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 Data Analysis Sheet L.1

Data analysis sheet for in-plane length measurements with two ends anchored
(or for an inside edge-to-inside edge length measurement)

Top view of a fixed-fixed beam test structure depicting the measurement to be made.

Figure L.1.1.  Top view of a fixed-fixed beam test structure depicting the measurement
to be made, where Edge 1 and Edge 2 are considered inside edges.

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) = / /

   
   

 

Table 1 - Preliminary ESTIMATES

Description
1 material =    

material
2 design length = µm

design length
3 magnification = × magnification
4 orientation = 
    		orientation on the chip
5 calx = x-calibration factor (for the given magnification)
6 interx = µm interferometer's maximum field of view (for the given magnification)
7 σxcal = µm one sigma uncertainty in a ruler measurement (for the given magnification)
8 xres = µm resolution of the interferometer in the x-direction
9 calz = z-calibration factor (for the given magnification)
10 aligned?      alignment ensured ?
11 leveled?      data leveled ?


                                       

 

Table 2 - INPUTS (uncalibrated values)

Notes
12 x1max (i.e., x1upper) = µm  
13 x1min (i.e., x1lower) =  µm (x1min > x1max)
14 x2min (i.e., x2lower) = µm (x2min > x1min)
15 x2max (i.e., x2upper) =   µm (x2max > x2min)


                                     

 

Table 3 - OUTPUTS (calibrated values)

Equation
16 Lmin = µm Lmin =  ( x2min – x1min ) * calx
17 Lmax = µm Lmax = ( x2max – x1max ) * calx
18 L = µm in plane length
L =  (Lmin + Lmax ) / 2
       
19 uL = µm uL = ( Lmax – Lmin ) / 6
20 uxcal = µm uxcal = (σxcal / interx) * ( L / calx )
21 uxres = µm uxres = xres * calx / 1.732
22 uc = µm combined standard uncertainty
uc = SQRT [ uL2 + uxcal2 + uxres2]

Report the results as follows:  Since it can be assumed that the possible estimated values are either
approximately uniformly distributed or Gaussian with approximate standard deviation uc, the length
is believed to lie in the interval L ± uc with a level of confidence of approximately 68 %
assuming a Gaussian distribution. 

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 design length should be between 0 µm and 1050 µm.
3. The measured value for L is more than 3uc from the design length.
4. Is the magnification appropriate given the design length ?
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.
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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 Electronics Division is within the Electronics and Electrical Engineering Laboratory.
The MNT Project (http://www.eeel.nist.gov/812/MNT/index.html) is within the Enabling Devices and ICs Group.

Date created: 12/4/2000
Last updated: 6/2/2009
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