Factors in Electrochemical Nanostructure Fabrication Using Electron

Journal of The Electrochemical Society, 151 共3兲 G175-G180 共2004兲

G175

0013-4651/2004/151共3兲/G175/6/$7.00 © The Electrochemical Society, Inc.

Factors in Electrochemical Nanostructure Fabrication Using Electron-Beam Induced Carbon Masking T. Djenizian,*,z L. Santinacci,a,* and P. Schmuki** Department of Materials Science, LKO, University of Erlangen-Nuremberg, D-91058 Erlangen, Germany The present work investigates the fabrication of Au nanostructures using the masking effect of carbon patterns deposited by the electron-beam 共E-beam兲 of a scanning electron microscope for electrochemical reactions. E-beam induced deposition is based on the decomposition of residual hydrocarbon species 共molecules from the pump oil兲 to create a solid deposit at the point of impact of the E-beam. Subsequently, such E-beam deposited matter is used to completely block the electrochemical deposition of Au in the nanometer scale. In this work, several factors affecting the resolution of the process are studied. Electrochemical conditions as well as control of the E-beam C-deposit are investigated to optimize the lateral resolution of the process. Especially, it is demonstrated that the beam energy used for depositing the C-mask plays a crucial role in fabricating Au nanostructures in the sub-50 nm range. © 2004 The Electrochemical Society. 关DOI: 10.1149/1.1643744兴 All rights reserved. Manuscript received April 2, 2003. Available electronically February 5, 2004.

Miniaturization of materials in the nanometer scale has attracted the entire semiconductor industry as well as a large community of scientists and engineers because of the explosion of potential applications leading to significant, fundamentally new advances in different fields including physics, chemistry, materials science, and biology. To date, optical lithography is the main technique used for the integrated circuit 共IC兲 industry, but the current strategies employed are blocked by optical diffraction. Thus, new approaches and alternative techniques have been developed to downsize the dimensions of structures 共see, e.g., reports on the LIGA process,1 microcontact printing,2 and proximal probe lithography3-6兲. For a large overview see Ref. 7. Particle beam lithography and especially electron-beam lithography 共EBL兲 are approaches that have been widely investigated to produce structures in the sub-100 nm range.8-16 The process steps of such resist-based techniques are essentially the same as those used for photolithography, except that the pattern on the resist is obtained by scanning the focused particle beam directly across the surface. Due to a very high resolution, EBL is mainly used to produce masks and prototype nanoelectronic device fabrication.17,18 Electron-beam-induced deposition 共EBID兲 is an approach using a beam of electrons to produce 3D nanostructures. This single-step direct writing technique is carried out in a conventional or modified scanning electron microscope 共SEM兲 or transmission electron microscope 共TEM兲. The principle is based on the focused electronbeam-induced decomposition of adsorbed precursor molecules introduced into the vacuum chamber of the E-beam instrument. If the precursor species used are metallorganic compounds, the materials obtained show a nanocomposite structure with metal nanocrystals of variable size embedded in an amorphous matrix. The main constituents of the matrix are C and the metal present in the precursor molecules. Due to the combination of high resolution and 3D structures formation, EBID is highly appreciated in the field of exploratory nanodevice fabrication and has recently moved towards applications for production of conducting lines,19 X-ray mask repair,20 photonic crystals,21 and a wide range of devices.22-24 When the precursor species used are only the residual hydrocarbon molecules issued from pump oil, a carbonaceous deposit is obtained at the E-beam treated locations. In previous work, the chemical composition of such an E-beam deposited compounds has been investigated by Auger electron spectroscopy 共AES兲.25 The derivative of the Auger spectrum obtained from this material was compared with Auger spectra obtained from pure graphite and chemical vapor deposition

* Electrochemical Society Student Member. ** Electrochemical Society Active Member. a

Permanent address: EPFL, LTP, Department of Materials Science, CH1015 Lausanne, Switzerland. z E-mail: [email protected]

