Browse Prior Art Database

Morphological estimation of tip geometry for scanned probe microscopy

IP.com Disclosure Number: IPCOM000125638D
Original Publication Date: 1994-Dec-20
Included in the Prior Art Database: 2005-Jun-09

Publishing Venue

National Institute of Standards and Technology

Related People

John S. Villarrubia: INVENTOR

Abstract

Morphological constraints inherent in the imaging process limit the possible shapes of the tip with which any given tunneling microscope or atomic force microscope image could have been taken. Broad tips do not produce narrow image protrusions. Therefore, feature sizes within the image may be used to place an upper bound on the size of the tip. In this paper, mathematical morphology is used to derive, for each point on an image, a corresponding bounding surface for the tip. The actual tip must be equal to or smaller than the largest tip which satisfies all of the constraints. Example calculations are performed, demonstrating that if the imaged specimen contains sharp features and high relief, the tip shape deduced by this method will be a good estimate of the actual one. Once known, the tip geometry can be "deconvoluted" from images to recover parts of the actual surface which were accessible to the tip.

This text was extracted from a PDF file.
At least one non-text object (such as an image or picture) has been suppressed.
This is the abbreviated version, containing approximately 9% of the total text.

Page 1 of 14

Surface Science 321, (1994) 287..

Morphological estimation of tip geometry for scanned probe microscopy

J.S. Villarrubia

National Institute of Standards and Technology, Gaithersburg, MD 20899, USA

May 6,1994 (revised 8/8/94)

Morphological constraints inherent in the imaging process limit the possible shapes of the tip with which any given tunneling microscope or atomic force microscope image could have been taken. Broad tips do not produce narrow image protrusions. Therefore, feature sizes within the image may be used to place an upper bound on the size of the tip. In this paper, mathematical morphology is used to derive, for each point on an image, a corresponding bounding surface for the tip. The actual tip must be equal to or smaller than the largest tip which satisfies all of the constraints. Example calculations are performed, demonstrating that if the imaged specimen contains sharp features and high relief, the tip shape deduced by this method will be a good estimate of the actual one. Once known, the tip geometry can be "deconvoluted" from images to recover parts of the actual surface which were accessible to the tip.

1. Introduction

Accurate measurement of sub-µm features is important to a variety of scientific and technological problems. Biolo- gists and organic chemists would like to compare images of organic molecules to calculated models[1]. Material scientists would like to make surface roughness[2] and grain size determinations[3]. The Semiconductor Industry Association has identified critical dimension metrology at this scale as an important item on the critical path to the next generation of electronics[4].

Among the most promising techniques available are scanned probe microscopies (SPM) such as scanning tun- neling microscopy (STM) and atomic force microscopy (AFM), which operate by testing the height of the surface at each point with a mechanical probe. These techniques routinely achieve nanometer or even atomic resolution on fLat surfaces. Efforts are underway to construct instruments in which tip position is monitored by interferometry or calibrated capacitance gauges[5,6], raising the hope of making surface measurements with unprecedented accu- racy.

However, in these techniques the shape of the tip is "con- volved" (strictly speaking, dilated) with the surface, pro- ducing significant distortions in measurements of surfaces with relief. For example, if a parabolic tip with 20 nm

radius is used to image a 1 µm high line, the apparent width at the base of the line will be 400 nm greater than the true width as a result of tip interaction. This becomes a serious error as line widths significantly less than 1 µm become possible. Due to its widespread use in industrial settings, it is worth noting that in stylus profiling issues of tip shape are important in much the same way[7], albeit at a somewhat poorer resolution.

One way of characterizing this problem is to note that an SPM measurement of the width, , of th...