Data Analysis Sheet SH.2

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Data analysis sheet for step height measurements from two 3-D data sets taken during the same data session.

a) b)

Figure SH.2.1. 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, Reflecting Films Using an Optical Interferometer."

date data taken (optional)   =
identifying words (optional)   =
filename of first 3-D data set (optional) =
filename of second 3-D data set (optional) =

Nomenclature:
    "L" and "M" refer to the test structure number ("1," "2," "3," etc.),
    "X" and "Y" refer to the platform letter ("A," "B," "C," etc.),
    "r" refers to the reference platform,
    "W" and "E" directionally indicate which reference platform, and
    the data traces are "a," "b," and "c".

Uncalibrated REFERENCE PLATFORM INPUTS (in mm)
First Data Set				Second Data Set
1a	platLrWa=	4a	platLrEa=	1b	platMrWa=	4b	platMrEa=
2a	platLrWb=	5a	platLrEb=	2b	platMrWb=	5b	platMrEb=
3a	platLrWc=	6a	platLrEc=	3b	platMrWc=	6b	platMrEc=

Calibrated REFERENCE PLATFORM CALCULATIONS (in mm)
First Data Set				Second Data Set
7a	platLr=	8a	s_plat_L_r=	7b	platMr=	8b	s_platMr=

Note 1: platLr = AVE(platLrWa, platLrWb, platLrWc, platLrEa, platLrEb, platLrEc)*cal_z
Note 2: s_platLr = STDEV(platLrWa, platLrWb, platLrWc, platLrEa, platLrEb, platLrEc)*cal_z
Note 3: The calculations for the second data set are similar to the calculations for the first data set
given in Notes 1 and 2.

Uncalibrated PLATFORM INPUTS (in mm)
First Data Set		Second Data Set
9a	platLXa=	9b	platMYa =
10a	platLXb =	10b	platMYb =
11a	platLXc =	11b	platMYc =

Calibrated PLATFORM CALCULATIONS (in mm)
First Data Set		Second Data Set
12a	platLX =	12b	platMY =
13a	s_platLX =	13b	s_platMY =
14a	u_WplatLX =	14b	u_WplatMY =
15a	u_certLX =	15b	u_certMY =
16a	u_repeatLX =	16b	u_repeatMY =
17a	u_driftLX =	17b	u_driftMY =
18a	u_linearLX =	18b	u_linearMY =
19a	u_platLX =	19b	u_platMY =

Note 4: platLX = cal_z*AVE(platLXa, platLXb, platLXc) - platLr
Note 5: s_platLX = cal_z*STDEV(platLXa, platLXb, platLXc)
Note 6: u_WplatLX = SQRT(s_platLX²+s_platLr²)
Note 7: u_certLX = |s_cert*platLX / cert|
Note 8: u_repeatLX= |z_repeat*platLX / (2*1.732*z₆)|
Note 9: u_driftLX = |z_drift*cal_z*platLX / (2*1.732*cert)|
Note 10: u_linearLX= |z_perc*platLX / (1.732*100)|
Note 11: u_platLX = SQRT(u_WplatLX²+u_certLX²+u_repeatLX²+u_driftLX²+u_linearLX²)
Note 12: The calculations for the second data set are similar to the calculations for the first data set
given in Notes 4 through 11, inclusive.

Calibrated OUTPUTS (in mm)
	stepL_XM_Y	u_c
20

Note 13: stepL_XM_Y= platMY-platLX
Note 14: u_c= SQRT(u_platLX²+u_platMY²)
Note 15: The numerical values of the platform inputs in Data Sheet SH.1 are identical to the numerical values of the platform inputs in this data sheet. The resulting values for stepN_XY in Data Sheet SH.1 and stepL_XM_Y in this data sheet are comparable, yet the value for u_c in this data sheet is larger than the u_c value in Data Sheet SH.1. This implies that step-height measurements from one 3-D data set (as calculated in Data Sheet SH.1) are preferred to step-height measurements from two 3-D data sets (as calculated in this data sheet).

Modify the input data, given the information supplied in any flagged statement below, if applicable, then recalculate:
1.		Please completely fill out the Preliminary Inputs Table.
2.		Is the magnification appropriately greater than 2.5×?
3a.		Alignment has not been ensured for the first data set.
3b.		Alignment has not been ensured for the second data set.
4a.		Data has not been leveled for the first data set.
4b.		Data has not been leveled for the second data set.
5.		The value for cert should be between 0.000 µm and 15.000 µm.
6.		The value for s_cert should be between 0.000 µm and 0.100 µm.
7.		The value for z_repeat should be between 0.000 µm and 0.050 µm.
8.		The value for z₆ should be between (cert - 0.100 µm)/cal_z and (cert + 0.100 µm)/cal_z.
9.		The value for z_drift should be between 0.000 µm and 0.050 µm.
10.		The value for cal_z should be between 0.900 and 1.100, but not equal to 1.000.
11.		The value for z_perc should be between 0.0 and 3.0, inclusive.
12.		The reference platform inputs have not been provided.
13.		More reference platform inputs are required for standard deviation calculations.
14.		The reference platform inputs should be between -0.010 µm and 0.010 µm.
15.		The values for platLr and platMr should be between -0.007 µm and 0.007 µm.
16.		The values for s_platLr and s_platMr should be less than 0.010 µm.
17.		The platform inputs have not been provided.
18.		More platform inputs are required for standard deviation calculations.
19.		The platform inputs should be between -2.500 µm and 2.500 µm.
20.		The values for platLX and platMY should be between -2.500 µm and 2.500 µm.
21.		The values for s_platLX and s_platMY should be less than 0.010 µm.
22.		The value for stepL_XM_Y should be between -2.500 µm and 2.500 µm.
23.		The value for u_c should be less than 0.030 µm.

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Date created: 3/4/2006
Last updated: 1/11/2008