共CVD兲 deposited diamond which were taken as references. According to the literature, it has been found that E-beam deposited material is carbon-containing.26,27 More specifically, the spectrum reveals the presence of sp2 - and sp3 -bonded C. This amorphous structure of C, so-called diamond-like carbon 共DLC兲 exhibits electrical properties comparable to diamond.28,29 Recently, it has been reported that such E-beam induced C deposit can be used as a negative resist for electrochemical reactions, i.e., it has been demonstrated that E-beam C deposit in the nanometer range in thickness can block completely and selectively electrodeposition of metals on Si surfaces30,31 as well as the electrochemical etching of Si.32 This C masking effect has also been employed to fabricate TiO2 structures on Ti surfaces.25 In this work, several factors such as the electrochemical conditions and E-beam parameters affecting the resolution of the process are investigated in order to fabricate nanostructures. It is demonstrated that under optimized electrochemical conditions the lateral resolution of the process strongly depends on the E-beam parameters and especially the beam energy used for depositing the C-mask. Experimental Experiments were carried out on n-type Si共100兲 wafers with a resistivity of 5-8 ⍀ cm. The wafers were cleaved to samples of 1.2 ⫻ 1.2 cm and were degreased by subsequently sonicating in acetone, isopropanol, methanol, and rinsed with deionized water. The samples were dipped in 1% HF for 30 s to remove the air-formed native oxide layer and to H terminate the Si surface. Finally the samples were rinsed in deionized water and dried under a nitrogen stream. InGa eutectic 共99.99%兲 was smeared on the back side of the samples to establish an ohmic contact. Samples were patterned using a JEOL 6400 thermionic emission SEM equipped with the lithography software Elphy Quantum and a beam blanker provided by Raith GmbH. On each of the sample array of 10 lines, 50 ␮m in length, equidistantly spaced 共1.5 ␮m兲 were deposited with increasing electron doses, nC/cm2 with 0.1 ⭐ n ⭐ 1. During the deposition the pressure of the chamber was 10⫺4 Pa, the working distance was set to 10 mm, and the probe current was constant and equal to 10 pA at 5 keV and 50 pA at 20 keV. Then, samples were pressed against a 10 mm diameter O-ring of an electrochemical cell which consisted of a conventional threeelectrodes configuration. Platinum gauze served as a counter electrode, and a Ag/AgCl electrode (E ⫽ 236.3 mV vs. SHE兲 was used as a reference electrode. Deposition of Au was achieved by potentiostatic experiments in a 10 mM KAu共CN兲2 ⫹ 1 M KCl electrolyte 共pH 8.5兲. The electrochemical cell was always placed in a black box in order to avoid any noncontrolled photoelectrochemical effects. Chemical characterization of the E-beam deposit was carried out by AES using the C peak at 270 eV and the Si peak at 1621 eV. AES spectra were acquired on a Perkin-Elmer 670 spectrometer. Topog-

G176


raphy of the samples after E-beam treatments was obtained by atomic force microscopy 共AFM兲 using Pico SPM from Molecular Imaging driven by a Nanoscope E controller from Digital Instruments used in the contact mode and equipped with a 100 ␮m piezoscanner and an ultrasharp silicon tip. Capacitance measurements were performed with a Zahner IM6 setup 共Zahner Elektrik, Kronach, Germany兲. A potential ramp was applied in the anodic direction for n-type Si with a step of 65 mV and the amplitude of perturbation was 10 mV. The Mott-Schottky plots were recorded in the frequency range of 1 kHz. Current transients and potentiostatic experiments were carried out with an EG&G PAR 273A model. Results and Discussion Deposition of the C mask.—In order to characterize the C distribution over the surface, AES line scans were acquired as a function of the distance perpendicular to the two series of C lines. Figures 1a and b show the scanning AES experiments performed on a Si sample carrying the ten C lines written with 5 and 20 keV beam energy, respectively. In both cases, the results clearly indicate the presence of the ten C lines. It has to be pointed out that the C and Si intensities are complementary, i.e., the intensity of the Si peaks decreases when the intensity of the Auger C peaks increases suggesting that the amount of C increases with increasing electron dose. Figures 2a and b show the height and width of the C lines taken from the corresponding AFM profiles 共Fig. 2c and d兲. The height value was taken at the maximum and the linewidth was defined as the full width at half-maximum 共fwhm兲 of the Gaussian cross section. In all cases, the C linewidth tends to reach a limiting value for electron doses higher than 0.4 C/cm2 whereas lineheight increases with increasing electron dose suggesting that a high aspect ratio is achieved through the E-beam-induced deposition technique. In agreement with the fact that the higher the beam energy, the smaller the spot size, it is apparent that the width of the deposits increased with decreasing beam energy. It can be pointed out that the linewidths are much broader than the estimated probes size 共less than 100 nm兲, which confirms that the deposition of carbon is determined not only by the primary E-beam size, but also by the distribution of the scattering electrons emitted from the substrate.33-35 Electrochemical investigations.—The description of the interface according to the model of Gerischer can be used to determine the range of potential for electrochemical metal deposition as well as to describe the mechanism involved.36 First, the determination of the flatband potential (V FB) is required to obtain the schematic representation of the interface according to the model of Gerischer. The flatband potential corresponds with the potential of zero excess charge in the space-charge layer of the semiconductor. It can be determined by an extrapolation of the so-called Mott-Schottky plot of the capacity measurements, namely a plot of 1/C 2 vs. the externally applied voltage.37,38 The Mott-Schottky relation is given by Eq. 1 1 2 ⫽ 共 V ⫺ V FB兲 C2 ␧␧ 0 eN D

