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Quantifying surface modification events from scanning force microscopy images
ARTICLE IN PRESS Ultramicroscopy 109 (2009) 1044–1051
Contents lists available at ScienceDirect
Ultramicroscopy journal homepage: www.elsevier.com/locate/ultramic
Quantifying surface modification events from scanning force microscopy images G. Roe a, L. McDonnell b, a b
School of Science, Galway-Mayo Institute of Technology, Galway, Ireland Centre for Surface & Interface Analysis, Department of Applied Physics & Instrumentation, Cork Institute of Technology, Rossa Avenue, Cork, Ireland
a r t i c l e in f o
PACS: 68.37.Ps Keywords: Scanning force microscopy Quantification Surface modification
a b s t r a c t Scanning force microscopy (SFM) is widely used to monitor surfaces and surface modification processes. Some surface modification processes involve the addition (or removal) of discrete entities to (or from) a surface in circumstances where the absolute number of entities is related to some aspect of the process. A two-dimensional surface characterisation parameter – the surface area ratio (SAR) – was previously developed as a means of quantifying such modification and can be readily obtained from SFM images. Simulations have shown that the SAR parameter is superior for quantification purposes to conventional surface roughness parameters such as roughness average Sa, the area equivalent of Ra. Key features of SAR are as follows: its linear dependence with coverage; dependence of linearity slope on coverage mechanism; and its independence from the form, waviness or roughness of the underlying surface. A further advantage of this method is its simplicity given that the SAR parameter is readily obtained from SFM images. Simulations of adsorption onto flat surfaces have been validated using SFM images of polystyrene spheres adsorbed onto mica. & 2009 Elsevier B.V. All rights reserved.
1. Introduction Since its invention [1], scanning force microscopy (SFM) has been widely used to image surface topography and has proved to be an excellent technique to monitor surfaces and their modification. SFM offers a number of advantages over traditional microscopies: the potential for spatial resolution at the atomic scale; a lateral range that encompasses those of optical and electron microscopies; the ability to image in air, liquid or vacuum; and the absence of any technique-specific sample preparation requirements. In addition, image contrast in SFM is derived from actual height measurements of surface topography and thus three-dimensional shape and size data can be obtained directly from SFM images. This is unlike conventional optical and scanning electron microscopies where image contrast is generated by topographic slopes, thereby restricting metrology to lateral dimensions. Differences in the characterisation of surface topography by SEM and SFM are described elsewhere [e.g. 2] and will not be discussed further here. When quantifying SFM images, it must be recognised that the heights of surface features can only be correctly measured when (i) the SFM tip has unrestricted access to at least one side of the feature and (ii) there is no distortion of the sample by the tip (or
Corresponding author. Tel.:+353 21 4326442; fax:+353 21 4345355.
E-mail address: [email protected] (L. McDonnell). 0304-3991/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.ultramic.2009.03.022
vice versa) during imaging. Of course, the SFM tip shape will always be added to the lateral dimensions of surface features and thus lateral quantification will require the SFM tip dimensions to be determined so that the images can be deconvoluted. Finally, images can only be validly quantified when the scanning force microscope has been calibrated. Some surface modification processes involve adding (or removing) discrete entities to (or from) a surface in circumstances where the absolute number of entities, or topographic events, is related to some aspect of the process, for example, the adsorption of proteins [3] and in solid phase assays based on SFM detection of binding events [4–7]. There are two distinct approaches to quantifying the occurrence of such events within SFM images. The local approach uses particle detection software to isolate and then count each event [5–8], whilst the competing global approach interprets changes in three-dimensional surface roughness parameters calculated for the entire image [4,9]. With the particle detection approach, the first step is to isolate the events from the background by applying a planar threshold to the image. As image contrast within conventional optical and scanning electron microscopes is often dominated by the shorter wavelength slopes of the sample topography (the longer wavelengths that comprise the background being considerably suppressed during imaging), planar thresholding is often effective in separating the events from the background. However, such an approach is not well suited to SFM images as they generally have non-planar backgrounds that a planar threshold cannot
ARTICLE IN PRESS G. Roe, L. McDonnell / Ultramicroscopy 109 (2009) 1044–1051
distinguish from surface modification events, particularly when such events are relatively small. This is a similar problem to the difficulties in quantifying photographic images where non-uniform background lighting has been used [8]. The non-planar background in SFM images arises because image contrast is generated not just by the surface topography but also by surface form, sample tilt and the curved trajectory of the piezoelectric scanner. Thus, before a planar threshold can be applied to such SFM images these unwanted contrast contributions must be removed. Unfortunately, image processing procedures that identify and remove the longer-wavelength image background are quite complex, time consuming, generally very user intensive and often introduce image artifacts. Using the global approach, there are several surface characterisation parameters available for consideration [9]. Average roughness Sa, root-mean-square roughness Sq, and the area equivalents of the linear surface characterisation parameters Ra and Rq are typical of the parameters routinely used to quantify surface roughness from SFM images [10]. The principal limitation in using the Sa or Sq parameters is that, by definition, they can only measure surface amplitudes. For example, two-dimensionally sinusoidal surfaces of identical peak amplitude have the same Sa or Sq values regardless of the wavelength of the surface. Of course, altering the spatial distribution of the amplitudes (from say sine to square), whilst retaining the same peak amplitude, will increase the values of the Sa and Sq parameters. However, such changes arise from the amplitude differences between the surfaces, rather than from the lateral differences, there being more higher amplitudes when the spatial distribution is changed from sine to square. Area-derived two-dimensional surface characterisation parameters respond to both lateral and amplitude differences and therefore reflect, more fully, the character of a surface, as well as the changes that occur therein. However, as surfaces with completely different wavelengths and amplitudes can have the same areas, such parameters do not uniquely describe a surface. Absolute surface area and Sdr, the developed surface ratio [9], are two examples of area-derived two-dimensional surface roughness parameters in current use. Previously [11], we introduced an alternative surface characterisation parameter – the surface area ratio, SAR – where SAR is the ratio of the absolute surface area of the substrate after surface modification (e.g. adsorption) to the absolute surface area of the substrate before surface modification. This definition is presented schematically in Fig. 1. Whilst we have demonstrated elsewhere [12] that the SAR parameter
SAR =
1045
varies linearly with the number of ferritin molecules bound onto anti-ferritin sensor surfaces, a detailed study of how the SAR parameter is affected by the surface modification mechanism and by the substrate topography has not published. In the work presented here, the SAR and Sa parameters were calculated from simulated SFM images as spheres were ‘‘adsorbed’’ on top of three different substrate topographies by three different coverage mechanisms. The results of the simulations were compared to the SAR and Sa values calculated from real SFM images of polystyrene spheres adsorbed onto mica. The good agreements obtained between the simulated and real images for this particular case and in the case of [12] have validated the SAR parameter as an effective method of quantifying surface modification events from SFM images.
