**2. Experimental**

#### *2.1. Material and Sample Preparation*

The GaAs samples investigated in this study were cut into dimensions of ~10 × 10 mm, from a monocrystalline wafer obtained from a local manufacturer—The Gallium Arsenide Company Slovakia, CMK Ltd. (Zarnovica, Slovakia). Detailed information on the material, provided by the manufacturer, is shown in Table 1.

For the irradiation experiment and subsequent PAS characterisation, in a total, six pairs of samples were required, while one sample pair served as a reference. Two samples were destroyed during the cutting of the sample (Figure 1), and some samples were damaged and thus could not be used for the study evaluated during the proton irradiation.

**Figure 1.** As-prepared test samples of the GaAs as per Table 1 for the irradiation experiment.


**Table 1.** Specification of the studied GaAs samples.

#### *2.2. Proton Irradiation Experiment*

The proton irradiation experiment was performed using the 6 MV Tandetron tandem accelerator at the STU University Science Park CAMBO located in Trnava (Figure 2). The accelerator is used for a wide range of ion irradiation studies including H, He, and heavy ion irradiation. The maximum achievable energy for proton irradiation is 12 MeV and the maximum flux, depending on beam scanning area, which can reach up to 10<sup>14</sup> cm<sup>−</sup>2.s−<sup>1</sup> [16].

**Figure 2.** The 6 MV Tandetron ion accelerator at the Advanced Technologies Research Institute, Slovak University of Technology [17].

The actual irradiation times and corresponding proton fluxes shown in Table 2 were proposed according to the availability of the accelerator, in order to obtain a wide range of proton fluxes that will be increasing logarithmically. While different target fluences were initially considered for this experiment, finally a fluence of 10<sup>16</sup> cm<sup>−</sup><sup>2</sup> was selected to be achieved by using five different fluxes (ranging from 10<sup>11</sup> to 11<sup>13</sup> cm<sup>−</sup>2.s−1). The energy of the protons in Figure 3 is discussed later in this chapter. The reasoning behind the selection of the fluence is based on the sensitivity of the PALS technique and it is illustrated in Figure 4.


**Table 2.** As-prepared test samples for the irradiation experiment.

Note, that in two cases (sets 2 and 4), the samples measured using the PAS technique were not identical in terms of the proton fluence received. The proton flux for these samples was calculated as the mean of the two nearest values.

**Figure 3.** SRIM-based calculation for the dpa with 5 MeV protons.

**Figure 4.** Fluence vs. irradiation times for different proton fluxes (beam currents) used in the experiment.

The irradiation temperature was kept near room temperature using a water-cooled sample stage. Figure 3 shows the simulated implantation profile and the values of displacement per atom (dpa) calculated according to the Norgett−Robinson−Torrens (NRT) [18] model using the "The Stopping and Range of Ions in Matter" (SRIM) data obtained according to the suggestion by Stoller [19] for the fluence of 10<sup>16</sup> cm<sup>−</sup><sup>2</sup> used in the present study.

The fundamental approach in this study assumed that the concentration of the radiation-induced point defects would be constant at a certain range of proton flux, but there is a sharp threshold at a certain level of proton flux above which the production of these defects will be diminished in the thermal effects produced by the dislocation cascades.

The SRIM code was used to compute the reference value of the produced concentration of radiation-induced vacancies. However, it is a common understanding that this tool does not consider the mobility of the displaced atoms and the results are obtained for 0 K temperature. Practically, there is always a temperature effect that reduces the number of actual concentrations of vacancies that survived the displacement cascades. Positron annihilation spectroscopy can effectively study this realistic assessment of the concentration of radiation-induced vacancies.

The energy of the charged particles plays a leading role in the type of defects, such as Frenkel pairs, as well as cascade and sub-cascaded collisions. In the presented experiments, energy of 5 MeV was used for the proton irradiation and the resulting sample modification. The corresponding SRIM profile is shown in Figure 3, together with the positron stopping profile obtained from the GEANT4 (GEometry ANd Tracking) simulation package [20]. The figure illustrates the sensitivity of this technique to the given (uneven) defect depth profile by providing the actual/corrected dpa profile, "visible" to 22Na positrons. Energy of 5 MeV was chosen so as to minimise the interaction of positrons with the displacement damage peak and the hydrogen peak produced at the end of the track region by protons capturing electrons.

As mentioned above, the reasoning for selecting the 10<sup>16</sup> cm<sup>−</sup><sup>2</sup> fluence is derived from Figure 4. This fluence can be obtained using realistic flux values and accelerator beam time availability.

#### *2.3. Positron Annihilation Spectroscopy Characterisation*

Among the numerous analytical techniques used in material irradiation studies, positron annihilation spectroscopy (PAS) is well known for its spectacular sensitivity to atomic-scale vacancy-type defects. Although the technique is sensitive to other types of defects (dislocations, grain boundaries and precipitates of certain elements), vacancy-type defects are typically the most attractive potential well in irradiated single crystals. The sensitivity of various PAS techniques to neutral vacancies ranges from ~5 × 10<sup>15</sup> cm<sup>−</sup><sup>3</sup> (detection limit) to ~10<sup>19</sup> cm<sup>−</sup><sup>3</sup> (positron trapping gets saturated). This sensitivity range was also considered in the selection of the target fluence in the present experiment.

The experimental characterisation of the irradiated samples was performed at the Slovak University of Technology in Bratislava at the Faculty of Electrical Engineering and Information Technology at the Institute of Nuclear and Physical Engineering. This institute has a dedicated PAS laboratory for positron annihilation spectroscopy equipped with one standalone positron lifetime spectrometer and one setup combining positron lifetime and coincidence Doppler broadening spectrometer. Both lifetime spectrometers are digital, based on three BaF2 scintillator detectors and DRS4 waveform digitising boards.

