PHYSICAL REVIEW A VOLUME 26. NUMBER 1 JULY 1982 Transmissionof 1 6-keV positrons through thin metal films Allen P. Mills, Jr. and RobertJ. Wilson Bell Laboratories, Murray Hill, NewJersey 07974 (Received 4 November 1980) We report measurements of the transmission of 1-6-keV energy positrons through films of AI, Cu, and Si up to 3000 A thick. Whenthe thickness is expressed in termsof mass per unit area,the transmission of Cu and Al is found to be the same within :t 10%. Within a :t20% precision we observe no effect having to do with the crystallinity of the materials. The median penetration depth of positrons in Al and Cu is found to vary with the energy E as E", with n = 1.60~g:A~ and 1.43~g:?I, respectively. Our measured median penetration depthsare significantly lessthan one would have expected from the calculation of Niem- inen and Oliva [R. M. Nieminenand J. Oliva, Phys.Rev. B 2.2,2226 (1980)] which seems to indicatethe importance of large-angle scattering effects. Our measurements canbecom- binedwith independent measurements of the energy dependence of the yield of positronium at a surface[K. G. Lynn, Phys. Rev. Lett. :4.4, 1330(1980) and K. G. Lynn and D. O. Welch,Phys.Rev. B 2b 99 (1980)] to obtain values for the positrondiffusion constant D+ in single-crystal metal samples.For example, we find D+(Al)=(O. 76:t0.14) cm2sec-1 and D+(Cu)=(1.06:t0.20) cm2sec-l. The former is in agreement with the deformation- potentialcalculationof Bergersen et al. [B. Bergersen, E. Pajanne, P. Kubica, M. J. Stott, and C. H. Hodges, Solid StateCommun. u. 1377 (1974)] if the positroneffectivemass in Al is m + = ( 1.59 :to. 12 )m.. Finally, we use our measurements to calculate the optimum thickness of transmitting positronmoderators for enhancing the brightness of slow positron beams. I. INTRODUCTION of the transmission probability for 1-6-keV energy positronsincident on thin films of AI, Cu, and Si. Beforepresenting the measurements, we must first ask if it is sensible to speak of positrons "stopping" in a metal. According to the calculations of Niem- inen and Oliva16 the rate of energyloss of a posi- tron in Al is dE/dt:==:;2X 1017(E/l000 eV)-1/2 eVsec-1 for E> 1000eV and reaches a maximum value of dE/dt:=::3X 1017 eVsec-1 at E:=:: 100eV. The total path length -1 E 6.s=fEmax dE dt (2E 1m )1/2dE (1) miD for positrons slowingdown from an energy E max to an energy Emin is roughly As = 500A(Emax/lOOOeVj2 (2) for Emin:==: 100 eV. While the positron is traveling along its path it will change its momentum as well as its energy, so ~ is an upper bound on how far the positron moves through the solid. At low ener- gies E < 30 eV, the energy loss rate is approximately Low-energy positions which havebeen implanted into a solid target in vacuum form a unique and sensitive probeof the surface regions of the solid.I,2 The positrons which diffuse to the surface may ei- ther become bound in the "image potential" well just outside the surface3-IO or be ejected into the vacuum as free positrons6 or positronium.7,11 The relative likelihood of these three channels is sensi- tive to submonolayer surface contamination and the branching ratios may be found, for example, from measurements of the energy spectrum of the annihi- lation y rays. On the other hand, the probability L (E) of a positron reaching the surface after being implanted with energyE depends on the positron diffusion constantD + and annihilation rate Yb in the bulk solid, the rate of trapping of positronsat crystalline defects y" and the depth profile p(x,E) of the positrons just after they stop in the solid.7,12-16 Information aboutthe parameters D+, Yb,and y, and their possible variation with depthx may be obtained from measurements of L (E) if the depthprofile is known. In order to obtain information about how posi- trons stop in a metal, we havemademeasurements 26 490