An overview on existing approaches for statistical modeling of bipolar transistors is given with emphasis on practically feasible statistical simulation of analog/h.f. circuits. A suitable approach is outlined and applied to both device simulation and experimental fab data.
I IntroductionToday's competitive semiconductor market demands a reduction of design and mask cost by first pass success for even high-frequency (h.f.) analog circuits. In addition, the demand for early market entry is forcing co-development of process and circuits (concurrent engineering). Thus, predictive modeling strategies have to be applied to provide early design kits with realistic simulation-based compact models.Variations in processing conditions during wafer fabrication cause unavoidable manufacturing tolerances, which are typically of random nature in a production process. One can distinguish between intra-die and interdie variations (e.g. j1][2][3]). The latter include variations that occur from die-to-die on a single wafer, from wafer-towafer within a single lot and from lot-to-lot over time (possibly due to shifting process conditions). Compared to these, intra-die variations occur only over small distances within a die and are thus much smaller.Tolerances in circuit manufacturing affect the yield of a product. They can be divided into parametric variations and into catastrophic failures. The latter, characterized by a non-functional circuit, need to be resolved by changing the processing procedures (incl. equipment, materials) or the design itself. In contrast, parametric variations are fundamentally unavoidable. Hence, they can only be minimized to a certain extent and subject to cost constraints. Parametric variations lead to functional yield, in which circuits are fundamentally functional but their electrical performance parameters may not meet the specifications, and to parametric yield, in which circuit performance varies within the specification limits.The ultimate goal is to optimize circuit yield while at the same time meeting the given circuit performance specifications; this goal is often referred to as yield optimization [1][2][3]. To allow the design of manufacturable circuits, the associated design tools and methodologies have to include process tolerances; the corresponding overall strategy is often called design for manufacturability (DfM) [3]; for instance, one of the strategies (design centering) aims at making the circuit behavior as insensitive to process variations as possible (e.g. [5][6]). DfM attempts to incorporate process tolerances into the design methodology, partially by using accurate simulation. To meet circuit performance specifications in a given process -often called (electrical) circuit optimization-, usually only the device layout is varied intentionally, while the vertical device structure (incl. dimensions and doping) is assumed to be unchanged. Compared to electrical optimization, yield optimization requires to include process tolerances in layout and device structure. Work on design centeri...