2. Experimental 2.1. Preparation of monolayers of polystyrene spheres Using the general method described by Van Cleef et al. [13], 1.07 mm diameter polystyrene (also referred to as latex) spheres (Sigma-Aldrich, Poole, England) were immobilised onto mica. Briefly, the polystyrene spheres were supplied in an aqueous suspension having a solids content of 10% and this solution was subsequently diluted with water in five steps within the range 1:10–1:100,000. A micropipette was used to deposit 0.1 ml aliquots of the diluted preparations onto freshly cleaved mica substrates (Agar Scientific, Stansted, England), which were then placed in a desiccator for 15–20 h. 2.2. Scanning force microscopy Scanning force microscopy was performed in air using an ExplorerTM instrument (Veeco Instruments, Santa Barbara, USA) equipped with SPMLab 3.06.06 image acquisition and processing software. The mica substrates were fixed to magnetic stainless steel sample holders using double-sided adhesive tape and placed onto the magnetised holder of a manual XY sample manipulator. The polystyrene sphere samples were imaged in contact mode using rectangular silicon cantilevers (Nanosensors, Wetzlar, Germany) with a nominal force constant of 0.32 N/m (manufacturer’s specification). The SFM tip radius was estimated experimentally to be approximately 20 nm. Images were typically acquired at line scan rates within the range 1.0–0.67 Hz. SAR and
surface area after surface modification surface area before surface modification
Fig. 1. Schematic representation of the definition of the SAR parameter.
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Sa values were calculated from SFM images using software written in MATLAB (The MathWorks, Natick, USA). In the SAR calculations, the SFM image of a blank mica sample was used to provide the surface area prior to surface modification.
3. Simulations 3.1. Model substrates and coverage mechanisms The adsorption of 10 nm diameter spheres onto three different substrate topographies, for three different coverage mechanisms, was simulated using MATLAB software. For all of the simulations reported herein, the substrates had dimensions of 1000 nm 1000 nm and were ‘‘imaged’’ with a spatial resolution of 1500 pixel 1500 pixel. It was assumed in the simulations that
the SFM tip was ideal, i.e. having vertical side walls and negligible diameter. The three substrate topographies simulated were as follows: Type A: a perfectly smooth substrate of flat form; Type B: a substrate of flat form with two-dimensional sinusoidal roughness of amplitude 1 nm and wavelength 10 nm; Type C: a substrate of flat form with (i) two-dimensional sinusoidal waviness of 200 nm wavelength and 10 nm amplitude and (ii) two-dimensional sinusoidal roughness of amplitude 1 nm and wavelength 10 nm. Three-dimensional views of the topographies of type B and type C substrates are shown in Fig. 2. The amplitudes of the roughness and the waviness are 10% and 100%, respectively, of the diameter of an adsorption event. In order to show the surface
Fig. 2. (a) Three-dimensional view of type B substrate consisting of a flat form with three-dimensional sinusoidal roughness of amplitude 1 nm and wavelength 10 nm. (b) Three-dimensional view of type C substrate consisting of a flat form, three-dimensional waviness of 200 nm amplitude and 10 nm amplitude with three-dimensional sinusoidal roughness of amplitude 1 nm and wavelength 10 nm.
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2.5 Type II
Type I Type III
SAR
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Coverage of Surface by Spheres (%) Fig. 3. Schematic representation of the three coverage mechanisms: (a) Type I (random); (b) Type II (close-packed linear); (c) Type III (close-packed spiral). The open circle indicates the next adsorption site.
4.5 4 3.5
random coverage for which spheres are placed at random but not allowed to contact; Type II: close-packed linear coverage that starts in a corner and proceeds linearly and continuously, on a row by row basis, until the substrate is fully covered; Type III: close-packed spiral coverage that starts in the centre and proceeds by continuous spiral growth until the spiral circumference meets the edge of the substrate.
3 Sa (nm)
detail, only 200 nm 200 nm portions of the simulated type B and type C substrates are shown in Fig. 2. The three adsorption coverage mechanisms simulated were as follows:
2.5 2
Type I:
The three coverage mechanisms are illustrated schematically in Fig. 3. In all cases, adsorption was restricted to a single layer on top of the substrate. Type I coverage is similar to the random sequential adsorption (RSA) models [14,15], which are typical of protein adsorption onto many surfaces [16,17]. Types II and III coverages have relevance to two-dimensional crystal growth and dissolution. For the six cases described above, SAR and Sa parameters were calculated for coverages from zero to the maximum possible for the specific coverage mechanism. 3.2. Results of simulations Fig. 4 shows the results of the simulations of (a) the SAR parameter and (b) the Sa parameter for the three different coverage mechanisms on a type A (flat) substrate. From Fig. 4(a), it can be seen for all cases that SAR increases linearly with coverage, with the slope of the SAR versus coverage graph depending quite significantly on the coverage mechanism. Intuitively, the increase in the SAR value is to be expected; as coverage progresses, the smooth substrate topography is replaced by that of the relatively rough overlayer. Consequently, the surface area and thus SAR increase with increased coverage. SAR increases most rapidly with coverage in the case of type I (random) coverage because adsorption events are always isolated in this model. Unlike the basic RSA model, contact is not allowed in type I coverage and so every adsorption event contributes the maximum
1.5 1
−−− Type I Coverage −−− Type II Coverage −+− Type III Coverage
0.5 0
0
10
20
30 40 50 60 70 80 Coverage of Surface by Spheres (%)
90
100
Fig. 4. Simulations of (a) the SAR parameter and (b) the Sa parameter for the three different coverage mechanisms on a type A substrate.
