Abstract

We present a geometrical model of atomic topography with which to obtain a quantitative assessment of surface roughness. A series of two- and three-dimensional atomic surface roughness equations with sufficiently realistic parameters is developed to permit quantitative comparison with scanning-tunneling microscope and atomic-force microscope (AFM) experimental results. The model is sufficiently simple that one can easily use it to interpret experimental data. Tables are provided with estimated values for two- and three-dimensional rms atomic surface roughness in pure metal crystals and ionic crystals based on the atomic surface roughness equations. We use these roughness equations to determine the roughness of cleaved muscovite mica [essentially, KAl2(OH)2Si3AlO10]; the calculated values for both two- and three-dimensional roughness are consistent with those obtained in our AFM measurements. In addition, we demonstrate both theoretically and experimentally that atomic surface roughness is never zero.

© 2000 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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1998 (1)

J. Yu, Y. Namba, “Atomic surface roughness,” Appl. Phys. Lett. 73, 3607–3609 (1998).
[CrossRef]

1997 (1)

1996 (2)

J. Yu, J. L. Cao, Y. Namba, Y. Y. Ma, “Surface roughness characterization of soft x-ray multilayer films on the nanometer scale,” J. Vac. Sci. Technol. B 14, 42–47 (1996).
[CrossRef]

I. Yoshida, T. Sugita, K. Sasaki, H. Hori, “Studies of cleaved surfaces of phyllo-silicates (talc, phlogopite and muscovite) by using AFM and LEED,” J. Surf. Sci. Soc. Jpn. 17, 30–36 (1996; in Japanese).

1995 (6)

T. Sugita, I. Yoshida, “Studies of cleaved surfaces of layered semi-metals, graphite and phyllo-silicates,” J. Surf. Sci. Soc. Jpn. 16, 664–672 (1995; in Japanese).

Y. Sugawara, M. Ohta, H. Ueyama, S. Morita, “Defect motion on an InP(110) surface observed with noncontact atomic force microscopy,” Science 270, 1646–1648 (1995).
[CrossRef]

M. Ohta, H. Ueyama, Y. Sugawara, S. Morita, “Contrast of atomic-resolution images from a noncontact ultrahigh-vacuum atomic force microscope,” Jpn. J. Appl. Phys. 34, L1692–L1694 (1995).
[CrossRef]

Y. Sugawara, M. Ohta, H. Ueyama, S. Morita, “Atomic-resolution imaging of ZnSSe (110) surface with ultrahigh-vacuum atomic force microscope (UHV-AFM),” Jpn. J. Appl. Phys. 34, L462–L464 (1995).
[CrossRef]

J. M. Bennett, M. M. Tehrani, J. Jahanmir, J. C. Podlesny, T. L. Balter, “Topographic measurements of supersmooth dielectric films made with a mechanical profiler and a scanning force microscope,” Appl. Opt. 34, 209–212 (1995).
[CrossRef] [PubMed]

J. M. Bennett, J. Jahanmir, J. C. Podlesny, T. L. Balter, D. T. Hobbs, “Scanning force microscope as a tool for studying optical surfaces,” Appl. Opt. 34, 213–230 (1995).
[CrossRef] [PubMed]

1994 (3)

J. Yu, L. Hou, W. Sh. Ma, J. L. Cao, J. Y. Yu, J. E. Yao, “Nanometer characterization of single point diamond-turned mirrors on the micrometer and sub-micrometer scale,” J. Vac. Sci. Technol. B 12, 1835–1838 (1994).
[CrossRef]

M. Ohta, Y. Sugawara, K. Hontani, S. Morita, F. Osaka, M. Suzuki, H. Nagaoka, S. Mishima, T. Okada, “Atomically resolved image of cleaved GaAs (110) surface observed with an ultrahigh vacuum atomic force microscope,” Jpn. J. Appl. Phys. 33, L52–L54 (1994).
[CrossRef]

F. J. Giessibl, “Atomic force microscopy in ultrahigh vacuum,” Jpn. J. Appl. Phys. 33, 3726–3734 (1994).
[CrossRef]

1993 (2)

F. Ohnesorge, G. Binning, “True atomic resolution by atomic force microscopy through repulsive and attractive forces,” Science 260, 1451–1456 (1993).
[CrossRef] [PubMed]

J. E. Griffith, D. A. Grigg, “Dimensional metrology with scanning probe microscopes,” J. Appl. Phys. 74, R83–R109 (1993).
[CrossRef]

1992 (2)

T. Suntola, “Atomic layer epitaxy,” Thin Solid Films 216, 84–89 (1992).
[CrossRef]

G. Bining, “Force microscopy,” Ultramicroscopy 42–44, 7–15 (1992).
[CrossRef]

1989 (1)

B. Drake, C. B. Prater, A. L. Weisenhorn, S. A. C. Gould, T. R. Albrecht, C. F. Quate, D. S. Cannell, H. G. Hansma, P. K. Hansma, “Imaging crystals, polymers, and processes in water with the atomic force microscope,” Science 243, 1586–1589 (1989).
[CrossRef] [PubMed]

1987 (1)

Y. Aoyagi, “Atomic-layer growth of GaAs by modulated-continuous-wave laser metalorganic vapor-phase epitaxy,” J. Vac. Sci. Technol. B 5, 1460–1464 (1987).
[CrossRef]

1986 (2)

1985 (2)

