Investigation of Position-Dependent Signal Propagation Delay in Large-Pitch AC-LGAD Using a Two-Dimensional Transmission-Line Model

This paper presents a study of position-dependent signal propagation delay in large-pitch pixelated AC-coupled Low-Gain Avalanche Detectors (AC-LGADs). In AC-LGADs, a continuous resistive ${\mathrm{N}}^{+}$ layer and segmented AC-coupled readout electrodes enable charge sharing and simultaneous timing and position measurements. However, lateral signal transport in the resistive layer can introduce a position-dependent delay in the measured signal arrival time. In this work, an IHEP-designed pixel AC-LGAD was characterized using a two-dimensional picosecond laser scan. The measured leading-edge arrival time shows an approximately linear dependence on an effective propagation distance, with a delay slope of about $194.7\pm 1.3\mathrm{ps}/\mathrm{mm}$ for the tested device. After applying a position-dependent delay correction, the sigma of the combined arrival-time distribution over the scanned region is reduced from 88.3 ps to 48.6 ps. To interpret the observed delay, an equivalent two-dimensional lossy transmission-line model is developed for the continuous resistive layer. The model provides a semi-quantitative description of the leading-edge delay and indicates that, within the measured signal bandwidth, the transport is dominated by the resistive term and is therefore dispersive and diffusion-like. A distributed SPICE network including the pad-area response and capacitive charge sharing provides a complementary circuit-level cross-check of the approximately linear distance dependence. These results quantify the propagation-induced timing delay in large-pitch AC-LGADs and provide guidance for timing correction and future optimization of the resistive-layer sheet resistance.