Self-consistent autocorrelation for finite-area bias correction in roughness measurement

TL;DR

This paper introduces two practical, self-consistent bias correction methods for autocorrelation functions in AFM roughness measurements, improving accuracy in finite-area data analysis.

Contribution

It develops novel bias correction approaches based on self-consistent autocorrelation formulations, addressing a gap in practical correction methods for AFM data.

Findings

Both correction methods effectively reduce bias in simulated data.

Experimental data confirms the methods improve roughness parameter estimates.

The approaches are easy to implement in practical AFM data processing.

Abstract

Scan line levelling, a ubiquitous and often necessary step in AFM data processing, can cause a severe bias on measured roughness parameters such as mean square roughness or correlation length. Although bias estimates have been formulated, they aimed mainly at assessing the severity of the problem for individual measurements. Practical bias correction methods are still missing. This work exploits the observation that the bias of autocorrelation function (ACF) can be expressed in terms of the function itself, permitting a self-consistent formulation. From this two correction approaches are developed, both with the aim to obtain convenient formulae which can be easily applied in practice. The first modifies standard analytical models of ACF to incorporate, in expectation, the bias and thus actually match the data the models are used to fit. The second inverts the relation between true and estimated ACF to realise a model-free correction. Both are tested using simulated and experimental data and found effective.