amount of additional surface area. In type II and type III coverage mechanisms, contact occurs for every adsorption event and thus the surface area contribution of each adsorption event is reduced compared with the case of random adsorption. Furthermore, in type III (close-packed spiral) coverage, contact alternates from one to two spheres as growth progresses. Consequently, this coverage mechanism contributes more additional area for every other adsorption event than type II (row growth) mechanism and so the slope for type III coverage is larger than that for type II coverage. Unlike the SAR parameter, the Sa parameter (Fig. 4(a)) is nonlinear for all three cases, increasing with coverage to a maximum at around 50% and then decreasing with further increases in coverage. The behaviour of the Sa parameter is very similar for all three substrates; being intrinsically insensitive to surface wavelengths, the Sa parameter is not affected per se by the lateral disposition of adsorption events. Increased coverage affects Sa in two ways: firstly, the amplitudes of the surface topography are changed; and secondly, the mean level of the surface is raised. These latter two effects account for the small deviations observed in the values of the Sa parameter for the three coverage mechanisms as coverage approaches 50%. Fig. 5 shows the results of the simulations of (a) the SAR parameter and (b) the Sa parameter for the three different coverage mechanisms on a type B (rough) substrate. The effect
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Fig. 5. Simulations of (a) the SAR parameter and (b) the Sa parameter for the three different coverage mechanisms on a type B substrate.
of substrate roughness on the SAR response as compared to the response when the substrate is perfectly flat (Fig. 4) is minimal. The SAR response to all three coverage mechanisms shows the same characteristics as previously observed. The main difference is that the slope of each of the coverage mechanisms is reduced very slightly. This difference may be explained by the fact that the area increases arising from increasing coverage are now being divided by the greater initial surface area generated by the roughness of the substrate. The results predict that substrate roughness does not significantly affect the ability to measure coverage using SAR. It is also clear from Fig. 5(b) that the substrate roughness has a minimal effect on the Sa responses to the coverage mechanisms. The most obvious difference being that the initial Sa value in each of the cases is now not zero, but of a value that reflects the initial amplitude of the roughness of the substrate before the commencement of coverage. There are also now slight discrepancies between the individual responses for each of the coverage mechanisms and this may be explained in terms of the spheres either sitting into topographic hollows or onto topographic peaks on the substrate, to greater or lesser extents, with each of the coverage mechanisms. Such considerations also give rise to an expectation of a slight loss of repeatability with the Sa response for the random coverage mechanism.
Fig. 6. Simulations of (a) the SAR parameter and (b) the Sa parameter for the three different coverage mechanisms on a type C substrate.
Fig. 6 shows the results of the simulations of (a) the SAR parameter and (b) the Sa parameter for the three different coverage mechanisms on a type C (wavy) substrate. As can be seen from Fig. 6(a), the simulations still predict an essentially linear response of SAR to increasing coverage. On the other hand, Fig. 6(b) shows that the simulations predict that the response of the Sa parameter will be very non-linear for all types of coverage mechanism. Furthermore, the simulation run to run repeatability of Sa for type I (random) coverage is very poor, as shown in Fig. 7(a). The changes in the Sa value for the surface, as it becomes covered with spheres, produce variable increases, or indeed in some cases decreases, in the overall Sa value depending on whether the added sphere locates at a topographical peak or trough. In contrast, the response of SAR to increasing random coverage of a surface is found to be invariant, to a high degree, from simulation run to simulation run as shown in Fig. 7(b).
4. Intercomparison with experimental results A dried mica substrate coated with polystyrene spheres (dilution of 1:100,000) was examined using contact mode SFM. A single layer of close-packed polystyrene spheres was selected
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Fig. 8. A selection of four SFM images of a polystyrene monolayer.
Fig. 7. Three consecutive simulations of (a) the Sa parameter and (b) the SAR parameter for the three different coverage mechanisms on a type C substrate.