J. Nishizawa, “Molecular layer epitaxy,” J. Electrochem. Soc. 132, 1197–1200 (1985).
[CrossRef]

J. Tersoff, D. R. Hamann, “Theory of the scanning tunneling microscope,” Phys. Rev. 31, 805–813 (1985).
[CrossRef]

1982 (1)

G. Binning, H. Rohrer, Ch. Gerber, E. Weibel, “Surface studies by scanning tunneling microscopy,” Phys. Rev. Lett. 49, 57–61 (1982).
[CrossRef]

1979 (1)

1976 (1)

R. D. Shannon, “Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides,” Acta Crystallogr. A 32, 751–767 (1976).
[CrossRef]

1969 (1)

R. D. Shannon, C. T. Prewitt, “Effective ionic radii in oxides and fluorides,” Acta Crystallogr. A 25, 925–946 (1969).

1952 (1)

L. H. Ahrens, “The use of ionization potentials,” Geochem. Cosmochim. Acta 2, 155–169 (1952).
[CrossRef]

Ahrens, L. H.

L. H. Ahrens, “The use of ionization potentials,” Geochem. Cosmochim. Acta 2, 155–169 (1952).
[CrossRef]

Albrecht, T. R.

B. Drake, C. B. Prater, A. L. Weisenhorn, S. A. C. Gould, T. R. Albrecht, C. F. Quate, D. S. Cannell, H. G. Hansma, P. K. Hansma, “Imaging crystals, polymers, and processes in water with the atomic force microscope,” Science 243, 1586–1589 (1989).
[CrossRef] [PubMed]

Aoyagi, Y.

Balter, T. L.

Benatar, L.

R. Howland, L. Benatar, Practical Guide to Scanning Probe Microscopy (Park Scientific Instruments, Sunnyvale, Calif., 1993–1996).

Bendat, J. S.

J. S. Bendat, A. G. Piersol, Random Data: Analysis and Measurement Procedures (Wiley-Interscience, New York, 1971).

Bennett, J. M.

Bining, G.

G. Bining, “Force microscopy,” Ultramicroscopy 42–44, 7–15 (1992).
[CrossRef]

Binning, G.

F. Ohnesorge, G. Binning, “True atomic resolution by atomic force microscopy through repulsive and attractive forces,” Science 260, 1451–1456 (1993).
[CrossRef] [PubMed]

G. Binning, C. F. Quate, Ch. Gerber, “Atomic force microscope,” Phys. Rev. Lett. 56, 930–933 (1986).
[CrossRef]

G. Binning, H. Rohrer, Ch. Gerber, E. Weibel, “Surface studies by scanning tunneling microscopy,” Phys. Rev. Lett. 49, 57–61 (1982).
[CrossRef]

Cannell, D. S.

B. Drake, C. B. Prater, A. L. Weisenhorn, S. A. C. Gould, T. R. Albrecht, C. F. Quate, D. S. Cannell, H. G. Hansma, P. K. Hansma, “Imaging crystals, polymers, and processes in water with the atomic force microscope,” Science 243, 1586–1589 (1989).
[CrossRef] [PubMed]

Cao, J. L.

J. Yu, J. L. Cao, Y. Namba, Y. Y. Ma, “Surface roughness characterization of soft x-ray multilayer films on the nanometer scale,” J. Vac. Sci. Technol. B 14, 42–47 (1996).
[CrossRef]

J. Yu, L. Hou, W. Sh. Ma, J. L. Cao, J. Y. Yu, J. E. Yao, “Nanometer characterization of single point diamond-turned mirrors on the micrometer and sub-micrometer scale,” J. Vac. Sci. Technol. B 12, 1835–1838 (1994).
[CrossRef]

J. Yu, L. Hou, J. Wei, J. E. Yao, J. L. Cao, J. Y. Yu, “Scanning tunneling microscope to evaluate supersmooth surface roughness,” in Current Developments in Optical Design and Optical Engineering II, R. E. Fischer, W. J. Smith, eds., Proc. SPIE1752, 123–131 (1992).
[CrossRef]

Celotta, R. J.

Dragoset, R. A.

R. A. Dragoset, R. D. Young, H. P. Layer, S. R. Mielczarek, E. C. Teague, R. J. Celotta, “Scanning tunneling microscopy applied to optical surfaces,” Opt. Lett. 11, 560–562 (1986).
[CrossRef] [PubMed]

R. A. Dragoset, T. V. Vorburger, “Scanning tunneling microscopy of a diamond-turned surface and a grating replica,” in Metrology: Figure and Finish, B. Truax, ed., Proc. SPIE749, 54–58 (1986).

Drake, B.

B. Drake, C. B. Prater, A. L. Weisenhorn, S. A. C. Gould, T. R. Albrecht, C. F. Quate, D. S. Cannell, H. G. Hansma, P. K. Hansma, “Imaging crystals, polymers, and processes in water with the atomic force microscope,” Science 243, 1586–1589 (1989).
[CrossRef] [PubMed]

Elson, J. M.

Gerber, Ch.

G. Binning, C. F. Quate, Ch. Gerber, “Atomic force microscope,” Phys. Rev. Lett. 56, 930–933 (1986).
[CrossRef]

G. Binning, H. Rohrer, Ch. Gerber, E. Weibel, “Surface studies by scanning tunneling microscopy,” Phys. Rev. Lett. 49, 57–61 (1982).
[CrossRef]

Giessibl, F. J.

F. J. Giessibl, “Atomic force microscopy in ultrahigh vacuum,” Jpn. J. Appl. Phys. 33, 3726–3734 (1994).
[CrossRef]

Gould, S. A. C.

