Limits of topographic measurement by the scanning tunnelling and atomic force microscopes

SUMMARY Parameters describing the topographic character of a surface (height, surface wavelength, slope and curvature) can be derived from equivalent sinusoidal profiles. The response of a surface‐measuring instrument may be modelled in terms of instrument parameters such as stylus radius, and scanning range and resolution. The performance of the instrument may then be mapped as a zone in amplitude‐wavelength (AW) space to show the sinusoidal profiles it is capable of measuring. In a first‐order analysis the STM and AFM are considered as equivalent to contact‐stylus instruments with a notional stylus radius equal to the tip radius plus the gap. Comparisons between different instruments and types of instrument are readily made by mapping in AW space. The error arising from convolution of the sinusoidal profile with that of the finite tip may be quantified and plotted as contours in AW space.