and a suitable 100 mm 100 mm area of the boundary between the layer and the mica substrate was imaged. Using the SPMLab 3.06.06 (Veeco Instruments, Santa Barbara CA, USA) image processing software the image was planar levelled using the 3point algorithm of the SPMLab 3.06.06 software. Then, 19 15 mm 15 mm area zoom images were obtained, ranging from a region free of polystyrene spheres (the blank sample) through to a region full of polystyrene spheres (100% coverage). The number of polystyrene spheres in each image was counted manually and converted into % coverage. Fig. 8 shows a selection of four SFM images from the coverage range. The SAR and Sa parameters were calculated for the 19 SFM images and Fig. 9 shows how these parameters vary with coverage. The mica substrate can be considered flat relative to the dimensions of the latex spheres, thereby corresponding to a type A substrate, whilst the coverage mechanism corresponds to the close-packed type II coverage. The corresponding simulations are shown in Fig. 4. Due to the differences in scale between the real substrates, the real adsorption events and those simulated, quantitative comparisons between the results of simulations and experiments cannot be made. Nevertheless, the SAR parameter increases linearly as the coverage increases from about 10% to about 80%, as predicted by the simulations (compare Fig. 9(a) with
Fig. 4(a)). The departures from the predicted linearity at the lowest and highest coverage values can be easily explained. The non-linearity at the low end of the coverage range is due to the arrival of the edge of the polystyrene monolayer within the image. The arrival of the edge introduces a large amount of extra surface area and this in turn produces a sharp initial increase in SAR with coverage. Once the edge has been introduced in its entirety into the image, the extra surface area introduced by extending the monolayer into the image is less than that introduced by its entrance. This reduction in the additional surface area is due to the fact that the tip, being real, cannot access the sides of latex spheres within the monolayer that are entirely surrounded by other spheres. Therefore, spheres within the monolayer produce less additional image surface area compared to those at the edge. This ‘‘edge effect’’ is not observed in the simulations of type II coverage on a type A substrate as the model assumes a perfect (negligible) tip. As a result, practically all of the sides of all the spheres in the simulated monolayer are ‘‘imaged’’ and contribute equivalent additional surface area. Similar effects occur at high coverages as the edge of the monolayer leaves the image. Simulations (not shown) made with a ‘‘real’’ tip have confirmed that the above effects arise from tip imaging. The Sa versus surface coverage curve obtained for the same series of images of increasing coverage by the monolayer of polystyrene spheres over the mica substrate is also very similar to that predicted by the simulations of type II coverage on a type A substrate (compare Fig. 9(b) with Fig. 4(b)). The variation of Sa with coverage is observed to be non-linear and, as predicted by the simulations, has a maximum at about 50% coverage.. Clearly, Sa is insensitive to change of coverage in the region of 50% coverage and furthermore this parameter cannot provide unambiguous coverage values (other than at the maximum value). The most obvious difference between the simulation (Fig. 4(b)) and the experiment (Fig. 9(b)) is in the end point. The model predicts a relatively higher end point value than the maximum Sa value actually obtained. The reason for this discrepancy may once again be explained by the fact that the model assumes a perfect
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amount of particles will be unaffected by the coverage mechanism or indeed by changes in the coverage mechanism. Similar behaviour was observed for the Sq parameter (results not shown here) and this is not surprising given that the Sq parameter is simply the root-mean-square version of the Sa parameter. The above predictions are not surprising given that the Sa and Sq parameters are intrinsically insensitive to surface wavelengths, as remarked earlier. On the other hand, a linear relationship between SAR and coverage is predicted for all cases of adsorption and coverage. Furthermore, as a measure of the number of binding events on a surface, SAR is predicted to be insensitive to the type of topography of the surface upon which the binding events are occurring. However, SAR is sensitive to the coverage mechanism of the binding events, in that different coverage mechanisms give different slopes for each of the linear relationships between SAR and coverage observed for the three coverage mechanisms. The above simulations have been experimentally confirmed to a large degree in the case of type II coverage (linear) of a type A substrate (flat). Furthermore, previously reported experiments [12] validated simulations of type I coverage (random) of a type B substrate (rough). The good agreement between the simulated and actual images has validated the SAR parameter as an effective method of quantifying surface modification events from SFM images. One current application of the SAR parameter is in immunoassays based on SFM detection [12]. Other potential applications include scanning probe microscopy studies of crystal growth and dissolution and the adsorption of species onto single crystal surfaces. With regard to the latter applications, it should be noted that the sensitivity of the SAR parameter is determined by the additional surface contributed by each new topographic event. As the scale of the topographic event approaches that of the substrate’s features the SAR parameter will become increasingly insensitive. However, the sensitivity can be recovered by using suitably blunt SFM tips to image the topographic events [12]. Provided that the topographic events are sufficiently isolated with respect to the SFM tip size, tip imaging will magnify the additional surface area whilst attenuating the surface area of the substrate. A future publication will present the results of a detailed study of the effect on SFM tip radius on the behaviour of the SAR parameter, as well as additional validation experiments.
Coverage (%) Fig. 9. Graphs of (a) SAR and (b) Sa versus coverage obtained from nineteen SFM images of the polystyrene monolayer cited in Fig. 8.
tip and hence can, for example, access and image the mica substrate in the gaps between the spheres. This leads to a rougher image surface being produced by the simulations compared with the experiment and so the simulated image gives a higher Sa value than the experimental image.
5. Conclusion In the work presented here, the SAR and Sa parameters were calculated from simulated SFM images as spheres were ‘‘adsorbed’’ onto three different substrate topographies by three different coverage mechanisms. The simulations predicted nonlinear Sa responses for all the three coverage mechanisms simulated. Sa was also predicted to be highly sensitive to the topography of the substrate. Interestingly, the simulations predict that the Sa parameter for a given substrate covered by a particular
Acknowledgements The authors wish to acknowledge the assistance of A. Ward in preparing the polystyrene spheres sample. The latter stages of this work were supported by the Technological Sector Research Programme of the Department of Education and Science under the National Development Plan 2000–2006. References [1] G. Binnig, C.F. Quate, Ch. Gerber, Phys. Rev. Lett. 56 (1986) 930–933. [2] J.E. Castle, P.A. Zhdan, J. Phys. D: Appl. Phys. 30 (1997) 722–740. [3] A.P. Quist, L.P. Bjo¨rck, C.T. Reimann, S.O. Oscasson, B.U.R. Sundqvist, Surf. Sci. 325 (1995) L406–L412. [4] A. Perrin, V. Lanet, A. Theretz, Langmuir 13 (1997) 2557–2563. [5] S.R. Nettikadan, J.C. Johnson, C. Mosher, C.E. Henderson, Biochem. Biophys. Res. Commun. 311 (2003) 540–545. [6] S.R. Nettikadan, J.C. Johnson, S.G. Vengasandra, J. Muys, E. Henderson, Nanotechnology 15 (2004) 383–389. [7] A. Perrin, A. Theretz, V. Lanet, S. Vialle, B. Mandrand, J. Immunol. Methods 224 (1999) 77–87. [8] J.C. Russ, The Image Processing Handbook, second ed., CRC Press, Boca Raton, FL, 1994. [9] K.J. Stout, P.J. Sullivan, P.J. Dong, E. Mainsah, N. Luo, T. Mathia, H. Zahouani, The development of methods for the characterisation of roughness in three
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[10] [11] [12] [13]
dimensions, Publication no. EUR15178EN of the Commission of the European Communities, Luxembourg, 1994, ISBN:0-7044-1313-2. K. Carneiro, C.P. Jensen, J.F. Jørgensen, J. Garnaes, Ann. CIRP 44 (1995) 517–522. G. Roe, L. McDonnell, E.M. Cashell, Scanning 19 (1997) 168–169. G. Roe, L. McDonnell, Ultramicroscopy 105 (2005) 196–203. M. Van Cleef, S.A. Holt, G.S. Watson, S. Myhra, J. Microsc. 181 (1996) 2–9.
