Quantitative electrical homogeneity assessment of nanowire transparent electrodes

The homogeneous distribution of electric current (electrical homogeneity) is not guaranteed in nanowire electrodes but is crucial for the stability of the electrode and actually desirable in most applications. Despite the relevance of this feature, it is common practice to perform qualitative assessments at the electrode scale, thus masking local effects. To address this issue, we have developed a computational strategy to aid in the design of nanowire electrodes with improved electrical homogeneity. Nanowire electrodes are modeled as two-dimensional networks of stick and junction resistors (with resistance R_w and R_j, respectively) to simulate the electric conduction process. Electrodes are discretized into regular grids of squares and the electrical power of the network contained in each square is computed. The mismatch between the areal power density of the entire electrode and that of the squares provides a quantitative electrical homogeneity evaluation. Repeating the analysis with squares of different size yields an evaluation that spans across length scales. A scalar indicator, coined the homogeneity index, summarizes the results of the multiscale evaluation. The proposed strategy is employed to assess the electrical homogeneity of silver nanowire electrodes through the analysis of scanning electron microscopy images. Our results agree with the outcomes of the experimental assessment performed on the same electrodes. Parametric studies are performed by varying nanowire content and nanowire-to-junction resistance ratio R_w/R_j. We observe that a significant reduction of contact resistance is not necessary to ensure a high degree of homogeneity. The ideal condition of negligible junction resistance (R_w ≫ R_j) leads to the best-case scenario, a situation which is closely approached if R_w ≈ R_j (15% difference at the most in terms of homogeneity index).