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Data Analysis Sheet T.3

Data analysis sheet for thickness measurements in MEMS processes using optomechanical
technique.

a) 

b) 

Figure T.3.1.  For a fixed-fixed beam test structure a) a design rendition and b) a cross-sectional side
view of a pegged beam.

To obtain the measurements in this data sheet, consult the following:
[1]  J.C. Marshall, "New Optomechanical Technique for Measuring Layer Thickness in MEMS Processes,"
Journal of Microelectromechanical Systems, Vol. 10, No. 1, March 2001.
[2]  SEMI MS2, "Test Method for Step Height Measurements of Thin Films."

Note:  A stylus profilometer is typically used to measure A. 
            An optical interferometer is typically used to measure B.
            The platforms are assumed to be reflective with no secondary fringe effect.

date data taken (optional) = / /

 
 
 
 
   

Table 1 - Preliminary INPUTS

 

  

To Measure A

 To Measure B

Description
1 mat =

 
  
    

 composition of the thin film layer
2 test
structure =

            
 
                   

test structure being measured
3 design
length =

µm

 design length
(needed for test structure identification purposes only)
4 which?

       
  
      
     

which test structure on the test chip where "first" corresponds to the topmost test structure in the column or array that has the specified length?
5 orient =

     
    
  
  
  

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

alignment ensured?
8 levelN = data leveled?
9 µm µm certified value of physical step height used for calibration
10 µm µm certified one sigma uncertainty of the certified physical step height used for calibration
11 N = 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 6N = µm µm the uncalibrated average of the six calibration measurements from which zrepeat was found
13 N = 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 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
15 N = % % 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

µm

 anchor etch depth
17

µm

 range of the anchor etch depth (as provided by the processing facility)
18

µm

 estimated value for the dimension J (if known); otherwise input 0.0 µm
19

µm

 estimated value for the combined standard uncertainty of Jest (if Jest is known and inputted); otherwise input 0.0 µm
20 µm the uncalibrated surface roughness of platX measured as the smallest of all the values obtained for σplatXt.  (However, if the surfaces of platX, platY, and platZ all have identical compositions, then it is measured as the smallest of all the values obtained for σplatXt, σplatYt1, σplatYt2, and σplatZt in which case σroughX = σroughY = σroughZ.)
21 µm the uncalibrated surface roughness of platY measured as the smallest of all the values obtained for σplatYt1 and σplatYt2.  (However, if the surfaces of platX, platY, and platZ all have identical compositions, then it is measured as the smallest of all the values obtained for σplatXt, σplatYt1, σplatYt2, and σplatZt in which case σroughX = σroughY = σroughZ.)
22 µm the uncalibrated surface roughness of platZ measured as the smallest of all the values obtained for σplatZt.  (However, if the surfaces of platX, platY, and platZ all have identical compositions, then it is measured as the smallest of all the values obtained for σplatXt, σplatYt1, σplatYt2, and σplatZt in which case σroughX = σroughY = σroughZ.)

Nomenclature:
    "platX" refers to the height measurement taken from the top of the underlying layer,
    "platY" refers to the height measurement taken from the top of the anchor,
    "platZ" refers to the height measurement taken from the top of the pegged portion of the beam,
    "t" indicates which data trace ("a," "b," or "c"), and
    "N" indicates which measurement ("A" or "B").

 

Table 2 - MINIMUM AND DELTA HEIGHT MEASUREMENTS
Uncalibrated PLATFORM INPUTS
(in µm) used to find A
typically with a stylus profilometer		 Uncalibrated PLATFORM INPUTS
(in µm) used to find B
typically with an optical interferometer
23 29 35 41
24 30 36 42
25 31 37 43
26 32 38 44
27 33 39 45
28 34 40 46
Note 1:  The platform height measurements are platXt, platYt1, platYt2, and platZt.
Note 2:  The standard deviations of the platform height measurements are σplatXt, σplatYt1, σplatYt2, and σplatZt.
                                      

                                    


Table 3a - Calibrated OUTPUTS (in µm) 

47 54
48 55
49 56
50  
51
52
53
Note 3:  At = (platYt1-platXt)*calzA
 Note 4:  Bt = (platZt-platYt2)*calzB
Note 5:  σplatXave= calzA*AVE(σplatXa, σplatXb, σplatXc)
Note 6:  σplatY1ave= calzA*AVE(σplatYa1, σplatYb1, σplatYc1)
Note 7:  σplatY2ave= calzB*AVE(σplatYa2, σplatYb2, σplatYc2)
Note 8:  σplatZave= calzB*AVE(σplatZa, σplatZb, σplatZc)

Table 3b - Calibrated OUTPUTS (in µm)
 

N

 uLstepN uWstepN ucertN urepeatN udriftN ulinearN ucstepN
57 A =
58 B =
Note 9:  N = AVE (Na, Nb, Nc)
Note 10:  uLstepA = SQRT[(σplatXave-calzA*σroughX)2+(σplatY1ave-calzA*σroughY)2]
Note 11:  uLstepB = SQRT[(σplatY2ave-calzB*σroughY)2+(σplatZave-calzB*σroughZ)2]
Note 12:  uWstepN = σstepN = STDEV(Na, Nb, Nc)
Note 13:  ucertN = |scertN*N / certN|
Note 14:  urepeatN = |zrepeatN*N / (2*1.732*z6N)|
Note 15:  udriftN = |(zdriftN*calzN)*N / (2*1.732*certN)|
Note 16:  ulinearN = |zpercN*N / (1.732)|
Note 17:  ucstepN = SQRT(uLstepN2+uWstepN2+ucertN2+urepeatN2+udriftN2+ulinearN2)
Table 3c - Calibrated OUTPUTS (in µm)
59 C = ucC =
60 J = ucJ =
61 aa = ucaa =
62 ab = ucab =
63 a = uca =
Note 18:  C = A + B    and  ucC = SQRT(ucstepA2 + ucstepB2)
 Note 19:  J = B - H     and  ucJ = SQRT(ucstepB2 + ucH2)    where   ucH = ΔH / 6
Note 20:  aa = A + H  and  ucaa = SQRT(ucstepA2 + ucH2)
Note 21:  ab = C - Jest   and  ucab = SQRT(ucC2 + ucJest2)
Note 22:  The thickness of the suspended layer, a, is the value specified for aa or ab
               (whichever has the smaller combined standard uncertainty value)
               unless Jest=0 in which case a = aa.
Note 23:  Each of the standard uncertainty components is obtained using a Type B analysis.

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 uca, the thickness
is believed to lie in the interval a ± uca 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. the magnifications appropriately greater than 2.5×?
4a.
4b.
5a.
5b.
6.
7.
8.
9. N - 0.100 µm)/calzN and (certN + 0.100 µm)/calzN and not equal to 0.0 µm.
10. N  should be between 0.000 µm and 0.050 µm, inclusive.
11. N should be between 0.900 and 1.100, but not equal to 1.000.
12. N should be between 0.0 % and 3.0 %, inclusive.
13. ΔH, Jest, and ucJest should be greater than or equal to 0.0 µm and less than 0.50 µm.
14.
15.  
16.
17. platYt2, and platZt) should be between -2.500 µm and 2.500 µm.
18.
19.
20.
21.
22.
23. a should be greater than A and less than C.

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Date created: 2/10/2008
Last updated: 1/8/2010