2l na f2 ð5Þ multislice method. In reality, the wavefield is attenuated and phase shifted according to the refractive index d(x, y, z) þ ib(x, r ¼ 2·812 × 10¹15 m is the classical radius of the electron, e y, z)ateachpoint(x,y,z) through the volume of the object, and n is the volume density of atoms. For collections of a and diffraction governs the propagation of the wavefield from atoms which are amorphous on a scale of the soft X-ray z to z þ dz. In the multislice method, we imagine slicing the wavelength l, the refractive indices can be calculated from a object into a number of discrete slabs of finite thickness Dz sum weighted by the volume density of each type of atom (see Fig. 3). If we represent the wavefield entering one slab as present: wi(x, y), the exiting wavefield is then multiplied by the total n ð f þ if Þ n ð f þ if Þð6Þattenuation and phase shift which would be imposed upon a a 1 2 → a;i 1;i 2;i z ray travelling through the Dz thickness of the slab at the point X 0 We use here the tabulation of (f1 þ if2)ofHenkeet al. (1993). (x, y), giving a modulated wavefield wi (x, y)of The relationship for attenuation of Eq. (2) can then be used to 0 w1ðx;yÞ¼wiðx;yÞexp½¹kbðx; yÞDzÞ exp½ikdðx; yÞDzÿ: ð8Þ calculate the spectrum reaching the specimen region follow- This wavefield is then assumed to propagate a distance Dz ing transmission through a 100-nm thick Si3N4 window ¹3 through free space before it enters the next slab. This (r ¼ 3·44 g cm ) coated with 100 nm of Al2O3 (r ¼ 3·96 g cm¹3), followed by 1 mm of water. The resulting modi- propagation operation can be calculated by convolution of fication to the source blackbody spectrum is shown in Fig. 2. the wavefield wi with a propagator function, which can be implemented as (Collier et al., 1971):
¹1 0 2 2 3.3. Multislice propagation wi þ 1ðx; yÞ¼FT fFTfwiðx; yÞg exp½¹iliDzð1 ¹ fx ¹ fy Þÿg We now model the transmission of the X-ray wavefield ð9Þ through the specimen region. Since this region is not where FT indicates a Fourier transform, FT¹1 is an inverse uniform, we must consider diffraction effects using a Fourier transform, and fx and fy are spatial frequencies. multislice calculation (see, e.g. (Cowley & Moodie, 1957; Hare & Morrison, 1994). This calculation will be carried out separately for each of many wavelengths throughout the 3.4. Photon statistics illumination spectrum, where X-ray optical constants are tabulated at a multiplicative spacing in energy E with We now have an estimate of the wavefield w entering
Eiþ1 ¼ 1·016 Ei. the resist at each of the discrete wavelengths li which We can model the diffraction effects assuming spatially coherent radiation at each wavelength. Because the ultimate resolution limit of contact microradiography is at least an order of magnitude larger than the wavelength, most of the signal from a feature will be contained within a narrow angular range. Given that the specimen must be placed in close proximity to the photoresist, all interference effects will be confined within a small transverse distance. For example, with d ¼ 10 nm structures at l ¼ 3 nm and with a z ¼ 1 mm sample-to-resist gap, far-field diffraction fringes 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 mutual Fig. 3. Schematic representation of the multislice method used to coherence over submicrometre transverse distances. propagate the wavefield through the sample.
