Nondestructive thickness measurement of biological layers at the nanoscale by simultaneous topography and capacitance imaging

Nanoscale capacitance images of purple membrane layers are obtained simultaneously to topography in a nondestructive manner by operating alternating current sensing atomic force microscopy in jumping mode. Capacitance images show excellent agreement with theoretical modeling and prove to be a noninvasive method for measuring the thickness of purple membrane layers beyond the single monolayer limit with nanoscale lateral spatial resolution. With the ability of spatially resolving the capacitance while preserving the sample from damaging, this technique can be applied for nanoscale thickness measurement of other biological layers and soft materials in general.


Nondestructive thickness measurement of biological layers at the nanoscale by simultaneous topography and capacitance imaging
Ignacio Casuso, a͒ Laura Fumagalli, and Gabriel Gomila Nanoscale capacitance images of purple membrane layers are obtained simultaneously to topography in a nondestructive manner by operating alternating current sensing atomic force microscopy in jumping mode.Capacitance images show excellent agreement with theoretical modeling and prove to be a noninvasive method for measuring the thickness of purple membrane layers beyond the single monolayer limit with nanoscale lateral spatial resolution.With the ability of spatially resolving the capacitance while preserving the sample from damaging, this technique can be applied for nanoscale thickness measurement of other biological layers and soft materials in general.© 2007 American Institute of Physics.͓DOI: 10.1063/1.2767979͔2][3] In its development, a main issue concerns the nondestructive measurement of the biolayer thickness with submonolayer thickness vertical resolution and submicrometric spatial lateral resolution.Standard thin film characterization techniques such as optical ellipsometry, reflectance spectroscopy, 4 and capacitance metrology 5,6 are not suitable for this purpose as they offer in all cases lateral resolution beyond the micrometer.
8][9] This technique has shown nanoscale spatial resolution in simultaneous capacitance and topographic imaging, thus enabling the evaluation of thin film thickness at the nanoscale. 10However, until now, ac CS-AFM has been implemented in conventional AFM contact mode, which precludes its application to soft materials, such as biological layers, due to the large lateral shear forces inherent to this scanning mode.
In the present letter we describe the first implementation of ac CS-AFM in jumping mode ͑JM͒, 11,12 and show its use as a nondestructive technique for nanoscale capacitance imaging and thickness characterisation of biological layers and soft materials, in general, that enables individual capacitance characterization at fix points of the sample in control of the applied force and time of measurement in addition to minimal shear forces during lateral motion.
The experimental setup developed consists of a commercial AFM ͑Nanotec Electronica S.L.͒ connected to a fully customized amplifier, 13 which allows simultaneous topographic and low-noise dc and ac current measurements.Images are produced by jumping a conductive tip biased with respect to the sample at each image point following the sequence: tip retraction, lateral displacement, and approach down to contact, as schematically shown in Fig. 1, and described elsewhere. 11In this way, the probe produces mini-mum lateral shear forces on the samples during the scan while allowing for simultaneous contact electrical measurements.The electric current flowing through the tip is acquired at each image point by the WSXM software 14 during the period of the cycle when the tip is in contact with the sample surface, together with the conventional AFM signals, thus producing four simultaneous images: topography, dc current, ac resistance, and capacitance.With respect to dc current measurements, ac current measurements are much more technically demanding as one has to measure extremely small capacitance variations ͑attofarad range͒ in the presence of a large stray contribution ͑ϳ100 fF range͒. 7In order to reach this capacitance sensitivity we either set long acquisition times per point or average out several consecutive measurements taken on the same line scan.
As a model system of biological layer, we used purple membrane ͑PM͒ layers, a two-dimensional crystal lattice naturally present in the cell membrane of Halobacterium Salinarum. 15PM is composed of a lipid bilayer and a single protein species, the Bacteriorhodopsin ͑bR͒, in a lipid-toprotein ratio of 10 ͑mol/ mol͒.][18] Patches of PM containing wild type bR were deposited onto a flat gold film evaporated on a mica substrate and dried under N 2 ͑g͒ flow.To avoid large current values, a resistor of 120 M⍀ was added in series with the sample.All the measurements were performed under dry N 2 ͑g͒ conditions and using conductive diamond coated tips ͑CDT force modulation mode Nanosensors™, nominal radius of 100-200 nm and spring constant of 2.8 N / m͒.
