Chengfu Ma, Yuhang Chen, and Wenhao Huang

AFFILIATIONS 1 Key Laboratory of Precision Scientific Instrumentation of Anhui Higher Education Institutes,Department of Precision Machinery and Precision Instrumentation,University of Science and Technology of China,Hefei 230026,China

2CAS Key Laboratory of Mechanical Behavior and Design of Materials,Department of Precision Machinery and Precision Instrumentation,University of Science and Technology of China,Hefei 230026,China

ABSTRACT Atomic force microscopy (AFM) is increasingly being used as a fundamental tool for dimensional measurements at the nanoscale in the laboratory and in industry.Since the environmental temperature is not controlled in many measurements,or is even varied on purpose,quantificatio of its effects on AFM dimensional measurements is needed.In this paper,the influence of the temperature in the entire environment of the AFM(excluding only the controller and computer)and that in the local environment around the tip–sample are investigated.The results show that lateral dimensional measurements are affected mainly by the entire environmental temperature.However,vertical measurements are influence by the temperature of both the entire environment and the local environment.The effects become significan for temperatures higher than some threshold,here between 35 and 40° C.

KEYWORDS Atomic force microscopy,Environmental temperature,Dimensional measurement,Pitch,Height

I.INTRODUCTION

Since its invention,atomic force microcopy (AFM)1has emerged as a versatile tool in a wide range of research fields Although many of their applications are based on their capabilities for high-resolution topographic imaging,as well as for measurements of various properties of materials,2–4AFMs are increasingly being employed for quantitative metrological measurements,especially in the semiconductor industry.5Surface roughness6and feature dimensions,7,8including height,width,and pitch,are common measurements.This has led to a need to standardize AFMs for dimensional measurements.9For this purpose,metrological AFMs have been developed,10–13and these provide a traceability to the SI unit of length by using integrated optical interferometers for calibration.Physical transfer standards calibrated by metrological AFMs can then be used to calibrate normal AFMs.

In addition,dimensional measurements using AFMs are influ enced by many factors,and these require quantification Nonlinearity,hysteresis and creep of the scanners,tip convolution,environmental factors,and data processing are the main sources of uncertainty.14Among these,environmental factors,especially thermal effects,are widely recognized but have not been sufficientl well studied.15The thermal drift effect and methods for its compensation have been studied.16,17However,investigations into how the environmental temperature affects dimensional measurements are still lacking.This has become an urgent task,considering that most AFMs are operated without stringent control of the environmental temperature,and in some cases measurements at different temperatures are carried out on purpose.18,19The working temperature may influenc the behavior of microscope components.For instance,the strain coefficient of the piezoelectric ceramics used in AFM scanners depend on the working temperature,20and these coefficient are directly related to AFM dimensional measurements.To address this issue,we report here our work to experimentally quantify environmental temperature effect on AFM dimensional measurements,in the framework of the TC201/SC9 Subcommittee of the International Organization for Standardization(ISO).

II.EXPERIMENTAL METHODS

The experiments were performed on four types of commercial AFMs in various institutions.As shown in Fig.1,the environmental temperature was controlled by two means.(1)In local chamber control(type A),a small chamber was used together with a sample heating stage to control the temperature in the local environment containing only the sample and the AFM probe.(2)In whole chamber control(type B),the temperature was controlled in a large chamber containing the whole AFM,excluding only the controller and the computer.Measurements were carried out at temperatures ranging between 10 and 60° C,which may vary among different AFMs owing to technical constraints,with a step of 5° C.For local temperature control,a cycle of heating and cooling was performed.However,only the heating process was applied in the case of whole temperature control,considering the relatively long period for a passive cooling process that was required.In addition,measurements were carried out at each step after the set temperature was reached,with a±0.1° C fluctuatio over 5 min.

Dimensional measurements were performed on onedimensional (1D) and two-dimensional (2D) calibration gratings.At each temperature step,topographic imaging was performed on a grating using the tapping mode with a scan rate of 1 Hz.The scan sizes were chosen to cover around fiv pitches and sampled by 512 pixels × 512 lines.Typical topographic images of 2D and 1D gratings are shown in Figs.2(a) and 2(b),respectively.The 2D gratings were placed with their edges parallel to the scanning axes.The 1D gratings,however,were placed obliquely in order to introduce pitch measurements in both the fast and slow scanning axes.The measured pitches in the fast (xpitch) and slow (ypitch)scanning axes and the height were analyzed.Before that,flattenin of the images was performed by fittin a plane though three points on the same level using the software Gwyddion.To determine the pitch values,fiv evenly distributed profile were extracted in each axis and fitte by a sine function[Fig.2(c)].The pitch values were then obtained by averaging the fittin periods.As shown in Fig.2(d),the height values were determined from the height distributions of the topography images using Gwyddion.

FIG.1. Schematic illustration of the local chamber (type A) and whole chamber(type B)temperature control methods.

FIG.2. (a) and (b) Topographic images of 2D and 1D gratings,respectively.(c)Height profil fitte by a sine function.(d) Height distribution of a topographic image.