᭧ 1998 The Royal Microscopical Society, Journal of Microscopy, 191, 159–169 SOFT X-RAY CONTACT MICROSCOPY 163 represent the illumination spectrum; the intensity is then where hc/l is the photon energy, k ¼ 2p/l is the wave given by I(x, y) ¼ S|w|2. We must next confront the fact number, b is the absorptive part of the refractive index of the that the irradiance distribution which reaches the photo- photoresist as given by Eq. (5), Dx,y is the calculation pixel resist involves a finite number of photons. For a numerical size, and rr is the density of the resist. calculation, the irradiance distribution has already been When an X-ray photon is absorbed in the photoresist spatially discretized. Therefore, at a wavelength li and a PMMA, an Auger electron is usually generated which will position Dx,y(i, j), we can calculate the integer number of then produce a number of low energy (10–1000 eV) photons hNi which are present. This number was calculated electrons by collisions. Many of these electrons will break as if there are no statistical fluctuations in the signal, so we the polymer chain of the photoresist, thereby lowering must also include Poisson fluctuations. For hNiՆ 25, this the effective molecular weight in that region. When placed can be well approximated by a Gaussian distribution with a in a solvent, the resist will be dissolved according to the variance s2 of s ¼ √hNi. Given a computer routine which local molecular weight. The net result is that the generates pseudo-random numbers n on a Gaussian dissolution rate R(D) is dose dependent, and it can be distribution with a mean of zero and a variance of 1, the approximated by shot-noise-included signal N is g RðDÞ¼R0ðD=D0Þ : ð12Þ N ¼hNiþn hNi: ð10Þ Various measurements of R0 and D0 can be found in the We also impose the constraint NpՆ0 for those rare cases literature (Hawryluk et al., 1975; Spiller & Feder, 1977; when the Gaussian approximation to the Poisson distribu- Shinozaki, 1988). In X-ray holography experiments, it has tion would give N < 0· been found that the highest resolution photoresist images are obtained when low concentration developer is used (1:5 methyl isobutyl ketone in isopropyl alcohol), in which case 3.5. Resist exposure ¹4 ¹1 4 values of R0 ¼ 2·3 × 10 nm s , D0 ¼ 10 Gy, and g ¼ 2·2 We now have the shot-noise-included number of photons N can be estimated from the literature (Jacobsen, 1988). at each wavelength li and pixel Dx,y(i, j). We must next calculate the effect of this exposure on the photoresist. The 3.6. Resist development fraction of photons absorbed in a thickness dt of resist is –d(I/ Having computed the exposure and therefore the dis- 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 solution rate of the resist volume, we must now simulate the development of the resist. A common model for this hc 1 process is to assume that development proceeds into the DðzÞ¼N 2kb e¹2kb;z; ð11Þ l D2r resist along the direction of the local surface normal. In the x;yr
Fig. 4. Illustration of the resist development model. (a) For each point on the resist surface, the normal vector is first calculated. The depth of 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 ends of the normal vectors define a deformed surface. The height of this new surface is linearly interpolated onto the regular grid points and used as the representation of the surface profile for the subsequent etching step.
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Fig. 5. Estimate of the resist wall slope resulting from development of a step exposure. As the resist is etched, a step on the surface is produced. In the next etching time interval, the step is etched downward by a distance R1Dt and rightward by a distance R2Dt. In the limit of a large number of short time intervals, this model ¹1 predicts a wall slope angle of ∠ A Ϸ tan (R1/R2). 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, and at the maximum (dashed line) sphere-to-resist gap of 1000 nm. case of a computer calculation on a discrete grid of points, the surface normal direction is calculated at each grid point, and a ‘ray’ is drawn with a length given by product of R (D) and the time step Dt. The ends of these ‘rays’ generate a new surface and the height of this When two regions of the photoresist have different etching surface on regular grid points is interpolated to produce rates R1 and R2, the developed resist profile will have a –1 the surface profile for the next iteration in the slope with an angle ∠ A Ϸ tan (R1/R2), if R1 q R2 (see calculation cycle (Fig. 4). The end result is that the Fig. 5). Our two-dimensional resist development simulation shape of the resist surface is simulated as a function of routine gives results that are in agreement with this simple development time. one-dimensional model (see Fig. 6). To check this in the –1 2 –1 We have tested the resist development simulation by simulation, we used R1 ¼ 20 nm s , and R ¼ 5nms modelling the development of a step-shaped exposure. with 256 × 256 pixels size of 2 nm.
Fig. 6. Simulated development of two 2-D rect functions. The dissolution rate is assumed to be either 5 or 20 nm s¹1 (a). The calculated resist profiles after 5, 15 and 30 s of development are shown in (b), (c) and (d), respectively. The square shaped surface profile emerges in (b), and with further development the side-cutting effect of wet etching is evident in (c), until in (d) the final resist shape becomes triangular due to the sideways development. The ∠ A measured from the slightly curved side walls in (d) is Ϸ 75, in agree- ment with the expected tan¹1 (20/5) Ϸ 76.
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Fig. 8. The spectrally integrated dosage deposited on photoresist as a function of the sample-resist gap and the linear distance along the line of the protein spheres (from the 2-D calculation). For the five different sized objects shown here at different scales, many general characteristics of the gap-dependent exposure pattern scale from one exposure to another though there are detailed differences. The image alteration due to Fresnel diffraction is evident in all the graphs and becomes more pronounced for smaller feature sizes. As the gap becomes larger than the scale of the sphere-to-sphere distance, the exposure pattern appears to show not three spheres, but more complex and narrower structures.
