A semiconductor construction, comprising: a semiconductor substrate comprising a monocrystalline semiconductor material; a plurality of isolation regions (12, 14, 16) within the semiconductor material and extending along a defined longitudinal direction, a plurality of lines (65, 67) extending substantially orthogonally to the isolation regions; an array of pillars (70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90) extending upwardly from the monocrystalline semiconductor material, the array comprising columns along the defined longitudinal direction and rows along a defined horizontal direction which is substantially orthogonal to the defined longitudinal direction; the columns of the array being between the isolation regions (12, 14, 16) and along longitudinally-extending strips of the monocrystalline semiconductor material, the pillars comprising mesas of the monocrystalline semiconductor material extending upwardly from the longitudinally-extending strips; a first set of source/drain regions at upper regions of the pillars; a second set of source/drain regions (151, 153); a set of channel regions between the first and second sets of source/drain regions; and a plurality of gateline rows (144, 146, 148) extending along the defined horizontal direction; the gateline rows extending along the rows of the array of pillars; the gateline rows, channel regions, and first and second sets of source/drain regions forming a plurality of transistor devices; individual transistor devices comprising a first source/drain region of the first set, a second source/drain region of the second set, a channel region extending from the first source/drain region to the second source/drain region, and a gate within the gateline row and proximate the channel region, characterised by: the isolation regions being recessed within the semiconductor material and spaced from one another for complete isolation by the longitudinally-extending strips of the monocrystalline semiconductor material; the lines having dielectric regions over the isolation regions and semiconductor sections (95, 97) between the dielectric regions; and the second set of source/drain regions (151, 153) being within the semiconductor sections of the lines. a semiconductor substrate comprising a monocrystalline semiconductor material; a plurality of isolation regions (12, 14, 16) within the semiconductor material and extending along a defined longitudinal direction, a plurality of lines (65, 67) extending substantially orthogonally to the isolation regions; an array of pillars (70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90) extending upwardly from the monocrystalline semiconductor material, the array comprising columns along the defined longitudinal direction and rows along a defined horizontal direction which is substantially orthogonal to the defined longitudinal direction; the columns of the array being between the isolation regions (12, 14, 16) and along longitudinally-extending strips of the monocrystalline semiconductor material, the pillars comprising mesas of the monocrystalline semiconductor material extending upwardly from the longitudinally-extending strips; a first set of source/drain regions at upper regions of the pillars; a second set of source/drain regions (151, 153); a set of channel regions between the first and second sets of source/drain regions; and a plurality of gateline rows (144, 146, 148) extending along the defined horizontal direction; the gateline rows extending along the rows of the array of pillars; the gateline rows, channel regions, and first and second sets of source/drain regions forming a plurality of transistor devices; individual transistor devices comprising a first source/drain region of the first set, a second source/drain region of the second set, a channel region extending from the first source/drain region to the second source/drain region, and a gate within the gateline row and proximate the channel region, characterised by: the isolation regions being recessed within the semiconductor material and spaced from one another for complete isolation by the longitudinally-extending strips of the monocrystalline semiconductor material; the lines having dielectric regions over the isolation regions and semiconductor sections (95, 97) between the dielectric regions; and the second set of source/drain regions (151, 153) being within the semiconductor sections of the lines. the isolation regions being recessed within the semiconductor material and spaced from one another for complete isolation by the longitudinally-extending strips of the monocrystalline semiconductor material; the lines having dielectric regions over the isolation regions and semiconductor sections (95, 97) between the dielectric regions; and the second set of source/drain regions (151, 153) being within the semiconductor sections of the lines.