A

mpaa0fvg©

K

1

atfOomipo

0d

Available online at www.sciencedirect.com

Precision Engineering 32 (2008) 182–185

An optical profilometer for characterizing complexsurfaces under high vacuum conditions

K. Fladischer a, D. Litwin b, J. Galas b, A.E. Weeks c, D.A. MacLaren d,R. Lammegger a, H. Sormann e, W.E. Ernst a, B. Holst a,∗

a Institute of Experimental Physics, Graz University of Technology, Petersgasse 16, 8010 Graz, Austriab INOS-Institute of Applied Optics, Kamionkowska 18, 03-805 Warsaw, Poland

c Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 OHE, United Kingdomd Department of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom

e Institute of Theoretical and Computational Physics, Graz University of Technology,Petersgasse 16, 8010 Graz, Austria

Received 30 March 2007; accepted 3 August 2007Available online 19 August 2007

bstract

The requirements for high precision metrology devices have increased rapidly in recent years. Furthermore, the applications are spreading toany new branches of science and technology. Hence new demands are appearing which are related not only to classical parameters such as

recision and speed but also to other factors including the environment in which the measurements must be performed. In this paper we presentnew device for measuring complex surface profiles of samples held under high vacuum conditions. The surface profile is obtained by scanning

n optical sensor, held in air, across a standard view-port. The sensor has a lateral resolution of 25 �m and a perpendicular distance resolution of.12 �m over a range of 3 mm. The maximum scanning area is a circle, 30 mm in diameter. The device was developed to characterize silicon wafers

or use as mirrors for atom optical applications. The mirrors are formed by bending the silicon under an applied electric field, which requires highacuum conditions to prevent arc discharge. In the last part of the paper we discuss how simulations can be used to determine the required samplingrid spacing for obtaining the surface profile shape with a given accuracy.

2007 Elsevier Inc. All rights reserved.

eywords: Topography; Optical distance sensor; Surface profile; Silicon wafer; High vacuum; Electrostatic deformation; Scanning helium microscope

aodacfsmt

. Introduction

Several methods exist for measuring the topography ofspherical and complex surfaces. They can be separated intoactile and optical methods. Tactile methods are unsuitable forragile samples and are usually not as fast as optical methods.ptical methods can be separated into two further groups: meth-ds where the whole surface is measured at once and scanningethods. Classical interferometers such as the Mach–Zender

nterferometer [1] belong to the first approach. The underlyingrinciple for classical interferometers is that a complete interfer-gram of the surface relative to a reference surface is obtained

∗ Corresponding author. Tel.: +43 316 873 8644; fax: +43 316 873 8655.E-mail address: bodil@cantab.net (B. Holst).

aaltsep

141-6359/$ – see front matter © 2007 Elsevier Inc. All rights reserved.oi:10.1016/j.precisioneng.2007.08.001

t once. The problem of applying this method to an asphericalr complex surface is that such surfaces typically require a largeynamic range, such that use of a flat reference surface leads tohigh fringe density. This can be avoided by using wavefront

ompensation elements, but then a suitable element is requiredor each surface form [2]. Consequently, it is not easy to mea-ure a range of different surfaces and for complex surfaces theethod of choice is often a scanning system. Most scanning sys-

ems measure either the local distance to the surface, the slope,nd/or the curvature [3]. The slope/curvature methods have thedvantage of being largely independent of the position and angu-ar orientation of the sensor relative to the surface, as long as

he lateral correlation is not affected [2]. Distance measuringystems are generally more sensitive to positional and angularrrors. Systems with up to four distance sensors have been pro-osed for compensation [3]. A recent paper demonstrates the

n Engineering 32 (2008) 182–185 183

pee

sdtobicTtsmo1tuctt

ecaovaaaFms

dtbhnmap

2

dTpptMpipo

FVt

oisust6slo

ttwcnttobs

3

fivvetsr

K. Fladischer et al. / Precisio

ossibility of eliminating not only the positional and angularrrors (related to the scanning stage) but also systematic sensorrrors [4].