4. Model calculations 4.1. Effect of Fresnel diffraction during exposure The model described above has been used to consider three It is important to know the extent to which Fresnel main factors which affect resolution in contact microscopy: diffraction degrades the image during exposure. To study Fresnel diffraction, shot noise and development (wet this effect, we used the multislice method described earlier. etching). These effects will be considered in turn. The sample was assumed to consist of three spheres of
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Fig. 9. Simulation of exposure and develop- ment of protein spheres and rods of dia- meter s, separated by a distance s with s ¼ 38, 40, 42 and 44 nm, from left to right in (a). The exposure pattern shown in (b) reflects the effect of shot noise, while the images (c) through (f) show the resist surface calculated following the development time indicated. Compared with image (c), the resist surface in (f) is smoother, but some high-resolution fea- tures are lost during the additional 48 s of development. We have used the following parameters in the calculation: dosage ¼ 2·06 MGray, sample–resist gap ¼ 1 mm, g ¼ 2·2, and pixel size ¼ 2 nm. protein of diameter s (s ¼ 10–50 nm) separated by a microscopy. To reliably produce images representing the distance s and the X-ray exposure spectrum was assumed sample, the sample to resist distance should ideally be on the to be as in Fig. 2. The spectra of X-ray reaching the same scale as the desired feature resolution. photoresist for the cases of 20 and 1000 nm sample-to-resist gap are shown in Fig. 7. The resulting exposure-vs.-gap 4.2. Effect of shot noise and wet etching images are shown in Fig. 8. The remarkable point of this figure is how three simple structures appear to produce a wide The simulation method described above was also used to variety of images at even submicrometre gap d2. In a sense, study the effect of shot noise and wet etching on the one is seeing more complex manifestations of the well-known observed ‘images’. In this case, the specimen was assumed Arago’s spot behind an opaque absorber. These figures clearly to consist of protein spheres and cylinders with diameters illustrate that knowledge of the specimen-to-resist distance is ranging from 30 to 50 nm as indicated. crucial for interpreting high-resolution images in contact Figure 9(a) and (b) shows a set of test objects with size of
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Fig. 10. Etching of poorly resolved lines. The effective etching rate is higher at the peak than the valley because of higher contact area with the developer, resulting in the reduction of the peaks and hence the contrast.
38, 40, 42 and 44 nm, and the resulting exposure pattern. following argument (see Fig. 10): when low contrast peaks Figure 9(c–f) shows the resist profile at four development of poorly resolved features emerge, they expose a larger times. In this calculation, the parameters used were: surface contact area to the developer than the nearby valley, dosage ¼ 2·06 MGrey, g ¼ 2·2, sample-resist gap ¼ 1 mm, leading to higher effective local etching rate; they are and pixel size ¼ 2 nm. therefore etched preferentially. This process will continue Several observations can be made concerning Fig. 9. In until the effective dissolution rate of the peaks is equal to Fig. 9(b), the cylinders can be distinguished from shot noise that of the valley. At this time, either the peaks are no even for the smallest, 38 nm diameter. However, in all cases longer peaks (the feature is lost) or the final contrast is the spherical structures are difficult to discern. With the reduced to a degree determined by the size of the peak and onset of wet etching, the largest cylinders and spheres become the contrast in dissolution rate. After such time, further recognizable owing to the g ¼ 2·2 nonlinear response of the development will not alter the contrast. PMMA. As the exposure time is increased, the presence of the This behaviour is summarized in Fig. 11, where we largest cylinders becomes even more pronounced, although plotted the normalized contrast (height difference between the separation between them becomes less distinct. the peak and valley) as a function of feature size and For the smallest (38 nm) features, the simulations development time. The contrast of small features will reach indicate that they are observable after 6 s of development, its maximum value after a short development time and will but progressively less visible after longer times. At 54 s, it is be reduced by further development. This indicates that there not possible to tell that the object consisted of two small is an optimum development time for a certain feature size, cylinders. Similarly, cylinders of other sizes show good when the feature is resolved with maximum contrast. Such contrast at 6 and 18 s and reduced contrast with further optimum time was determined from data in Fig. 11 and is development. This effect, which is included in the model of plotted as a function of the feature size in Fig. 12. This resist development described above, can be explained by the graph is approximately linear and its intercept on the feature size axis can be loosely defined as the resolution limit (Ϸ 30 nm in this case) of the contact print under this particular exposure condition. The calculation results of Fig. 9 show that small and low contrast 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.
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