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[14] J. Feder, J. Theor. Biol. 87 (1980) 237. [15] J. Feder, I. Giaever, J. Colloid Interface Sci. 87 (1980) 144. [16] Y. Yuan, M.R. Oberholzer, A.M. Lenhoff, Colloids Surf. A: Physicochem. Eng. Aspects 165 (2000) 125–141. [17] J. Talbot, G. Tarjus, P.R. Van Tassel, P. Viot, Colloids Surf. A: Physicochem. Eng. Aspects 165 (2000) 287–324.
Contents lists available at ScienceDirect
Ultramicroscopy journal homepage: www.elsevier.com/locate/ultramic
Quantifying surface modification events from scanning force microscopy images G. Roe a, L. McDonnell b, a b
School of Science, Galway-Mayo Institute of Technology, Galway, Ireland Centre for Surface & Interface Analysis, Department of Applied Physics & Instrumentation, Cork Institute of Technology, Rossa Avenue, Cork, Ireland
a r t i c l e in f o
PACS: 68.37.Ps Keywords: Scanning force microscopy Quantification Surface modification
a b s t r a c t Scanning force microscopy (SFM) is widely used to monitor surfaces and surface modification processes. Some surface modification processes involve the addition (or removal) of discrete entities to (or from) a surface in circumstances where the absolute number of entities is related to some aspect of the process. A two-dimensional surface characterisation parameter – the surface area ratio (SAR) – was previously developed as a means of quantifying such modification and can be readily obtained from SFM images. Simulations have shown that the SAR parameter is superior for quantification purposes to conventional surface roughness parameters such as roughness average Sa, the area equivalent of Ra. Key features of SAR are as follows: its linear dependence with coverage; dependence of linearity slope on coverage mechanism; and its independence from the form, waviness or roughness of the underlying surface. A further advantage of this method is its simplicity given that the SAR parameter is readily obtained from SFM images. Simulations of adsorption onto flat surfaces have been validated using SFM images of polystyrene spheres adsorbed onto mica. & 2009 Elsevier B.V. All rights reserved.
1. Introduction Since its invention [1], scanning force microscopy (SFM) has been widely used to image surface topography and has proved to be an excellent technique to monitor surfaces and their modification. SFM offers a number of advantages over traditional microscopies: the potential for spatial resolution at the atomic scale; a lateral range that encompasses those of optical and electron microscopies; the ability to image in air, liquid or vacuum; and the absence of any technique-specific sample preparation requirements. In addition, image contrast in SFM is derived from actual height measurements of surface topography and thus three-dimensional shape and size data can be obtained directly from SFM images. This is unlike conventional optical and scanning electron microscopies where image contrast is generated by topographic slopes, thereby restricting metrology to lateral dimensions. Differences in the characterisation of surface topography by SEM and SFM are described elsewhere [e.g. 2] and will not be discussed further here. When quantifying SFM images, it must be recognised that the heights of surface features can only be correctly measured when (i) the SFM tip has unrestricted access to at least one side of the feature and (ii) there is no distortion of the sample by the tip (or
Corresponding author. Tel.:+353 21 4326442; fax:+353 21 4345355.
E-mail address: [email protected] (L. McDonnell). 0304-3991/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.ultramic.2009.03.022
vice versa) during imaging. Of course, the SFM tip shape will always be added to the lateral dimensions of surface features and thus lateral quantification will require the SFM tip dimensions to be determined so that the images can be deconvoluted. Finally, images can only be validly quantified when the scanning force microscope has been calibrated. Some surface modification processes involve adding (or removing) discrete entities to (or from) a surface in circumstances where the absolute number of entities, or topographic events, is related to some aspect of the process, for example, the adsorption of proteins [3] and in solid phase assays based on SFM detection of binding events [4–7]. There are two distinct approaches to quantifying the occurrence of such events within SFM images. The local approach uses particle detection software to isolate and then count each event [5–8], whilst the competing global approach interprets changes in three-dimensional surface roughness parameters calculated for the entire image [4,9]. With the particle detection approach, the first step is to isolate the events from the background by applying a planar threshold to the image. As image contrast within conventional optical and scanning electron microscopes is often dominated by the shorter wavelength slopes of the sample topography (the longer wavelengths that comprise the background being considerably suppressed during imaging), planar thresholding is often effective in separating the events from the background. However, such an approach is not well suited to SFM images as they generally have non-planar backgrounds that a planar threshold cannot
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distinguish from surface modification events, particularly when such events are relatively small. This is a similar problem to the difficulties in quantifying photographic images where non-uniform background lighting has been used [8]. The non-planar background in SFM images arises because image contrast is generated not just by the surface topography but also by surface form, sample tilt and the curved trajectory of the piezoelectric scanner. Thus, before a planar threshold can be applied to such SFM images these unwanted contrast contributions must be removed. Unfortunately, image processing procedures that identify and remove the longer-wavelength image background are quite complex, time consuming, generally very user intensive and often introduce image artifacts. Using the global approach, there are several surface characterisation parameters available for consideration [9]. Average roughness Sa, root-mean-square roughness Sq, and the area equivalents of the linear surface characterisation parameters Ra and Rq are typical of the parameters routinely used to quantify surface roughness from SFM images [10]. The principal limitation in using the Sa or Sq parameters is that, by definition, they can only measure surface amplitudes. For example, two-dimensionally sinusoidal surfaces of identical peak amplitude have the same Sa or Sq values regardless of the wavelength of the surface. Of course, altering the spatial distribution of the amplitudes (from say sine to square), whilst retaining the same peak amplitude, will increase the values of the Sa and Sq parameters. However, such changes arise from the amplitude differences between the surfaces, rather than from the lateral differences, there being more higher amplitudes when the spatial distribution is changed from sine to square. Area-derived two-dimensional surface characterisation parameters respond to both lateral and amplitude differences and therefore reflect, more fully, the character of a surface, as well as the changes that occur therein. However, as surfaces with completely different wavelengths and amplitudes can have the same areas, such parameters do not uniquely describe a surface. Absolute surface area and Sdr, the developed surface ratio [9], are two examples of area-derived two-dimensional surface roughness parameters in current use. Previously [11], we introduced an alternative surface characterisation parameter – the surface area ratio, SAR – where SAR is the ratio of the absolute surface area of the substrate after surface modification (e.g. adsorption) to the absolute surface area of the substrate before surface modification. This definition is presented schematically in Fig. 1. Whilst we have demonstrated elsewhere [12] that the SAR parameter
SAR =
1045
varies linearly with the number of ferritin molecules bound onto anti-ferritin sensor surfaces, a detailed study of how the SAR parameter is affected by the surface modification mechanism and by the substrate topography has not published. In the work presented here, the SAR and Sa parameters were calculated from simulated SFM images as spheres were ‘‘adsorbed’’ on top of three different substrate topographies by three different coverage mechanisms. The results of the simulations were compared to the SAR and Sa values calculated from real SFM images of polystyrene spheres adsorbed onto mica. The good agreements obtained between the simulated and real images for this particular case and in the case of [12] have validated the SAR parameter as an effective method of quantifying surface modification events from SFM images.
