Why Curvy Design Now? Manufacturing Is Possible And Scaling Needs It

Have you ever seen roots or tree branches take a 90-degree turn? Have you ever seen a river that takes a 90-degree turn? Nature doesn’t do 90-degree turns, or for that matter any sharp angle turns – not even 135 degrees. Yet the entire chip-design infrastructure is based on the Manhattan assumption of 90-degree turns. While it would take time to change, is there any doubt that a curvilinear (curvy) chip, if magically made possible, would be smaller, faster, and use less power?

An expert panel during the 60^th Design Automation Conference in 2023 addressed why the idea of curvy design is now a topic for research. The panel was moderated by Aki Fujimura, CEO of D2S, and combined expertise throughout the design chain with John Kibarian, CEO of PDF Solutions, Ezequiel Russell, Senior Director of Mask Technology at Micron, Andrew Kahng, Distinguished Professor at UCSD, and Steve Teig, CEO of Perceive. The entire panel presentation is available here.

Aki Fujimura opened the panel with a critical observation that today’s GPU workstation has 340,000,000 times more computational capability than in the early days of Manhattan design, circa 1985. While the photomask segment has been leading the way, it’s time to rethink EDA.

Manufacturing curvy photomasks is now possible

GPU-accelerated, curvilinear inverse lithography technology (ILT) software combined with the latest multi-beam mask writers are enabling curvy masks today. Until multi-beam mask writers came about, the prior generation of variable shaped beam (VSB) mask writers were practically able to write only axis-parallel rectangles or 45-degree triangles. Curvy mask shapes are used to help increase process windows for wafer lithography purely for manufacturability reasons, but the ability to create curvy masks also happens to enable curvy target shapes on the wafer, as shown in figure 1. Enabling curvy masks, in turn, will enable curvy designs. This is the first piece of the puzzle as to “why curvy now?” Curvy designs are manufacturable now because curvy masks are manufacturable now.

Fig. 1: Multi-beam mask writers combined with GPU-accelerated ILT enable curvy masks.

Taking a step back, what is meant by a curvy target shape? Not all curvy shapes are curvy design shapes in our (arbitrary) definition. The intent of curvy design is to design shapes that are manufacturable shapes. Transistor layers are going to be unidirectional and uniform, especially as transistors become vertical at the very leading-edge nodes. So, what we mean by curvy design refers to intra-connect (connecting transistors inside standard cells) and inter-connect (connecting standard cell inputs and outputs to other standard cell inputs and outputs) being curvy routes.

Curvy routes will not necessarily be uniform width, but they are curvilinear metal paths for electrons to travel from outputs of transistors to inputs of transistors. The middle picture in figure 2 is curvy (non-Manhattan), but not curvy design. The intent of curvy design is to have target shapes on the wafer that are manufacturable, so the diagonal route with rounded corners (as shown on the right) is a viable curvy design target.

Fig. 2: Curvy design requires wafer targets that are manufacturable.

Proof points in the curvy direction

Aki referenced several past proof points for curvy design benefits, including Tal Dayan’s Ph.D. thesis on any angle-routing (called rubber band routing) from 1997, which shows an average of 30% or more via reduction (figure 3). In the 2000s, several companies including Agere, ATI and Toshiba demonstrated that the X Architecture reduced wire length by 30%, leveraging routing in only the 45-degree direction (figure 4).

Fig. 3: Any angle-routing research projected significant via reduction.

Fig. 4: X Architecture demonstrated 30% wire length reduction.

Scaling techniques today need curvy design to address wiring congestion

John Kibarian, CEO of PDF Solutions, provided his perspective on the panel as to “why now?” for curvy design. John founded PDF Solutions in 1991, took the company public in 2001, and is known as a pioneer in yield management. Recalling the time of the X Architecture, John observed that lithography was the engine driving the chip industry to scale and for many it was perhaps easier to move from 90nm to 65nm than to adopt X. Today, as shown in figure 5, with pitch scaling projected to slow, other techniques are needed such as device scaling with CFETs, library scaling, back-side power, and other circuit and system techniques. John pointed out that library track height will continue to drop, leading to increased wiring congestion. Wire-length reduction techniques such as curvy design are needed to enable these scaling techniques.

Fig. 5: Wire length reduction techniques needed to reduce congestion as CFET, library scaling, backside power are adopted.

Vias are the enemy: Curvy design can reduce vias

Steve Teig, CEO of Perceive, also on the panel, illustrated the potential benefits of curvy design. Steve is a visionary technologist whose work has impacted industries ranging from software and semiconductors to biotechnology and machine learning. During his career in EDA, he was the principal inventor of Tangate’s P&R algorithms and later of the X Architecture. Now, as CEO of his second fabless semiconductor company, Steve added a unique perspective to the panel. Steve pointed out to the audience that vias are the enemy by causing congestion, increased wire length, and design conservatism. He gave a simple example, shown in figure 6, to illustrate how curvy design connections reduce via counts by as much as 50%. John Kibarian added his perspective that vias are difficult to yield, so reducing them directly improves yield.

Fig. 6: Illustration of via count reduction with curvy design.

Sounds great! So, when can I use curvy design?

If you reduce the number of vias, you reduce the die size and cost while improving yield.  This is very compelling – so what will it take? What are the barriers and challenges to curvy design? It was stated early in the panel that, today, the design infrastructure leading up to the photomask handoff is based on Manhattan angles and hasn’t changed in over 40 years. Andrew Kahng brought the perspective that curvy design is yet another exciting paradigm but there have been past ideas in the same genre. What will make this movie different? Micron is already targeting and using curvy shapes for masks as Ezequiel Russell explained on the panel. Die size/cost reduction are big selling points, according to Ezequiel, but you will need to reduce the friction to adoption. It will take time, money, and motivation to move to curvy design. The next blog post will explore the panel’s perspective on the barriers and challenges to curvy design.