B. Drake, C. B. Prater, A. L. Weisenhorn, S. A. C. Gould, T. R. Albrecht, C. F. Quate, D. S. Cannell, H. G. Hansma, P. K. Hansma, “Imaging crystals, polymers, and processes in water with the atomic force microscope,” Science 243, 1586–1589 (1989).
[CrossRef] [PubMed]

Griffith, J. E.

J. E. Griffith, D. A. Grigg, “Dimensional metrology with scanning probe microscopes,” J. Appl. Phys. 74, R83–R109 (1993).
[CrossRef]

Grigg, D. A.

J. E. Griffith, D. A. Grigg, “Dimensional metrology with scanning probe microscopes,” J. Appl. Phys. 74, R83–R109 (1993).
[CrossRef]

Grim, R. E.

R. E. Grim, Clay Mineralogy, 2nd ed. (McGraw-Hill, New York, 1968).

Hamann, D. R.

J. Tersoff, D. R. Hamann, “Theory of the scanning tunneling microscope,” Phys. Rev. 31, 805–813 (1985).
[CrossRef]

Hansma, H. G.

B. Drake, C. B. Prater, A. L. Weisenhorn, S. A. C. Gould, T. R. Albrecht, C. F. Quate, D. S. Cannell, H. G. Hansma, P. K. Hansma, “Imaging crystals, polymers, and processes in water with the atomic force microscope,” Science 243, 1586–1589 (1989).
[CrossRef] [PubMed]

Hansma, P. K.

B. Drake, C. B. Prater, A. L. Weisenhorn, S. A. C. Gould, T. R. Albrecht, C. F. Quate, D. S. Cannell, H. G. Hansma, P. K. Hansma, “Imaging crystals, polymers, and processes in water with the atomic force microscope,” Science 243, 1586–1589 (1989).
[CrossRef] [PubMed]

Hobbs, D. T.

Hontani, K.

M. Ohta, Y. Sugawara, K. Hontani, S. Morita, F. Osaka, M. Suzuki, H. Nagaoka, S. Mishima, T. Okada, “Atomically resolved image of cleaved GaAs (110) surface observed with an ultrahigh vacuum atomic force microscope,” Jpn. J. Appl. Phys. 33, L52–L54 (1994).
[CrossRef]

Hori, H.

I. Yoshida, T. Sugita, K. Sasaki, H. Hori, “Studies of cleaved surfaces of phyllo-silicates (talc, phlogopite and muscovite) by using AFM and LEED,” J. Surf. Sci. Soc. Jpn. 17, 30–36 (1996; in Japanese).

Hou, L.

J. Yu, L. Hou, W. Sh. Ma, J. L. Cao, J. Y. Yu, J. E. Yao, “Nanometer characterization of single point diamond-turned mirrors on the micrometer and sub-micrometer scale,” J. Vac. Sci. Technol. B 12, 1835–1838 (1994).
[CrossRef]

J. Yu, L. Hou, J. Wei, J. E. Yao, J. L. Cao, J. Y. Yu, “Scanning tunneling microscope to evaluate supersmooth surface roughness,” in Current Developments in Optical Design and Optical Engineering II, R. E. Fischer, W. J. Smith, eds., Proc. SPIE1752, 123–131 (1992).
[CrossRef]

Howland, R.

R. Howland, L. Benatar, Practical Guide to Scanning Probe Microscopy (Park Scientific Instruments, Sunnyvale, Calif., 1993–1996).

Hurlbut, C. S.

C. Klein, C. S. Hurlbut, Manual of Mineralogy, 21st ed. (Wiley, New York, 1993).

Ishii, M.

Iwai, S.

Jahanmir, J.

Klein, C.

C. Klein, C. S. Hurlbut, Manual of Mineralogy, 21st ed. (Wiley, New York, 1993).

Layer, H. P.

Ma, W. Sh.

J. Yu, L. Hou, W. Sh. Ma, J. L. Cao, J. Y. Yu, J. E. Yao, “Nanometer characterization of single point diamond-turned mirrors on the micrometer and sub-micrometer scale,” J. Vac. Sci. Technol. B 12, 1835–1838 (1994).
[CrossRef]

Ma, Y. Y.

J. Yu, J. L. Cao, Y. Namba, Y. Y. Ma, “Surface roughness characterization of soft x-ray multilayer films on the nanometer scale,” J. Vac. Sci. Technol. B 14, 42–47 (1996).
[CrossRef]

Magonov, S. N.

S. N. Magonov, M.-H. Wangbo, Surface Analysis with STM and AFM—Experimental and Theoretical Aspects of Image Analysis (Verlagsgesellschaft, Weinheim, Germany, 1996); “Interpreting STM and AFM images” Adv. Mater. 6, 355–371 (1994).
[CrossRef]

Mattsson, L.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering, 2nd ed. (Optical Society of America, Washington, D.C., 1999).

Mielczarek, S. R.

Mishima, S.

M. Ohta, Y. Sugawara, K. Hontani, S. Morita, F. Osaka, M. Suzuki, H. Nagaoka, S. Mishima, T. Okada, “Atomically resolved image of cleaved GaAs (110) surface observed with an ultrahigh vacuum atomic force microscope,” Jpn. J. Appl. Phys. 33, L52–L54 (1994).
[CrossRef]

Morita, S.

