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Data Analysis Sheet SH.3

Data analysis sheet for step height measurements taken during different data sessions from two step height test structures.


a)                                                 b)

Figure SH.3.1.  For a CMOS step height test structure: a) a design rendition and b) a cross-section.

To obtain the following measurements, consult SEMI standard test method MS2 entitled
"Test Method for Step Height Measurements of Thin Films."


                                      

                                    

date first 3-D data set taken (optional) = / /
date second 3-D data set taken (optional) = / /


   
   
   


Table 1 - Preliminary INPUTS

 

   First Test
Structure		 Second Test
Structure

Description
1 proc =

 
   
       

which process?
2 which =      
 
      
    
      
     		      
 
      
    
      
     		For CMOS SRM chips, which test structure? 
For MUMPs chips, which quad?
3 which2 =       
 
     
   
      
     
 
   
     
     		      
 
      
    
      
     
 
   
     
     		Which platform, where "first" corresponds to the leftmost or bottommost platform in the test structure, counting the reference platform?
4 which3 =       
 
     
    
       		      
 
     
    
       		For CMOS chips, which iteration of the test structure where "first" corresponds to the topmost test structure in the column?
5 orient =   

   

 

 

 

   

   

 

 

 

orientation of the test structure on the test chip
6 mag = × × magnification
7 align =

alignment ensured?
8 level =

data leveled?
9 cert = μm μm certified value of physical step height standard used for calibration
10 σcert = μm μm certified one sigma uncertainty of the certified physical step height standard used for calibration
11 zrepeat(shs)= μm μm maximum uncalibrated range of the six calibration measurements taken before the data session at the same location on the physical step height or after the data session at the same location on the physical step height (whichever is larger)
12 z6 = μm μm the uncalibrated average of the six calibration measurements from which zrepeat(shs) was found
13 zdrift = μm μm uncalibrated drift in the calibration data (i.e., the uncalibrated positive difference between the average of the six calibration measurements taken before the data session at the same location on the physical step height and the average of the six calibration measurements taken after the data session at the same location on the physical step height)
14 calz = the z-calibration factor = the certified value of the physical step height standard divided by the average of the twelve calibration measurements taken at the same location on the physical step height
15 zperc = % % if applicable, over the instrument's total scan range, the maximum percent deviation from linearity, as quoted by the instrument manufacturer (typically less than 3%)
16 σroughLX= μm   the uncalibrated surface roughness of platLX measured as the smallest of all the values obtained for σplatLXt.  (However, if the surfaces of platLX, platMY, platLr, and platMr all have identical compositions, then it is measured as the smallest of all the values obtained for σplatLXt, σplatMYt, σplatLrDt, and σplatMrDt in which case σroughLX= σroughMY.)
17 σroughMY=  

μm

 the uncalibrated surface roughness of platMY measured as the smallest of all the values obtained for σplatMYt.  (However, if the surfaces of platLX, platMY, platLr, and platMr all have identical compositions, then it is measured as the smallest of all the values obtained for σplatLXt, σplatMYt, σplatLrDt, and σplatMrDt in which case σroughLX= σroughMY.)

                                      

                                    


Nomenclature:
    "L" and "M" refer to the test structure number ("1," "2," "3," etc.),
    "X" and "Y" refer to the platform letter ("A," "B," "C," etc.),
    "r" refers to the reference platform,
    "D" directionally indicates which reference platform ("N," "S," "E," or "W"), and
    "t" indicates which data trace ("a," "b," or "c").

Table 2a - Uncalibrated REFERENCE PLATFORM INPUTS (in μm)
First Test Structure Second Test Structure
1a 4a 1b 4b
2a 5a 2b 5b
3a 6a 3b 6b
 

Table 2b - Calibrated REFERENCE PLATFORM CALCULATIONS (in μm)
First Test Structure Second Test Structure
7a 8a 7b 8b
Note 1:  platLr = AVE(platLrWa, platLrWb, platLrWc, platLrEa, platLrEb, platLrEc) calz
Note 2:  splatLr = STDEV(platLrWa, platLrWb, platLrWc, platLrEa, platLrEb, platLrEc) calz
Note 3:  The calculations for the second test structure are similar to the calculations for the first test
structure given in Notes 1 and 2.

Table 3a - Uncalibrated PLATFORM INPUTS (in μm)
First Test Structure Second Test Structure
9a 9b
10a 10b
11a 11b
12a platLXa = 12b platMYa =
13a platLXb = 13b platMYb =
14a platLXc = 14b platMYc =
 

Table 3b - Calibrated PLATFORM CALCULATIONS (in μm)
First Test Structure Second Test Structure
15a 15b
16a 16b
17a platLXave = 17b platMYave =
18a 18b
19a 19b
20a 20b
21a 21b
22a 22b
23a 23b
24a 24b
Note 4:  platLX = calz AVE(platLXa, platLXb, platLXc) - platLr
Note 5:  splatLX = calz STDEV(platLXa, platLXb, platLXc)
Note 6:  σplatLXave = calz AVE(σplatLXa, σplatLXb, σplatLXc)
Note 7:  uLplatLX = σplatLXave - calz σroughLX
Note 8:  uWplatLX = SQRT(splatLX2+splatLr2)
Note 9:  ucertLX = |σcert platLX / cert|
Note 10:  urepeat(shs)LX = |zrepeat(shs) platLX / [2(1.732) z6]|
Note 11:  udriftLX = |(zdrift calz) platLX / [2(1.732) cert]|
Note 12:  ulinearLX = |zperc platLX / (1.732)|
Note 13:  uplatLX = SQRT(uLplatLX2+uWplatLX2+ucertLX2+urepeat(shs)LX2+udriftLX2+ulinearLX2)
                   (Each of the standard uncertainty components is obtained using a Type B analysis,
                except for uWplatLX, which uses a Type A analysis.)
Note 14:  The calculations for the second test structure are similar to the calculations for the first
test structure given in Notes 4 through 13, inclusive.

Table 4 - Calibrated OUTPUTS (in μm)
 
25
Note 15:  stepLXMY = platMY-platLX
 Note 16:  ucSH = SQRT(uplatLX2+uplatMY2)

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 ucSH, the step height is believed to lie in the interval stepLXMY ± ucSH (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. he Preliminary Inputs Table.
2.
3a.
3b.
4a.
4b.
5.
6.
7.
8.
9.
10.
11.
12.
13.  
14.
15.  
16.  
17.  
18.  
19.  
20.
21. σplatLXt and σplatMYt should be between 0.0 μm and 0.02 μm, inclusive.
22.
23.
24.
25.

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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: 3/4/2006
Last updated: 4/26/2013