关1兴

where V is the applied voltage, N D the doping concentration, ␧ is the dielectric constant in the direction normal to the surface, and ␧ 0 ⫽ 8.854•10⫺14 F cm⫺1 the permissivity of the vacuum. The extrapolation to 1/C 2 → 0 yields the flatband potential, and from the slope where the plot is linear the dopant concentration N D is deduced. It is found from the Mott-Schottky plot shown in Fig. 3 that V fb is approximately ⫺1.0 V 共Ag/AgCl兲 and N D ⫽ 1015 cm⫺3 . According to Eq. 2 E c,s ⫽ qV FB ⫹ kT ln

冉冊 NC ND

关2兴

Figure 1. AES profiles of two arrays of ten E-beam C lines deposited on n-type Si共100兲 using a beam energy of 5 共a兲 and 20 keV 共b兲. The two series of C lines were written with an increasing electron dose from left to right 共between 0.1 and 1 C/cm2兲.

where the effective density of states in the conduction band is N C ⫽ 2.8•1019 cm⫺3 , the lower level of the conduction band at the semiconductor surface (E c,s) is ⫺1.23 V 共Ag/AgCl兲 with respect to the flatband potential. Since the Fermi level of the semiconductor has to be adjusted to the equilibrium potential of the electrolyte (V eq ⫽ ⫺0.71 vs. Ag/AgCl at pH 8.5兲, the interfaces are in a depletion situation as shown in Fig. 4a. This schematic representation of the interface under open circuit potential 共OCP兲 condition is deduced from Eq. 3 E c,b ⫺ E F ⫽ kT ln

冉冊 NC ND

关3兴


G177

Figure 2. Dependence of the C line height 共a兲 and width 共b兲 on the electron dose taken from AFM profiles of two arrays of ten E-beam C lines deposited on n-type Si共100兲 using a beam energy of 5 共c兲 and 20 keV 共d兲.

where the lower level of the conduction band in the bulk semiconductor (E c,b) is approximately ⫺0.95 V 共Ag/AgCl兲 and the upper level of the valence band in the bulk semiconductor (E v,b) is approximately 0.15 V 共Ag/AgCl兲. The equilibrium potential is about ⫺0.71 V 共Ag/AgCl兲, so that the energy levels of the Au acceptor states are expected to overlap only with the conduction band. As there is no overlap of Au acceptor states with the valence band, electrons cannot be transferred from the semiconductor to the solution. Consequently, Au deposition cannot be observed under OCP condition. According to the model of Gerischer, deposition of Au occurs at higher cathodic voltages than V FB , i.e., when the interface is in an accumulation situation. Theoretically, cathodic voltages higher than V FB ⫽ ⫺1.0 V 共Ag/AgCl兲 are required to initiate the transfer of electrons from the electrolyte to the semiconductor via a conduction band mechanism. The accumulation situation is illustrated in Fig. 4b where an external voltage of ⫺1.6 V vs. Ag/AgCl is applied.

