A simulation study of repeatability and bias in the CD-SEM

The ability of a critical dimension scanning electron microscope (CD-SEM) to resolve differences in the widths of two lines is determined by measurement repeatability and any sample-dependent biases. In order to ascertain the dependence of these quantities upon eight different parameters specifying the sample geometry, instrument conditions, and noise, the MONSEL Monte Carlo electron simulator has been used to calculate secondary electron images for varying depth of focus, sample edge shape, electron beam spot size, and proximity of neighboring lines. To each of these images was added noise with varying total power (Le., root mean square noise) but with that power distributed across spatial frequencies so as to match the shape of the power spectral density measured in one or the other of two different commercial CD-SEMs in a fabrication facility environment. The edge positions from these. simulated noisy images were then "measured" as would be done in a CD-SEM, employing both commonly used (maximum derivative, regression to baseline, sigmoidal fit) and experimental (model-based library matching) edge location algorithms. Simulations were performed for 14400 different combinations of values for the eight parameters. From many repetitions of noise, the repeatability of such edge measurements was ascertained for each of these. Since in a simulation the true edge positions are known, the biases (i.e., average, or "systematic," errors) of these edge determinations were also determined. The noise amplitude, choice of edge detection algorithm, and beam size are significant factors in measurement repeatability. The CD-SEM's measurement repeatability may be an order of magnitude better than its spatial resolution. For some edge detection methods the bias is a. function of edge shape. This means that in a manufacturing environment in which the shape varies, there will be a random component of error that is not captured in the usual same-sample tests of instrument precision.