A semiconductor device manufacturing method therefor, and display device having the semiconductor device

The transistor includes a gate electrode, a gate insulating film over the gate electrode, an oxide semiconductor film over the gate insulating film, a source electrode and a drain electrode which are electrically connected to the oxide semiconductor film. The oxide semiconductor film includes a first oxide semiconductor film on the side of the gate electrode and a second oxide semiconductor film over the first oxide semiconductor film. The first oxide semiconductor film includes a first region in which the atomic ratio of In is higher than that of M (M is Ti, Ga, Sn, Y, Zr, La, Ce, Nd or Hf). The second oxide semiconductor film including a second area in which the atomic ratio of In is smaller than that of the first oxide semiconductor film. The second region includes a portion which is thinner than the first region.