An apparatus for growing a crystalline sheet from a melt, comprising: a first cold block assembly comprising: a first cold block; and a first shield surrounding the first cold block and being at an elevated temperature with respect to that of the first cold block, the first shield defining an opening disposed along a surface of the first cold block proximate a melt surface that defines a first cold area comprising a first width along a first direction of the first cold block, the first cold area operable to provide localized cooling of a first region of the melt surface proximate the first cold block; a second cold block assembly, the second cold block assembly comprising: a second cold block; and a second shield surrounding the second cold block and being at a second elevated temperature with respect to the second cold block, the second shield defining a second opening disposed along a second surface of the second cold block proximate a second region of the melt surface and defining a second cold area, the apparatus being characterized in that the second surface comprising a curved shape arranged to, in the first direction, position outer regions of the second surface at a greater vertical distance from the melt surface than inner regions of the second surface; and a crystal puller arranged to draw a crystalline seed in a direction perpendicular to the first direction the second cold block assembly comprises two or more heating elements disposed along the second surface, the second cold block assembly operable to decrease power to at least one of the two or more heating elements so as to vary the second width to the third width with time. a first cold block assembly comprising: a first cold block; and a first shield surrounding the first cold block and being at an elevated temperature with respect to that of the first cold block, the first shield defining an opening disposed along a surface of the first cold block proximate a melt surface that defines a first cold area comprising a first width along a first direction of the first cold block, the first cold area operable to provide localized cooling of a first region of the melt surface proximate the first cold block; a first cold block; and a first shield surrounding the first cold block and being at an elevated temperature with respect to that of the first cold block, the first shield defining an opening disposed along a surface of the first cold block proximate a melt surface that defines a first cold area comprising a first width along a first direction of the first cold block, the first cold area operable to provide localized cooling of a first region of the melt surface proximate the first cold block; a second cold block assembly, the second cold block assembly comprising: a second cold block; and a second shield surrounding the second cold block and being at a second elevated temperature with respect to the second cold block, the second shield defining a second opening disposed along a second surface of the second cold block proximate a second region of the melt surface and defining a second cold area, the apparatus being characterized in that the second surface comprising a curved shape arranged to, in the first direction, position outer regions of the second surface at a greater vertical distance from the melt surface than inner regions of the second surface; and a second cold block; and a second shield surrounding the second cold block and being at a second elevated temperature with respect to the second cold block, the second shield defining a second opening disposed along a second surface of the second cold block proximate a second region of the melt surface and defining a second cold area, the apparatus being characterized in that the second surface comprising a curved shape arranged to, in the first direction, position outer regions of the second surface at a greater vertical distance from the melt surface than inner regions of the second surface; and a crystal puller arranged to draw a crystalline seed in a direction perpendicular to the first direction the second cold block assembly comprises two or more heating elements disposed along the second surface, the second cold block assembly operable to decrease power to at least one of the two or more heating elements so as to vary the second width to the third width with time.