VOLUME 44, +UMBER 22 PHYSICAL REVIEW LETTERS 2 JUNE 1980 dominant mechanisms causing a temperature- dependent resistivity between 1 to 5 'K. The cal- culated magnitudes of the electron-phonon scat- tering are too small to explain our data, and are without a mobility dependence. Their contribu- tions to our high-mobility samples may have pro- duced the curvature of p vs &, but theory predicts negligible contributions even in these cases. The anomalous scattering suggested by Kawaji' and also localization effects" will give a temperature dependence ™ 1n(1/&), which may also have con- tributed to this curvature. The effects of analyz- ing the data with such additional terms have been estimated and do not change our conclusions. Any observed effect attributed only to electron- phonon scattering should be shown to be independ- ent of mobility. The authors are indebted to Dr. Frank Stern for the identification and formulation of the es- sential physics in this problem. We are also grateful to Mr. Stanley Mroczkowski, Mr. Theo- dore Sabety, and Mr. Atul Goel for fabricating the devices, and to Dr. A. B. Fowler for informa- tive discussions. This research was supported in part by the U. S. Office of Naval Research un- der Grant No. N00014-76-C-1083. 'F. Stern, Crit. Rev. Solid State Sci. 4, 499 (1974). 2K. M; Cham and R. G. Wheeler, in Proceedings of the Third International Conference on Electronic Prop- erties of Two-Dimensional Systems, Lake Yamanaka, Japan, September, 1979 (to be published). 3Y. Kawaguchi and S. Kawaji, in Proceedings of the Third International Conference on Electronic Proper- ties of the Two-Dimensional Systems, Lake Yamanaka, Japan, September, 1979 {to be published). 4A. Hartstein, A. B. Fowler, and M. Albert, in Proceedings of the Third International Conference on Electronic Properties of the Two-Dimerisional Systems, Lake Yamanaka, Japan, September, 1979 (to be pub- lished). 'F. Stern, preceding Letter I. Phys. Rev. Lett. 44, 1469 (1980)] . F. Stern and W. E. Howard, Phys. Rev. 163, 816 (1967). 7P. F. Maldague, Surf. Sci. 73, 296 (1978). BH. Ezawa, S. Kawaji, T. Kuroda, and K. Nakamura, Surf. Sci. 24, 669 (1971). ~H. Ezawa, T. Kuroda, and K. Nakamura, Surf. Sci. 24, 654 (1971). Y. Matsumoto and Y. Uemura, Jpn. J. Appl. Phys. Supp1. 2, Pt. 2, 367 (1974). "E. Abrahams, 0. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 {1979) . Classical Local-Field Eff'ect in Reflectance from Adsorbed Overlayers Amitabha Bagehi and Ruben G. Barrera' Department of Physics and Astronomy, University of Maryland, College Park, 3faryland 20742 Basab B. Dasgupta Department of Physics, University of Wisconsin Parkside, -Xenosha, Wisconsin 53141 (Received 22 February 1980) The role of the local-field effect in differential reflectance spectroscopy is studied within a classical model for an ordered overlayer of a weakly adsorbed species on a metal substrate. Results for Ar on Al at two coverages strongly indicate the importance of the local-field effect in such optical studies. PACS numbers: 78.20. Dj, 73.60.Hy There has been a great deal of interest in re- cent years in the use of differential-ref lectivity methods to study the electronic properties of ad- sorbed objects on a variety of substrates. In par- ticular, experiments have been reported" on dif- ferential reflectance spectra from rare-gas atoms adsorbed on metallic and oxide surfaces down to submonolayer coverages. In this paper we report on the first quantitative and detailed study of the classical local-field effect in such systems, and its possible implications for the measurement of optical reflectance. Our results, showing a strik- ing correlation with experiments, suggest that the local-field effect is indeed quite important in surf ace reflectance spectroscopy. Although no systematic study of the role of the local-field ef- fect in this problem has been attempted in the past, ideas rather similar to ours have appeared 1980 The American Physical Society 1475