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 Data Analysis Sheet SG.1

Data analysis sheet for strain gradient measurements

Top view of cantilever test structure used to measure strain gradient.

Figure SG.1.1.  Top view of cantilever test structure used to measure strain gradient.

To obtain the following measurements, consult ASTM standard test method E 2246 entitled
"Standard Test Method for Strain Gradient Measurements of Thin, Reflecting Films
Using an Optical Interferometer."


filename of 3-D data set (optional)   = 
filename of 2-D data traces (optional) =
     
     
material =  Poly1       Poly2       stacked Poly1 and Poly2 
                 SiC-2       SiC-3   

design length = µm
which cantilever on the round robin test chip ?  First    Second     Third   
magnification = ×
orientation =  0 degree      90 degree
x
-calibration factor (for the given magnification) = calx =
maximum field of view (for the given magnification) = interx = µm
one sigma uncertainty in a ruler measurement (for the given mag) = σxcal = µm
resolution of the interferometer in the x-direction = xres µm
z-calibration factor (for the given magnification) = calz =
certified value of double-sided step height standard = cert = µm
standard deviation of step height measurements (on double-sided step height standard) = σzcal = µm
resolution of the interferometer in the z-direction = zres µm
peak-to-valley roughness of a flat and leveled surface of the sample material calculated to be the average of three or more measurements, each measurement of which is taken from a different 2-D data trace = Rtave = µm
alignment ensured ?   Yes      No
data leveled ?   Yes      No
Is this cantilever exhibiting stiction ?   Yes      No
           
If it is exhibiting stiction, do not fill out the remainder of this form.
                                     


INPUTS (uncalibrated values from Trace "a" or "e"):
              x1max (i.e., x1upper) = µm
              x1min (i.e., x1lower) = µm       
(x1min > x1max)

INPUTS (uncalibrated values from Trace "b")
              x1 = µm    z1 = µm   (x1ave < x1 * calx)
   
          x2 = µm    z2 = µm   (x1ave < x2 * calx)
   
          x3 = µm    z3 = µm   (x1ave < x3 * calx)

INPUTS (uncalibrated values from Trace "c")
              x1 = µm    z1 = µm   (x1ave < x1 * calx)
   
          x2 = µm    z2 = µm   (x1ave < x2 * calx)
   
          x3 = µm    z3 = µm   (x1ave < x3 * calx)

INPUTS (uncalibrated values from Trace "d")
              x1 = µm    z1 = µm   (x1ave < x1 * calx)
   
          x2 = µm    z2 = µm   (x1ave < x2 * calx)
   
          x3 = µm    z3 = µm   (x1ave < x3 * calx)


                                  

OUTPUTS (calibrated values):

           x1ave µm

            s               from Trace "c"
                    s = 1 (for downward bending cantilevers or
                             
if data was taken from the bottom of an upward bending cantilever)
                    s = −1 (for upward bending cantilevers unless

                                data was taken from the bottom of an upward bending cantilever
)

                      Rint µm    from Trace "b"
                        a   µm    from Trace "b"
                        b   µm    from Trace "b"

            sg m1    from Trace "b"

                      Rint µm    from Trace "c"
                        a   µm    from Trace "c"
                        b   µm    from Trace "c"

             sg
m
1    from Trace "c"
                      uW m1       from two or three traces
                      usamp m
1   from Trace "c"
                      uxcal
m
1     from Trace "c"
                      uzcal m
1     from Trace "c"
                      uzres
m
1     from Trace "c"
                      uxres
m
1     from Trace "c"
             
uc =  SQRT[uW2 + usamp2 + uxcal2 + uzcal2 + uzres2 + uxres2]
             uc m1   from two or three traces

                      Rint µm    from Trace "d"
                        a   µm    from Trace "d"
                        b   µm    from Trace "d"
            sg m
1    from Trace "d"


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.   For the round robin test chip, the design length should be 400, 450, 500, 550, 600, 650, 700, 750, or 800 mm.
    3.   Is the magnification appropriate given the design length ?
    4.   Magnifications at or less than 2.5× shall not be used.
    5.   Is 0.95 < calx < 1.05 but not equal to "1"?  If not, recheck your x-calibration.
    6.   The value for interx should be between
0 µm and 1500 µm.
    7.   The value f
or σxcal should be between 0 µm and 4 µm.
    8.   The value f
or xres should be between 0 µm and 1.57 µm.
    9.   Is 0.95 < calz < 1.05 but not equal to "1"?  If not, recheck your z-calibration.
  10.   The value for
σzcal should be between 0 µm and 0.050 µm.
  11.   The value for cert should be greater than 0 µm and less than 25 µm.

  12.   The value for zres should be greater than 0 µm and less than or equal to 0.005 µm. 
  13.   The value for
Rtave should be between 0 µm and 0.100 µm.
  14.   Alignment has not been ensured.
  15.   Data has not been leveled.

  16.   x1min should be greater than x1max.
  17.   The calibrated values for x1min and x1max are greater than 10 µm apart.
  18.   In Trace "b," the calibrated values of x1, x2, and x3 should be > x1ave.

  19.   In Trace "c," the calibrated values of x1, x2, and x3 should be > x1ave.
  20.   In Trace "d," the calibrated values of x1, x2, and x3 should be > x1ave.
  21.   In Traces "b," "c," and "d," the value for s is not the same.

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Date created: 12/4/2000
Last updated: 1/11/2008