In order to verify if deposition of Au on the Si surface is achieved for cathodic potentials, higher than V FB , a series of current transients at potentials in the range ⫺1.0 V 共Ag/AgCl兲 to ⫺1.6 V 共Ag/AgCl兲 was carried out 共Fig. 5兲. In accordance with the values of potentials obtained from the model of Gerischer, a significant cathodic current leading to Au deposition is only observed for applied potentials higher than V FB , whereas no Au deposit was obtained for samples polarized between V eq and ⫺1.0 V 共Ag/AgCl兲. Furthermore, the transients are characterized by an initial increase of the current density which is followed by a decay at longer times. The time corresponding to the current maximum decreases and the maximum current increases as the applied potential becomes more negative. These results are consistent with nucleation of 3D hemispherical clusters followed by diffusion-limited growth.39-41 For deposition potentials higher than ⫺1.5 V 共Ag/AgCl兲 an additional current due to the evolution of hydrogen is observed. The 3D island growth mechanism or Volmer-Weber mechanism has been already

G178


Figure 3. Mott-Schottky plot performed in 10 mM KAu(CN) 2 ⫹ 1 M KCl at 1 kHz.

observed for several systems42-47 and can be attributed to the relatively weak interaction energy between semiconductors and metals. The morphology of the gold deposits obtained after current transient experiments have been studied by SEM 共not shown兲. It has been observed that the density of nuclei as well as the size of the globular features depend strongly on the applied potential, i.e., the higher the cathodic applied potential, the larger the number of small crystallites. At a relatively low cathodic potential 共⫺1.1 V vs. Ag/AgCl兲 only a few crystallites with a typical feature size of 220 nm are deposited onto Si. Using a higher cathodic potential 共⫺1.6 V vs. Ag/AgCl兲 results in deposits entirely covering the Si surface with particles of a mean size of approximately 20 nm. Resolution of the process.—As the lateral resolution of the process at the edge of the C deposit depends strongly on the formation of a smooth and continuous film, the creation of a large number of small crystallites is required because the coalescence of islands in an earlier growth stage leads to homogeneous layers. Therefore, deposits are preferentially formed at high cathodic potential. Figures 6a and b show an Si sample carrying the two series of C patterns as described above after electrochemical deposition of Au. Electrochemical treatment consisted of a potential step to ⫺1.6 V 共Ag/AgCl兲 for 10 s. In accordance with our previous work, an E-beam C deposit in the nanometer range in thickness is sufficient to block the electrodeposition of Au and achieve a complete masking effect.30 From Fig. 6a, where C lines were deposited with a beam energy of 5 keV, it is apparent that independently of the electron dose the Au deposit between the C lines is homogeneous and smooth leading to an excellent lateral resolution. In contrast, if the C lines are written with a beam energy of 20 keV, the Au deposit becomes coarse between the patterns and the density of crystallites decreases when the electron dose increases. This so-called proximity effect48 observed for high electron doses is attributed to the backscattered electron 共BSE兲 induced C deposition partially blocking the electrodeposition of gold in the immediate vicinity of the predefined patterns. It is reported that the contribution of BSEs for conventional resists can cause pattern distortions and limit the ability to resolve critical dimensions, but it can be reduced using high beam energies much greater than 20 keV49 or membrane substrates.50 According to the literature, the size of the interaction volume between electrons

Figure 4. Schematic representations of the interface according to the model of Gerischer under OCP conditions 共a兲 and when an external voltage of ⫺1.6 V vs. Ag/AgCl is applied 共b兲. The interface is in a depletion situation for cathodic potentials lower than V FB and in an accumulation situation for applied potentials higher than V FB .

and the specimen is a function of the incident beam energy.51 As the beam energy is increased, the electrons can penetrate more deeply in the specimen and a more significant fraction of the incident electrons striking the surface re-emerge from the sample. Lateral scattering of the primary electrons as they penetrate the specimen gives rise to the narrowing of the distributions, the forward-scattering distribution. Backward scattering of electron from the substrate gives rise to the broader distribution, the backscattering distribution. The


G179

Figure 5. Current-time transients for the deposition of Au on n-type Si in 1 M KAu(CN) 2 ⫹ 1 M KCl.

