The standard evaluation method for measurement uncertainty recommended by the Guideline to the Expression of Uncertainty in Measurement (GUM) [1] meets difficulties when a complicated relationship exists between the measurands and their input parameters. In the past, so-called virtual instrument models, like e.g. the virtual CMM, have been developed to assist in the determination of task-specific measurement uncertainties.
The Virtual Scanning Force Microscopy (Virtual SFM) builds numerical models for the individual error sources in the SFM instrument and the environment, and imitates the change of the measurement data during the whole measurement procedure to reveal the influence of these error sources. It makes the whole analysis process more transparent to the user. In the simulation, the Monte Carlo method defined in the Supplement 1 to the GUM [2] is applied to obtain statistics for the measurement process.
After the mainframe building as well as the components development of the Virtual SFM was realized, we applied it to the commercial SFM Dimension 5000 and compared its uncertainty budget results with the values derived from real measurements, as a validation.
Because sufficient knowledge about the instrument is necessary for an exact simulation, calibrations and measurements are demanded to investigate this SFM before simulation. Besides conventional calibrations, a self-calibration method was achieved to map the geometry errors of the instrument precisely. The following calibrations and measurements were executed with SFM Dimension 5000:
- Self-calibration using a 2D grating to map the 2D systematic positioning errors of x-y plane
- Self-calibration using a wedge to measure the squareness between the z-axis and the x-y plane
- Calibrating the nonlinearity of the z-axis using a calibrated compact piezoelectric positioning stage (z-PPS)
- Measurement of the flatness in x-y plane
- Calibrating the scale factors of x-, y- and z-axis using 2D grating and step height
- Measurement of the drifts in x-, y- and z-axis
- Real-time measurement of the temperature, humidity and air pressure.
(a) | (b) |
Fig.1: Distribution of the simulation and measurement results: (a) simulation results, (b) measurement results
The simulation result of the Virtual SFM shows that such measurements can very well be simulated in the Virtual SFM to obtain the measurement uncertainty if some of the important SFM parameters are determined.
[1] 1995 Guide to the Expression of Uncertainty in Measurement 2nd edition (Geneva: International Organization for Standardization) ISBN 92-67-10188-9
[2] 2004 Draft GUM Supplement 1: numerical methods for the propagation of distributions, BIPM Joint Committee on Guides in Metrology
Kontakt
Abteilungsleiter
Dr. Harald Bosse
Telefon: (0531) 592-5010
E-Mail:
harald.bosse(at)ptb.de
Sekretariat
Kimberly Smith-Rösler
Telefon: (0531) 592-5011
Fax: (0531) 592-69 5011
E-Mail:
kimberly.smith-roesler(at)ptb.de
Anschrift
Physikalisch-Technische Bundesanstalt
Bundesallee 100
38116 Braunschweig