1072 Enrico Di Russo et al.


evaporated atom is too close in space and has a too similar time of flight of the first one, the double event would be counted as a single one. For the detector system used in this study, a second impact occurring <1.5 ns after the first one and at a distance of less than ~1.5mmon the detector would be undetected (Da Costa et al., 2012; Blum et al., 2016). The histograms of the frequencies of the detection distances


d associated with {Ga+,Ga+} couples is reported in Figure 6b. The data are extracted from a large data set containing ~19 million ions associated with multiple events (T=50 K; ϕ≈0.0025/0.0035 event/pulse; IR Elas=5.1nJ). Because Ga consists of two isotopes (69Ga and 71Ga), homo-isotopic and hetero-isotopic couples can be distinguished. The hetero- isotopic couples {69Ga, 71Ga} present a peak at 1.9mm. For homo-isotopic couples this peak shifts to 4.4mm and no cou- ples were detected below d=1.7mm, consistent with previous results on different ion species (Blum et al., 2016). This can be considered as a strong indication that pile-up phenomena occur for homo-isotopic hits. In fact, in an aDLD the spatial resolving power is 1.5mm (Da Costa et al., 2005, 2012). Below this dis- tance, signals related to simultaneous impacts of atoms with the same timeof flight (samemass) are convoluted in a single signal, making the detection of multi-hits impossible. In order to estimate the number of homo-isotopic Ga


pairs which were not detected in experiments, an analysis of isotopic abundances in Ga multi-hits was performed as fol- lows. We have restricted our approach to pairs of ions, neglecting higher order events (triplets, etc.). Ga comprises of two isotopes (69Ga and 71Ga) with nat-


ural abundances p1=60.1 and p2=39.9%, respectively (sub- scripts 1 and 2 stand for 69Ga and 71Ga isotopes, respectively). Given the isotope distribution of Ga, the probabilities of occurrence for each type of pairs (11, 22, 12) are, respectively, p1


2=0.36, p2 2=0,16, 2p1p2=0.48). The factor of 2


in the latter expression is due to the fact that 12 and 21 pairs are indiscernible; 52%ofGa pairs are homo-isotopic pairs and it is these pairs that will be subjected to pile-up effects. When there is no detection bias due to pile-effects, the


expected number of ion pairs that are detected (n) can be expressed as:


n=n11 + n12 + n22 with nii =n:p2 i with i=1; 2: n12 =2n:p1:p2;


(1) (2) (3)


where nii is the number of homo-isotopic pairs composed of isotopes i and n12 the number of hetero-isotopic pairs. In contrast to hetero-isotopic couples, the number of


detected homo-isotopic pairs nii′ (i=1, 2) is smaller than the


expected number (nij) because of pile-up effects (prime stands for measured amounts). From simple consideration, it is pos- sible to derive the expected number of homo-isotopic pairs nii from the measurement of n12 and finally to compute the bias rate τii =n0ii = nii, that is an evaluator of detection biases.


nii =n:p2 i With n=n12 = 2p1p2:


(4) (5)


As hetero-isotopic events are not affected by pile-up effects: n12 =n012:


τii =n0ii = nii =2n0ii:p1:p2 = p2 i :n012 : (6)


Thus, substituting equation (6) in equation (5) then equation (5) in equation (4) leads to a simple expression of the bias rate:


(7)


Note that the intrinsic detector efficiency equally affects hetero- and homo-isotopic pairs and subsequently does not intervene in this approach. Our data yield τ11=τ22≈0.4. The probability of bias is


were observed as a function of the field Feff. Taking into account the relativeamount of doubleGa detection eventswith respect to single impacts, the number of Ga ions that were not detected is estimated to be around 2% of the total amount of detected Ga+ ions.We can therefore conclude that the impact of Ga pile-up on the global composition is negligible throughout the whole interval of surface electric field explored in thiswork.However,APTusers should carefully estimate the impact of pile-up on their data, because this quantity also depends on the specific performances of the used detector. In order to assess whether correlated events are caused


independent of the nature of the isotope considered (i=1, 2) and consequently of the type of pair (11 or 22). However, the occurrence frequencies related to 11 and 22 pairs are different (p1


2≈0.36, p2 2≈0.16). No significant variations of τ11 and τ22


by the dissociation of molecular ions, the same data set containing ~19 million ions associated with multiple events was analyzed. Adopting the same approach described by Saxey, the correlation histogram was constructed in order to reveal the presence of dissociation processes (Saxey, 2011). Only one little dissociation track was found and associated with the following process (Fig. 7):


As2+


and As+ ions. It was estimated that this dissociation path involves ~0.8% of As3 Figure 3a, As3


where parent As3 2+ molecular ions correspond to 11% (~1%,


respectively) of the total amount of As ions detected at high (low, respectively) field conditions.


3 !As+ 2 + As+; (8)


2+ molecular ions are dissociated into As2+ 2+ molecular ions. As reported in


Figure 7. Detail of correlation histograms associated to the dis- sociation process. The data were obtained at the following experi- mental parameters: T=50 K; ϕ≈0.0025 ÷0.0035 event/pulse; IR Elas=5.1 nJ. The dataset contains ∼19 million of multiple events.


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