A semiconductor-on-insulator structure including first and second layers which are attached to one another either directly or through one or more intermediate layers. The first layer includes a substantially single crystal germanium semiconductor material while the second layer comprises a glass or a glass-ceramic material having a linear coefficient thermal of expansion (25-300.degree. C.) which is within the range of +/-20.times.10.sup.-7/.degree. C. of the linear coefficient thermal of expansion of the germanium first layer.