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|---|---|---|---|---|---|---|---|
| 2<\/td>\n | undefined <\/td>\n<\/tr>\n | ||||||
| 4<\/td>\n | CONTENTS <\/td>\n<\/tr>\n | ||||||
| 7<\/td>\n | FOREWORD <\/td>\n<\/tr>\n | ||||||
| 9<\/td>\n | INTRODUCTION <\/td>\n<\/tr>\n | ||||||
| 10<\/td>\n | Figures Figure 1 \u2013 Spatial resolution of magnetic stray field characterizationtechniques and their possible maximum scan area <\/td>\n<\/tr>\n | ||||||
| 11<\/td>\n | 1 Scope 2 Normative references 3 Terms and definitions 3.1 General terms <\/td>\n<\/tr>\n | ||||||
| 12<\/td>\n | 3.2 General terms related to magnetic stray field characterization <\/td>\n<\/tr>\n | ||||||
| 13<\/td>\n | 3.3 Terms related to the measurement method described in this document <\/td>\n<\/tr>\n | ||||||
| 18<\/td>\n | 3.4 Key control characteristics measured according to this document <\/td>\n<\/tr>\n | ||||||
| 19<\/td>\n | 3.5 Symbols and abbreviated terms <\/td>\n<\/tr>\n | ||||||
| 20<\/td>\n | 4 General 4.1 Measurement principle, general <\/td>\n<\/tr>\n | ||||||
| 21<\/td>\n | Figure 2 \u2013 Field measurement with finite-size sensors <\/td>\n<\/tr>\n | ||||||
| 22<\/td>\n | 4.2 Application to scanning systems, discretization 4.3 Preparation of the measurement setup 4.4 Measurement principle, MFM 4.4.1 General Figure 3 \u2013 Schematic MFM setup <\/td>\n<\/tr>\n | ||||||
| 23<\/td>\n | 4.4.2 Field detection process 4.4.3 Lever correction function FLCF <\/td>\n<\/tr>\n | ||||||
| 24<\/td>\n | Figure 4 \u2013 Lever correction function (FLCF) in Fourier space <\/td>\n<\/tr>\n | ||||||
| 25<\/td>\n | 4.4.4 Effective magnetic charge density of the tip 4.4.5 Characteristics of the MFM FICF Figure 5 \u2013 Lever correction function (FLCF) and distance losses <\/td>\n<\/tr>\n | ||||||
| 26<\/td>\n | 4.4.6 Concept of calibration by deconvolution Figure 6 \u2013 Instrument calibration function (FICF ) in real and Fourier space. Line plots of the partial Fourier space (absolute value, left) and real space (right). <\/td>\n<\/tr>\n | ||||||
| 27<\/td>\n | 4.4.7 Regularized deconvolution approach <\/td>\n<\/tr>\n | ||||||
| 28<\/td>\n | 4.5 MFM setup key control characteristics 4.5.1 General <\/td>\n<\/tr>\n | ||||||
| 29<\/td>\n | 4.5.2 Cantilever spring constant C Tables Table 1 \u2013 MFM setup key control characteristics <\/td>\n<\/tr>\n | ||||||
| 30<\/td>\n | 4.5.3 Cantilever resonance quality factor Q 4.5.4 Sensitivity of the detection and analysis electronics Figure 7 \u2013 Typical resonance curve of a cantilever <\/td>\n<\/tr>\n | ||||||
| 31<\/td>\n | 4.5.5 Measurement height 4.5.6 Scan size, pixel resolution 4.5.7 Canting angle of the cantilever in the setup 4.5.8 Magnetization orientation of the tip Figure 8 \u2013 Typical amplitude\u2013distance plot of a cantileverwith the linear transition region indicated <\/td>\n<\/tr>\n | ||||||
| 32<\/td>\n | 4.5.9 Regularized deconvolution 4.6 Ambient conditions during measurement 4.7 Reference samples 4.7.1 General 4.7.2 “Well-known” and calculable reference sample 4.7.3 Band domain patterns as self-referencing calibration samples Table 2 \u2013 Ambient conditions key control characteristics <\/td>\n<\/tr>\n | ||||||
| 33<\/td>\n | 4.7.4 Detailed stray field calculation procedure for perpendicularly magnetized band domain reference samples Figure 9 \u2013 Band domain reference sample <\/td>\n<\/tr>\n | ||||||
| 34<\/td>\n | Table 3 \u2013 Stray field estimation key control characteristics <\/td>\n<\/tr>\n | ||||||
| 35<\/td>\n | Table 4 \u2013 Stray field estimation protocol <\/td>\n<\/tr>\n | ||||||
| 36<\/td>\n | 5 Measurement procedure for calibrated magnetic field measurements 5.1 Calibrated stray field measurement of a sample under test <\/td>\n<\/tr>\n | ||||||
| 37<\/td>\n | 5.2 Detailed description of the measurement and calibration procedure 5.3 Measurement protocol <\/td>\n<\/tr>\n | ||||||
| 38<\/td>\n | Table 5 \u2013 Measurement protocol <\/td>\n<\/tr>\n | ||||||
| 39<\/td>\n | 5.4 Measurement reliability 5.4.1 Artefacts in MFM measurements 5.4.2 Artefacts resulting from strong stray field samples <\/td>\n<\/tr>\n | ||||||