2. Experimental 2.1. Preparation of monolayers of polystyrene spheres Using the general method described by Van Cleef et al. [13], 1.07 mm diameter polystyrene (also referred to as latex) spheres (Sigma-Aldrich, Poole, England) were immobilised onto mica. Briefly, the polystyrene spheres were supplied in an aqueous suspension having a solids content of 10% and this solution was subsequently diluted with water in five steps within the range 1:10–1:100,000. A micropipette was used to deposit 0.1 ml aliquots of the diluted preparations onto freshly cleaved mica substrates (Agar Scientific, Stansted, England), which were then placed in a desiccator for 15–20 h. 2.2. Scanning force microscopy Scanning force microscopy was performed in air using an ExplorerTM instrument (Veeco Instruments, Santa Barbara, USA) equipped with SPMLab 3.06.06 image acquisition and processing software. The mica substrates were fixed to magnetic stainless steel sample holders using double-sided adhesive tape and placed onto the magnetised holder of a manual XY sample manipulator. The polystyrene sphere samples were imaged in contact mode using rectangular silicon cantilevers (Nanosensors, Wetzlar, Germany) with a nominal force constant of 0.32 N/m (manufacturer’s specification). The SFM tip radius was estimated experimentally to be approximately 20 nm. Images were typically acquired at line scan rates within the range 1.0–0.67 Hz. SAR and
surface area after surface modification surface area before surface modification
Fig. 1. Schematic representation of the definition of the SAR parameter.
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Sa values were calculated from SFM images using software written in MATLAB (The MathWorks, Natick, USA). In the SAR calculations, the SFM image of a blank mica sample was used to provide the surface area prior to surface modification.
3. Simulations 3.1. Model substrates and coverage mechanisms The adsorption of 10 nm diameter spheres onto three different substrate topographies, for three different coverage mechanisms, was simulated using MATLAB software. For all of the simulations reported herein, the substrates had dimensions of 1000 nm 1000 nm and were ‘‘imaged’’ with a spatial resolution of 1500 pixel 1500 pixel. It was assumed in the simulations that
the SFM tip was ideal, i.e. having vertical side walls and negligible diameter. The three substrate topographies simulated were as follows: Type A: a perfectly smooth substrate of flat form; Type B: a substrate of flat form with two-dimensional sinusoidal roughness of amplitude 1 nm and wavelength 10 nm; Type C: a substrate of flat form with (i) two-dimensional sinusoidal waviness of 200 nm wavelength and 10 nm amplitude and (ii) two-dimensional sinusoidal roughness of amplitude 1 nm and wavelength 10 nm. Three-dimensional views of the topographies of type B and type C substrates are shown in Fig. 2. The amplitudes of the roughness and the waviness are 10% and 100%, respectively, of the diameter of an adsorption event. In order to show the surface
Fig. 2. (a) Three-dimensional view of type B substrate consisting of a flat form with three-dimensional sinusoidal roughness of amplitude 1 nm and wavelength 10 nm. (b) Three-dimensional view of type C substrate consisting of a flat form, three-dimensional waviness of 200 nm amplitude and 10 nm amplitude with three-dimensional sinusoidal roughness of amplitude 1 nm and wavelength 10 nm.
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2.5 Type II
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random coverage for which spheres are placed at random but not allowed to contact; Type II: close-packed linear coverage that starts in a corner and proceeds linearly and continuously, on a row by row basis, until the substrate is fully covered; Type III: close-packed spiral coverage that starts in the centre and proceeds by continuous spiral growth until the spiral circumference meets the edge of the substrate.
