This invention discloses methods, materials, and devices for making and screening combinatorial libraries to identify semi-conducting and thermoelectric materials. The disclosed method includes preparing a combinatorial library of materials, and identifying library members that are semiconductors. The method may include determining a thermoelectric figure of merit, ZT, for each member of a second combinatorial library of materials. The method determines ZT by applying an oscillatory voltage across the library members, measuring power dissipated by library members, and calculating ZT from the power dissipated. The method may also include isolating single-phase materials of the semiconducting library members. The present invention also discloses an apparatus for discovering thermoelectric materials using combinatorial techniques. The apparatus includes a first combinatorial library of materials comprised of thin films arrayed on a substrate, and a device for identifying semiconducting members of the first combinatorial library. In addition, the apparatus may include a device for measuring ZT—a voltage source for applying an oscillatory electrical potential across members of a second combinatorial library arrayed on a substrate, and a device for measuring the resulting power dissipated by library members. The apparatus may also include a device for isolating single-phase materials of library members that were identified as semiconductors.