a method of fabricating a semiconductor structure . according to one aspect of the invention , on a first semiconductor substrate , a first compositionally graded si 1 - x ge x buffer is deposited where the ge composition x is increasing from about zero to a value less than about 20 %. then a first etch - stop si 1 - y ge y layer is deposited where the ge composition y is larger than about 20 % so that the layer is an effective etch - stop . a second etch - stop layer of strained si is then grown . the deposited layer is bonded to a second substrate . after that the first substrate is removed to release said first etch - stop si 1 - y ge y layer . the remaining structure is then removed in another step to release the second etch - stop layer . according to another aspect of the invention , a semiconductor structure is provided . the structure has a layer in which semiconductor devices are to be formed . the semiconductor structure includes a substrate , an insulating layer , a relaxed sige layer where the ge composition is larger than approximately 15 %, and a device layer selected from a group consisting of , but not limited to , strained - si , relaxed si 1 - y ge y layer , strained s 1 - z ge z layer , ge , gaas , iii - v materials , and ii - vi materials , where ge compositions y and z are values between 0 and 1 .