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Data Analysis Sheet SH.3.a

Data analysis sheet for step height measurements taken during different data sessions from two step height test structures with a more detailed calculation of ucSH, which includes the repeatability component, urepeat(samp).


a)                                                           b)

Figure SH.3.a.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 temp =

°

 temperature during measurement (should be held constant)
2 relative humidity =

relative humidity during measurement (if not known, enter -1)
3 proc =

 
   
       

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

   

 

 

 

   

   

 

 

 

orientation of the test structure on the test chip
8 mag = × × magnification
9 align =

alignment ensured?
10 level =

data leveled?
11 cert = μm μm certified value of physical step height standard used for calibration
12 σcert = μm μm certified one sigma uncertainty of the certified physical step height standard used for calibration
13 σ6ave = μm μm maximum of two uncalibrated values (σbefore and σafter) where σbefore is the standard deviation of six measurements taken across the physical step height standard before the data session and σafter is the standard deviation of six measurements taken across the physical step height standard after the data session
14 z6ave = μm μm uncalibrated average of the six calibration measurements used to calculate σ6ave
15 σ6same= μm μm maximum of two uncalibrated values (σsame1 and σsame2) where σsame1 is the standard deviation of six measurements taken on the physical step height standard at the same location before the data session and σsame2 is the standard deviation of six measurements taken at this same location after the data session
16 z6same = μm μm uncalibrated average of the six calibration measurements used to calculate σ6same
17 zdrift = μm μm uncalibrated drift in the calibration data (i.e., the uncalibrated positive difference between the average of the six measurements taken before the data session at the same location on the physical step height and the average of the six measurements taken after the data session at the same location on the physical step height)
18 calz = the z-calibration factor (for the given magnification)
19 zlin = % % if applicable, the maximum relative deviation from linearity over the instrument's total scan range, as quoted by the instrument manufacturer (typically less than 3%)
20 σrepeat(samp)=

%

 step height relative repeatability standard deviation obtained from step height test structures fabricated in a process similar to that used to fabricate the sample
21 sroughLX= μm   the uncalibrated surface roughness of platLX measured as the smallest of all the values obtained for splatLXt.  (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 splatLXt, splatMYt, splatLrDt, and splatMrDt in which case sroughLX= sroughMY.)
22 sroughMY=  

μm

 the uncalibrated surface roughness of platMY measured as the smallest of all the values obtained for splatMYt.  (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 splatLXt, splatMYt, splatLrDt, and splatMrDt in which case sroughLX= sroughMY.)

                                      

                                    


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 indicates a 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 s 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
25a 25b
26a 26b
Note 4:  platLX = calz AVE(platLXa, platLXb, platLXc) - platLr
Note 5:  splatLX = calz STDEV(platLXa, platLXb, platLXc)
Note 6:  splatLXave = calz AVE(splatLXa, splatLXb, splatLXc)
Note 7:  uLplatLX = SQRT[splatLXave2 - (calz sroughLX)2]
Note 8:  uWplatLX = SQRT(splatLX2+splatLr2)
Note 9:  ucertLX = |σcert platLX / cert|
Note 10:  ucalLX = |σ6ave platLX / z6ave|
Note 11:  urepeat(shs)LX = |σ6same platLX /  z6same|
Note 12:  udriftLX = |(zdrift calz) platLX / [2(1.732) cert]|
Note 13:  ulinearLX = |zlin platLX / (1.732)|
Note 14:  urepeat(samp)LX= |σrepeat(samp) platLX |
Note 15:  uplatLX = SQRT(uLplatLX2+uWplatLX2+ucertLX2+ucalLX2+urepeat(shs)LX2
                                                                   +udriftLX2+ulinearLX2+urepeat(samp)LX2)
       (Each of the standard uncertainty components is obtained using a Type B analysis, except
       for uWplatLX, ucalLX, urepeat(shs)LX, and urepeat(samp)LX which use a Type A analysis.)
Note 16:  The calculations for the second test structure are similar to the calculations for the first
test structure given in Notes 4 through 15, inclusive.

Table 4 - Calibrated OUTPUTS (in μm)
 
27
Note 17:  stepLXMY = platMY-platLX
 Note 18:  ucSH = SQRT(uplatLX2+uplatMY2)

Report the results as follows:  Since it can be assumed that the estimated values of the uncertainty
components are either 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. The value for temp should be between 19.4 ° and 21.6 °, inclusive.
3. The value for relative humidity (if known) should be between 0 % and 60 %, inclusive.
4.
5a.
5b.
6a.
6b.
7.
8.
9. σ6ave σ6same
10.
11.
12.
13.
14. The value for
15.
16.  
17.
18.  
19.  
20.  
21.  
22.  
23.
24. splatLXt and splatMYt should be between 0.0 μm and 0.02 μm, inclusive.
25.
26.
27.
28.

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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