3 Sa (nm)
detail, only 200 nm 200 nm portions of the simulated type B and type C substrates are shown in Fig. 2. The three adsorption coverage mechanisms simulated were as follows:
2.5 2
Type I:
The three coverage mechanisms are illustrated schematically in Fig. 3. In all cases, adsorption was restricted to a single layer on top of the substrate. Type I coverage is similar to the random sequential adsorption (RSA) models [14,15], which are typical of protein adsorption onto many surfaces [16,17]. Types II and III coverages have relevance to two-dimensional crystal growth and dissolution. For the six cases described above, SAR and Sa parameters were calculated for coverages from zero to the maximum possible for the specific coverage mechanism. 3.2. Results of simulations Fig. 4 shows the results of the simulations of (a) the SAR parameter and (b) the Sa parameter for the three different coverage mechanisms on a type A (flat) substrate. From Fig. 4(a), it can be seen for all cases that SAR increases linearly with coverage, with the slope of the SAR versus coverage graph depending quite significantly on the coverage mechanism. Intuitively, the increase in the SAR value is to be expected; as coverage progresses, the smooth substrate topography is replaced by that of the relatively rough overlayer. Consequently, the surface area and thus SAR increase with increased coverage. SAR increases most rapidly with coverage in the case of type I (random) coverage because adsorption events are always isolated in this model. Unlike the basic RSA model, contact is not allowed in type I coverage and so every adsorption event contributes the maximum
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Fig. 4. Simulations of (a) the SAR parameter and (b) the Sa parameter for the three different coverage mechanisms on a type A substrate.
amount of additional surface area. In type II and type III coverage mechanisms, contact occurs for every adsorption event and thus the surface area contribution of each adsorption event is reduced compared with the case of random adsorption. Furthermore, in type III (close-packed spiral) coverage, contact alternates from one to two spheres as growth progresses. Consequently, this coverage mechanism contributes more additional area for every other adsorption event than type II (row growth) mechanism and so the slope for type III coverage is larger than that for type II coverage. Unlike the SAR parameter, the Sa parameter (Fig. 4(a)) is nonlinear for all three cases, increasing with coverage to a maximum at around 50% and then decreasing with further increases in coverage. The behaviour of the Sa parameter is very similar for all three substrates; being intrinsically insensitive to surface wavelengths, the Sa parameter is not affected per se by the lateral disposition of adsorption events. Increased coverage affects Sa in two ways: firstly, the amplitudes of the surface topography are changed; and secondly, the mean level of the surface is raised. These latter two effects account for the small deviations observed in the values of the Sa parameter for the three coverage mechanisms as coverage approaches 50%. Fig. 5 shows the results of the simulations of (a) the SAR parameter and (b) the Sa parameter for the three different coverage mechanisms on a type B (rough) substrate. The effect
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Fig. 5. Simulations of (a) the SAR parameter and (b) the Sa parameter for the three different coverage mechanisms on a type B substrate.
of substrate roughness on the SAR response as compared to the response when the substrate is perfectly flat (Fig. 4) is minimal. The SAR response to all three coverage mechanisms shows the same characteristics as previously observed. The main difference is that the slope of each of the coverage mechanisms is reduced very slightly. This difference may be explained by the fact that the area increases arising from increasing coverage are now being divided by the greater initial surface area generated by the roughness of the substrate. The results predict that substrate roughness does not significantly affect the ability to measure coverage using SAR. It is also clear from Fig. 5(b) that the substrate roughness has a minimal effect on the Sa responses to the coverage mechanisms. The most obvious difference being that the initial Sa value in each of the cases is now not zero, but of a value that reflects the initial amplitude of the roughness of the substrate before the commencement of coverage. There are also now slight discrepancies between the individual responses for each of the coverage mechanisms and this may be explained in terms of the spheres either sitting into topographic hollows or onto topographic peaks on the substrate, to greater or lesser extents, with each of the coverage mechanisms. Such considerations also give rise to an expectation of a slight loss of repeatability with the Sa response for the random coverage mechanism.
Fig. 6. Simulations of (a) the SAR parameter and (b) the Sa parameter for the three different coverage mechanisms on a type C substrate.
Fig. 6 shows the results of the simulations of (a) the SAR parameter and (b) the Sa parameter for the three different coverage mechanisms on a type C (wavy) substrate. As can be seen from Fig. 6(a), the simulations still predict an essentially linear response of SAR to increasing coverage. On the other hand, Fig. 6(b) shows that the simulations predict that the response of the Sa parameter will be very non-linear for all types of coverage mechanism. Furthermore, the simulation run to run repeatability of Sa for type I (random) coverage is very poor, as shown in Fig. 7(a). The changes in the Sa value for the surface, as it becomes covered with spheres, produce variable increases, or indeed in some cases decreases, in the overall Sa value depending on whether the added sphere locates at a topographical peak or trough. In contrast, the response of SAR to increasing random coverage of a surface is found to be invariant, to a high degree, from simulation run to simulation run as shown in Fig. 7(b).
4. Intercomparison with experimental results A dried mica substrate coated with polystyrene spheres (dilution of 1:100,000) was examined using contact mode SFM. A single layer of close-packed polystyrene spheres was selected
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Fig. 8. A selection of four SFM images of a polystyrene monolayer.
Fig. 7. Three consecutive simulations of (a) the Sa parameter and (b) the SAR parameter for the three different coverage mechanisms on a type C substrate.
