A　third-order　quasi-cubic　silicon　film　potential　function　in　the　vertical　direction　is　assumed　for　FD-SOI　device,　and　the　surface　potential　formula　is　obtained　via　solving　the　two-dimensional　Poisson　equation　in　the　subthreshold　region.　The　surface　potential　model　in　the　deep-submicrometer　FD　device　is　presented　by　introducing　some　new　parameters　to　describe　the　DIBL　effect.　Based　on　it,　a　drain　current　model　in　the　subthreshold　region　is　developed,　which　can　predict　the　accurate　sub-threshold　drain　current　characteristics.　The　models　are　verified　by　comparing　with　the　two-dimensional　device　simulator,　MEDICI.