Achieving maximum hardness in semi-coherent multilayer thin films with unequal layer thickness

Abstract

Sources of plastic strengthening in [0 0 1] epitaxial Cu/Ni multilayer thin films are examined using measurements of in-plane lattice parameter and hardness (H) for films of different bilayer period (Λ) and Ni volume fraction (% Ni). Similar to other investigations, H for 50% Ni–50% Cu films increases with decreasing bilayer period down to Λ = 20 nm, where interfaces are coherent. A new finding is that H for semi-coherent films increases with % Ni. This strategy yields the largest reported H for this system (5.2 GPa for 60% Ni/40% Cu, Λ = 60 nm), showing that smaller is not always stronger. The rationale for the increased H is the development of a large interfacial dislocation density during the elasto-plastic transition to fully plastic yield. This strengthens Cu/Ni interfaces to slip propagation. The results are interpreted with a dislocation-based model that furnishes estimates of interfacial dislocation line energies, pinning strengths to confined layer slip, and interface barrier strengths to slip transmission.

Introduction

Numerous experiments document an increase in hardness (H) of metallic multilayer thin films with decreasing individual layer thickness (h). In the regime h < 50 nm, H ∼ h⁻ⁿ, where n is typically less than 0.5, signifying a deviation from the classic Hall–Petch relationship [1], [2], [3], [4], [5]. This departure has been attributed to the discrete (small) number of pile-up dislocations against interfaces, culminating with confined layer slip (CLS) of single dislocation loops with decreasing h [2], [6], [7], [8], [9]. In this regime, dislocation-based CLS models require empirical fitting parameters to match hardness data [2], [10], [11]. Ultimately, the CLS model breaks down when h is so small that interfaces cannot confine single loops.

Computational approaches suggest that multilayer film hardness is intimately coupled to the nature of interfaces. During CLS, a fundamental quantity is the line energy of dislocations deposited along interfaces [7], [8], [12]. Peierls analyses suggest that such energies are small if interfaces are readily able to absorb and delocalize incoming dislocations [13]. For coherent iso-structural Cu/Ni films, atomistic studies show that interfaces are relatively weak barriers to transmission due to contiguous slip systems; instead, the primary source of dislocation confinement is coherency stress, which alternates in sign from one layer to another [11], [14], [15]. At the continuum scale, dislocation dynamics analyses suggest that local dislocation–dislocation interactions increase the critical resolved shear stress for CLS and thus provide a mechanism for hardening [16], [17], [18]. However, such models employ a fixed core cutoff and thus do not account for core spreading or other nonlinear phenomena observed in atomistic and Peierls simulations.

A principal aim of this work is to examine sources of plastic strengthening in epitaxial A/B multilayer thin films as a function of bilayer period and volume fractions of the A/B constituents. The approach is to couple experimental measurements of H and in-plane lattice parameters in Cu/Ni films with recent dislocation-based modeling [19]. The model partitions strategies for strengthening into two modes: increasing resistance to confined layer slip and increasing resistance to slip transmission across interfaces. These two orthogonal modes of loop expansion are intimately coupled to interfacial quantities, such as the line energy (w) to deposit dislocations at interfaces, pinning resistance (τ_pin) to confined layer slip and resistance (τ_i) to slip propagation across interfaces. Specific goals are to determine the variation in these quantities with interfacial dislocation density and to contrast how coherent vs. semi-coherent multilayer thin films derive their plastic strength.

This work provides specific advances to the experimental and modeling literature. First, hardness data is often presented with little quantitative description of the underlying microstructure [2], [4], [5], [20] and only for equal layer thickness (50% Ni–50% Cu) [4], [5], [20], [21], [22], [23], [24]. Here, hardness measurements are complemented by X-ray and transmission electron microscopy characterization to confirm texture, grain morphology and in-plane lattice strains prior to indentation. Films with unequal layer thickness (e.g. 60% Ni–40% Cu) are considered, and the results validate a hypothesis that H increases with % Ni at larger Λ (60 nm) [9]. This provides an alternate strengthening approach to the usual method of decreasing Λ at fixed % Ni and it yields a Cu/Ni film with maximum hardness (H = 5.2 GPa, adhered to [0 0 1] Si). The results confirm assumptions that in-plane stress decreases monotonically with increasing Λ [7], [9], [20], [25] and suggest appropriate values of dislocation prelogarithmic factors to adopt in dislocation dynamics simulations [12], [26], [27].