Warm starting Gaussian processes for efficient electrical characterization of semiconductors

Abstract

Current approaches for performing electrical characterization are too slow to meet the demands of modern semiconductors. This problem is exacerbated as the complexity of the chip designs increases. We present a machine learning based methodology for performing the characterization more efficiently by avoiding redundant drain current - gate voltage (𝐼𝑑−𝑉𝑔) measurements. The proposed methodology combines physics informed Gaussian Process Regression (PI-GPR) and Active Sampling (AS) techniques to dynamically determine a limited but representative subset of 𝐼𝑑−𝑉𝑔 points using prior knowledge. The value of the proposed method was verified through a variety of device designs, maskset, and process variations of the complementary field effect transistor architecture; a total of 1000 devices were tested. We show that the proposed PI-GPR is significantly faster than standard (cold start) GPR in all tested cases and speeds up the conventional characterization process by six times while maintaining threshold voltage accuracy within a maximum absolute error of 25 millivolts, and subthreshold slope within a maximum absolute error of 25 millivolts per decade.