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Data Analysis Sheet SH.1

Data analysis sheet for step height measurements from one step height test structure.


a)                                                   b)


Figure SH.1.1.  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 data taken (optional) = / /


   
   
 

Table 1 - Preliminary INPUTS

Data Set Prelims

Description

1 proc =

   

       

which process?
2 which =        

    

        

      

         

       

which step height measurement, test structure, or quad?
3 orient =      

  

 

orientation of the test structure on the test chip
4 × magnification
5 align =
 
alignment ensured?
6 level =
 
data leveled?
7

µm

certified value of physical step height used for calibration
8 µm certified one sigma uncertainty of the certified physical step height used for calibration
9 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)
10 µm the uncalibrated average of the six calibration measurements from which zrepeat was found
11 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)
12 the z-calibration factor = the certified value of the physical step height divided by the average of the twelve calibration measurements taken at the same location on the physical step height
13 % 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%)
14 σ µm the uncalibrated surface roughness of platNX measured as the smallest of all the values obtained for σplatNXt.  (However, if the surfaces of platNX, platNY, and platNr all have identical compositions, then it is measured as the smallest of all the values obtained for σplatNXt, σplatNYt, and σplatNrDt in which case σroughNX=σroughNY.)
15 σ µm the uncalibrated surface roughness of platNY measured as the smallest of all the values obtained for σplatNYt (However, if the surfaces of platNX, platNY, and platNr all have identical compositions, then it is measured as the smallest of all the values obtained for σplatNXt, σplatNYt, and σplatNrDt in which case σroughNX=σroughNY.)

                                      

                                    


Nomenclature:
    "N" refers 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, and
    "t" indicates which data trace ("a," "b," or "c").
 

Table 2 - Platform INPUTS and CALCULATIONS

Uncalibrated PLATFORM INPUTS (in µm) Calibrated CALCULATIONS (in µm)
1 7 13
2 8 14
3 9 15
4 σ 10 σ  
5 σ 11 σ 16 σ
6 σ 12 σ 17 σ

Note 1:  stepNXYt = calz*(platNYt-platNXt)
Note 2:  σplatNXave = calz*AVE(σplatNXa, σplatNXb, σplatNXc)
Note 3:  
σplatNYave = calz*AVE(σplatNYa, σplatNYb, σplatNYc)

Table 3 - Calibrated OUTPUTS (in µm)

   

18
Note 4:  stepNXY = AVE(stepNXYa, stepNXYb, stepNXYc)
Note 5:  uLstep = SQRT[(
σplatNXave- calz*σroughNX)2 + (σplatNYave- calz*σroughNY)2]
Note 6:  uWstep = sstepNXY = STDEV(stepNXYa, stepNXYb, stepNXYc)
Note 7:  ucert = |scert*stepNXY / cert|
Note 8:  urepeat = |zrepeat*stepNXY / (2*1.732*z6)|
Note 9:  udrift = |(zdrift*calz)*stepNXY / (2*1.732*cert)|
Note 10:  ulinear = |zperc*stepNXY / (1.732)|
Note 11:  uc = SQRT(uLstep2+uWstep2+ucert2+urepeat2+udrift2+ulinear2)

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 step
height is believed to lie in the interval stepNXY ± 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.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12. σroughNX and σroughNY should be greater than 0.0 µm and less than or equal to the smallest measured value for σplatNXt and σplatNYt, respectively.
13.
14.
15.  
16. σplatNXt and σplatNYt should be between 0.00 µm and 0.025 µm, inclusive.
17.
18.

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Date created: 3/4/2006
Last updated:
6/2/2009