Transistor-Level Analysis of Dynamic Delay Models

Abstract

Delay estimation is a crucial task in digital circuit design as it provides the possibility to assure the desired functionality, but also prevents undesired behavior very early. For this purpose elaborate delay models like the Degradation Delay Model (DDM) and the Involution Delay Model (IDM) have been proposed in the past, which facilitate accurate dynamic timing analysis: Both use delay functions that determine the delay of the current input transition based on the time difference T to the previous output one. Currently, however, extensive analog simulations are necessary to determine the (parameters of the) delay function, which is a very time-consuming and cumbersome task and thus limits the applicability of these models. In this paper, we therefore thoroughly investigate the characterization procedures of a CMOS inverter on the transistor level in order to derive analytical expressions for the delay functions. Based on reasonably simple transistor models we identify three operation regions, each described by a different estimation function. Using simulations with two independent technologies, we show that our predictions are not only accurate but also reasonably robust w.r.t. variations. Our results furthermore indicate that the exponential fitting proposed for DDM is actually only partially valid, while our analytic approach can be applied on the whole range. Even the more complex IDM is predicted reasonably accurate.

Gain and Pain of a Reliable Delay Model

“…One point deliberately neglected in this paper is accuracy. Investigations by Öhlinger et al [4] and Maier et al [7] revealed that deriving appropriate description is a nontrivial task. Furthermore, characterizing each single gate by relying heavily on analog simulations is computationally expensive.…”