The Rise of 3D IC Technology
3D Integrated Circuit (3D IC) technology is rapidly transforming the landscape of semiconductor design. By stacking circuits vertically and utilizing the z-axis, designers gain an additional dimension of integration that extends the benefits of Moore’s Law—despite the increasing physical limitations of traditional 2D scaling. This vertical architecture allows for higher logic density, shorter interconnects, and improved performance per watt, offering a pathway to continue performance scaling in an era where transistor miniaturization is approaching atomic limits.
However, while the benefits are substantial, 3D IC design introduces new fabrication and architectural challenges. Chief among them is the vertical interconnect problem—creating connections between stacked layers without consuming excessive die area or introducing signal integrity issues. Each through-silicon via (TSV) or vertical micro-bump used to link layers effectively blocks usable circuit area on all intervening layers, which makes every additional connection a costly architectural decision.
The Challenge of Binary Circuits in 3D Stacks
Traditional binary arithmetic circuits—such as adders and multipliers—pose a particular challenge for 3D IC design. Binary operations rely on carry propagation, which inherently demands dense and immediate connectivity between digits. This requirement becomes problematic in 3D layouts, where vertical interconnects are expensive, power-hungry, and spatially intrusive. The more tightly coupled the logic, the harder it becomes to physically separate layers without suffering performance or layout penalties.
As a result, binary systems are not naturally optimized for spatial separation across layers, making them less than ideal for exploiting the full advantages of 3D ICs. The need for numerous, arbitrary interconnections between logic blocks across different vertical layers works against the goal of minimizing TSVs and maximizing silicon utilization.
Modular Computation: A Natural Fit for 3D IC Architectures
Modular computation, based on the Residue Number System (RNS), offers a compelling alternative that aligns naturally with the goals of 3D IC design. In RNS, each digit (modulus) operates independently and does not require carry propagation to or from adjacent digits. This independence allows each modulus to be implemented on a separate physical layer of the IC stack, dramatically reducing the need for vertical interconnects.
Even when inter-layer communication is needed—for example, to orchestrate digit-wise crossbar routing—the design remains highly structured. A crossbar bus, implemented identically at each layer, can be efficiently fabricated using repeating, symmetrical routing patterns. This self-similarity is a significant architectural advantage: it simplifies design, improves layout regularity, and reduces the cost and complexity of fabrication.
By using modular arithmetic, entire arithmetic units—including matrix multipliers, ALUs, and accumulators—can be distributed across layers with minimal wiring overhead. This approach maximizes the benefit of vertical stacking while maintaining high-speed, low-power arithmetic operations. It also opens the door to scalable, high-precision computation in vertical form factors—an important consideration for AI, signal processing, and edge computing devices where space and efficiency are critical.