As mentioned above, the experiment was designed for optimal utilisation of a conventional 22Na positron source with a continuous energy spectrum of positrons ranging from 0 to 540 keV. The actual positron stopping profile, as well as the displacement damage profile adjusted to the spectrum of positron probes, is shown in Figure 3.

For the present research, we used positron annihilation lifetime spectroscopy (PALS), which enables qualitative and quantitative characterisation of vacancy-type defects in crystalline materials. The physical principle of the PALS technique is based on positron trapping by defects and the fact that the positron lifetime depends on the nature and size of this defect. PALS is a widely used microstructural characterisation technique based on the measurement of changes in the time of positrons trapped by lattice defects. Both the size and concentration of defects can be obtained from the positron lifetime spectrumby evaluating the lifetime values and intensities of individual components. The values of the positron lifetimes are well-known for most semiconductors, and the evaluation of the results can be supported by a broad range of published data that are both theoretically and experimentally obtained.

#### **3. Results and Discussion**

The positron annihilation lifetime spectra were evaluated using the LT10 program developed by Giebel and Kansy [21]. The spectra were decomposed into two components. The first component characterises the material bulk lifetime t1 (reduced by trapping at defects) and the second component corresponds to lattice defects t2, here considered as monovacancies. The lifetime of the second component was fixed at a value of 295 ps, reported for a mono-vacancies in undoped GaAs [22], while the lifetime of the first component, together with both intensities (I1, I2), was left as a free parameter. The average positron lifetime (tAVG), as the statistically most reliable parameter independent of the fitting model, was calculated for all of the lifetime data. The concentration of vacancies was calculated according to the procedure described in detail, for instance, in [23]. The obtained results are shown in Table 3. The concentration of vacancies NV was directly calculated from the positron trapping rate kv via a constant of proportionality, the so-called trapping coefficient of 1 × 10<sup>15</sup> s<sup>−</sup><sup>1</sup> [22].

The results plotted in Figure 5 show that the proton flux ranges between 10<sup>11</sup> and 10<sup>12</sup> cm<sup>−</sup>2.s−<sup>1</sup> lead to about the same concentration of monovacancies in 5 ± 1 × 10<sup>16</sup> cm<sup>−</sup>3. This value is fairly reasonable compared with the SRIM simulation, which estimates the vacancy concentration for the given fluence on the level 2.56 × 10<sup>17</sup> cm<sup>−</sup>3. The discrepancy is given by the fact that SRIM does not account for the thermal recombination of vacancies, so SRIM always overestimates the actual damage to the lattice. Considering the aim of this paper, it is interesting to compare the observed vacancy production with other types of irradiation experiments involving PALS analysis. The paper by Sagatova et al. [24] on 8

MeV electron irradiated GaAs reported vacancy concentrations of 1.6 and 2.8 × 10<sup>16</sup> cm<sup>−</sup><sup>3</sup> for samples exposed to 1000 and 1500 kGy radiation. As the latter dose was obtained by 8.37 × 10<sup>15</sup> cm<sup>−</sup><sup>2</sup> electron fluence, i.e., close to the proton fluence 1 × 10<sup>16</sup> cm<sup>−</sup><sup>2</sup> reported in this paper, one can compare the impact of two different types of radiation. Such a comparison suggests that these two types of radiation introduce a similar resulting displacement damage, with only a slightly higher (~factor of 2) concentration of vacancies produced by protons. It is important to note that the analysis was aimed at the ion track region and not the damage peak in both cases.


**Table 3.** Experimental results of the PAS.

**Figure 5.** The concentration of radiation-induced vacancies in the studied GaAs samples as obtained from the PALS experiments. The concentration predicted by SRIM for 0 K is also indicated.

As can be further seen from Figure 5, at a certain level of proton flux (> 10<sup>12</sup> s<sup>−</sup><sup>1</sup> cm<sup>−</sup>3) the concentration of radiation-induced vacancies dropped sharply, suggesting that the new displacement damage cascades were initiated while the previous cascades were still active.

On the other hand, it is reasonable to assume that proton fluxes lower than ~10<sup>11</sup> s<sup>−</sup><sup>1</sup> m<sup>−</sup><sup>3</sup> would lead to a defect concentration near the saturation range indicated in the figure. From this, we can conclude that proton flux below ~10<sup>12</sup> s<sup>−</sup><sup>1</sup> cm<sup>−</sup><sup>3</sup> provides a meaningful radiation condition for the accelerated ageing studies in semiconductors planned for application in harsh radiation environments.

This is an important observation for numerous future experiments as it suggests that long exposure to a mild radiation environment can be, to some extent, simulated experimentally by short-term exposure to much more severe radiation conditions. Such a significant shortening of the irradiation experiment can significantly save costs related to beamtime at irradiation facilities.

It is important to note that the observed flux effect could be very different from the flux effect reported for neutron irradiation experiments on reactor pressure vessel (RPV) steels and other types of complex materials, where a higher flux leads to a more significant vacancy-type defect production [25]. Unlike the present experiment, the microstructure of irradiated RPV steels suffers from additional segregation and precipitation of certain elements (such as Cu or P), which the radiation-induced vacancies may be associated with. While the microstructural evolution of semiconductors is relatively simple compared with the nuclear structural materials, the number of published reports on the flux effect in these materials is significantly smaller.

In this study, the electrical properties of the semiconductors were not investigated, but it is reasonable to assume that the concentration of the free charge carriers would result in similar conclusions. However, this will be investigated in more detail in our forthcoming study, additionally including wide-bandgap semiconductors.