In this paper an optical profilometer for measuring complexurfaces under ultra-high-vacuum conditions is presented. Theevice was originally developed to characterize and optimizehe profile of electrostatically bent silicon wafers. Fields of therder of 107 V/m are required to bend the wafers, well above thereakdown field in air. The deflected wafers are used as focus-ng elements for atoms in a new type of matter-wave microscopeurrently under development: the scanning helium microscope.he operating principle is similar to that of a scanning elec-

ron microscope: a focused beam of neutral helium atoms iscanned across a surface, and the scattered atoms give infor-ation about the sample topography. The potential advantages

f this new tool are the low energy of the helium atoms (about000 times less than electrons for a similar wavelength) and thathe atoms are uncharged. This means that the instrument can besed to investigate fragile and insulating samples that are diffi-ult to image with existing techniques. Detailed descriptions ofhe design and implementation of the atom-optical mirrors andhe scanning helium microscope are given in [5–8].

Characterization and optimization of mirror profiles is nec-ssary prior to using a mirror in the microscope. Due to theomplexity of the measuring conditions it was decided to usesimple, single distance sensor design. The sensor is placed

utside the vacuum chamber and profiles the sample through aiew-port. This has the advantage of making the system easier todjust and, in addition, keeps the vacuum chamber small. A dis-dvantage is that the sensor cannot be put as close to the surfaces would otherwise have been the case, lowering the resolution.or example, we could not copy the device of Schulz [2], whicheasures aspherical surfaces using the curvature and allows the

urface to be characterized with a height accuracy of 0.4 nm.The construction of the profilometer presented here is

escribed in detail in Section 2. Section 3 demonstrates howhe systematic errors from the sensors and translation stages cane compensated by using an error map. In Section 4 it is shownow the overall accuracy can be modeled on the basis of theoise of the error map and the spacing of the sampling grid. Theodeling can be used to determine the required grid spacing fordesired accuracy. In Section 5, silicon wafer measurements areresented. The paper finishes with a conclusion in Section 6.

. The optical profilometer

Fig. 1 shows a scale drawing of the optical profilometerevice, operating typically at a pressure around 10−7 mbar.he vacuum chamber (Fig. 1A) is a standard CF-150 cross-iece. The vacuum is maintained during operation by an ionump (TiTan TM Ion pump, Gamma Vacuum, Fig. 1F). Forhe optical sensing a commercial sensor is used (IFS 2400-3,

icro-Epsilon, Fig. 1C). This sensor is based on the confocal

rinciple: a white light source is focused onto the sample, wheret is reflected. Different wavelengths focus at slightly differentoints and consequently a distance can be assigned dependingn which wavelength comes to an exact focus. The resolution

TTGp

ig. 1. Overview drawing (to scale) of the optical profilometer device. (A)acuum chamber with sample, (B) view-port, (C) optical sensor, (D and E)

ranslation stages, and (F) ion pump.

f the sensor is 0.12 �m averaging over a sample area of 25 �mn diameter. The perpendicular measuring range is 3 mm. Thisensor type is normally used in air and has previously beensed to characterize the shape and thickness of undeformedilicon wafers [9,10], but was custom calibrated by the manufac-urer to measure through the view-port (Spectrosil, Lambda/2,0/40 scratch/digit, 30 arc sec parallelity, Fig. 1B). The sensor iscanned across the view-port by two precision motorised trans-ation stages (M-405.PD, PI, Fig. 1 D and E) stacked on eachther and controlled separately.

The silicon wafers are mounted approximately 0.5 mm fromhe vacuum side of the view-port and accessed from the rear sohat the position of the view port and the sensor remain constanthen the sample is changed. This is crucial for the error map

orrection since a repositioned view-port would necessitate aew error map to be taken. Also crucial is the reproducibility ofhe positioning of the sample holder, which has been machinedo an alignment tolerance of ±0.01 mm. As the sensor averagesver an area of 25 �m, we conclude that positioning errors cane ignored in the present case. For a detailed description of theample holder see [11].

