An isolation structure can include a structure material with thermal conductivity greater than silicon dioxide, yet electrical conductivity such that the structure material can replace silicon dioxide as an insulator. At least one column can extend to a target layer from a top surface of a semiconductor device near an active area of the device. At least one lateral portion can extend from the column(s) substantially parallel to the target layer and can extend between multiple columns in the target layer, such as in a cavity formed by lateral etching. The structure material can include, for example, aluminum nitride (AlN).