Semiconductor wafer, insulated gate field effect transistor, and method for producing semiconductor wafer

A semiconductor wafer comprising:

• a base wafer, a first crystalline layer, a second crystalline layer, and an insulating layer that are positioned in the stated order,
• the semiconductor wafer further comprising:
• a third crystalline layer positioned either between the first crystalline layer and the second crystalline layer or between the base wafer and the first crystalline layer,
• wherein
• the second crystalline layer is made of a crystal that either lattice matches or pseudo lattice matches a crystal making the first crystalline layer, and has a wider band gap than the crystal making the first crystalline layer,
• the third crystalline layer is made of a crystal that either lattice matches or pseudo lattice matches the crystal making the first crystalline layer, and has a wider band gap than the crystal making the first crystalline layer,
• the third crystalline layer includes a first atom that will be a donor or an acceptor, and
• when the third crystalline layer includes a first atom that will be a donor, the second crystalline layer includes a second atom that will be an acceptor, and
• when the third crystalline layer includes a first atom that will be an acceptor, the second crystalline layer includes a second atom that will be a donor.