© 1999 Macmillan Magazines Ltdletters to natureNATURE|VOL 399|24 JUNE 1999|www.nature.com 761interfacial dielectric constant will probably be between that of Si andSiO2. The altered dielectric layers are not accounted for in ourellipsometric measurements, in which we assume that the oxide hasonly the dielectric constant of bulk SiO2. This is probably whyellipsometry has underestimated the width of the oxides in Fig. 3.The probe localization is obtained by constructing a wavepacketwith a transverse momentum spread of more than a reciprocallattice vector, and consequently all electronic momentum informa-tion is lost (as required by the uncertainty principle). Thereforethese evanescent states responsible for tunnelling through the oxideand the states from the extended conduction band are treated on anequal footing, and cannot be separated in such a local measurement.In the simplest model, the silicon wavefunctions decay exponen-tially into the oxide barrier with a decay length for the evanescentstates, l(E), determined by the energy difference between theinterfacial state (E) and the conduction band edge of bulk SiO2,(Ec), as lE~=ÎEc2 E. The tunnelling current depends on theoverlap of the evanescent states from either interface. A satisfactorytunnelling barrier is formed when the oxide thickness t is 6l. Thissets an absolute minimum thickness of tmin 0:7 nm for an idealSiO2gate oxide. Interfacial roughness adds another 6jrto tmin. Thesmallest roughness for our thermally grown oxides was6jr 0:6 nm which puts a lower limit of 1.2 nm on the practicalSiO2gate oxide thickness. The induced gap states also place severeconstraints on the minimum allowed thickness for alternativedielectrics, many of which have large dielectric constants, butreduced bandgaps and hence longer decay lengths. Furthermore,there is the possibility of a reaction between the dielectric and thesilicon substrate to form a silicon oxide interlayer. If the interlayerthickness exceeds 1.3 nm (and a typical native oxide is 2 nm thick),the gate capacitance is less than what could be obtained with a pureSiO2gate oxide. MReceived 20 January; accepted 8 April 1999.1. Semiconductor Industry Association The National Technology Roadmap for Semiconductors 71±81(Sematech, Austin, 1997).2. Timp, G. et al.inIEDM Technical Digest 615±618 (IEDM, San Francisco, 1998).3. Cryot-Lackmann, F. Sur le calcul de la cohesion et de la tension super®cielle des mataux de transitionpar une methode de liasions fortes. J. Phys. Chem. Solids 29, 1235±1243 (1968).4. Ourmazd, A., Taylor, D. W., Rentschler, J. 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Atomic scale observations of metal-induced gap states at {222} MgO/Cu interfaces.Phys. Rev. Lett. 80, 4741±4744 (1998).18. Brown, G. E. Jr, Waychunas, G. A., Stohr, J. & Sette, F. Near-edge structure of oxygen in inorganicoxides: effect of local geometry and cation type. J. Phys. 47, (Colloque C8) 685±689 (1986).19. Wallis, D., Gaskell, P. H. & Brydson, R. Oxygen K near-edge spectra of amorphous silicon suboxides.J. Microsc. 180, 307±312 (1993).20. Zangwill, A. Physics at Surfaces (Cambridge Univ. Press, New York, 1988).Acknowledgements. We thank D. R. Hammann, M. S. Hybertsen, P. Rez, J. Neaton and B. Batlogg fordiscussions, and J. Silcox and M. Thomas for access to the Cornell Center for Materials Research STEM.Funding for the operation and acquisition of the STEM was provided by the NSF. Upgrades were foundedby the US Air Force Of®ce of Scienti®c Research. The X-ray diffraction was performed on X16B at theNational Synchrotron Light Source.Correspondence and requests for materials should be addressed to D.A.M. (e-mail: [email protected]).Molecular mechanistic originof the toughness ofnatural adhesives, ®bresand compositesBettye L. Smith*², Tilman E. SchaÈffer³², Mario Viani*,James B. Thompson*, Neil A. Frederick*, Johannes Kindt*,Angela Belcher§, Galen D. Stuckyk, Daniel E. Morse¶& Paul K. Hansma** Department of Physics, k Department of Chemistry and Materials, and¶ Department of Molecular, Cellular, and Developmental Biology,University of California at Santa Barbara, California 93106, USA³Department of Molecular Biology, Max-Planck-Institute for BiophysicalChemistry, 37070 GoÈttingen, Germany§ Department of Chemistry, The University of Texas at Austin, Austin,Texas 78712, USA²These authors contributed equally to this work.........................................................................................................................Natural