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 Data Analysis Sheet L.6

Data analysis sheet for in-plane deflection measurements from released part to fixed location

Top view of a portion of the pointer test structure depicting the measurement to be made.

Figure L.6.1.  Top view of a portion of the pointer test structure depicting the measurement to be made.

To obtain the following measurements, consult ASTM standard test method E 2244 entitled
"Standard Test Method for In-Plane Length Measurements of Thin, Reflecting Films
Using an Optical Interferometer."


date data taken (optional) = / /

   
   
   
 
filename of 2-D data traces (optional) =
                                                              

Table 1 - Preliminary ESTIMATES

Description

1 material =       
      
 
      
    
      
 
   

material

2 displacement = μm

designed displacement

3 which?             
      
     
          
which iteration of the test structure where "first" corresponds to the topmost or leftmost test structure in the column or array of the same material that has the specified designed displacement?
4 magnification = × magnification
5 orientation =               
      
    
orientation on the chip
6 calx = x-calibration factor (for the given magnification)
7 interx = μm interferometer's maximum field of view (for the given magnification)
8 σxcal = μm one sigma uncertainty in a ruler measurement (for the given magnification)
9 xres = μm uncalibrated resolution of the interferometer in the x-direction
10 calz = z-calibration factor (for the given magnification)
11 aligned?      alignment ensured ?
12 leveled?      data leveled ?


                                      

 

Table 2 - INPUTS (uncalibrated values)

Notes

13 x1max (i.e., x1lower) = μm  
14 x1min (i.e., x1upper) = μm (x1min > x1max)
15 x2min (i.e., x2lower) = μm        (x2min > x1min)
16 x2max (i.e., x2upper) = μm  (x2max > x2min)
       
17 sep = μm uncalibrated pixel-to-pixel spacing (for the given magnification)
18 which values?      Use 'lower' or 'upper' values for calculation ? 


                                            


OUTPUTS (calibrated values):

            D1-min =  ( x2minx1min ) calx μm
            D1-max = ( x2maxx1max ) calx μm

            D1 =  (D1-min + D1-max ) / 2 = μm
                    
uD = (D1-max D1-min ) / 6 = μm
                     uxcal = (σxcal / interx) ( D1 / calx ) = μm
                     uxres
= xres cal
x / 1.732 = μm
            ucD = SQRT [ uD2 + uxcal2 + uxres2] = μm

            D1low (using lower values) = ( x2lower x1lower ) calx = μm
                     uD-low =
[2 (sep) calx] / 3 = μm
                     uxcal-low = (σxcal / interx) ( D1low / calx= μm

            ucDlow = SQRT [ uD-low2 + uxcal-low2 + uxres2] = μm

            D1up (using upper values) = ( x2upper
x1upper ) calx = μm
            
         uD-up = [2 (sep) calx] / 3 = μm
                     uxcal-up = (σxcal / interx) ( D1up / calx= μm

            ucDup = SQRT [ uD-up2 + uxcal-up2 + uxres2] = μm


           (Each of the standard uncertainty components is obtained using a Type B analysis.)

Report the results as follows:  Since it can be assumed that the estimated values of the uncertainty
components are approximately uniformly or Gaussianly distributed with approximate combined standard
uncertainty ucD, the in-plane deflection is believed to lie in the interval D1 ± ucD (expansion factor k=1)
representing a level of confidence of approximately 68 %. 

Modify the input data, given the information supplied in any flagged statement below, if applicable, then recalculate:
1. Please fill out the entire form.
2. The designed displacement is typically 0.0 μm.
3. The measured value for D1 is 10 μm greater than the designed displacement.
4. Is the magnification appropriate given the value for D1 ?
5. Magnifications at or less than 2.5× shall not be used.
6.  Is 0.95 < calx < 1.05 but not equal to "1" ?  If not, recheck your x-calibration.
7. The value for interx should be between 0 μm and 1500 μm.
8. The value for σxcal should be between 0 μm and 4 μm.
9. The value for xres should be between 0 μm and 1.57 μm.
10.  Is 0.95 < calz < 1.05 but not equal to "1" ?  If not, recheck your z-calibration.
11. Alignment has not been ensured.
12. Data has not been leveled.
13. x1min should be greater than x1max.
14. x2min should be greater than x1min.
15. x2max should be greater than x2min.
16. The calibrated values for x1min and x1max are greater than 10 μm apart.
17. The calibrated values for x2min and x2max are greater than 10 μm apart.
18. sep should be between 0 μm and 1.57 μm.

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Email questions or comments to mems-support@nist.gov.

NIST is an agency of the U.S. Commerce Department.
The Semiconductor and Dimensional Metrology Division is within the Physical Measurement Laboratory.
The MEMS Measurement Science and Standards Project is within the Nanoscale Metrology Group.

Date created: 12/4/2000
Last updated: 4/26/2013