Handbook of Modern Coating Technologies

Measuring techniques

By analogy with the usual technique with foil sources, for slow positrons, the method of measuring Doppler broadening can be applied. Outside the sample chamber, a Ge detector is installed next to the sample. Since the energy of annihilation radiation is sufficient for Y-rays to span a thin stainless steel wall, it becomes possible to measure Doppler broaden­ing. As explained earlier in Section 5.3, to identify defects and measure the concentration of defects, you can use the line shape parameters S and W. Depending on the depth of positron implantation (positron beam energy), these annihilation parameters are measured in a slow positron system. Another advantage of a system with a slow positron beam, in addition to sensitivity to depth, is the quality of the Doppler broadening of the annihilation peak because, in such a geometry of the experiment, neither Compton nor other background radi­ation is superimposed on the peak, because the spectral background is not affected by the generation of Y-rays in the source. In addition, the contribution of the positron source, which is present due to annihilation in the source foil in conventional technology, is absent in the Doppler spectrum.

The estimation of positron lifetime is a more suitable tool for the identification of valence orbitals of various types of defects and determination of their concentration than the Doppler broadening measuring technique. In a system with a slow positron beam, the regu­lar setup with start and stop detectors cannot be used as the source of Y-rays has low power (see Section 5.3). In this case, the annihilation events in the sample cannot be correlated with the number of emitted Y-rays. Moreover, the positron lifetime in the sample is much shorter than the flight time. Only with the help of pulsed beams from a specially developed FS that supplies a starting pulse can a positron be measured. To date, such a technique has been implemented only in a few laboratories, for example, in Munich [145,146] and Tsukuba [147] and is expensive in electronic form. Sperr and Kogel in 1997 discussed the performance limit of pulsed positron beams [139].

In a setup with a slow positron beam, in addition to measurements of Doppler broaden­ing and lifetime, a two-dimensional angular correlation of annihilation radiation is possible to measure. Analysis of the thin epitaxial layers or interfaces, as well as the electronic struc­ture of surface layers, is an advantage of this technique [133,148].

In an experiment with back diffusion using a system of slow positron beams, in addition to measuring the positron lifetime and momentum distribution, the defect density can be determined. Using the near-surface relative amount of positronium or annihilation para­meters on the surface, it is possible to calculate the fraction of positrons fs), which diffuse back in the direction to the surface. Only on the surface of the semiconductor can positro- nium form, since the annihilation parameters in the volume usually differ from the surface annihilation parameters. Not only the diffusion coefficient and implantation depth, but also the relative number of backscattered positrons depends on the concentration of defects, as positrons that were trapped cannot reach the surface of the sample. The quantity f is mea­sured as a function of the incident positron energy. The capture speed as a function of depth can be calculated using the fitting procedure. The lack of data on the nature of positron traps is the main disadvantage of this procedure. Parallel measurement of Doppler broadening and positron lifetime is also recommended. On the other hand, based on the results of back diffusion experiments, the total capture rate for most positron traps can be derived. Therefore for very highly positron-saturated regions, the defect concentration can also be determined, as was shown for ion-implanted silicon by Eichler et al. in 1997 [133].

Defect depth profiling

It is necessary to have data on the distribution of positron implantation to construct a depth profile of defects depending on the incident positron energy for different annihilation para­meters. In the next section, profiles obtained experimentally and by Monte Carlo simulation will be presented. Using computer programs, profiles of the depth of defects are calculated. Profile calculation procedures are also described in Section 5.4.2.

5.Б.4.2 Positron implantation profiles

Variations of the positron energy allow determining the concentration of defects as a func­tion of the penetration depth z, that is, the measurement of the defect depth profile. The implantation and penetration profiles P(z;E) of the monoenergetic positrons with energy E can be calculated using the following equation:

In honor of the initial experiments on electronic implantation of Makhov, the profile of positron implantation was named (see references cited in the monograph [133]). Monte Carlo simulations can be used to theoretically calculate the parameters of this profile [149,150]. The dependence of the parameters A and r on the material using a number of Monte Carlo calculations was shown by Ghosh [133,148]. By formula (6), it is possible to cal­culate the positron depth distribution after thermalization when diffusion began. Fig. 5—13F shows examples of such Makhov profiles. When superposed on the diffusion profile of posi­trons, well-defined defect structures from the relatively deep area of the sample are eroded, which imposes limitations on the measurement of defect depth profiles for high positron energies. Different values of A and r were obtained depending on the Monte Carlo methods used [148]. Slight deviations were found from the main characteristics of profile of the posi­tron implantation, which was described by Makhov analytical profile. These deviations necessitated approximation of the profile thus obtained by parameterizing function £ [151].

Leung et al. and Gebauer et al. experimentally determined parameters of the Makhov profile (Fig. 5—13F) [152,153]. They are presented in Fig. 5—13G. Parameters of the profile of implantation were deduced using the dependence between E and S for amorphous Si layers, with the sample thickness being determined independently by studying the cross-section in a SEM. Using a molecular beam epitaxy method, a-Si layers 120—1000 nm thick were depos­ited on a buffer layer from SiO2, which was prepared by the thermal oxidation at 1000°C. The curves for the S parameter were calculated by the VEPFIT software package using sys­tematic variation of A and Makhov profile's r parameters [154]. Fit of the positron annihila­tion data, zfit, and thickness calculated by scanning electron microscopy, zjSEM, were used to calculate the standard deviation X for each (A, r) pair:

For all five measured S(E) profiles (Fig. 5—13G), the deviation £ is averaged in formula (8). For the parameters of the Makhov profile, the minimum deviation r = 1.7 6 0.05 and A = 2.75 6 0.25 mg/cm2 keV_r (Fig. 5—13H) was found by Gebauer et al. (see references cited in [152]). Monte Carlo simulation results by Gauche in 1995 [148] are in good agree­ment with these parameters.

Calculations of S took into account all five curves plotted in Fig. 5—13G. The minimal deviation is indicated by the shaded area in Fig. 5—13H at point r = 1.7 6 0.05 and A = 2.75 6 0.25 mg/cm2 keV_r [152].