A semiconductor device formed in a silicon-on-insulator substrate includes a silicon channel region located between silicon source and drain regions, and a low-carrier-concentration layer that underlies the channel region. The low-carrier-concentration layer makes contact with both the channel region and the source region. The channel region and the low-carrier-concentration layer are of the same conductive type, but the low-carrier-concentration layer is doped to have a lower carrier concentration than the channel region. The low-carrier-concentration layer eliminates the floating substrate effect, because carriers that would otherwise accumulate in the channel region can escape through the low-carrier-concentration layer into the source region.