Efficient Transient Device Simulation with AWE Macromodels and Domain Decomposition (Special Issue on 1993 VLSI Process and Device Modeling Workshop (VPAD93))

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Numerical simulation of multiple semiconductor devices is necessary to analyze dynamic two-and three-dimensional interactions among devices in CMOS inverters, SRAM cells, and other more complicated gates. With the advent of complete 3D process simulation, an alternative to brute-force transient device simulation must be found for large contiguous silicon regions. Our approach differs from brute-force methods in that we focus not on the time-step control but rather on the latency in the system. By latency, we do not mean that activity within parts of the simulation has ceased or has reached a steady state. Rather, we imply that a simpler form of the solution, a macromodel, can be used to decouple the problem into smaller subproblems. This means that while integrating at a particular time-step, the system of device equations needs only to be solved for a subset of nodes, whereas the node device variables approximated by macromodels are treated as fixed boundary conditions. This drastically reduces the size of the system of equations to be solved at each time-step and allows each node to have a different time-step. Because the responses have exponential-like behavior, we aim to approximate carrier and potential values with closedform exponential macromodels during a time interval. To assure the accuracy of the simulation, we implement several error formula which predict the range of validity of this interval. Moreover, this approach takes advantage of a standard workstation environment (e.g. SparcStation, DECstation, RS6000). This method has been successfully exploited in circuit simulators like SAMSON, which relies on a sophisticated predictor/corrector scheme based on Gear's backward-differentiation formulae (BDF) and depends on partitioning the circuit by inspection. The device simulation problem differs because the partitioning can not be performed by inspection, and the overhead of implementing multi-order BDF would negate the advantage of the decoupling. Instead, we propose the event-driven simulator, AWETOPSY (Asymptotic Waveform Evaluation for Transient Optimized and Partitioned Simulation) that uses automatic partitioning (domain decomposition) and a straightforward second-order integration scheme that we call the power method in conjunction with exponentially-based macromodeling of Asymptotic Waveform Evaluation to exploit the latency. Although Asymptotic Waveform Evaluation (AWE) was originally developed to simplify the solution of linear circuits, we have adapted it to transient device simulation.
社団法人電子情報通信学会の論文
1994-02-25

Efficient Transient Device Simulation with AWE Macromodels and Domain Decomposition (Special Issue on 1993 VLSI Process and Device Modeling Workshop (VPAD93))

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