and a suitable 100 mm 100 mm area of the boundary between the layer and the mica substrate was imaged. Using the SPMLab 3.06.06 (Veeco Instruments, Santa Barbara CA, USA) image processing software the image was planar levelled using the 3point algorithm of the SPMLab 3.06.06 software. Then, 19 15 mm 15 mm area zoom images were obtained, ranging from a region free of polystyrene spheres (the blank sample) through to a region full of polystyrene spheres (100% coverage). The number of polystyrene spheres in each image was counted manually and converted into % coverage. Fig. 8 shows a selection of four SFM images from the coverage range. The SAR and Sa parameters were calculated for the 19 SFM images and Fig. 9 shows how these parameters vary with coverage. The mica substrate can be considered flat relative to the dimensions of the latex spheres, thereby corresponding to a type A substrate, whilst the coverage mechanism corresponds to the close-packed type II coverage. The corresponding simulations are shown in Fig. 4. Due to the differences in scale between the real substrates, the real adsorption events and those simulated, quantitative comparisons between the results of simulations and experiments cannot be made. Nevertheless, the SAR parameter increases linearly as the coverage increases from about 10% to about 80%, as predicted by the simulations (compare Fig. 9(a) with
Fig. 4(a)). The departures from the predicted linearity at the lowest and highest coverage values can be easily explained. The non-linearity at the low end of the coverage range is due to the arrival of the edge of the polystyrene monolayer within the image. The arrival of the edge introduces a large amount of extra surface area and this in turn produces a sharp initial increase in SAR with coverage. Once the edge has been introduced in its entirety into the image, the extra surface area introduced by extending the monolayer into the image is less than that introduced by its entrance. This reduction in the additional surface area is due to the fact that the tip, being real, cannot access the sides of latex spheres within the monolayer that are entirely surrounded by other spheres. Therefore, spheres within the monolayer produce less additional image surface area compared to those at the edge. This ‘‘edge effect’’ is not observed in the simulations of type II coverage on a type A substrate as the model assumes a perfect (negligible) tip. As a result, practically all of the sides of all the spheres in the simulated monolayer are ‘‘imaged’’ and contribute equivalent additional surface area. Similar effects occur at high coverages as the edge of the monolayer leaves the image. Simulations (not shown) made with a ‘‘real’’ tip have confirmed that the above effects arise from tip imaging. The Sa versus surface coverage curve obtained for the same series of images of increasing coverage by the monolayer of polystyrene spheres over the mica substrate is also very similar to that predicted by the simulations of type II coverage on a type A substrate (compare Fig. 9(b) with Fig. 4(b)). The variation of Sa with coverage is observed to be non-linear and, as predicted by the simulations, has a maximum at about 50% coverage.. Clearly, Sa is insensitive to change of coverage in the region of 50% coverage and furthermore this parameter cannot provide unambiguous coverage values (other than at the maximum value). The most obvious difference between the simulation (Fig. 4(b)) and the experiment (Fig. 9(b)) is in the end point. The model predicts a relatively higher end point value than the maximum Sa value actually obtained. The reason for this discrepancy may once again be explained by the fact that the model assumes a perfect
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amount of particles will be unaffected by the coverage mechanism or indeed by changes in the coverage mechanism. Similar behaviour was observed for the Sq parameter (results not shown here) and this is not surprising given that the Sq parameter is simply the root-mean-square version of the Sa parameter. The above predictions are not surprising given that the Sa and Sq parameters are intrinsically insensitive to surface wavelengths, as remarked earlier. On the other hand, a linear relationship between SAR and coverage is predicted for all cases of adsorption and coverage. Furthermore, as a measure of the number of binding events on a surface, SAR is predicted to be insensitive to the type of topography of the surface upon which the binding events are occurring. However, SAR is sensitive to the coverage mechanism of the binding events, in that different coverage mechanisms give different slopes for each of the linear relationships between SAR and coverage observed for the three coverage mechanisms. The above simulations have been experimentally confirmed to a large degree in the case of type II coverage (linear) of a type A substrate (flat). Furthermore, previously reported experiments [12] validated simulations of type I coverage (random) of a type B substrate (rough). The good agreement between the simulated and actual images has validated the SAR parameter as an effective method of quantifying surface modification events from SFM images. One current application of the SAR parameter is in immunoassays based on SFM detection [12]. Other potential applications include scanning probe microscopy studies of crystal growth and dissolution and the adsorption of species onto single crystal surfaces. With regard to the latter applications, it should be noted that the sensitivity of the SAR parameter is determined by the additional surface contributed by each new topographic event. As the scale of the topographic event approaches that of the substrate’s features the SAR parameter will become increasingly insensitive. However, the sensitivity can be recovered by using suitably blunt SFM tips to image the topographic events [12]. Provided that the topographic events are sufficiently isolated with respect to the SFM tip size, tip imaging will magnify the additional surface area whilst attenuating the surface area of the substrate. A future publication will present the results of a detailed study of the effect on SFM tip radius on the behaviour of the SAR parameter, as well as additional validation experiments.
Coverage (%) Fig. 9. Graphs of (a) SAR and (b) Sa versus coverage obtained from nineteen SFM images of the polystyrene monolayer cited in Fig. 8.
tip and hence can, for example, access and image the mica substrate in the gaps between the spheres. This leads to a rougher image surface being produced by the simulations compared with the experiment and so the simulated image gives a higher Sa value than the experimental image.
5. Conclusion In the work presented here, the SAR and Sa parameters were calculated from simulated SFM images as spheres were ‘‘adsorbed’’ onto three different substrate topographies by three different coverage mechanisms. The simulations predicted nonlinear Sa responses for all the three coverage mechanisms simulated. Sa was also predicted to be highly sensitive to the topography of the substrate. Interestingly, the simulations predict that the Sa parameter for a given substrate covered by a particular
Acknowledgements The authors wish to acknowledge the assistance of A. Ward in preparing the polystyrene spheres sample. The latter stages of this work were supported by the Technological Sector Research Programme of the Department of Education and Science under the National Development Plan 2000–2006. References [1] G. Binnig, C.F. Quate, Ch. Gerber, Phys. Rev. Lett. 56 (1986) 930–933. [2] J.E. Castle, P.A. Zhdan, J. Phys. D: Appl. Phys. 30 (1997) 722–740. [3] A.P. Quist, L.P. Bjo¨rck, C.T. Reimann, S.O. Oscasson, B.U.R. Sundqvist, Surf. Sci. 325 (1995) L406–L412. [4] A. Perrin, V. Lanet, A. Theretz, Langmuir 13 (1997) 2557–2563. [5] S.R. Nettikadan, J.C. Johnson, C. Mosher, C.E. Henderson, Biochem. Biophys. Res. Commun. 311 (2003) 540–545. [6] S.R. Nettikadan, J.C. Johnson, S.G. Vengasandra, J. Muys, E. Henderson, Nanotechnology 15 (2004) 383–389. [7] A. Perrin, A. Theretz, V. Lanet, S. Vialle, B. Mandrand, J. Immunol. Methods 224 (1999) 77–87. [8] J.C. Russ, The Image Processing Handbook, second ed., CRC Press, Boca Raton, FL, 1994. [9] K.J. Stout, P.J. Sullivan, P.J. Dong, E. Mainsah, N. Luo, T. Mathia, H. Zahouani, The development of methods for the characterisation of roughness in three
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