Yu Gu, Yuqing Zhang, Xiaobao Xu
Abstract Transparent electrodes must provide both optical access and lateral electrical transport, yet high optical transparency often comes at the cost of increased sheet resistance. Here we develop a current-spreading transport framework that connects this optical-electrical constraint to lateral sheet conduction coupled to vertical current injection. We model the electrode as a two-dimensional conducting sheet coupled to a local vertical current law, and show that the relevant design length is the operating-point-dependent spreading length L s (V 0 )=[ R s f'(V 0 )] -1/2 . Numerical examples for ohmic and PN-diode vertical responses show that high sheet resistance can still be compatible with nearly uniform current injection when the lateral dimension is small compared with L s . For larger areas, metal grids reduce the local spreading distance but introduce a second constraint set by finite grid-line resistance, with a grid length scale L g ∼ ( G g R s L s ) 1/2 . The resulting criteria translate material-level transparency constraints into transport and grid-geometry rules for transparent electrodes in optoelectronic devices.