We first obtained simultaneous topographic and dc current images in jumping mode of the PM patches in order to verify its insulating and homogeneous nature.Figure 2 shows characteristic images obtained by applying a 3 nN force and a dc bias of 100 mV.
The topographic image ͓Fig.2͑a͔͒ reveals a PM patch formed by an ϳ5 nm thick monolayer ͑PM 1 ͒ which is double folded in some regions ͑PM 2 ͒.The corresponding dc current image ͓Fig.2͑b͔͒ shows current levels through the PM patch ͑dark region͒ below the amplifier resolution ͑ϳ0.3 pA͒, surrounded by a highly conductive region corresponding to the gold substrate with current levels up to 0.8 nA ͑here the current level is limited by the series resis-tor͒.The irregular conductivity of the gold is due to the contamination residues from the PM solution, which impedes a good electrical contact with the gold substrate in some regions.The PM patch shows a low voltage uniform insulating nature, compatible with a pure capacitive behavior.During several hours of JM scanning no appreciably deformation of the biological layer was observed, thus proving the ability of jumping mode to perform simultaneous topographic and electric measurements without destroying or appreciably deforming the biological layer.
Simultaneous topographic and capacitance images obtained on a small portion of the PM patch shown in Fig. 2͑a͒ are shown in Fig. 3. Measurements have been taken at the same applied force ͑3 nN͒, with an applied sinusoidal voltage of 0.7 V rms amplitude and 92 kHz frequency, and 0 V dc bias.The images have been taken at low scan rate ͑143 ms/ pixel͒ to reach high capacitance resolution ͓below 3 aF in Fig. 3͑b͔͒.Figure 3 clearly shows a direct correlation between membrane topography and capacitance, thus show-ing the ability of ac CS-AFM in jumping mode to image both properties simultaneously.This correlation between topography and capacitance is further evidenced through the profiles taken along one scanning line ͓Figs.3͑c͒ and 3͑d͔͒, in which a capacitance variations of a few attofarads precisely tracks the topography profile of the monolayer PM 2 over the first layer PM 1 .The integrity of the PM membrane patch has remained unaffected again during the imaging process.Importantly, we remark that before Fig. 3 no other nanoscale capacitance image on a biological specimen had ever been reported.
Higher capacitance sensitivity ͑around 1 aF͒ can be obtained by averaging out a number of consecutive scans taken on the same line.An example is shown in Fig. 4. We note that further slowing down the scan speed to increase capacitance sensitivity is subject to scan instabilities.The profiles shown in Figs.4͑c͒ and 4͑d͒ have been obtained by averaging out nine consecutive scans taken at a scan speed of 56 ms/ pixel on a PM patch showing three overlapping layers ͓Fig 4͑a͔͒ and using a different AFM probe.We found that the averaged topographic and capacitance profiles ͓Figs.4͑c͒ and 4͑d͔͒ show again an excellent correlation, but this time with lower capacitance noise.The results reported in Figs. 3 and 4 can be interpreted in a quantitative way and hence used to accurately determine the membrane thickness with nanoscale lateral and vertical spatial resolutions.We remark that while here the reference thickness h 0 could be also obtained from the larger area topographic image in general this will not be the case.The technique reported here will then constitute a powerful and nondestructive method to assess the thickness of the biolayers.To this aim, a theoretical model of the tip/membrane/ gold substrate capacitance as a function of layer thickness under dry conditions is necessary.This model can be obtained from a recent derivation of the electrostatic force acting on a conductive tip in close proximity to a thin dielectric film, 19 where h is the layer thickness, its dielectric constant, z the tip-thin film distance, and V the tip-electrode substrate voltage.The tip capacitance as a function of tip-membrane distance and membrane thickness is then given by C apex ͑z,h͒ ϵ ͵ 2F͑z,h͒ where K͑R͒ is a constant value depending on the tip radius.
