time was 20 min. The full pattern covers an area of about With additional enhancements of this technique, further 100 um X200 um, and is quite uniform across the entire applications can be envisioned. Elimination or removal of area. The lattice constant of the pattern, A/2 or 212. 78 nm, the background will result in the creation of an array of iso- was considered to be known more accurately than the hori- lated nanoscale metal dots on a surface. These could be used zontal calibration of the AFM, so this value was used to put to study, e.g., transport phenomena, or quantum dot effects if the horizontal dimensions of the image on an absolute scale. fabricated on a semiconductor. Further, they could be used as Also shown in Fig. 2 are two line scans, showing the an etch mask to transfer the pattern to a substrate material shape of the features in two directions. These line scans have allowing extension of the fabrication techniques to other ma- been put on a true vertical scale, including the background terials. Improvement of the resolution, which should be pos- level, by normalizing the surface topography to the average sible down to the 10 nm level, could lead to the possibility of deposition thickness of 20 nm, estimated (with an accuracy scanning the substrate during deposition, creating almost any of about +5 nm)from previous characterizations of the desired pattern, replicated within each unit cell of the lattice deposition rate. Line scans such as the ones depicted in Fig. across the substrate. Furthermore, the interference of many 2 and others taken at a variety of locations on the sample standing waves incident from a range of angles with con- indicate that(without correction for AFM tip shape)the fea- trolled phase could be used to generate more complex pat- tures are 13+1 nm high, and have a full-width at half maxi- terns mum of 80+10 nm. The cause of the slight asymmetry in This work is supported in part by the Technology Ad line scan A-A is unknown, though we believe it to be an ministration of the U.s. Department of Commerce, and by AFM artifact the National Science Foundation under grant no. PhY As the line scans indicate, the regions between the fea- 9312572 Z.J. J acknowledges support of a National Re- tures are also covered with chromium. This background is a search Council postdoctoral fellowship result of other isotopes in the atomic beam which are not affected by the laser light(16% of the atoms), atoms which are transferred to the metastable D-state during the optical G. Timp, R. E Behringer, D. M. Tennant, J E. Cunningham, M. Prentiss, collimation step(an estimated 7% of the atoms), and atom and K. K Berggren, Phys. Rev. Lett. 69, 1636(1992) 2J. J. McClelland, R. E. Scholten, E. C. Palm, and R.J. Celotta, Science that are in the high velocity tail of the Maxwell-Boltzmann 62,877(1993) velocity distribution emerging from the chromium evapora- R.E. Scholten, J.J. McClelland, E C Palm, A. Gavrin, and R J. Celotta, tion source. Scan B-B appears to have a slightly higher See, e. g, Electron-beam, X-ray and lonbeam Sub-i reter Lithogra background level, arising we believe because it samples the phies for Maniyfactuiring I, SPIE Proc. Vol. 1671, edited by M. Peckerar saddle regions of the standing wave, while a -A' samples the (SPIE, Bellingham, WA, 1992) true nodes SR E. Scholten, R. Gupta, J. J. McClelland, and R. J. Celotta(to be pub. Various mechanisms could be implemented to reduce the 6]. P. Gordon and A Ashkin, Phys. Rev.A21,1606(1980);JDalibard and ackground seen in Fig. 2, if desired. For example, the un- C. Cohen-Tannoudji, J. Opt. Soc. Am. B 2, 1707(1985) high velocity atoms, could be removed from the beam by a waves E+=(iE +yE2)e kr-ur E-r-(Ei+ye)e-f(lr+ ung desirable isotopes and D-level atoms, as well as some of the The net electric field can be determined by combining the four trave laser deflection process. Alternatively, it is possible that a E+,-(rEtie)e uniform etch of the chromium surface as deposited could El and E, are the complex electric