A crystalline thin structure (104, 204, 404) is grown on a surface (108, 228) of a substrate (112, 208, 400) by depositing molecules (136, 220) from a molecular precursor to a lateral growth front (144, 224) of the structure using a crystal grower (116, 200). In one embodiment, the crystal grower comprises a solution (124) containing the molecular precursor in a solvent (140). Molecules are added to the lateral growth front by moving one or both of the free surface (120, 120') of the solution and deposition surface relative to the other at a predetermined rate. In another embodiment, the crystal grower comprises a mask (212) that includes at least one opening (216). Precursor molecules are vacuum deposited via a molecular beam (236) at the growth front (228) of the crystalline thin structure (204) as one or both of the opening and surface are moved relative to the other at a predetermined rate.