The capacitance variation as a function of a change in membrane thickness ⌬h with respect to a given thickness of reference h 0 can then be evaluated as Equation ͑3͒ holds true provided that the dielectric constant of the layer is homogeneous and that R ӷ h 0 , h 0 + ⌬h, as in the present case.Note that within this approximation the local capacitance due to a change in thickness is independent from the dielectric constant and only depends on the sample thickness.The measured capacitance in an ac CS-AFM experiment includes in addition a contribution from the stray capacitance variation that can be approximated by a linear function of the profile changes, 7 thus giving Equation ͑4͒ can be used to interpret quantitatively the capacitance measurements and to extract from them the biolayer thickness.To this end, we first determine the stray capacitance rate c stray and the tip radius R from the capacitance-distance curves on bare gold shown in Fig. 4͑b͒ as reported elsewhere. 7For the two tips used in the experiments we obtain c stray = 0.19± 0.05 aF/ nm, R Fig. 3 = 300± 30 nm, and R Fig. 4 = 90± 9 nm.Then, we obtain the thickness variation ⌬h from the simultaneously measured topographic profile ͓Figs.3͑c͒ and 4͑c͔͒.Finally, we fit the measured capacitance to Eq. ͑4͒ by adjusting the only re-maining free parameter, the thickness of the first PM layer ͑PM 1 ͒, h 0 .We obtain h 0 = 5.0± 0.8 nm and h 0 =5±1 nm in both cases from data in Figs.3͑d͒ and 4͑d͒.The agreement between theoretical and experimental data is excellent in both cases.The obtained thickness of the reference layer ͑5 nm͒ perfectly fits the thickness of the bottom PM monolayer ͑PM 1 ͒ measured from the larger area topographic image ͓Figs.2͑a͒ and 4͑a͔͒.In addition, the extracted value of the membrane thickness proves to be independent from the electrical tip radius of the measuring probe.These results then demonstrate the ability of simultaneous topographic and capacitance measurements to provide membrane layer thickness values at the nanoscale.
In summary, we have demonstrated the ability of ac current-sensing AFM operated in jumping mode to map simultaneously the topography and capacitance of biological layers without damaging them.We have shown that by means of these measurements the biolayer thickness can be determined with high precision at the nanoscale.With the ability of spatially resolving the capacitance while preserving the sample from damaging, this technique can be applied for nanoscale thickness measurement of other biological layers and soft materials in general Financial support by BFU2006-04656/BMC and NAN2004-09415-C05-01 grants of the Spanish MEC is acknowledged.The authors are grateful to M. Sampietro and G. Ferrari ͑Politecnico di Milano͒ for the electronic circuitry and to Nanotec Electronica S.L. for assistance in the AFM setup. 1 Departament d'Electrònica, Universitat de Barcelona and Laboratori de Nanobioenginyeria-IBEC, Parc Científic de Barcelona, Barcelona, Spain 08028 Esteve Padrós Unitat de Biofísica, Department de Bioquímica i de Biologia Molecular, Facultat de Medicina i Centre d'Estudis en Biofísica, Universitat Autònoma de Barcelona, Barcelona, Spain 08193 ͑Received 30 May 2007; accepted 9 July 2007; published online 7 August 2007͒

FIG. 2 .
FIG.2.Simultaneous topographic ͑a͒ and dc current ͑b͒ images of a PM patch on a gold substrate measured by dc CS-AFM in jumping mode with 100 mV applied bias.Profiles of ͑c͒ topography and ͑d͒ direct current corresponding to the dashed lines in the images are also shown.The PM patch is formed by an ϳ5 nm thick monolayer ͑PM 1 ͒ which is double folded in some regions ͑PM 2 ͒.