Принципы нанометрологии, страница 5

160Type ER2 – rectangular groove standard .............................. 160Type ER3 – circular groove standard .................................... 161Type ES – sphere/plane measurement standard ................... 162Type CS – contour standard.................................................. 163Type CG1 – X/Y crossed grating ........................................... 163Type CG2 – X/Y/Z grating standard .....................................

164Results of a comparison of different instrumentsused to measure a sinusoidal sample ................................... 166Schematic image of a typical scanning probe system,in this case an AFM .............................................................. 179Block diagram of a typical SPM ............................................ 182Noise results from an AFM. The upper image shows anexample of a static noise investigation on a bare siliconwafer. The noise-equivalent roughness is Rq ¼ 0.013 nm.For comparison, the lower image shows the wafer surface:scan size 1 mm by 1 mm, Rq ¼ 0.081 nm ............................

184Schematic of the imaging mechanism of spherical particleimaging by AFM. The geometry of the AFM tip prevents‘true’ imaging of the particle as the apex of the tip is not incontact with the particle all the time and the final image isa combination of the tip and particle shape. Accuratesizing of the nanoparticle can only be obtained from theheight measurement ............................................................. 185Definition of the pitch of lateral artefacts:(a) 1D and (b) 2D .................................................................. 187Schematic of a force curve (a) and force-distancecurve (b) .................................................................................

190Schematic illustration of the strong capillary forcethat tends to drive the tip and sample together duringimaging in air ........................................................................ 194(a) TEM image of nominal 30 nm diameter gold nanoparticles; (b) using threshold to identify the individualparticles; (c) histogram of the measured diameters ............. 205TEM image of 150-nm-diameter latex particles. Thisimage highlights the drawback to TEM size measurementusing TEM or SEM. The first is that a white ‘halo’surrounds the particle. Should the halo area be included inthe size measurement? If so there will be a difficulty indetermining the threshold level.

The second is theparticles are aggregated, again making sizing difficult......... 206FiguresFigure 8.1Figure 8.2Figure 8.3Figure 8.4Figure 8.5Figure 8.6Figure 8.7Figure 8.8Figure 8.9Figure 8.10Figure 8.11Figure 8.12Figure 8.13Figure 8.14Figure 8.15Figure 8.16Figure 8.17Figure 8.18Figure 8.19Figure 8.20Figure 8.21Figure 8.22Figure 8.23Separation of surface texture into roughness, wavinessand profile.............................................................................. 214Primary (top), waviness (middle) and roughness (bottom)profiles ................................................................................... 215Maximum profile peak height, exampleof roughness profile ...............................................................

218Maximum profile valley depth, example of roughnessprofile ..................................................................................... 219Height of profile elements, example of roughnessprofile .....................................................................................

220The derivation of Ra ............................................................. 221Profiles with positive (top), zero (middle) and negative(bottom) values of Rsk (reprinted from ASME B46.11995, by permission of the American Society ofMechanical Engineers. All rights reserved) .......................... 222Profiles with low (top) and high (bottom) values of Rku(reprinted from ASME B46.1-1995, by permission of theAmerican Society of Mechanical Engineers. All rightsreserved) ................................................................................ 223Width of profile elements ..................................................... 224Material ratio curve ...............................................................

225Profile section level separation ............................................. 226Profile height amplitude distribution curve ......................... 227Amplitude distribution curve ............................................... 227Epitaxial wafer surface topographies in differenttransmission bands: (a) the raw measured surface;(b) roughness surface (short scale SL-surface) S-filter ¼0.36 mm (sampling space), L-filter ¼ 8 mm); (c) wavysurface (middle scale SF-surface) S-filter ¼ 8 mm,F-operator; and (d) form error surface (long scale formsurface), F-operator ...............................................................

231Areal material ratio curve ..................................................... 240Inverse areal material ratio curve ......................................... 240Void volume and material volume parameters .................... 242Example simulated surface ................................................... 245Contour map of Figure 8.18 showing criticallines and points ..................................................................... 245Full change tree for Figure 8.19 ............................................

246Dale change tree for Figure 8.19 .......................................... 247Hill change tree for Figure 8.19 ............................................ 247Line segment tiling on a profile ............................................ 253xxixxiiFiguresFigure 8.24Figure 8.25Figure 9.1Figure 9.2Figure 9.3Figure 9.4Figure 9.5Figure 9.6Figure 9.7Figure 9.8Figure 9.9Figure 9.10Figure 9.11Figure 9.12Figure 10.1Figure 10.2Figure 10.3Inclination on a profile .........................................................

254Tiling exercises for area-scale analysis ................................. 256A typical moving bridge CMM ............................................. 264CMM configurations............................................................. 265Illustration of the effect of different measurementstrategies on the diameter and location of a circle. Themeasurement points are indicated in red; the calculatedcircles from the three sets are in black and the centres areindicated in blue .................................................................... 271Schema of the kinematic design of the Zeiss F25 CMM .... 273Schema of the NMM ............................................................

275Schema of the NMM measurement coordinatemeasuring principle .............................................................. 276Silicon micro-scale probe designed by [34], produced bychemical etching and vapour deposition .............................. 277The fibre probe developed by PTB. Notice the secondmicrosphere on the shaft of the fibre; this gives accuratemeasurement of variations in sample ‘height’(z axis) [38] ............................................................................ 278A vibrating fibre probe. The vibrating end forms a ‘virtual’tip that will detect contact with the measurement surfacewhile imparting very little force [41] ....................................

279Vertical AFM probe for MEMS sidewall investigation [44].... 280Miniature CMM performance verification artefacts.(a) METAS miniature ball bar, (b) PTB ball plate, (c) PTBcalotte plate, (d) PTB calotte cube, (e) Zeiss halfsphereplate ....................................................................................... 282Straightness (xTx) measurement of the F25 with the CAAcorrection enabled ................................................................. 284Comparative plot of described surface interaction forces,based on the following values: R ¼ 2 mm; U ¼ 0.5 V;g ¼ 72 mJ$m2; H ¼ 1018 J; e ¼ r ¼ 100 nm.

Physicalconstants take their standard values: e0 ¼ 8.854 1012C2$N1$m2; h ¼ 1.055 1034 m2$kg$s1 andc ¼ 3 108 m$s1 ................................................................ 299Schema of the NPL low-force balance .................................. 300Experimental prototype reference cantilever array –plan view ............................................................................... 302FiguresFigure 10.4 Images of the NPL C-MARS device, with detailof its fiducial markings; the 10 mm oxide squaresform a binary numbering system along the axisof symmetry .......................................................................... 303Figure 10.5 Computer model of the NPL Electrical Nanobalancedevice.

The area shown is 980 mm 560 mm.Dimensions perpendicular to the plane have beenexpanded by a factor of twenty for clarity ............................ 305Figure 10.6 Schema of a resonant force sensor – the nanoguitar ........... 306xxiiiThis page intentionally left blankTablesTable 3.1Table 3.2Table 4.1Table 4.2Table 4.3Table 6.1Table 7.1Table 7.2Table 7.3Table 8.1Table 8.2TableTableTableTableTable8.38.48.58.68.7Sources of seismic vibration and correspondingfrequencies [27] ......................................................................... 48Possible sources of very-low-frequency vibration .....................