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 Data Analysis Sheet L.4

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

Top view of ring test structure depicting the measurement to be made.

Figure L.4.1.  Top view of ring test structure depicting the measurement to be made,
where Edge 1 and Edge 2 are considered outside 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 which ring?      
    
     
        
       
    
    		which ring (from left-to-right or top-to-bottom) on the test chip ?  
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 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., x2upper) = µm (x2min > x1min)
16 x2max (i.e., x2lower) = µm   (x2max > x2min)


                                    
 

Table 3 - OUTPUTS (calibrated values)

Notes
17 Lmin = µm Lmin =  ( x2min − x1min ) * calx
18 Lmax =  µm Lmax = ( x2max − x1max ) * calx
19 L = µm in-plane length
L =  (Lmin + Lmax ) / 2
       
20 uL = µm uL = (Lmax − Lmin ) / 6
21 uxcal = µm uxcal = (σxcal / interx) * ( L / calx )
22 uxres = µm uxres = xres * calx / 1.732
23 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. Is the magnification appropriate for the given measurement ?
3. Magnifications at or less than 2.5× shall not be used.
4. Is 0.95 < calx < 1.05 but not equal to "1" ?  If not, recheck your x-calibration.
5. The value for interx should be between 0 µm and 1500 µm.
6. The value for σxcal should be between 0 µm and 4 µm.
7. The value for xres should be between 0 µm and 1.57 µm.
8.  Is 0.95 < calz < 1.05 but not equal to "1" ?  If not, recheck your z-calibration.
9. Alignment has not been ensured.
10. Data has not been leveled.
11. x1min should be greater than x1max.   
12. x2min should be greater than x1min.
13. x2max should be greater than x2min.
14. The calibrated values for x1min and x1max are greater than 10 µm apart.
15. The calibrated values for x2min and x2max are greater than 10 µm apart.
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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: 6/2/2008