A source trench and a drain trench are asymmetrically formed in a top semiconductor layer comprising a first semiconductor in a semiconductor substrate. A second semiconductor material having a narrower band gap than the first semiconductor material is deposited in the source trench and the drain trench to form a source side narrow band gap region and a drain side narrow band gap region, respectively. A gate spacer is formed and source and drain regions are formed in the top semiconductor layer. A portion of the boundary between an extended source region and an extended body region is formed in the source side narrow band gap region. Due to the narrower band gap of the second semiconductor material compared to the band gap of the first semiconductor material, charge formed in the extended body region is discharged through the source and floating body effects are reduced or eliminated.