Median implantation depth and implantation profile of 3–18 keV positrons in amorphous polymers

Abstract

Most applications of positron beams require knowledge of the implantation characteristics for an appropriate interpretation of the experimental data. In this work, the median implantation depth as a function of implantation energy, z 1/2 (E), of 3-18 keV positrons and their implantation profile P(z,E) in a total of 13 thin films of atactic polystyrene, poly͑styrene-co-acrylonitrile͒, and polymethylmethacrylate spin coated onto a silicon substrate were determined from positron lifetime measurements using a pulsed, low-energy positron beam. z 1/2 (E) and P(z,E) were determined from the measurement of the ortho-positronium yield obtained from the intensity I 3 of the long lifetime. z 1/2 (E) was parametrized with the commonly used power-law fit z 1/2 (E) ϭ(A/)E n , with and E in units of g cm Ϫ3 and keV, respectively, yielding Aϭ2.81(Ϯ0.2) g cm Ϫ2 and n ϭ1.71(Ϯ0.05). Excellent agreement between amorphous polymer and literature data on Al and Cu suggests that the median implantation depth of positrons for low-to medium-Z materials in the studied energy range is independent of structure and only a function of mass density. Fitting of the Makhovian implantation profile to the experimental data suggested that the value of the parameter m varies between 1.7 and 2.3, systematically increasing with z at constant implantation energy, but is independent of the implantation energy. Using an equation proposed by Baker et al., the experimental data of 12 of the 13 studied polymer films could be described with a slightly better agreement than the Makhovian equation.

Experimental progress in positronium laser physics

“…This renders them difficult to produce and fragile. Moreover, they are intrinsically inefficient compared to reflection geometries because the stopping profile of a positron beam will follow a Mahkovian like distribution [252,306,307] and it is not generally possible to implant positrons in such a way that more than half of the beam will cross the exit surface. Some transmission targets have been demonstrated.…”

“…For Ps atoms produced in porous silica targets the emission rate into vacuum (where the density will be significantly reduced) is expected to be on the order of 100 MHz [126], and thus we might expect that the Ps-Ps scattering rate must be similar to this in order for such interactions to take place; this implies Ps densities of 10 16 cm −3 . For positrons implanted into porous silica targets the resulting Ps density can be estimated using Mahkovian stopping profiles [306,307], and by considering Ps emission rates [126]. Typical parameters in the high-density experiments [288,290,362] were a stopping distance of ≈100 nm, and a beam areal density up to 10 × 10 10 cm s −1 , leading to instantaneous Ps densities approaching the required …”

Positronium formation via excitonlike states on Si and Ge surfaces

“…We show here that e-h formation by the slowing down of the incident positrons may also populate the same electronic states, and that as a result the amount of Ps emitted from a pSi surface depends on the incident positron beam characteristics in an unusual way. That is, while the Ps fraction usually depends on the beam energy only via the positron implantation depth (and subsequent diffusion back to the surface [39,40]), in the case of p-Si this dependence is modified to reflect the formation of e-h pairs, which will increase in number with the beam energy, but at the same time tend to decrease in effectiveness due to the lateral spreading associated with diffusion to the surface from increasing depths. Moreover, if the positron beam density is high enough then e-h pairs produced by one positron may affect the rate at which another positron is able to form Ps, resulting in a Ps fraction that depends on the beam density.…”

Reseaching the PVT properties and gradient energy coefficient with different parameters of Polystyrene (PS910

“…(14)- (15), we can determine the scaling parameters, , , P V T    , and the structural parameter 3c/s, which can be obtained by superimposing experimental P-V-T data on the theoretical , , P V T surface. Having these parameters at hand, we can compute the hole fraction, h(V,T)=1-y, of the lattice model (as a measure of the free volume [14]). …”

“…These parameters are simultaneity fitting of the density data with the theory using the coupled Eqs. (13)- (14). Table1 shows these computed parameters with the average and maximum relative percentage error in volume given by …”