Original Methods for Diffusion Measurements in Polycrystalline Thin Films

Abstract

With the development of nanotechnologies, the number of industrial processes dealing with the production of nanostructures or nanoobjects is in constant progress (microelectronics, metallurgy). Thus, knowledge of atom mobility and the understanding of atom redistribution in nanoobjects and during their fabrication have become subjects of increasing importance, since they are key parameters to control nanofabrication. Especially, todays materials can be both composed of nanoobjects as clusters or decorated defects, and contain a large number of interfaces as in nanometer-thick film stacking and buried nanowires or nanoislands. Atom redistribution in this type of materials is quite complex due to the combination of different effects, such as composition and stress, and is still not very well known due to experimental issues. For example, it has been shown that atomic transport in nanocrystalline layers can be several orders of magnitude faster than in microcrystalline layers, though the reason for this mobility increase is still under debate. Effective diffusion in nanocrystalline layers is expected to be highly dependent on interface and grain boundary (GB) diffusion, as well as triple junction diffusion. However, experimental measurements of diffusion coefficients in nanograins, nanograin boundaries, triple junctions, and interfaces, as well as investigations concerning diffusion mechanisms, and defect formation and mobility in these different diffusion paths are today still needed, in order to give a complete picture of nanodiffusion and nanosize effects upon atom transport. In this paper, we present recent studies dealing with diffusion in nanocrystalline materials using original simulations combined with usual 1D composition profile measurements, or using the particular abilities of atom probe tomography (APT) to experimentally characterize interfaces. We present techniques allowing for the simultaneous measurement of grain and GB diffusion coefficients in polycrystals, as well as the measurement of nanograin lattice diffusion and triple junction diffusion. We also show that laser-assisted APT microscopy is the ideal tool to study interface diffusion and nanodiffusion in nanostructures, since it allows the determination of 1D, 2D and 3D atomic distributions that can be analyzed using diffusion analytical solutions or numerical simulation.

Atom Probe Tomography Studies on the Cu(In,Ga)Se₂ Grain Boundaries

“…Furthermore, Letellier et al 36 reported for nickel-based superalloys that the local magnification effect increases continuously as the GB approaches an orientation parallel to the tip axis (z axis). This may explain why the width of the GB is only slightly enlarged compared to other studies 37 .…”

Anomalous B diffusion profiles in nanocrystalline Si

“…As can be seen in Figure 2, this model cannot reproduce the experimental profiles shown in Figure 1. Even considering B cluster dissolution or taking into account B GB segregation [19,20], the end of the B profiles cannot be reproduced before B atoms have reached the nc-Si/SiO 2 interface. The B diffusion coefficient variation with B concentration in Si grains cannot explain the B profiles measured in nc-Si at these temperatures (6800°C).…”

“…In this model, the B atoms are considered to be incorporated in the Si grain after the lateral migration of the GB. From the literature, D gb was set to 2.74 Â 10 À15 cm 2 s À1 in GBs at 700°C [15] (experiments support that GB diffusion is identical in immobile and mobile GBs [21]) and D g was adjusted according to the simulation results [8,9,19,20]. In order to fit the experimental profiles, we set D g = 4.33 Â 10 À19 cm 2 s À1 (Eq.…”

“…At point defect equilibrium, GB diffusion coefficients (D gb ) were found to be constant at given temperature, and for B diffusion in Si GBs D gb = 0.8 exp(À2.6 eV/k B T) cm 2 s À1 [15]. Figure 2 shows the results of two-dimensional (2-D) finite-element simulations of B diffusion in the nc-Si layer considering the Fisher geometry [18] with a grain width of 50 nm and a GB size of 0.5 nm [8,9,19,20], as well as considering the B diffusion coefficients D B and D gb and the electrical effects in grains given in the literature and described above (Eqs. (1)-(4)).…”

“…The B diffusion coefficient variation with B concentration in Si grains cannot explain the B profiles measured in nc-Si at these temperatures (6800°C). The Fisher geometry we used does not take into account the fact that GBs were mobile during annealing despite a constant average grain size [18], though mobile GBs were shown to have a significant impact on diffusion profiles in polycrystalline layers [19,20]. Figure 3 presents simulations of B diffusion in the nc-Si layer considering the same assumptions as for the simulations presented in Figure 2, but also considering GB migration [19,20] and a constant diffusion coefficient in grains (D g ).…”