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 Data Analysis Sheet RS.2

Data analysis sheet for residual strain measurements with more detailed calculations of the combined standard uncertainty, uc

Top view of fixed-fixed beam used to measure residual strain.

Figure RS.2.1.  Top view of fixed-fixed beam used to measure residual strain.

To obtain the following measurements, consult ASTM standard test method E 2245 entitled
"Standard Test Method for Residual Strain Measurements of Thin, Reflecting Films
Using an Optical Interferometer" and NISTIR 7291 entitled "MEMS Length and Strain
Round Robin Results with Uncertainty Analysis."

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    (therefore, t =  µm )
design length = µm
which fixed-fixed beam on the round robin test chip ?  First    Second     Third   
magnification = ×
orientation =  0 degree      90 degree
x-calibration factor (for the given magnification) = calx =
interferometer's 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 step height standard = cert = µm
certified one sigma uncertainty of certified value of step height standard = scert = µm
maximum range of the six calibration measurements taken before the data session or after the data session (whichever is larger) = zrepeat = µm
Is the mean value of the six calibration measurements used to obtain zrepeat greater than or less than the mean value of all twelve calibration measurements ?    greater than      less than      (Therefore, ameanz = ).
drift in the calibrated data (i.e., the absolute value of the mean value of the six calibration measurements taken before the data session minus the mean value after the data session) = zdrift = µm
percent quoted by interferometer manufacturer for the maximum deviation from linearity of the data scan over the total scan range divided by 1 % such that it is unitless = zperc =
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
surface 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= Rave = µm
alignment ensured ?   Yes      No
data leveled ?   Yes      No
Is this fixed-fixed beam 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)
              x2min (i.e., x2lower)  = µm           (x2min > x1min)
              x2max (i.e., x2upper) = µm           (x2max > x2min)

INPUTS (uncalibrated values from Trace "b"):
              x1F = µm    z1F = µm   (x1ave < x1F * calx)
              x2F = µm    z2F = µm   (inflection point)
                                                                                           ( x1F < x2F < x3F )
              x3F = µm    z3F = µm   (most deflected point)
                                                                                          ( x1S = x3F ; z1S = z3F )
              x2S = µm    z2S = µm   (inflection point)
              x3S = µm    z3S = µm   ( x3S * calx < x2ave )
                                                                                          ( x1S < x2S < x3S )

INPUTS (uncalibrated values from Trace "c"): 
              x1F = µm    z1F = µm   (x1ave < x1F * calx)
              x2F = µm    z2F = µm   (inflection point)
                                                                                           ( x1F < x2F < x3F )
              x3F = µm    z3F = µm   (most deflected point)
                                                                                            ( x1S = x3F ; z1S = z3F )
              x2S = µm    z2S = µm   (inflection point)
              x3S = µm    z3S = µm   ( x3S  * calx < x2ave )
                                                                                           ( x1S < x2S < x3S )

INPUTS (uncalibrated values from Trace "d"): 
              x1F = µm    z1F = µm   (x1ave < x1F * calx)
              x2F = µm    z2F = µm   (inflection point)
                                                                                          ( x1F < x2F < x3F )
              x3F = µm    z3F = µm   (most deflected point)
                                                                                           ( x1S = x3F ; z1S = z3F )
              x2S = µm    z2S = µm   (inflection point)
              x3S = µm    z3S = µm   ( x3S  * calx < x2ave )
                                                                                           ( x1S < x2S < x3S )

                                      

OUTPUTS (calibrated values):
            x1ave =  µm            x2ave =  µm
             L      =  µm
                         Lmax = ( x2max − x1max ) * calx
                         Lmin = ( x2min − x1min ) * calx
                         uLL  =  ( Lmax − Lmin ) / 6 =  µm
                         uLxcal  = ( σxcal / interx ) * ( L / calx ) = µm
                         uLxres  = xres* calx / 1.732 =  µm
             ucL   =  SQRT[uLL2 + uLxcal2 + uLxres2]  =  µm
             s        =                    from Trace "c"
                          s = 1       (for downward bending fixed-fixed beams)
                         s = −1     (for upward bending fixed-fixed beams)

                             AF   =  µm      from Trace "b"
                           w1F   =             from Trace "b"
                             AS   =  µm      from Trace "b"
                           w3S   =              from Trace "b"
             xeF   =  µm            from Trace "b"
             xeS   =  µm            from Trace "b"
            εr0    =  × 10-6       from Trace "b"
            εr     =    × 10-6       from Trace "b"

