The invention provides a method of forming an electronic device from a lamina that has a coefficient of thermal expansion that is matched or nearly matched to a constructed metal support. In some embodiments the method comprises implanting the top surface of a donor body with an ion dosage to form a cleave plane followed by exfoliating a lamina from the donor body. After exfoliating the lamina, a flexible metal support that has a coefficient of thermal expansion with a value that is within 10% of the value of the coefficient of thermal expansion of the lamina is constructed on the lamina. In some embodiments the coefficients of thermal expansion of the metal support and the lamina are within 10% or within 5% of each other between the temperatures of 100 and 600 ° C.