. The error map

Several factors influence the performance of the optical pro-lometer. Systematic error contributions arise from: (i) theiew-port, as the sensor is calibrated for the center of theiew-port only and thickness variations will give a systematicrror; (ii) reproducible out-of-plane movements of the transla-ion stages. Random errors arise from: (i) the resolution of theensor; (ii) vibrations; (iii) temperature fluctuations; (iv) non-eproducible out-of-plane movement of the translation stages.

he systematic errors can be compensated using an error map.he random errors limit the ultimate precision of the device.iven that the sensor averages over an area of 25 �m, the in-lane positioning errors of the translation stages are negligible

184 K. Fladischer et al. / Precision Eng

Fig. 2. The mean distance variation (z) from a flat reference plane across themeasuring range of the instrument. The data has been obtained by scanningacross an optical flat (λ/10) several times and fitting a Gaussian curve at eachpa0

atp

t4owamcpsFtt

Faaw

it2orsst

4

tvopsmttt

shcetwtaiotw

osition. The long-range movement in and out of the reference plane can bettributed to the translation stage spindles. The spacing of the contour lines is.2 �m.

nd measures can be implemented to minimise vibrational andhermal fluctuations. Hence, for the error map only the out-of-lane distance measurement errors are taken into account.

In order to determine the magnitude of the error contribu-ions, the silicon wafer was replaced with an optical flat (Linos,0 mm in diameter, flatness λ/10), and several scans across theptical flat were carried out. Based on these scans, two mapsere compiled displaying the mean distance variation (z) fromflat reference plane (Fig. 2) and the spread (σ) of the distanceeasured at each position (Fig. 3) (for each position a Gaussian

urve was fitted). Figs. 2 and 3 comprise the error map of therofilometer. When a silicon wafer is scanned, the distance mea-

ured at each point is corrected with the corresponding value inig. 2 and an error bar assigned corresponding to the σ-value at

hat point (Fig. 3).The long-range movement in and out-of-planehat can be seen in Fig. 2 can be attributed to the lead screws

ig. 3. The spread (σ) at each measurement point for the distance variation fromflat reference plane (see Fig. 2). It can be seen that one of the stages has two

reas where the out-of-plane positioning is less reproducible than elsewhere (thehite stripes).The spacing of the contour lines is 0.05 �m.

ttsmtttbpospuatTrt

5

e

ineering 32 (2008) 182–185

n the translation stages. The manufacturer guarantees that eachranslation stage has an out-of-plane movement of less than ±�m; no information is provided regarding the reproducibility

f this out-of-plane movement. In fact the movement is quiteeproducible in most places as can be seen in Fig. 3. The whitetripes in the figure indicate that the horizontal stage has twoections where the out-of-plane positioning is less reproduciblehan elsewhere.

. Determining the required sample rate

Having obtained the error map, the next step is to determinehe required sampling grid spacing. This will depend on the indi-idual measurement problem. We present here, as an example,ne approach suitable for our application. Our ultimate aim is torovide a focusing mirror, which will focus a helium beam to apot in the nanometer range when a particular mirror area is illu-inated. Hence, we need the profilometer to be able to measure

he profiles of the silicon wafers with an accuracy which allowshe prediction of the size of a focused spot with a diameter inhis range.

Our approach was as follows: We wish to compare the bentilicon profile with the shape of an ideal ellipsoidal mirror. Aeight-map based on the ideal ellipsoidal shape was thereforealculated [5]; (z = f (x, y)) where (x, y) is the base mirror ref-rence plane and z the height variations from that plane similaro the figures displayed in this paper. Several thousand data setsere generated with a statistical noise corresponding to a cer-

ain standard deviation (σ) in the distance measurement (z) andcertain sampling grid spacing in the (x, y) plane. For simplic-

ty we kept σ constant over the whole area. Ten σ values andne sampling grid spacing (0.25 mm) were chosen. Based onhis, all cases can be calculated, since the error scales with

√N,

here N is the number of measuring points. Each data set washen fitted with a fourth-order polynomial and compared withhe fourth-order polynomial expansion of the ideal ellipsoidalhape. This enabled us to evaluate the aberrations directly. Theost sensitive parameters were the fourth-order terms where

he relative deviations between the simulated coefficients andhe ideal coefficients were typically more than 100%. Data forhe average relative deviation of the x2y2-coefficient (M2,2) cane seen in Fig. 4. It turned out that given a σ of 1 �m, a sam-ling grid spacing of 0.5 mm (corresponding to a sampling timef 30 min for the whole mirror) is sufficient to determine thehape with the desired accuracy. The accuracy was tested byerforming ray-tracing, simulating the illumination of a partic-lar mirror area using the calculated polynomials. Data for theverage relative deviation of the x2y2-coefficient (M2,2) usinghe 0.5 mm sampling grid spacing can also be found in Fig. 4.he data shows the expected

√N behaviour. The larger the

equired illuminated area, the more precise the coefficients haveo be.

