A three-dimensional monocrystalline silicon thin-film solar cell substrate having a structure defined by a plurality of square-based inverted pyramidal cavities, comprising: a free-standing, self-supporting three-dimensional monocrystalline silicon thin-film substrate comprising a plurality of inverted pyramidal structures defined by a plurality square-based inverted pyramidal cavities, said free-standing, self-supporting three-dimensional monocrystalline silicon thin-film substrate further comprising a first side and a second side, said first side having a three-dimensional surface topography comprising ridges of said plurality of square-based inverted pyramidal cavities and said second side having a three-dimensional surface topography comprising the apices of said plurality of square-based inverted pyramidal cavities, said ridges of said plurality of square-based inverted pyramidal cavities comprising a plurality of interconnected continuous ridges on said three-dimensional monocrystalline silicon thin-film substrate and defining base openings of said square-based inverted pyramidal cavities; and said plurality of square-based inverted pyramidal cavities comprising single-sized larger inverted pyramidal cavities and single-sized smaller inverted pyramidal cavities, said single-sized larger pyramidal cavities and said single-sized smaller inverted pyramidal cavities being arranged in a regular staggered alternance pattern on said free-standing, self-supporting three-dimensional monocrystalline silicon thin-film solar cell substrate, wherein said regular staggered alternance pattern substantially increases the mechanical rigidity of said three-dimensional monocrystalline silicon thin-film solar cell substrate by preventing formation of continuous long straight line ridges that define the openings of a large number of pyramidal cavities on said free-standing, self-supporting three-dimensional monocrystalline silicon thin-film solar cell substrate, wherein said free-standing, self-supporting three-dimensional monocrystalline silicon thin-film solar cell substrate has a thickness in the range of 5 to 60μm. a free-standing, self-supporting three-dimensional monocrystalline silicon thin-film substrate comprising a plurality of inverted pyramidal structures defined by a plurality square-based inverted pyramidal cavities, said free-standing, self-supporting three-dimensional monocrystalline silicon thin-film substrate further comprising a first side and a second side, said first side having a three-dimensional surface topography comprising ridges of said plurality of square-based inverted pyramidal cavities and said second side having a three-dimensional surface topography comprising the apices of said plurality of square-based inverted pyramidal cavities, said ridges of said plurality of square-based inverted pyramidal cavities comprising a plurality of interconnected continuous ridges on said three-dimensional monocrystalline silicon thin-film substrate and defining base openings of said square-based inverted pyramidal cavities; and said plurality of square-based inverted pyramidal cavities comprising single-sized larger inverted pyramidal cavities and single-sized smaller inverted pyramidal cavities, said single-sized larger pyramidal cavities and said single-sized smaller inverted pyramidal cavities being arranged in a regular staggered alternance pattern on said free-standing, self-supporting three-dimensional monocrystalline silicon thin-film solar cell substrate, wherein said regular staggered alternance pattern substantially increases the mechanical rigidity of said three-dimensional monocrystalline silicon thin-film solar cell substrate by preventing formation of continuous long straight line ridges that define the openings of a large number of pyramidal cavities on said free-standing, self-supporting three-dimensional monocrystalline silicon thin-film solar cell substrate, wherein said free-standing, self-supporting three-dimensional monocrystalline silicon thin-film solar cell substrate has a thickness in the range of 5 to 60μm.