Y. Sugawara, M. Ohta, H. Ueyama, S. Morita, “Atomic-resolution imaging of ZnSSe (110) surface with ultrahigh-vacuum atomic force microscope (UHV-AFM),” Jpn. J. Appl. Phys. 34, L462–L464 (1995).
[CrossRef]

M. Ohta, H. Ueyama, Y. Sugawara, S. Morita, “Contrast of atomic-resolution images from a noncontact ultrahigh-vacuum atomic force microscope,” Jpn. J. Appl. Phys. 34, L1692–L1694 (1995).
[CrossRef]

Y. Sugawara, M. Ohta, H. Ueyama, S. Morita, “Defect motion on an InP(110) surface observed with noncontact atomic force microscopy,” Science 270, 1646–1648 (1995).
[CrossRef]

M. Ohta, Y. Sugawara, K. Hontani, S. Morita, F. Osaka, M. Suzuki, H. Nagaoka, S. Mishima, T. Okada, “Atomically resolved image of cleaved GaAs (110) surface observed with an ultrahigh vacuum atomic force microscope,” Jpn. J. Appl. Phys. 33, L52–L54 (1994).
[CrossRef]

Nagaoka, H.

M. Ohta, Y. Sugawara, K. Hontani, S. Morita, F. Osaka, M. Suzuki, H. Nagaoka, S. Mishima, T. Okada, “Atomically resolved image of cleaved GaAs (110) surface observed with an ultrahigh vacuum atomic force microscope,” Jpn. J. Appl. Phys. 33, L52–L54 (1994).
[CrossRef]

Namba, Y.

J. Yu, Y. Namba, “Atomic surface roughness,” Appl. Phys. Lett. 73, 3607–3609 (1998).
[CrossRef]

J. Yu, J. L. Cao, Y. Namba, Y. Y. Ma, “Surface roughness characterization of soft x-ray multilayer films on the nanometer scale,” J. Vac. Sci. Technol. B 14, 42–47 (1996).
[CrossRef]

Nishizawa, J.

J. Nishizawa, “Molecular layer epitaxy,” J. Electrochem. Soc. 132, 1197–1200 (1985).
[CrossRef]

Nussbaumer, H. J.

H. J. Nussbaumer, Fast Fourier Transform and Convolution Algorithms (Springer-Verlag, Berlin, 1982); R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1986).
[CrossRef]

Ohnesorge, F.

F. Ohnesorge, G. Binning, “True atomic resolution by atomic force microscopy through repulsive and attractive forces,” Science 260, 1451–1456 (1993).
[CrossRef] [PubMed]

Ohta, M.

Y. Sugawara, M. Ohta, H. Ueyama, S. Morita, “Atomic-resolution imaging of ZnSSe (110) surface with ultrahigh-vacuum atomic force microscope (UHV-AFM),” Jpn. J. Appl. Phys. 34, L462–L464 (1995).
[CrossRef]

M. Ohta, H. Ueyama, Y. Sugawara, S. Morita, “Contrast of atomic-resolution images from a noncontact ultrahigh-vacuum atomic force microscope,” Jpn. J. Appl. Phys. 34, L1692–L1694 (1995).
[CrossRef]

Y. Sugawara, M. Ohta, H. Ueyama, S. Morita, “Defect motion on an InP(110) surface observed with noncontact atomic force microscopy,” Science 270, 1646–1648 (1995).
[CrossRef]

M. Ohta, Y. Sugawara, K. Hontani, S. Morita, F. Osaka, M. Suzuki, H. Nagaoka, S. Mishima, T. Okada, “Atomically resolved image of cleaved GaAs (110) surface observed with an ultrahigh vacuum atomic force microscope,” Jpn. J. Appl. Phys. 33, L52–L54 (1994).
[CrossRef]

Okada, T.

M. Ohta, Y. Sugawara, K. Hontani, S. Morita, F. Osaka, M. Suzuki, H. Nagaoka, S. Mishima, T. Okada, “Atomically resolved image of cleaved GaAs (110) surface observed with an ultrahigh vacuum atomic force microscope,” Jpn. J. Appl. Phys. 33, L52–L54 (1994).
[CrossRef]

Osaka, F.

M. Ohta, Y. Sugawara, K. Hontani, S. Morita, F. Osaka, M. Suzuki, H. Nagaoka, S. Mishima, T. Okada, “Atomically resolved image of cleaved GaAs (110) surface observed with an ultrahigh vacuum atomic force microscope,” Jpn. J. Appl. Phys. 33, L52–L54 (1994).
[CrossRef]

Pauling, L.

L. Pauling, The Nature of the Chemical Bond, 3rd ed. (Cornell U. Press, Ithaca, N.Y., 1960).

Piersol, A. G.

J. S. Bendat, A. G. Piersol, Random Data: Analysis and Measurement Procedures (Wiley-Interscience, New York, 1971).

Podlesny, J. C.

Povarennykh, A. S.

A. S. Povarennykh, Crystal Chemical Classification of Minerals, J. E. S. Bradley, transl. (Plenum, New York, 1972), Vol. 1, p. 42.

Prater, C. B.

B. Drake, C. B. Prater, A. L. Weisenhorn, S. A. C. Gould, T. R. Albrecht, C. F. Quate, D. S. Cannell, H. G. Hansma, P. K. Hansma, “Imaging crystals, polymers, and processes in water with the atomic force microscope,” Science 243, 1586–1589 (1989).
[CrossRef] [PubMed]

Prewitt, C. T.

R. D. Shannon, C. T. Prewitt, “Effective ionic radii in oxides and fluorides,” Acta Crystallogr. A 25, 925–946 (1969).

Quate, C. F.