. Silicon wafer measurements

As a final demonstration we present a measurement of anlectrostatically deformed silicon wafer, carried out with our

K. Fladischer et al. / Precision Eng

Fig. 4. The curves show the relative deviation of the x2y2 coefficient for thesimulated data (σM2,2sim ) from the ideal x2y2 mirror coefficient (M2,2ideal) independence of the standard deviation of the simulated data (σDistance). Curvesare shown for two sampling grid spacings (0.25 and 0.5 mm).

F1

naagv

6

aTiTopt

A

NFcdcta

R

[

ig. 5. Scan of a 50 �m thick silicon wafer with an applied field of 1.12 ×06 V/m. The contour line spacing is 10 �m.

ew device. Fig. 5 shows a measurement of a wafer with an

pplied field of 1.12 × 106 V/m. The central deflection area ist a depth of 150 �m which corresponds to a realistic focusingeometry whilst asymmetries in the profile arise from thicknessariations in the ultrathin wafer [12].

[[

ineering 32 (2008) 182–185 185

. Conclusion

In this paper we present an optical profilometer for char-cterizing complex surfaces under high vacuum conditions.he device is based on an optical sensor. The scanning area

s a circle, 30 mm in diameter, and the sensor range is 3 mm.he lateral resolution of the sensor is 25 �m and the accuracyf the device in measuring the surface height distribution isresently within ±1 �m. The accuracy is primarily limited byhe translation stages.

cknowledgments

This work was supported by the European Commission, FP6,EST ADVENTURE program, Project INA, Contract 509014.urther support was obtained from the Polish Ministry of Edu-ation and Science. We are grateful to C. Jaritz for providing therawing of the profilometer in Fig. 1 and R. Balsod for his skilledraftmanship in fabricating the mirror assembly. The Insti-ute of Electronic Materials Technology (www.itme.edu.pl/) iscknowledged for having supplied 50 �m thick Si(1 1 1) wafers.

eferences

[1] MacLaren DA, Goldrein HT, Holst B, Allison W. Phase-stepping opticalprofilometry of atom mirrors. J Phys D 2003;36:1842–9.

[2] Schulz M. Topography measurements by a reliable large-area curvaturesensor. Optik 2001;112(2):86–90.

[3] Weingartner I, Elster C. System of four distance sensors for high-accuracymeasurements of topography. Prec Eng 2004;28:164–70.

[4] Elster C, Weingartner I, Schulz M. Coupled distance sensor systems forhigh-accuracy topography measurement: Accounting for scanning stageand systematic sensor errors. Prec Eng 2005;30:32–8.

[5] MacLaren DA, Allison W, Holst B. Single crystal optic elements for heliumatom microscopy. Rev Sci Inst 2000;71(7):2625–34.

[6] Holst B, Allison W. An atom-focusing mirror. Nature 1997;390:244.[7] Buckland JR, Holst B, Allison W. Helium reflectivity of the Si(1 1 1)-

(1 × 1)H surface for use in atom optical elements. Chem Phys Lett1999;303:107–10.

[8] Barredo D, Calleja F, Weeks AE, Nieto P, Hinarejos JJ, Laurent G, et al.Si(1 1 1)-H(1 × 1): a mirror for atoms characterized by AFM, STM, Heand H2 diffraction. Surf Sci 2007;601:24–9.

[9] Litwin D, Galas J, Kozlowski T, Sitarek S. Measurements of the geometricalcharacteristics of the silicon wafer for a helium microscope focusing mirror.Proc SPIE 2005;5948:177–84.

10] Galas J, Litwin D, Sitarek S, Surma B, Piatkowski B, Miros A. Interfer-ometric and confocal techniques for testing of silicon wafers. Proc SPIE

2006;6188:61880C.

11] Weeks AE, MacLaren DA, Allison WA. Rev Sci Instrum, in preparation.12] Sass J, Mazur K, Surma B, Eichhorn F, Litwin D, Galas J, et al. X-ray studies

of ultra-thin Si wafers for mirror application. Nucl Instrum Methods PhysRes B 2006;253:236–40.