                             AF   =  µm      from Trace "c"
                           w1F   =             from Trace "c"
                             AS   =  µm      from Trace "c"
                           w3S   =              from Trace "c"
             xeF   =  µm             from Trace "c"
             xeS   =  µm             from Trace "c"
             εr0   =  × 10-6        from Trace "c"
             εr    =    × 10-6        from Trace "c"
                          uRave    =    × 10-6      from Trace "c"
                         unoise    =    × 10-6      from Trace "c"
                         uW    =    × 10-6          from two or three traces
                         uxcal    =    × 10-6        from Trace "c"
                         uL    =    × 10-6           from Trace "c"
                         ucert    =    × 10-6        from Trace "c"
                         urepeat    =    × 10-6        from Trace "c"
                         udrift    =    × 10-6        from Trace "c"
                         ulinear    =    × 10-6        from Trace "c"
                         uzres    =    × 10-6        from Trace "c"
                         uxres    =    × 10-6        from Trace "c"
                         uxresL    =    × 10-6        from Trace "c"
             uc    = SQRT[uRave2 + unoise2 + uW2 + uxcal2 + uL2 + ucert2 + urepeat2 + udrift2 + ulinear2 + uzres2 + uxres2 + uxresL2]
             uc    =    × 10-6        from two or three traces

                             AF   =  µm      from Trace "d"
                           w1F   =             from Trace "d"
                             AS   =  µm      from Trace "d"
                           w3S   =              from Trace "d"
             xeF   =  µm             from Trace "d"
             xeS   =  µm             from Trace "d"
            εr0    =  × 10-6        from Trace "d"
            εr     =    × 10-6        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 thickness value is different than what the fabricator specified.
    3.   For the round robin test chip, the design length should be 400, 450, 500, 550, 600, 650, 700, 750, or 800 mm. 
    4.   The measured value for L is more than 3ucL from the design length.
    5.   Is the magnification appropriate given the design length ?
    6.   Magnifications at or less than 2.5× shall not be used.
    7.   Is 0.95 < calx < 1.05 but not equal to "1"?  If not, recheck your x-calibration.
    8.   The value for interx should be between 0 µm and 1500 µm.
    9.   The value for sxcal should be between 0 µm and 4 µm.
  10.   The value for xres should be between 0 µm and 1.57 µm.
  11.   Is 0.95 < calz < 1.05 but not equal to "1"?  If not, recheck your z-calibration.
  12.   The value for cert should be greater than 0 µm and less than 25 µm.
  13.   The value for scert should be between 0 µm and 0.100 µm.
  14.   The value for zrepeat should be between 0 µm and 0.070 µm.
  15.   The value for zdrift should be between 0 µm and 0.010 µm.
  16.   The value for zperc should be between 0 and 3.
  17.   The value for zres should be greater than 0 µm and less than or equal to 0.005 µm.
  18.   The value for Rtave should be between 0 µm and 0.100 µm and greater than Rave.
  19.   The value for Rave should be between 0 µm and 0.020 µm.
  20.   Alignment has not been ensured.
  21.   Data has not been leveled.
  22.   x1min should be greater than x1max.
  23.  x2min should be greater than x1min.
  24.   x2max should be greater than x2min.
  25.   The calibrated values for x1min and x1max are greater than 10 µm apart.
  26.   The calibrated values for x2min and x2max are greater than 10 µm apart.
  27.   In Traces "b," "c," and "d," the value for s is not the same.
  28.   x1ave should be < (x1F * calx) in all traces.
  29.   (x3S * calx) should be < x2ave in all traces.
  30.   In all traces, make sure ( x1F < x2F < x3F ).
  31.   In all traces, make sure ( x1S < x2S < x3S ).
  32.   For Trace "b," | [(x2F*calx) − xeF ] | = µm.  This should be < 5 µm.
                     If it is not, choose (x2F, z2F) such that (x2F * calx) is closer to xeF = µm.
  33.   For Trace "b," | [(x2S*calx) − xeS ] | =  µm.  This should be < 5 µm.
                     If it is not, choose (x2S, z2S) such that (x2S * calx) is closer to xeS = µm.
  34.   For Trace "c," | [(x2F*calx) − xeF ] | = µm.  This should be < 5 µm.
                     If it is not, choose (x2F, z2F) such that (x2F * calx) is closer to xeF = µm.
  35.   For Trace "c," | [(x2S*calx) − xeS ] | =  µm.  This should be < 5 µm.
                     If it is not, choose (x2S, z2S) such that (x2S * calx) is closer to xeS = µm.
  36.   For Trace "d," | [(x2F*calx) − xeF ] | =  µm.  This should be < 5 µm.
                     If it is not, choose (x2F, z2F) such that (x2F * calx) is closer to xeF = µm.
  37.   For Trace "d," | [(x2S*calx) − xeS ] | =  µm.  This should be < 5 µm.
                     If it is not, choose (x2S, z2S) such that (x2S * calx) is closer to xeS = µm.

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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: 1/11/2008