B. Drake, C. B. Prater, A. L. Weisenhorn, S. A. C. Gould, T. R. Albrecht, C. F. Quate, D. S. Cannell, H. G. Hansma, P. K. Hansma, “Imaging crystals, polymers, and processes in water with the atomic force microscope,” Science 243, 1586–1589 (1989).
[CrossRef] [PubMed]

G. Binning, C. F. Quate, Ch. Gerber, “Atomic force microscope,” Phys. Rev. Lett. 56, 930–933 (1986).
[CrossRef]

Rohrer, H.

G. Binning, H. Rohrer, Ch. Gerber, E. Weibel, “Surface studies by scanning tunneling microscopy,” Phys. Rev. Lett. 49, 57–61 (1982).
[CrossRef]

Sasaki, K.

I. Yoshida, T. Sugita, K. Sasaki, H. Hori, “Studies of cleaved surfaces of phyllo-silicates (talc, phlogopite and muscovite) by using AFM and LEED,” J. Surf. Sci. Soc. Jpn. 17, 30–36 (1996; in Japanese).

Shannon, R. D.

R. D. Shannon, “Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides,” Acta Crystallogr. A 32, 751–767 (1976).
[CrossRef]

R. D. Shannon, C. T. Prewitt, “Effective ionic radii in oxides and fluorides,” Acta Crystallogr. A 25, 925–946 (1969).

Sugawara, Y.

Y. Sugawara, M. Ohta, H. Ueyama, S. Morita, “Defect motion on an InP(110) surface observed with noncontact atomic force microscopy,” Science 270, 1646–1648 (1995).
[CrossRef]

M. Ohta, H. Ueyama, Y. Sugawara, S. Morita, “Contrast of atomic-resolution images from a noncontact ultrahigh-vacuum atomic force microscope,” Jpn. J. Appl. Phys. 34, L1692–L1694 (1995).
[CrossRef]

Y. Sugawara, M. Ohta, H. Ueyama, S. Morita, “Atomic-resolution imaging of ZnSSe (110) surface with ultrahigh-vacuum atomic force microscope (UHV-AFM),” Jpn. J. Appl. Phys. 34, L462–L464 (1995).
[CrossRef]

M. Ohta, Y. Sugawara, K. Hontani, S. Morita, F. Osaka, M. Suzuki, H. Nagaoka, S. Mishima, T. Okada, “Atomically resolved image of cleaved GaAs (110) surface observed with an ultrahigh vacuum atomic force microscope,” Jpn. J. Appl. Phys. 33, L52–L54 (1994).
[CrossRef]

Sugita, T.

I. Yoshida, T. Sugita, K. Sasaki, H. Hori, “Studies of cleaved surfaces of phyllo-silicates (talc, phlogopite and muscovite) by using AFM and LEED,” J. Surf. Sci. Soc. Jpn. 17, 30–36 (1996; in Japanese).

T. Sugita, I. Yoshida, “Studies of cleaved surfaces of layered semi-metals, graphite and phyllo-silicates,” J. Surf. Sci. Soc. Jpn. 16, 664–672 (1995; in Japanese).

Suntola, T.

T. Suntola, “Atomic layer epitaxy,” Thin Solid Films 216, 84–89 (1992).
[CrossRef]

Suzuki, M.

M. Ohta, Y. Sugawara, K. Hontani, S. Morita, F. Osaka, M. Suzuki, H. Nagaoka, S. Mishima, T. Okada, “Atomically resolved image of cleaved GaAs (110) surface observed with an ultrahigh vacuum atomic force microscope,” Jpn. J. Appl. Phys. 33, L52–L54 (1994).
[CrossRef]

Teague, E. C.

Tehrani, M. M.

Tersoff, J.

J. Tersoff, D. R. Hamann, “Theory of the scanning tunneling microscope,” Phys. Rev. 31, 805–813 (1985).
[CrossRef]

Ueki, T.

Ueyama, H.

Y. Sugawara, M. Ohta, H. Ueyama, S. Morita, “Atomic-resolution imaging of ZnSSe (110) surface with ultrahigh-vacuum atomic force microscope (UHV-AFM),” Jpn. J. Appl. Phys. 34, L462–L464 (1995).
[CrossRef]

Y. Sugawara, M. Ohta, H. Ueyama, S. Morita, “Defect motion on an InP(110) surface observed with noncontact atomic force microscopy,” Science 270, 1646–1648 (1995).
[CrossRef]

M. Ohta, H. Ueyama, Y. Sugawara, S. Morita, “Contrast of atomic-resolution images from a noncontact ultrahigh-vacuum atomic force microscope,” Jpn. J. Appl. Phys. 34, L1692–L1694 (1995).
[CrossRef]

Vorburger, T. V.

R. A. Dragoset, T. V. Vorburger, “Scanning tunneling microscopy of a diamond-turned surface and a grating replica,” in Metrology: Figure and Finish, B. Truax, ed., Proc. SPIE749, 54–58 (1986).

Wangbo, M.-H.

S. N. Magonov, M.-H. Wangbo, Surface Analysis with STM and AFM—Experimental and Theoretical Aspects of Image Analysis (Verlagsgesellschaft, Weinheim, Germany, 1996); “Interpreting STM and AFM images” Adv. Mater. 6, 355–371 (1994).
[CrossRef]

Wei, J.

