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The last important characteristic of VLSI design is that it has no depth in its spatial geometry. Circuits are always specified in two dimensions and are not made into solid models. Two possible contradictory views to this depth-free characteristic are the issues of time and multiple circuit layers. Time is the extra dimension that must be considered by some circuit-analysis tools. However, time is not represented as a full extra dimension because that would be very memory-inefficient. Also, circuit structure does not change with time so there is no need to show it as a physical relation. Rather, time is an abstract view of a circuit, as was discussed previously.
Multiple circuit layers add the only true extra spatial dimension to circuitry. IC design must accommodate the multiple layers of the fabrication process, and printed circuitry often uses multilayer boards to allow wires to cross. However, circuitry does not extend in the third dimension to the extent that it exists in the first two. Even process designers, who explore new layering combinations for integrated circuits, must limit the space above the wafer that a design may use. Some people have concerned themselves with the possibility of truly three-dimensional integrated circuits in which signals extend arbitrarily far in three-space, forming a design volume rather than a design plane [Koppelman and Wesley]. The ability to manufacture such designs is not a near prospect so full three-dimensional design methods are not considered here.
The ability of a human to do three-dimensional design is additionally limited by both the depth-free nature of most human interface devices and the inability of a human to keep track of complex three-dimensional interactions. Notice that even in the design of buildings, architects use only two-dimensional sketches from above (called the plan view), from the side (called the elevation view), and from fixed angles (called perspective views). Although the limitation of graphic displays, plots, and input devices seems to be more serious than that of the ability of human perception, it is still a human limit that keeps us from being able to use three-dimensional devices effectively. Therefore, given the ability to fabricate true three-dimensional circuits, one would still find CAD systems using two-dimensional interaction and designing in slices that could be interconnected. For the present, it can be assumed that the third dimension--that of multiple layers--is a pseudodimension of multiple parallel planes. This is more than two-dimensional, but has many simplifications that make it less complicated than three-dimensional.
This same environment of design, (using a limited set of two-dimensional planes) can be found in a very different field: that of cartoon animation. The backdrop is the deepest plane and each animated character has a separate plane in front of the backdrop. There are no complex interactions between these planes: Objects in the closest plane always obscure those in deeper planes. In the animation business, this style of graphics is referred to as two-and-one-half-dimensional and the term applies well to VLSI design.
The advantages of two-and-one-half-dimensional graphics over full three-dimensional graphics are that many display algorithms are simpler and faster. In fact, many color displays are built for two-and-one-half-dimensional graphics and efficiently implement nonintersecting planes. Chapter 9, Graphics, discusses algorithms that can be used on such hardware.
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