spatial distributions of forward scattered electrons 共FSEs兲 and BSEs are generally assumed to be Gaussian48 and depend strongly on the E-beam energy, i.e., the higher the accelerating voltage, the narrower the FSEs distribution and the broader the BSEs distribution. The disk from which electrons are backscattered from the substrate can be established through the determination of the KanayaOkayama range.52 At low beam energy 共5 keV兲, the BSEs distribution becomes narrower, as broad in space as the forward scattered component 共Fig. 7a兲 so that the region to which the BSEs can escape is limited to a disk of approximately 0.47 ␮m in diameter. Thus, independent of the electron dose used, confined C lines with welldefined borders are deposited as depicted in Fig. 7b. As the energy of the incident electrons is greater 共20 keV兲, the interaction volume increases dramatically 共approximately 4.7 ␮m兲. Thus, the circular region where BSEs re-emerge is significantly larger than the area exposed by the incident beam and FSEs 共Fig. 7a兲. As a consequence, the region where adsorbed hydrocarbons decompose is considerably larger than the defined pattern locations. Since the contribution of the BSEs overexpose a large area, a diffuse C fog builds up in the vicinity of the beam impact and can hinder subsequent electrodeposition of Au. The amount of this additional C deposit increases with increasing electron dose and with reducing spacing between patterns because C fog overlapping occurs as depicted in Fig. 7b. From these results, it is clearly apparent that BSEs play a crucial role. At lowbeam energy, the resolution of the process is mainly governed by the BSEs exposure and independent of the electron dose used, the resolution obtained at the edges of the C lines is excellent. At high beam energy, BSEs overexpose a large area and a relatively low electron dose is required to decrease the contribution of BSEs and achieve good lateral resolution. In order to explore the lower size limit of the process, a Si sample carrying two perpendicular arrays of C lines with decreasing spacing were written with a 1 C/cm2 electron dose using a 5 keV beam energy. In this case, a low beam energy was chosen in order to dismiss a possible C fog overlapping by reducing the spacing between patterns. Subsequently, electrodeposition of Au was performed by a potentiostatic experiment 关⫺1.6 V 共Ag/AgCl兲 for 10 s兴. Figure 8 shows that the features reveal a coherent formation of clusters completely separated by the C lines. The size of the dots decreases by decreasing the distance between the C lines and deposition of clusters in the sub-50 nm range can be achieved.

Figure 6. SEM images of Au deposits on a Si surface carrying the two arrays of C lines as in Fig. 1. Au deposition was carried out in 10 mM KAu(CN) 2 ⫹ 1 M KCl at pH 8.5 by a potential step to ⫺1.6 V vs. Ag/AgCl for 10 s.

Conclusions Under optimized electrochemical conditions, it has been shown that the E-beam energy used for depositing C-masks plays a crucial role. C patterns written with a relatively high beam energy 共20 keV兲 revealed the presence of a C background in the vicinity of the predefined patterns. The amount of this additional C increases with increasing electron dose. It is assumed that the large disk from which BSEs re-emerge from the sample have enough energy to decompose organic molecules adsorbed at the Si surface. As a consequence, such C fog surrounding the patterns can partially block electrodeposition of Au. Thus, poor resolution is obtained at the edges of the C lines not only for high electron dose but also when the background overlapping occurs by reducing the spacing between the patterns. Decreasing the spatial distribution of the BSEs by decreasing the beam energy can dismiss this overexposure. As BSEs mainly govern the patterning independent of the electron dose, the resolution of the process is considerably improved. In this case, Au clusters in the sub-50 nm range were successfully fabricated.

G180


Figure 7. Schematic representation of the spatial distributions of the forward scattered electrons 共FSEs兲 and the back scattered electrons 共BSEs兲 for a beam energy of 5 and 20 keV 共a兲 and the corresponding spatial distribution of C 共b兲.

Figure 8. SEM image of Au dots fabricated by the E-beam induced C masking technique. A Si sample carrying two perpendicular arrays of C lines with decreasing spacing, written with a 1 C/cm2 electron dose using a 5 keV beam energy was electrochemically treated by a potentiostatic experiment 关⫺1.6 V 共Ag/AgCl兲 for 10 s兴. The size of the Au nanostructures decreases by decreasing the distance between the C lines. Au dots in the sub-50 nm range in size can be fabricated.