J. Yu, L. Hou, J. Wei, J. E. Yao, J. L. Cao, J. Y. Yu, “Scanning tunneling microscope to evaluate supersmooth surface roughness,” in Current Developments in Optical Design and Optical Engineering II, R. E. Fischer, W. J. Smith, eds., Proc. SPIE1752, 123–131 (1992).
[CrossRef]

Weibel, E.

G. Binning, H. Rohrer, Ch. Gerber, E. Weibel, “Surface studies by scanning tunneling microscopy,” Phys. Rev. Lett. 49, 57–61 (1982).
[CrossRef]

Weisenhorn, A. L.

B. Drake, C. B. Prater, A. L. Weisenhorn, S. A. C. Gould, T. R. Albrecht, C. F. Quate, D. S. Cannell, H. G. Hansma, P. K. Hansma, “Imaging crystals, polymers, and processes in water with the atomic force microscope,” Science 243, 1586–1589 (1989).
[CrossRef] [PubMed]

Wells, A. F.

A. F. Wells, Structural Inorganic Chemistry, 5th ed. (Clarendon, Oxford, 1991).

Yao, J. E.

J. Yu, L. Hou, W. Sh. Ma, J. L. Cao, J. Y. Yu, J. E. Yao, “Nanometer characterization of single point diamond-turned mirrors on the micrometer and sub-micrometer scale,” J. Vac. Sci. Technol. B 12, 1835–1838 (1994).
[CrossRef]

J. Yu, L. Hou, J. Wei, J. E. Yao, J. L. Cao, J. Y. Yu, “Scanning tunneling microscope to evaluate supersmooth surface roughness,” in Current Developments in Optical Design and Optical Engineering II, R. E. Fischer, W. J. Smith, eds., Proc. SPIE1752, 123–131 (1992).
[CrossRef]

Yoshida, I.

I. Yoshida, T. Sugita, K. Sasaki, H. Hori, “Studies of cleaved surfaces of phyllo-silicates (talc, phlogopite and muscovite) by using AFM and LEED,” J. Surf. Sci. Soc. Jpn. 17, 30–36 (1996; in Japanese).

T. Sugita, I. Yoshida, “Studies of cleaved surfaces of layered semi-metals, graphite and phyllo-silicates,” J. Surf. Sci. Soc. Jpn. 16, 664–672 (1995; in Japanese).

Young, R. D.

Yu, J.

J. Yu, Y. Namba, “Atomic surface roughness,” Appl. Phys. Lett. 73, 3607–3609 (1998).
[CrossRef]

J. Yu, J. L. Cao, Y. Namba, Y. Y. Ma, “Surface roughness characterization of soft x-ray multilayer films on the nanometer scale,” J. Vac. Sci. Technol. B 14, 42–47 (1996).
[CrossRef]

J. Yu, L. Hou, W. Sh. Ma, J. L. Cao, J. Y. Yu, J. E. Yao, “Nanometer characterization of single point diamond-turned mirrors on the micrometer and sub-micrometer scale,” J. Vac. Sci. Technol. B 12, 1835–1838 (1994).
[CrossRef]

J. Yu, L. Hou, J. Wei, J. E. Yao, J. L. Cao, J. Y. Yu, “Scanning tunneling microscope to evaluate supersmooth surface roughness,” in Current Developments in Optical Design and Optical Engineering II, R. E. Fischer, W. J. Smith, eds., Proc. SPIE1752, 123–131 (1992).
[CrossRef]

Yu, J. Y.

J. Yu, L. Hou, W. Sh. Ma, J. L. Cao, J. Y. Yu, J. E. Yao, “Nanometer characterization of single point diamond-turned mirrors on the micrometer and sub-micrometer scale,” J. Vac. Sci. Technol. B 12, 1835–1838 (1994).
[CrossRef]

J. Yu, L. Hou, J. Wei, J. E. Yao, J. L. Cao, J. Y. Yu, “Scanning tunneling microscope to evaluate supersmooth surface roughness,” in Current Developments in Optical Design and Optical Engineering II, R. E. Fischer, W. J. Smith, eds., Proc. SPIE1752, 123–131 (1992).
[CrossRef]

Acta Crystallogr. A (2)

R. D. Shannon, C. T. Prewitt, “Effective ionic radii in oxides and fluorides,” Acta Crystallogr. A 25, 925–946 (1969).

R. D. Shannon, “Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides,” Acta Crystallogr. A 32, 751–767 (1976).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

J. Yu, Y. Namba, “Atomic surface roughness,” Appl. Phys. Lett. 73, 3607–3609 (1998).
[CrossRef]

Geochem. Cosmochim. Acta (1)

L. H. Ahrens, “The use of ionization potentials,” Geochem. Cosmochim. Acta 2, 155–169 (1952).
[CrossRef]

J. Appl. Phys. (1)

J. E. Griffith, D. A. Grigg, “Dimensional metrology with scanning probe microscopes,” J. Appl. Phys. 74, R83–R109 (1993).
[CrossRef]

J. Electrochem. Soc. (1)

J. Nishizawa, “Molecular layer epitaxy,” J. Electrochem. Soc. 132, 1197–1200 (1985).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Surf. Sci. Soc. Jpn. (2)

T. Sugita, I. Yoshida, “Studies of cleaved surfaces of layered semi-metals, graphite and phyllo-silicates,” J. Surf. Sci. Soc. Jpn. 16, 664–672 (1995; in Japanese).

I. Yoshida, T. Sugita, K. Sasaki, H. Hori, “Studies of cleaved surfaces of phyllo-silicates (talc, phlogopite and muscovite) by using AFM and LEED,” J. Surf. Sci. Soc. Jpn. 17, 30–36 (1996; in Japanese).

