{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,4]],"date-time":"2026-09-04T05:17:00Z","timestamp":1788499020843,"version":"build-2803163510"},"reference-count":21,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T00:00:00Z","timestamp":1788307200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12275290"],"award-info":[{"award-number":["12275290"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["W2543001"],"award-info":[{"award-number":["W2543001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"award":["12275290"],"award-info":[{"award-number":["12275290"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"award":["W2543001"],"award-info":[{"award-number":["W2543001"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2023YFA1605901"],"award-info":[{"award-number":["2023YFA1605901"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2023YFA1605900"],"award-info":[{"award-number":["2023YFA1605900"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>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 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\u00b11.3ps\/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.<\/jats:p>","DOI":"10.3390\/s26175566","type":"journal-article","created":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T07:53:11Z","timestamp":1788335591000},"page":"5566","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Investigation of Position-Dependent Signal Propagation Delay in Large-Pitch AC-LGAD Using a Two-Dimensional Transmission-Line Model"],"prefix":"10.3390","volume":"26","author":[{"given":"Houqian","family":"Ding","sequence":"first","affiliation":[{"name":"Department of Physics, Nanjing University, Nanjing 210093, 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Proc."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1780","DOI":"10.1109\/LED.2019.2943242","article-title":"Demonstration of 200-, 100-, and 50-\u03bcm pitch resistive AC-coupled silicon detectors with 100% fill-factor for 4D particle tracking","volume":"40","author":"Mandurrino","year":"2019","journal-title":"IEEE Electron Device Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"168009","DOI":"10.1016\/j.nima.2022.168009","article-title":"Optimization of capacitively coupled Low Gain Avalanche Diode (AC-LGAD) sensors for precise time and spatial resolution","volume":"1048","author":"Kita","year":"2023","journal-title":"Nucl. Instrum. Methods Phys. Res. A"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"165319","DOI":"10.1016\/j.nima.2021.165319","article-title":"Resistive AC-coupled silicon detectors: Principles of operation and first results from a combined analysis of beam test and laser data","volume":"1003","author":"Tornago","year":"2021","journal-title":"Nucl. Instrum. Methods Phys. Res. A"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"P05001","DOI":"10.1088\/1748-0221\/17\/05\/P05001","article-title":"Characterization of BNL and HPK AC-LGAD sensors with a 120 GeV proton beam","volume":"17","author":"Heller","year":"2022","journal-title":"J. Instrum."},{"key":"ref_9","unstructured":"Cartiglia, N. (2022, January 2\u20134). Spatial and temporal resolution of FBK RSD2 sensors. Proceedings of the 17th \u201cTrento\u201d Workshop on Advanced Silicon Radiation Detectors, Freiburg, Germany. Available online: https:\/\/indico.cern.ch\/event\/1096847\/contributions\/4742361\/attachments\/2400282\/4104935\/Cartiglia_TREDI.pdf."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"P06013","DOI":"10.1088\/1748-0221\/18\/06\/P06013","article-title":"First survey of centimeter-scale AC-LGAD strip sensors with a 120 GeV proton beam","volume":"18","author":"Madrid","year":"2023","journal-title":"J. Instrum."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2134","DOI":"10.1109\/TNS.2023.3289032","article-title":"The performance of large-pitch AC-LGAD with different N+ dose","volume":"70","author":"Li","year":"2023","journal-title":"IEEE Trans. Nucl. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"169203","DOI":"10.1016\/j.nima.2024.169203","article-title":"The performance of AC-coupled Strip LGAD developed by IHEP","volume":"1062","author":"Sun","year":"2024","journal-title":"Nucl. Instrum. Methods Phys. Res. A"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.nima.2017.01.021","article-title":"Beam test results of a 16 ps timing system based on ultra-fast silicon detectors","volume":"850","author":"Cartiglia","year":"2017","journal-title":"Nucl. Instrum. Methods Phys. Res. A"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Christopoulos, C. (1995). The Transmission-Line Modeling Method: TLM, IEEE Press.","DOI":"10.1109\/9780470546659"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1545","DOI":"10.1109\/TCAD.2003.818373","article-title":"The power grid transient simulation in linear time based on 3-D alternating-direction-implicit method","volume":"22","author":"Lee","year":"2003","journal-title":"IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"163479","DOI":"10.1016\/j.nima.2020.163479","article-title":"Analysis and numerical design of Resistive AC-Coupled Silicon Detectors (RSD) for 4D particle tracking","volume":"959","author":"Mandurrino","year":"2020","journal-title":"Nucl. Instrum. Methods Phys. Res. A"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.nima.2015.04.025","article-title":"Design optimization of ultra-fast silicon detectors","volume":"796","author":"Cartiglia","year":"2015","journal-title":"Nucl. Instrum. Methods Phys. Res. A"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.nima.2016.03.093","article-title":"Ultra-fast silicon detectors (UFSD)","volume":"831","author":"Sadrozinski","year":"2016","journal-title":"Nucl. Instrum. Methods Phys. Res. A"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"166739","DOI":"10.1016\/j.nima.2022.166739","article-title":"Optimization of the gain layer design of ultra-fast silicon detectors","volume":"1033","author":"Siviero","year":"2022","journal-title":"Nucl. Instrum. Methods Phys. Res. A"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"170208","DOI":"10.1016\/j.nima.2025.170208","article-title":"nLGAD gain response to low-penetrating particles","volume":"1072","author":"Villegas","year":"2025","journal-title":"Nucl. Instrum. Methods Phys. Res. A"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"170808","DOI":"10.1016\/j.nima.2025.170808","article-title":"Time resolution limits in silicon sensors from Landau fluctuations and electronics noise","volume":"1080","author":"Riegler","year":"2025","journal-title":"Nucl. Instrum. Methods Phys. Res. 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