III.RESULTS AND DISCUSSION

The resultingxpitch,ypitch,and height values are shown as functions of the temperature in Fig.3.The measurements in Figs.3(a)–3(c) were performed with local temperature controls on Bruker Icon,AR Cypher,and Park NX 10 AFMs,respectively,while those in Fig.3(d) were carried out in a whole temperature control chamber on a Shimadzu SPM-9700 AFM.It can be seen from the results that in the cases with local chamber control,the temperature does not influenc thex-andy-pitch measurements significantly The measured pitches vary with largest fluctuation of approximately 0.043μm and 0.207μm for the whole procedures in Figs.3(a)and 3(b),respectively.The fluctuation are thus no larger than approximately 1%and 2%of the mean pitch values in Figs.3(a)and 3(b),respectively.For the case of Fig.3(c),increases in the measuredxandypitches can be observed during the heating process,as well as in the following cooling process.Such continuous increments of the measuredxandypitches during the whole procedure imply that the system may be still in the“warm-up”process.However,the deviation magnitudes are still as small as those in Fig.3(b),considering their similar pitches.Additionally,it can be seen that the local chamber temperature affects the height measurements considerably.This can be seen particularly from Fig.3(a),where a steady decrease in the measured height values is observed with increasing local chamber temperature.Significan changes in the measured heights can also be found in Fig.3(b)at temperatures greater than 35° C,even without a regular trend.The effect is relatively slight for the case of Fig.3(c),where the measurement was carried out over a range of lower temperatures compared with the other cases.Furthermore,from Fig.3(d),the environmental temperature in the whole chamber is found to have obvious effects on all three-dimensional measurements.Both the measured pitches,in both the fast and slow scan directions,and the measured heights do not vary so much at lower temperatures,but decrease significantl with increasing temperature after 40° C.

FIG.3.Average values of x pitch,y pitch,and height(with standard deviations shown as error bars)as functions of temperature for measurements on(a)Bruker Icon,(b)AR Cypher,(c)Park NX10,and(d)Shimadzu SPM-9700 AFMs.The measurements in(a)–(c)were performed with local temperature control and those in(d)with whole chamber control.

Considering that gratings with different pitches and heights were used in the experiments,here we normalize all the data by the values at 30° C of the heating processes,which are set as benchmarks,to allow a clearer comparison between the different cases.The resulting relative variations are displayed in Fig.4.It can be clearly seen again that the temperature variations in the local chambers do not have a significan influenc on the pitch measurements.However,for the case of whole chamber control,almost 4% decreases are observed for the measured pitches as the temperature is increased from 40° C to 50° C.This can be explained by the fact that most of the AFM components,including thexandyscanners,were outside the local chamber and therefore not affected by the temperature variations.The environmental temperature in the whole chamber,however,impacted directly on the AFM piezoelectric scanners,whose strain coefficient change with temperature.20A similar influenc can be seen for both thexandyscanners at higher temperatures.In addition,considerable deviations of the height measurements can be found in both cases of temperature control in local and whole chambers.For temperatures above a threshold of somewhere between 35 and 40° C,the measured heights are seen to decrease steadily with increasing temperature or to deviate abruptly.Since the height measurements are also influence by high temperatures in the local chamber,we suggest that the influenc may originate from variations in the tip–sample interaction due,for example,to reduction of water film on the sample surface as a result of evaporation at such temperatures.However,this should be further investigated and is beyond the scope of this paper.

It should be mentioned that the dimensions of gratings may also change with environmental temperature owing to thermal expansion.For the silicon gratings in our measurements,a thermal expansion coefficien of 2.6×10−6° C−1at room temperature21can be assumed for the investigated temperature range.However,we derive from our experiments expansion coefficient of as large as about −1.0×10−3° C−1.For instance,the measured pitches and the heights vary by respectively about −1.9×10−3° C−1and about −4.0× 10−3° C−1in the range of 30–50° C for the whole chamber control case in Fig.3(d).For the case of local temperature control such as in Fig.3(a),a comparable coefficien of about −3.1 × 10−3° C−1is derived for height measurement in the range of 22–55° C.The measured dimensions contract rather than expand with increasing temperature,with much larger coefficient than those for the thermal expansion of the material.Therefore,we conclude that the thermal expansion of the material plays a negligible role in the observed effects.In addition,from the fact that the lateral dimensional measurements were mainly influence by the temperature in the whole chamber containing the AFM scanners,but little in the local chamber control cases,we suggest that the effects originate from the thermal properties of the piezoelectric scanners.Indeed,studies have shown that the strain coefficient of piezoelectric materials are influ enced by the working temperature.20,22Accurate dimensional measurements under different environmental temperatures can therefore only be achieved by recalibrating AFM piezoelectric scanners for each temperature.Experiments with both the whole and local chamber controls on the same AFM apparatus are needed to better confir this.In the present study,however,investigations had to be performed on different instruments owing to technical restrictions.

FIG.4.Measured(a)x pitch,(b)y pitch,and(c)height values plotted in the form of relative variations as functions of the temperature in the control chamber.

IV.CONCLUSIONS

We conclude that the temperature in the entire environment of an AFM has significan influence on both its lateral and vertical dimensional measurements.The temperature in the local environment in the vicinity of the tip–sample,however,mainly affects the height measurements.The effects of environmental temperature become significan for temperatures larger than some threshold,here between 35 and 40° C.We suggest that for measurements applied at nonstandard temperatures,calibrations of the AFM are required for accurate dimensional measurements.

ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China(No.51675504)and the Fundamental Research Funds for the Central Universities(No.WK2090000022).We thank S.J.Cho from Park Systems Corp.,S.Wu from Tianjin University,and Q.Chen from Shimadzu Corp.for their technical support.

The data in this paper should not be regarded as performance comparisons of the identifie commercial AFM instruments.

The authors declare that they have no competing interests.