Statistical aspects of tuning simulators to noisy data

The purpose of TCAD tools is to reduce the cost of developing new semiconductor technologies by replacing real wafers with simulations. If the process flows and device structures can be simulated accurately, then new device designs can be analyzed using simulations instead of real wafers. However, due to uncertainty in material coefficients and deficiencies in the physical models, process and device simulators often fail to provide the accuracy necessary for predictive device design, thereby limiting the impact of TCAD on device development cost. To address this problem, process and device simulators are often tuned to match experimental data, i.e. the simulator coefficients are adjusted such that the simulator outputs match experimentally measured data. However, the experimental data to which the simulators are tuned contain noise due to both process variation and measurement noise. Since tuning parameters are adjusted such that the simulator outputs, which are deterministic, match the experimental data, the uncertainty in the data implies uncertainty in the optimal values of the tuning parameters. This paper presents a methodology for tuning to uncertain and sparse experimental data and estimating the tuning parameter distribution based on the experimental data uncertainty. This distribution can be used to determine whether there is enough data to generate confidence in the optimal values of the tuned parameters. Additionally, we show how the tuned parameter distribution can be used to estimate the uncertainty in simulations conducted at conditions other than those used for tuning.