field amplitudes determining the mag- nitude and polarization state of a wave traveling in the +i-direction, E3 remove the background before eliminating the features com- and E4 are the corresponding amplitudes for a wave traveling in the pletely +y-direction, and d is the relative temporal phase for the two waves. See, This work demonstrates that laser-focused atomic depo- e.g, J D. Jackson, Classical Electrodynamics, 2nd ed (Wiley, New York, sition can be successfully used to create a uniform, two-$AHemmerich,D.Schropp, Jr,and TWHansch,Phys.Rev.A44,1910 1975),pp.273f dimensional nanometer-scale pattern on a substrate. In its current form, the pattern shown in Fig. 2 could prove ex- G Grynberg, B. Lounis, P Verkerk, J-Y. Courtois, and C Salomon, Phys tremely useful as a calibration standard on the nanometer Rev.LeL70,2249(1993) J.J. McClelland, J. Opt. Soc. Am. B(in press) scale. The features represent essentially a"contact print"of fonogi the variation can be as much as a factor of 28.See, e.,VG a light wave the wavelength of which is tuned with ex Minogin and V.S. Letokhov, Laser Light Pressure on Atoms( Gordon and tremely high precision to an atomic resonance whose fre Breach, New York, 1987) quency is know with very high accuracy(about I ppm). Uncertainty estimates quoted in this paper are to be interpreted as one Thus, within the limits of some geometrical corrections that standard deviation combined random and systematic uncertainties unless can be kept very small (of order 10 ppm or less), the lattice uN. 1. Maluf, S. Y Chou, J. P McVittie, S. w.J. Kuan,. R. Allee, andR. F spacing accuracy is extremely high W. Pease, J. Vac. Sci. Technol. B 7, 1497(1989) 1380 Appl. Phys. Lett., Vol. 67, No. 10, 4 September 1995 Gupta et al Downloaded-v14-may-2008to7222.29.123.220.-redIstributionsubjecttoaip-licenseoncopyright;seehttp:/lapl.aiporglapl/copyrightjsptime was 20 min. The full pattern covers an area of about 100 mm3200 mm, and is quite uniform across the entire area. The lattice constant of the pattern, l/2 or 212.78 nm, was considered to be known more accurately than the hori￾zontal calibration of the AFM, so this value was used to put the horizontal dimensions of the image on an absolute scale. Also shown in Fig. 2 are two line scans, showing the shape of the features in two directions. These line scans have been put on a true vertical scale, including the background level, by normalizing the surface topography to the average deposition thickness of 20 nm, estimated ~with an accuracy of about 65 nm! from previous characterizations of the deposition rate. Line scans such as the ones depicted in Fig. 2 and others taken at a variety of locations on the sample indicate that ~without correction for AFM tip shape! the fea￾tures are 1361 nm high, and have a full-width at half maxi￾mum of 80610 nm. The cause of the slight asymmetry in line scan A–A8 is unknown, though we believe it to be an AFM artifact. As the line scans indicate, the regions between the fea￾tures are also covered with chromium. This background is a result of other isotopes in the atomic beam which are not affected by the laser light ~16% of the atoms!, atoms which are transferred to the metastable D-state during the optical collimation step ~an estimated 7% of the atoms!, and atoms that are in the high velocity tail of the Maxwell-Boltzmann velocity distribution emerging from the chromium evapora￾tion source. Scan B–B8 appears to have a slightly higher background level, arising we believe because it samples the saddle regions of the standing wave, while A–A8 samples the true nodes. Various mechanisms could be implemented to reduce the background seen in Fig. 2, if desired. For example, the un￾desirable isotopes and D-level atoms, as well as some of the high velocity atoms, could be removed from the beam by a laser deflection process. Alternatively, it is possible that a uniform etch of the chromium surface as deposited could remove the background before eliminating the features com￾pletely. This work demonstrates