A method for making a semiconductor device may include forming first and second semiconductor regions laterally adjacent one another and each comprising a first semiconductor material. The method may further include forming an in-situ doped, punch-through stopper layer above the second semiconductor region comprising the first semiconductor material and a first dopant, and forming a semiconductor buffer layer above the punch-through stopper layer, where the punch-through stopper layer includes the first semiconductor material. The method may also include forming a third semiconductor region above the semiconductor buffer layer, where the third semiconductor region includes a second semiconductor material different than the first semiconductor material. In addition, at least one first fin may be formed from the first semiconductor region, and at least one second fin may be formed from the second semiconductor region, the punch-through stopper layer, the semiconductor buffer layer, and the third semiconductor region.