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Data Analysis Sheet T.3

Data analysis sheet for thickness measurements in a surface-micromachining MEMS
process using an optomechanical technique.

a) 

b) 

Figure T.3.1.  For a cantilever 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 (optional) = / /

 
 
 
 
   
comments (optional) =

Table 1 - Preliminary INPUTS

 

 

To Measure A

To Measure B

Description

1 tempN = temperature during measurement (should be held constant)
2 relative
humidityN
=
% % relative humidity during measurement (if not known, enter -1)
3 mat =

 
  
    

composition of the thin film layer
4 test
structure
=

            
 
                   

test structure being measured
5 design
length
=

μm

design length
(needed for test structure identification purposes only)
6 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?
7 orient =

     
    
  
  
  

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

alignment ensured?
10 levelN = data leveled?
11 μm μm certified value of physical step height standard used for calibration
12 μm μm certified one sigma uncertainty of the certified physical step height standard used for calibration
13 6aveN= μm μm maximum of two uncalibrated values (before and after) where before is the standard deviation of six measurements taken across the physical step height standard before the data session and after is the standard deviation of six measurements taken across the physical step height standard after the data session
14 = μm μm uncalibrated average of the six calibration measurements used to calculate 6ave
15 6sameN= μm μm maximum of two uncalibrated values (same1 and same2) where same1 is the standard deviation of six measurements taken on the physical step height standard at the same location before the data session and same2 is the standard deviation of six measurements taken at this same location after the data session
16 = μm μm uncalibrated average of the six calibration measurements used to calculate 6same
17 N = 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 standard and the average of the six measurements taken after the data session at this same location)
18 the z-calibration factor (for the given magnification)
19 in = % % 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 % % 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

μm

anchor etch depth
22

μm

range of the anchor etch depth (as provided by the processing facility)
23

μm

estimated value for the dimension J (if known); otherwise input 0.0 μm
24

μm

estimated value for the combined standard uncertainty of Jest (if Jest is known and inputted); otherwise input 0.0 μm
25 μm uncalibrated surface roughness of platX measured as the smallest of all the values obtained for splatXt.  (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 splatXt, splatYt1, splatYt2, and splatZt in which case sroughX = sroughY = sroughZ.)
26 μm uncalibrated surface roughness of platY measured as the smallest of all the values obtained for splatYt1 and splatYt2.  (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 splatXt, splatYt1, splatYt2, and splatZt in which case sroughX = sroughY = sroughZ.)
27 μm uncalibrated surface roughness of platZ measured as the smallest of all the values obtained for splatZt.  (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 splatXt, splatYt1, splatYt2, and splatZt in which case sroughX = sroughY = sroughZ.)

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
28 34 40 46
29 35 41 47
30 36 42 48
31 37 43 49
32 38 44 50
33 39 45 51
Note 1:  The platform height measurements are
platXt, platYt1, platYt2, and platZt.
Note 2:  The standard deviations of the platform height measurements are splatXt, splatYt1, splatYt2, and splatZt.

                                      

                                    


Table 3a - Calibrated OUTPUTS (in μm) 

52 59
53 60
54 61
55  
56
57
58
Note 3:  At = (platYt1-platXt) calzA
Note 4:  Bt = (platZt-platYt2) calzB
Note 5
:  
splatXave= calzA AVE(splatXa, splatXb, splatXc)
Note 6
:  s
platY1ave= calzA AVE(splatYa1, splatYb1, splatYc1)
Note 7: 
splatY2ave= calzB AVE(splatYa2, splatYb2, splatYc2)
Note 8
:  
splatZave= calzB AVE(splatZa, splatZb, splatZc)

Table 3b - Calibrated OUTPUTS (in μm)

 

N

uLstepN uWstepN ucertN ucalN urepeat(shs)N udriftN ulinearN urepeat(samp)N ucSHN
62 A =
63 B =
Note 9:  N = AVE (Na, Nb, Nc)
Note 10
:  uLstepA = SQRT[splatXave
2-(calzA
sroughX)2+splatY1ave2-(calzA sroughY)2]
Note 11:  uLstepB = SQRT[splatY2ave2-(calzB sroughY)2+splatZave2-(calzB sroughZ)2]
Note 12:  uWstepN =
σWstepN = STDEV(Na, Nb, Nc)
Note 13:  ucertN = |σcertN N / certN|

Note 14
:  ucalN = |σ6aveN N /
z6aveN|
Note 15:  urepeat(shs)N = |
σ6sameN N / z6sameN|
Note 16:  udriftN = |(zdrift
N calzN) N / [2(1.732) certN]|
Note 17:  ulinearN = |zlinN N / (1.732)|

Note 18
:  urepeat(samp)N =
σrepeat(samp)N |N|
Note 19:  ucSHN = SQRT(
uLstepN2+uWstepN2+ucertN2+ucalN2+urepeat(shs)N2+udriftN2
                                                                                                +ulinearN
2
+ urepeat(samp)N2)
              (Each of the uncertainty components is obtained using a Type B analysis, except for
                uWstepN, ucalN,
urepeat(shs)N, and urepeat(samp)N which use a Type A analysis.)
Table 3c - Calibrated OUTPUTS (in μm)
64 C = ucC =
65 J = ucJ =
66 aa = ucaa =
67 ab = ucab =
68 a = uca =
Note 20:  C = A + B    and  ucC = SQRT(ucSHA2 + ucSHB2)
Note 21:  J = B - H     and  ucJ = SQRT(ucSHB2 + ucH2)    where   ucH =
ΔH / 6
Note 22
:  aa = A + and  uc
aa = SQRT(ucSHA2 + ucH2)
Note 23
:  
ab = C - Jest   and  ucab = SQRT(ucC2 + ucJest2)
Note 24
:  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.  However, there may be instances, e.g., if the
               anchor etch depth is large and unknown, where
ab would be the better choice.
Note 25
:  Where ucH and ucJest are Type B components.

Ua = 2uca = μm       (expanded uncertainty)
3uca = μm
a
- Ua =   μm     (a lower bound for a)
a
+ Ua =   μm     (an upper bound for a)

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 uca, the thickness is believed to lie in the interval a ± uca (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.
2. The values for tempN should be between 19.4 and 21.6, inclusive.
3. The values for relative humidityN (if known) should be between 0 % and 60 %, inclusive.
4. The value for the design length should be greater than 0 μm and less than or equal to 1000 μm.
5. the magnifications appropriately greater than 2.5×?
6a.
6b.
7a.
7b.
8.
9.
10.
11. N - 0.150 μm)/calzN and (certN + 0.150 μm)/calzN and not equal to 0.0 μm.
12. N  should be between 0.000 μm and 0.100 μm, inclusive.
13. N should be between 0.900 and 1.100, but not equal to 1.000.
14.
15. σrepeat(samp)N should be between 0.0 % and 10.0 %, inclusive.
16. ΔH, Jest, and ucJest should be greater than or equal to 0.0 μm and less than 0.50 μm.
17.
18.  
19.
20. platYt2, and platZt) should be between -2.500 μm and 2.500 μm.
21.
22.
23.
24.
25.
26. a should be greater than A and less than C.

Return to Main MEMS Calculator Page.

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: 2/10/2008
Last updated:
4/26/2013