that laser-focused atomic depo￾sition can be successfully used to create a uniform, two￾dimensional nanometer-scale pattern on a substrate. In its current form, the pattern shown in Fig. 2 could prove ex￾tremely useful as a calibration standard on the nanometer scale. The features represent essentially a ‘‘contact print’’ of a light wave, the wavelength of which is tuned with ex￾tremely high precision to an atomic resonance whose fre￾quency is know with very high accuracy ~about 1 ppm!. Thus, within the limits of some geometrical corrections that can be kept very small ~of order 10 ppm or less!, the lattice spacing accuracy is extremely high. With additional enhancements of this technique, further applications can be envisioned. Elimination or removal of the background will result in the creation of an array of iso￾lated nanoscale metal dots on a surface. These could be used to study, e.g., transport phenomena, or quantum dot effects if fabricated on a semiconductor. Further, they could be used as an etch mask13 to transfer the pattern to a substrate material, allowing extension of the fabrication techniques to other ma￾terials. Improvement of the resolution, which should be pos￾sible down to the 10 nm level, could lead to the possibility of scanning the substrate during deposition, creating almost any desired pattern, replicated within each unit cell of the lattice across the substrate. Furthermore, the interference of many standing waves incident from a range of angles with con￾trolled phase could be used to generate more complex pat￾terns. This work is supported in part by the Technology Ad￾ministration of the U. S. Department of Commerce, and by the National Science Foundation under Grant no. PHY– 9312572. Z. J. J. acknowledges support of a National Re￾search Council postdoctoral fellowship. 1G. Timp, R. E. Behringer, D. M. Tennant, J. E. Cunningham, M. Prentiss, and K. K. Berggren, Phys. Rev. Lett. 69, 1636 ~1992!. 2 J. J. McClelland, R. E. Scholten, E. C. Palm, and R. J. Celotta, Science 262, 877 ~1993!. 3R. E. Scholten, J. J. McClelland, E. C. Palm, A. Gavrin, and R. J. Celotta, J. Vac. Sci. Technol. B 12, 1847 ~1994!. 4See, e.g., Electron-beam, X-ray and Ion-beam Sub-micrometer Lithogra￾phies for Manufacturing II, SPIE Proc. Vol. 1671, edited by M. Peckerar ~SPIE, Bellingham, WA, 1992!. 5R. E. Scholten, R. Gupta, J. J. McClelland, and R. J. Celotta ~to be pub￾lished!. 6 J. P. Gordon and A. Ashkin, Phys. Rev. A 21, 1606 ~1980!; J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 2, 1707 ~1985!. 7The net electric field can be determined by combining the four traveling waves E1x5(zˆE11yˆE2)ei(kx2vt) , E2x52(zˆE11yˆE2)e2i(kx1vt) , E1y5(xˆE31zˆE4)ei(ky2vt1f) , E2y52(xˆE31zˆE4)e2i(ky1vt2f) , where E1 and E2 are the complex electric field amplitudes determining the mag￾nitude and polarization state of a wave traveling in the 1xˆ-direction, E3 and E4 are the corresponding amplitudes for a wave traveling in the 1yˆ-direction, and f is the relative temporal phase for the two waves. See, e.g., J. D. Jackson, Classical Electrodynamics, 2nd ed. ~Wiley, New York, 1975!, pp. 273 ff. 8A. Hemmerich, D. Schropp, Jr., and T. W. Ha¨nsch, Phys. Rev. A 44, 1910 ~1991!. 9G. Grynberg, B. Lounis, P. Verkerk, J.-Y. Courtois, and C. Salomon, Phys. Rev. Lett. 70, 2249 ~1993!. 10 J. J. McClelland, J. Opt. Soc. Am. B ~in press!. 11For Cr, the variation can be as much as a factor of 28. See, e.g., V. G. Minogin and V. S. Letokhov, Laser Light Pressure on Atoms ~Gordon and Breach, New York, 1987!. 12Uncertainty estimates quoted in this paper are to be interpreted as one standard deviation combined random and systematic uncertainties unless otherwise indicated. 13N. I. Maluf, S. Y. Chou, J. P. McVittie, S. W. J. Kuan, . R. Allee, and R. F. W. Pease, J. Vac. Sci. Technol. B 7, 1497 ~1989!. 1380 Appl. Phys. Lett., Vol. 67, No. 10, 4 September 1995 Gupta et al. Downloaded¬14¬May¬2008¬to¬222.29.123.220.¬Redistribution¬subject¬to¬AIP¬license¬or¬copyright;¬see¬http://apl.aip.org/apl/copyright.jsp