J. Vac. Sci. Technol. B (3)

J. Yu, J. L. Cao, Y. Namba, Y. Y. Ma, “Surface roughness characterization of soft x-ray multilayer films on the nanometer scale,” J. Vac. Sci. Technol. B 14, 42–47 (1996).
[CrossRef]

Y. Aoyagi, “Atomic-layer growth of GaAs by modulated-continuous-wave laser metalorganic vapor-phase epitaxy,” J. Vac. Sci. Technol. B 5, 1460–1464 (1987).
[CrossRef]

J. Yu, L. Hou, W. Sh. Ma, J. L. Cao, J. Y. Yu, J. E. Yao, “Nanometer characterization of single point diamond-turned mirrors on the micrometer and sub-micrometer scale,” J. Vac. Sci. Technol. B 12, 1835–1838 (1994).
[CrossRef]

Jpn. J. Appl. Phys. (4)

M. Ohta, Y. Sugawara, K. Hontani, S. Morita, F. Osaka, M. Suzuki, H. Nagaoka, S. Mishima, T. Okada, “Atomically resolved image of cleaved GaAs (110) surface observed with an ultrahigh vacuum atomic force microscope,” Jpn. J. Appl. Phys. 33, L52–L54 (1994).
[CrossRef]

M. Ohta, H. Ueyama, Y. Sugawara, S. Morita, “Contrast of atomic-resolution images from a noncontact ultrahigh-vacuum atomic force microscope,” Jpn. J. Appl. Phys. 34, L1692–L1694 (1995).
[CrossRef]

Y. Sugawara, M. Ohta, H. Ueyama, S. Morita, “Atomic-resolution imaging of ZnSSe (110) surface with ultrahigh-vacuum atomic force microscope (UHV-AFM),” Jpn. J. Appl. Phys. 34, L462–L464 (1995).
[CrossRef]

F. J. Giessibl, “Atomic force microscopy in ultrahigh vacuum,” Jpn. J. Appl. Phys. 33, 3726–3734 (1994).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

J. Tersoff, D. R. Hamann, “Theory of the scanning tunneling microscope,” Phys. Rev. 31, 805–813 (1985).
[CrossRef]

Phys. Rev. Lett. (2)

G. Binning, H. Rohrer, Ch. Gerber, E. Weibel, “Surface studies by scanning tunneling microscopy,” Phys. Rev. Lett. 49, 57–61 (1982).
[CrossRef]

G. Binning, C. F. Quate, Ch. Gerber, “Atomic force microscope,” Phys. Rev. Lett. 56, 930–933 (1986).
[CrossRef]

Science (3)

F. Ohnesorge, G. Binning, “True atomic resolution by atomic force microscopy through repulsive and attractive forces,” Science 260, 1451–1456 (1993).
[CrossRef] [PubMed]

Y. Sugawara, M. Ohta, H. Ueyama, S. Morita, “Defect motion on an InP(110) surface observed with noncontact atomic force microscopy,” Science 270, 1646–1648 (1995).
[CrossRef]

B. Drake, C. B. Prater, A. L. Weisenhorn, S. A. C. Gould, T. R. Albrecht, C. F. Quate, D. S. Cannell, H. G. Hansma, P. K. Hansma, “Imaging crystals, polymers, and processes in water with the atomic force microscope,” Science 243, 1586–1589 (1989).
[CrossRef] [PubMed]

Thin Solid Films (1)

T. Suntola, “Atomic layer epitaxy,” Thin Solid Films 216, 84–89 (1992).
[CrossRef]

Ultramicroscopy (1)

G. Bining, “Force microscopy,” Ultramicroscopy 42–44, 7–15 (1992).
[CrossRef]

Other (15)

S. N. Magonov, M.-H. Wangbo, Surface Analysis with STM and AFM—Experimental and Theoretical Aspects of Image Analysis (Verlagsgesellschaft, Weinheim, Germany, 1996); “Interpreting STM and AFM images” Adv. Mater. 6, 355–371 (1994).
[CrossRef]

J. S. Bendat, A. G. Piersol, Random Data: Analysis and Measurement Procedures (Wiley-Interscience, New York, 1971).

Technical Committee ISO/TC 57, International Standard ISO 4287/1, “Surface roughness—terminology. 1. Surface and its parameters,” (Geneva, Switzerland1984).

R. Howland, L. Benatar, Practical Guide to Scanning Probe Microscopy (Park Scientific Instruments, Sunnyvale, Calif., 1993–1996).

J. Yu, L. Hou, J. Wei, J. E. Yao, J. L. Cao, J. Y. Yu, “Scanning tunneling microscope to evaluate supersmooth surface roughness,” in Current Developments in Optical Design and Optical Engineering II, R. E. Fischer, W. J. Smith, eds., Proc. SPIE1752, 123–131 (1992).
[CrossRef]

A. S. Povarennykh, Crystal Chemical Classification of Minerals, J. E. S. Bradley, transl. (Plenum, New York, 1972), Vol. 1, p. 42.

C. Klein, C. S. Hurlbut, Manual of Mineralogy, 21st ed. (Wiley, New York, 1993).

A. F. Wells, Structural Inorganic Chemistry, 5th ed. (Clarendon, Oxford, 1991).

R. A. Dragoset, T. V. Vorburger, “Scanning tunneling microscopy of a diamond-turned surface and a grating replica,” in Metrology: Figure and Finish, B. Truax, ed., Proc. SPIE749, 54–58 (1986).