Acknowledgments The authors acknowledge DFG and FAU for the financial support of this work. Helga Hildebrand is acknowledged for the AES experiments. University of Erlangen-Nuremberg assisted in meeting the publication costs of this article.

References 1. C. R. Friedrich, R. Warrington, W. Bacher, W. Bauer, P. J. Coane, J. Go¨ttert, T. Hanemann, J. Hausselt, M. Heckele, R. Knitter, J. Mohr, V. Pioter, H. J. RitzhauptKleiss, and R. Ruprecht, High Aspect Ratio Processing, in Microlithography, Micromachining and Microfabrication, SPIE, Vol. 2, P. Rai-Choudhory, Editor, p. 301 共1997兲.

2. Y. Xia, J. A. Rogers, K. E. Paul, and G. M. Whitesides, Chem. Rev. (Washington, D.C.), 99, 1823 共1999兲. 3. L. Stockman, I. Heyvaert, C. van Haesendonck, and Y. Bruynseraede, Appl. Phys. Lett., 62, 2935 共1993兲. 4. K. Matsumoto, M. Ishii, K. Segawa, Y. Oka, B. J. Vartanian, and J. S. Harris, Appl. Phys. Lett., 68, 34 共1996兲. 5. P. M. Campbell, E. S. Snow, and P. J. McMarr, Appl. Phys. Lett., 66, 1388 共1995兲. 6. L. Santinacci, T. Djenizian, and P. Schmuki, Appl. Phys. Lett., 79, 1882 共2001兲. 7. P. Schmuki, S. Maupai, T. Djenizian, L. Santinacci, A. Spiegel, and U. Schlierf, Encyclopedia of Nanoscience and Nanotechnology, Techniques in Electrochemical Nanotechnology, American Scientific Publishers, Stevenson Ranch, CA 共2003兲. 8. A. N. Broers, W. W. Molzen, J. J. Cuomo, and N. D. Wittels, Appl. Phys. Lett., 29, 596 共1976兲. 9. D. R. Allee, C. P. Umbach, and A. N. Broers, J. Vac. Sci. Technol. B, 9, 2838 共1991兲. 10. S. Matsui, T. Ichihashi, and M. Mito, J. Vac. Sci. Technol. B, 7, 1182 共1989兲. 11. D. R. Allee and A. Broers, Appl. Phys. Lett., 57, 2271 共1990兲. 12. X. Pan, D. R. Allee, A. Broers, Y. S. Tang, and C. W. Wilkinson, Appl. Phys. Lett., 59, 3157 共1991兲. 13. D. R. Allee, A. N. Broers, and R. F. W. Pease, Proc. IEEE, 79, 1093 共1991兲. 14. G. Simon, A. M. Haghiri Gosnet, F. Carcenac, and H. Launois, Microelectron. Eng., 35, 51 共1997兲. 15. W. Xu, J. Wong, C. C. Cheng, R. Johnson, and A. Scherer, J. Vac. Sci. Technol. B, 13, 2372 共1995兲. 16. H. G. Craighead, R. E. Howard, L. D. Jackel, and P. M. Mankiewich, Appl. Phys. Lett., 42, 38 共1983兲. 17. C. P. Umbach, S. Washburn, R. B. Laibowitz, and R. A. Webb, Phys. Rev. B, 30, 4048 共1984兲. 18. A. Muray, M. Scheinfein, M. Isaacson, and I. Adesida, J. Vac. Sci. Technol. B, 3, 367 共1985兲. 19. H. W. P. Koops, C. Scho¨ssler, A. Kaya, and M. Weber, J. Vac. Sci. Technol. B, 14, 4105 共1996兲. 20. K. T. Kohlmann von Platen, M. Thiemann, and W. H. Bru¨nger, Microelectron. Eng., 13, 279 共1991兲. 21. H. W. P. Koops, Proc. SPIE, 2849, 248 共1996兲. 22. H. W. P. Koops, E. Munro, J. Rouse, J. Kretz, M. Rudolph, M. Weber, and G. Dahm, Nucl. Instrum. Methods Phys. Res. B, 363, 1 共1995兲. 23. M. Weber, M. Rudolph, J. Kretz, and