| 40<\/td>\n | 5.4.3 Artefacts when measuring samples with low coercivity 5.4.4 Distortion of the domain structure Figure 10 \u2013 Artefacts that occur if the tip magnetization is switchedby the stray field of the sample Figure 11 \u2013 Artefacts if the sample domain orientation is switchedby a strong tip stray field <\/td>\n<\/tr>\n | ||||||
| 41<\/td>\n | 5.4.5 Contingency strategy 5.4.6 Strategies to improve the quality of the measurements 5.5 Uncertainty evaluation 5.5.1 General 5.5.2 Reference sample Figure 12 \u2013 Typical distortion of an MFM image: different domain widths <\/td>\n<\/tr>\n | ||||||
| 42<\/td>\n | 5.5.3 ICF determination 5.5.4 Calibrated field measurement <\/td>\n<\/tr>\n | ||||||
| 43<\/td>\n | 6 Data analysis \/ interpretation of results 6.1 Software for data analysis Table 6 \u2013 Uncertainty evaluation key control characteristics <\/td>\n<\/tr>\n | ||||||
| 44<\/td>\n | Table 7 \u2013 Software implementation of stray field calculation of band domain samples Table 8 \u2013 Software-based realization of calibrated measurement <\/td>\n<\/tr>\n | ||||||
| 45<\/td>\n | 7 Results to be reported 7.1 General 7.2 Product \/ sample identification 7.3 Test conditions 7.4 Measurement set-up specific information <\/td>\n<\/tr>\n | ||||||
| 46<\/td>\n | 7.5 Test results 8 Validity assessment 8.1 General aspects <\/td>\n<\/tr>\n | ||||||
| 47<\/td>\n | 8.2 Requirements 8.3 Example 8.3.1 Determination of the Instrument Calibration Function FICF <\/td>\n<\/tr>\n | ||||||
| 48<\/td>\n | Figure 13 \u2013 Normalized Fourier amplitudes of the measured referencesample signal \u0394\u03c6ref and the reference sample magnetic field <\/td>\n<\/tr>\n | ||||||
| 49<\/td>\n | 8.3.2 Calibrated measurement Figure 14 \u2013 Typical transfer functions in Fourier and real space for different values of the regularization parameter \u03b1 Figure 15 \u2013 Comparison of the reference sample signal \u0394\u03c6ref and the SUT signal \u0394\u03c6SUT <\/td>\n<\/tr>\n | ||||||
| 51<\/td>\n | Annex A (informative)Algorithm A.1 Mathematical basics A.1.1 Continuous Fourier transform versus discrete Fourier Transform A.1.2 Partial (two-dimensional) Fourier space A.1.3 Cross correlation theorem <\/td>\n<\/tr>\n | ||||||
| 52<\/td>\n | A.2 Magnetic fields in partial Fourier space A.2.1 Differentiation in partial Fourier space A.2.2 Magnetic fields in partial Fourier space A.3 Signal generation in magnetic force microscopy A.3.1 General <\/td>\n<\/tr>\n | ||||||
| 53<\/td>\n | A.3.2 MFM phase shift signal <\/td>\n<\/tr>\n | ||||||
| 54<\/td>\n | A.3.3 L-curve criterion for pseudo-Wiener filter-based deconvolution process <\/td>\n<\/tr>\n | ||||||
| 55<\/td>\n | Figure A.1 \u2013 Plot of the 2-norm of the residual as a functionof the regularization parameter Figure A.2 \u2013 Example of an L-curve Figure A.3 \u2013 Illustration of the curvature of the L-curveas a function of the regularization parameter <\/td>\n<\/tr>\n | ||||||
| 56<\/td>\n | Annex B (informative)Uncertainty evaluation B.1 Definition for instrument calibration B.2 Definition for calibrated field measurement <\/td>\n<\/tr>\n | ||||||
| 57<\/td>\n | B.3 A type uncertainty evaluation B.4 B type uncertainty evaluation B.4.1 General B.4.2 Propagation of uncertainty from the real to the Fourier domain <\/td>\n<\/tr>\n | ||||||
| 58<\/td>\n | B.4.3 Propagation of uncertainty from the Fourier to the real space domain <\/td>\n<\/tr>\n | ||||||
| 59<\/td>\n | B.4.4 Uncertainty propagation based on the Wiener filter <\/td>\n<\/tr>\n | ||||||
| 61<\/td>\n | B.4.5 Uncertainty evaluation for the tip calibration <\/td>\n<\/tr>\n | ||||||
| 62<\/td>\n | B.4.6 Uncertainty evaluation for the stray field evaluation <\/td>\n<\/tr>\n | ||||||
| 63<\/td>\n | B.5 Monte Carlo technique <\/td>\n<\/tr>\n | ||||||
| 64<\/td>\n | Bibliography <\/td>\n<\/tr>\n<\/table>\n","protected":false},"excerpt":{"rendered":" Nanomanufacturing. Key control characteristics – Traceable spatially resolved nano-scale stray magnetic field measurements. Magnetic force microscopy<\/b><\/p>\n |