The　rising　of　big　data　and　artificial　intelligence　applications　requires　embedded　memory　with　higher　density,　lower　power　consumption,　and　wider　bandwidth.　Embedded　dynamic　random-access　memory　(eDRAM)　are　one　of　the　promising　embedded　memory　technologies.　Recent　advances　in　thin-film　amorphous　oxide　semiconductor　field-effect　transistors　(AOSFET)　have　enabled　two-transistor-zero-capacitor　(2TOC)　gain　cell　eDRAMs　to　have　three-dimensional　integration　capability　and　ultra-long　retention　time.　However,　2TOC　gain　cell　eDRAMs　are　still　facing　read　accuracy　challenges.　In　this　paper,　we　explored　the　statistical　distribution　characteristics　of　storage　node　(SN)　charges　during　the　retention　and　read　phases　by　conducting　perturbation　analysis　on　the　2TOC　GC　eDRAM.　Furthermore,　we　proposed　a　retention　channel　model　and　a　read　channel　model　for　the　2TOC　GC　eDRAM.　The　Monte　Carlo　circuit　simulation　results　indicate　that　both　the　retention　channel　and　read　channel　can　well　describe　the　statistical　properties　of　retention　errors　and　read　errors　in　the　2TOC　GC　eDRAM.　Both　channel　models　can　be　used　to　enhance　the　overall　reliability　of　the　GC　eDRAM.　　©　2024　IEEE.