H. W. P. Koops, J. Vac. Sci. Technol. B, 13, 461 共1995兲. 24. C. Scho¨ssler and H. W. P. Koops, J. Vac. Sci. Technol. B, 16, 862 共1998兲. 25. T. Djenizian, J. Macak, and P. Schmuki, Mater. Res. Soc. Symp. Proc., 741, 79 共2002兲. 26. K. D. Childs, B. A. Carlson, L. A. LaVanier, J. F. Paul, W. F. Stickle and D. G. Watson, Handbook of Auger Electron Spectroscopy, Physical Electronics, Inc., Eden Prairie, MN 共1995兲. 27. P. Weightman, Rep. Prog. Phys., 45, 753 共1982兲. 28. N. Miura, A. Yamada, and M. Konagai, Jpn. J. Appl. Phys., Part 2, 36, L1275 共1997兲. 29. N. Miura, T. Numaguchi, A. Yamada, M. Konagai, and J. I. Shirakashi, Jpn. J. Appl. Phys., Part 2, 36, L1619 共1997兲. 30. T. Djenizian, L. Santinacci, and P. Schmuki, Appl. Phys. Lett., 78, 2840 共2001兲. 31. T. Djenizian, B. Petite, L. Santinacci, and P. Schmuki, Electrochim. Acta, 47, 891 共2001兲. 32. T. Djenizian, L. Santinacci, H. Hildebrand, and P. Schmuki, Surf. Sci., 524, 40 共2003兲. 33. P. C. Hoyle, J. R. A. Cleaver, and H. Ahmed, Appl. Phys. Lett., 64, 1448 共1994兲. 34. R. R. Kuntz and T. M. Mayer, J. Vac. Sci. Technol. B, 5, 427 共1986兲. 35. K. T. Kohlmann von Platen, J. Chlebek, M. Weiss, K. Reimer, H. Oertel, and W. H. Brunger, J. Vac. Sci. Technol. B, 11, 2219 共1993兲. 36. S. R. Morrison, Electrochemistry at Semiconductor and Oxidized Metal Electrodes, Plenum Press, New York 共1980兲. 37. N. F. Mott, in Proc. R. Soc. London, 171, 27 共1939兲. 38. W. Schottky, Z. Phys., 113, 367 共1939兲. 39. B. Scharifker and J. Mostany, J. Electroanal. Chem., 177, 13 共1984兲. 40. G. Gunawardena, G. Hills, I. Montenegro, and B. Scharifker, J. Electroanal. Chem., 138, 225 共1982兲. 41. B. Scharifker and G. Hills, Electrochim. Acta, 28, 879 共1983兲. 42. G. Scherb and D. M. Kolb, J. Electroanal. Chem., 396, 151 共1995兲. 43. P. M. Vereecken, K. Strubbe, and W. P. Gomes, J. Electroanal. Chem., 433, 19 共1997兲. 44. R. M. Stiger, S. Gorer, B. Craft, and R. M. Penner, Langmuir, 15, 790 共1999兲. 45. G. Oskam, D. van Heerden, and P. C. Searson, Appl. Phys. Lett., 73, 3241 共1998兲. 46. A. A. Pasa and W. Schwarzacher, Phys. Status Solidi A, 173, 73 共1999兲. 47. B. Rashkova, B. Guel, R. T. Po¨tzschke, G. Staikov, and W. J. Lorenz, Electrochim. Acta, 43, 3021 共1998兲. 48. T. H. P. Chang, J. Vac. Sci. Technol., 12, 1271 共1975兲. 49. L. D. Jackel, R. E. Howard, P. M. Mankiewich, H. G. Craighead, and W. Epworth, Appl. Phys. Lett., 45, 698 共1984兲. 50. W. W. Molzen, A. N. Broers, J. J. Cuomo, J. M. E. Harper, and R. B. Laibowitz, J. Vac. Sci. Technol., 16, 269 共1979兲. 51. J. I. Goldstein, D. E. Newbury, P. Echlin, D. C. Joy, A. D. Romig, C. Fiori, and E. Lifshin, Scanning Electron Microscopy and X-Ray Microanalysis, Plenum Press, New York 共1992兲. 52. K. Kanaya and S. Okayama, J. Phys. D, 5, 43 共1972兲.