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering, 2nd ed. (Optical Society of America, Washington, D.C., 1999).

L. Pauling, The Nature of the Chemical Bond, 3rd ed. (Cornell U. Press, Ithaca, N.Y., 1960).

H. J. Nussbaumer, Fast Fourier Transform and Convolution Algorithms (Springer-Verlag, Berlin, 1982); R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1986).
[CrossRef]

R. E. Grim, Clay Mineralogy, 2nd ed. (McGraw-Hill, New York, 1968).

Seiko Instruments, Inc., 1-8 Nakase, Mihama-ku, Chiba-shi, Chiba 261, Japan.

Olympus Optical Company, Ltd., 2-43-2 Hatagaya Shibuyaku, Tokyo 151, Japan; web site: http://www.olympus.co.jp .

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Figures (8)

Fig. 1
Fig. 1

Schematic illustration of interatomic interaction for (a) a STM and (b) a AFM.

Fig. 2
Fig. 2

Simulated atomic topography for (a) λ1 = λ2 and (b) λ1 > λ2, where λ1 and λ2 are the spatial wavelengths along the x and y axes, respectively.

Fig. 3
Fig. 3

Change in three-dimensional rms ionic surface roughness as a function of coordination number for selected cations.

Fig. 4
Fig. 4

(a) Close-packing representation of a SiO4 tetrahedron. (b) The fundamental unit on which the structure of all silicates is based consists of four O2- ions at the apexes of a regular tetrahedron, surrounding and coordinated by one Si4+ ion at the center. (c) Formation of phyllosilicates. Three of the oxygen atoms of a tetrahedron are shared with the adjoining tetrahedron; infinite flat sheets are formed of unit composition Si2O5. (Redrawn from Ref. 17.)

Fig. 5
Fig. 5

Schematic diagram (based on the research of Klein and Hurlbut17 and Grim35) of the structures and compositions of mica. (a) Basic structures are built from one octahedral and two tetrahedral sheets, giving T–O–T layers. (b) Development from phyllosilicate structures to mica structure. Aluminum substitutes for every fourth silicon atom, and a charge of significant magnitude is produced to bind univalent K+ cations in 12-coordination to T–O–T layers.

Fig. 6
Fig. 6

Two possible ways to obtain atomic structure from the cleavage of mica.20,21 (a) K+ ions are removed with the upper T–O–T layer, forming an equilateral-triangle–hexagonal ring arrangement. The equilateral triangle is 2.8 Å on a side. (b) K+ ions are left on the lower T–O–T layer in a hexagonal system separated by 5.2 Å.

Fig. 7
Fig. 7

(a) AFM image of the mica cleavage (top view) with a gray scale to indicate the range of surface heights. The nearly hexagonal array of light spots corresponds to the hexagonal rings of K+ ions in the cleavage plane shown in Fig. 6. (b) A–A profile with a spatial wavelength of 5.2 Å cut along the two adjacent apexes of K+ ions [see the A–A line in (a)]. (c) B–B profile with a spatial wavelength of 6.2 Å cut along the two separate apexes of K+ ions [see the B–B line in (a)].

Fig. 8
Fig. 8

AFM topographic maps of atomic structure on the mica cleavage: (a) 1.5 nm × 1.5 nm, (b) 3.0 nm × 3.0 nm, (c) 6.0 nm × 6.0 nm.

Tables (6)

Tables Icon

Table 1 Calculated Three-Dimensional rms Atomic Surface Roughnesses (in Å) for Pure-Metal Crystalsa

Tables Icon

Table 2 Calculated Three-Dimensional rms Atomic Surface Roughnesses (Å) for Several Common Ionic Crystalsa

Tables Icon

Table 3 Calculated Two-Dimensional rms Atomic Surface Roughnesses (Å) for Pure-Metal Crystalsa

Tables Icon

Table 4 Calculated Two-Dimensional rms Atomic Surface Roughnesses (Å) for Several Common Ionic Crystalsa

Tables Icon

Table 5 Theoretical and Measured Values of the Two-Dimensional Roughnesses for σ, R a , and P-V Along Apexes of K+ Ions for Mica Cleavage

Tables Icon

Table 6 Theoretical and Measured Values of the Three-Dimensional Roughnesses for σ, R a , and P-V for Mica Cleavage

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

zx=r2 sin2πλ x,
zx, y=r2 sin2πλ1 xsin2πλ2 y,
σ=1L0L z2xdx1/2,
Ra=1L0L |zx|dx.
P-V=maxzx-minzx.
σ=1nλ0nλr2 sin2πλ x2dx1/2=122 r.
Ra=1nλ0nλr2 sin2πλ xdx=1π r.
P-V=r.
σ:Ra:P-V=122 r:1π r:r=0.35:0.32:1.
σ=1SS Z2x, ydxdy1/2
Ra=1SS |zx, y|dxdy,
P-V=maxzx, y-minzx, y.
σ=1nλ1nλ2Sr2 sin2πλ1 xsin2πλ2 y2dxdy1/2=1nλ1nλ2r220nλ1 sin2πλ1 xdx×0nλ2 sin2πλ2 ydy1/2=14 r.
Ra=1nλ1nλ2Sr2 sin2πλ1 xsin2πλ2 ydxdy=1nλ1nλ2r20nλ1sin2πλ1 xdx 0nλ2sin2πλ2 ydy=2π2 r.
P-V=r.
σ:Ra:P-V=14 r:2π2 r:r=0.25:0.20:1.

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