NOVELTY - Method (I) of producing a first metal oxide layer on the solid substrate comprises: providing an organometallic solution, where the organometallic solution includes an organometallic compound dissolved in a complexing solvent; distributing the organometallic solution on a solid substrate; removing the complexing solvent; and producing the first metal oxide layer on the solid substrate.    USE - The methods are useful for synthesizing multilayer heterostructures (all claimed), which are useful in thin film photovoltaics and organic LEDs.    ADVANTAGE - The methods provide flexible solid substrates, which are not adversely affected by exposure to 150 degrees C.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are also included for:    (1) a multilayer heterostructure (A) (200) made by method (I) comprising: solid substrate (including organic polymer) (205) and metal oxide layer residing on solid substrate, where multilayer heterostructure has light transmittance greater than 80% in 430-750 nm, flexibility (including the multilayer heterostructure being capable of bending 90 degrees around a curve having a radius less than less than or equal to 5 inches without apparent fracturing of the metal oxide layer) at 20?C, and lag time of greater than or equal to 30 hours at 45 degrees C and 85% relative humidity (RH);    (2) multilayer heterostructure (B) made by methods (I) and (III) comprising: solid substrate; metal oxide layer; and organic polymer layer, where multilayer heterostructure has properties including lag time of greater than or equal to 100 hours and steady state water vapor transmission rate (WVTR) of less than or equal to 2.6x 103- g/m2.day at 45 degrees C and 85% RH, and flexibility (including multilayer heterostructure being capable of bending 90 degrees around curve having radius less than 5 inches without apparent fracturing of metal oxide layer) at 20 degrees C;    (3) method (II) of producing second organic polymer layer on second metal oxide layer comprising: providing organometallic solution as above per se; distributing organometallic solution on solid substrate at processing pressure of ambient atmospheric pressure; removing complexing solvent at less than or equal to 225 degrees C; producing first metal oxide layer on solid substrate at less than or equal to 225 degrees C; producing first organic polymer layer on first metal oxide layer by liquid coating process (including providing organic polymer solution (including organic polymer dissolved in solvent), distributing organic polymer solution on metal oxide layer at process pressure of ambient atmospheric pressure and removing solvent); distributing organometallic solution on first organic polymer layer at processing pressure of ambient atmospheric pressure; producing second metal oxide layer on first organic polymer layer at less than or equal to 225 degrees C; and producing a second organic polymer layer on the second metal oxide layer by the liquid coating process;    (4) a method (III) of producing organic polymer layer on metal oxide layer comprising: providing solution including organometallic compound dissolved in complexing solvent, and water (less than 1000 ppm); distributing solution on flexible solid substrate at process pressure of greater than 475 mb; removing complexing solvent; producing metal oxide layer on solid substrate; and producing organic polymer layer on metal oxide layer by liquid coating process (including providing organic polymer solution comprising organic polymer dissolved in solvent, distributing organic polymer solution on metal oxide layer at process pressure of greater than 475 mb and removing solvent);    (5) multilayer heterostructure (C) made by method (III) comprising: metal oxide layer residing on solid substrate; and organic polymer layer residing on metal oxide layer, where multilayer heterostructure has properties including light transmittance greater than 80% throughout wavelength of 430-750 nm, lag time of greater than or equal to 100 hours and WVTR of less than or equal to 2.6x 103- g/m2.day at 45 degrees C and 85% RH, and flexibility (including multilayer heterostructure being capable of bending 90 degrees around a curve having a radius less than 5 inches without apparent fracturing of the metal oxide layer) at 20 degrees C;    (6) method (IV) of producing organic polymer layer (216, 217, 218) on inorganic oxide layer (211, 212, 213) comprising: producing inorganic oxide layer on solid substrate by first liquid coating process at process pressure greater than 9.4 mb, where inorganic oxide layer has thickness of less than or equal to 200 nm; and producing organic polymer layer on the inorganic oxide layer by second liquid coating process at process pressure greater than 9.4 mb;    (7) multilayer heterostructure (D) made by method (IV) comprising: solid substrate; inorganic oxide layer residing on solid substrate; and organic polymer layer residing on inorganic oxide layer, where multilayer heterostructure has properties including light transmittance greater than 80% throughout a wavelength of 430-750 nm, a lag time of greater than or equal to 30 at 45 degrees C and 85% RH, and flexibility (including the multilayer heterostructure being capable of bending 90 degrees around a curve having a radius less than 5 inches without apparent fracturing of the inorganic oxide layer) at 20 degrees C; and    (8) method (V) second organic polymer layer on inorganic oxide layer comprising: producing an siloxane compound of formula (SiOx) (Y1) layer on a solid substrate by a first liquid coating process (including providing first blend including liquid combined with organo silicon compound and distributing first blend on solid substrate at process pressure of ambient atmospheric pressure), where solid substrate bends 90 degrees around curve having radius of less than or equal to 3 inches at 20 degrees C without apparent fracturing and the siloxane compound layer has thickness of less than or equal to 200 nm; producing first organic polymer layer on siloxane compound layer by second liquid coating process (including providing organic polymer solution including organic polymer dissolved in solvent, and distributing organic polymer solution on siloxane compound layer at process pressure of ambient atmospheric pressure); producing inorganic oxide layer on first organic polymer layer by third liquid coating process (including providing second blend including liquid combined with organo silicon compound or organometallic compound, and distributing second blend on first organic polymer layer at process pressure of ambient atmospheric pressure); producing second organic polymer layer on inorganic oxide layer by fourth liquid coating process (including providing organic polymer solution including organic polymer dissolved in solvent, and distributing organic polymer solution on inorganic oxide layer at process pressure of ambient atmospheric pressure; and producing second organic polymer layer on inorganic oxide layer by liquid coating process.    DESCRIPTION OF DRAWING(S) - The figure shows the schematic representation of the multilayer heterostructure.    Multilayer heterostructure (200)    Polyethylene naphthalate substrate (205)    Primary inorganic oxide layers (211, 212, 213)    Organic polymer layers (216, 217, 218)