High-performance semiconductor films with vertical compositions that are designed to atomic-scale precision provide the foundation for modern integrated circuitry and novel materials discovery. One approach to realizing such films is sequential layer-by-layer assembly, whereby atomically thin two-dimensional building blocks are vertically stacked, and held together by van der Waals interactions. With this approach, graphene and transition-metal dichalcogenides-which represent one- and three-atom-thick two-dimensional building blocks, respectively-have been used to realize previously inaccessible heterostructures with interesting physical properties. However, no large-scale assembly method exists at present that maintains the intrinsic properties of these two-dimensional building blocks while producing pristine interlayer interfaces, thus limiting the layer-by-layer assembly method to small-scale proof-of-concept demonstrations. Here we report the generation of wafer-scale semiconductor films with a very high level of spatial uniformity and pristine interfaces. The vertical composition and properties of these films are designed at the atomic scale using layer-by-layer assembly of two-dimensional building blocks under vacuum. We fabricate several large-scale, high-quality heterostructure films and devices, including superlattice films with vertical compositions designed layer-by-layer, batch-fabricated tunnel device arrays with resistances that can be tuned over four orders of magnitude, band-engineered heterostructure tunnel diodes, and millimetre-scale ultrathin membranes and windows. The stacked films are detachable, suspendable and compatible with water or plastic surfaces, which will enable their integration with advanced optical and mechanical systems.