A method of preparing a multilayer structure, the method comprising: etching a silicon layer of a silicon-on-insulator substrate in an ambient atmosphere comprising hydrogen chloride vapor or chloride vapor at an initial temperature of about 800°C or more, and decreasing the etching temperature to less than 600°C during or at the end of the silicon layer etching step with a ramp rate between about 5°C/s and about 20°C/s, wherein the silicon-on-insulator substrate comprises (i) a single crystal semiconductor handle layer comprising two major, generally parallel surfaces, one of which is a front surface of the single crystal semiconductor handle layer and the other of which is a back surface of the single crystal semiconductor handle layer, a circumferential edge joining the front and back surfaces of the single crystal semiconductor handle layer, a central plane between and parallel to the front surface and the back surface of the single crystal semiconductor handle layer, a central axis perpendicular to the central plane, and a bulk region between the front and back surfaces of the single crystal semiconductor handle layer, (ii) a dielectric layer in interfacial contact with the front surface of the single crystal semiconductor handle layer, and (ii) the silicon layer in interfacial contact with the dielectric layer, and further wherein the silicon layer is etched to a thickness between about 0.5 nanometer and about 4 nanometers, as measured along the central axis, and further wherein the etched silicon layer comprises a hydride-terminated surface; depositing a first layer comprising germanium on the etched silicon layer comprising the hydride-terminated surface; annealing the silicon-on-insulator substrate comprising the etched silicon layer and the first layer comprising germanium at a temperature and duration sufficient to interdiffuse germanium from the first layer into the etched silicon layer, to thereby yield a second layer comprising silicon and germanium having a formula of Si x Ge 1-x, wherein x is between about 0.2 and about 0.8, molar ratio; and depositing a third layer comprising silicon and germanium by epitaxial deposition on the second layer comprising silicon and germanium, wherein the third layer comprising silicon and germanium has a formula Si y Ge 1-y, wherein y is between about 0 and about 0.9, molar ratio. etching a silicon layer of a silicon-on-insulator substrate in an ambient atmosphere comprising hydrogen chloride vapor or chloride vapor at an initial temperature of about 800°C or more, and decreasing the etching temperature to less than 600°C during or at the end of the silicon layer etching step with a ramp rate between about 5°C/s and about 20°C/s, wherein the silicon-on-insulator substrate comprises (i) a single crystal semiconductor handle layer comprising two major, generally parallel surfaces, one of which is a front surface of the single crystal semiconductor handle layer and the other of which is a back surface of the single crystal semiconductor handle layer, a circumferential edge joining the front and back surfaces of the single crystal semiconductor handle layer, a central plane between and parallel to the front surface and the back surface of the single crystal semiconductor handle layer, a central axis perpendicular to the central plane, and a bulk region between the front and back surfaces of the single crystal semiconductor handle layer, (ii) a dielectric layer in interfacial contact with the front surface of the single crystal semiconductor handle layer, and (ii) the silicon layer in interfacial contact with the dielectric layer, and further wherein the silicon layer is etched to a thickness between about 0.5 nanometer and about 4 nanometers, as measured along the central axis, and further wherein the etched silicon layer comprises a hydride-terminated surface; depositing a first layer comprising germanium on the etched silicon layer comprising the hydride-terminated surface; annealing the silicon-on-insulator substrate comprising the etched silicon layer and the first layer comprising germanium at a temperature and duration sufficient to interdiffuse germanium from the first layer into the etched silicon layer, to thereby yield a second layer comprising silicon and germanium having a formula of Si x Ge 1-x, wherein x is between about 0.2 and about 0.8, molar ratio; and depositing a third layer comprising silicon and germanium by epitaxial deposition on the second layer comprising silicon and germanium, wherein the third layer comprising silicon and germanium has a formula Si y Ge 1-y, wherein y is between about 0 and about 0.9, molar ratio.