Data Analysis Sheet SH.2

Data analysis sheet for step height measurements taken during the same data session from two step height test structures.

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 Films."

date data taken (optional) = / /
identifying words (optional)   =
instrument used (optional)   =
fabrication facility (optional)   =
test chip name (optional)   =
test chip number (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,
    "D" directionally indicates which reference platform ("N," "S," "E," or "W"), and
    "t" indicates which data trace ("a," "b," or "c").

Table 2a - Uncalibrated REFERENCE PLATFORM INPUTS (in μm)
First Test Structure				Second Test Structure
1a	platLrWa=	4a	platLrEa=	1b	platMrWa=	4b	platMrEa=
2a	platLrWb=	5a	platLrEb=	2b	platMrWb=	5b	platMrEb=
3a	platLrWc=	6a	platLrEc=	3b	platMrWc=	6b	platMrEc=

Table 2b - Calibrated REFERENCE PLATFORM CALCULATIONS (in μm)
First Test Structure				Second Test Structure
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 test structure are similar to the calculations for the first test
structure given in Notes 1 and 2.

Table 3a - Uncalibrated PLATFORM INPUTS (in μm)
First Test Structure		Second Test Structure
9a	platLXa=	9b	platMYa =
10a	platLXb =	10b	platMYb =
11a	platLXc =	11b	platMYc =
12a	σ_platLXa =	12b	σ_platMYa =
13a	σ_platLXb =	13b	σ_platMYb =
14a	σ_platLXc =	14b	σ_platMYc =

Table 3b - Calibrated PLATFORM CALCULATIONS (in μm)
First Test Structure		Second Test Structure
15a	platLX =	15b	platMY =
16a	s_platLX =	16b	s_platMY =
17a	σ_platLXave =	17b	σ_platMYave =
18a	u_LplatLX =	18b	u_LplatMY =
19a	u_WplatLX =	19b	u_WplatMY =
20a	u_certLX =	20b	u_certMY =
21a	u_{repeat(shs)LX} =	21b	u_{repeat(shs)MY} =
22a	u_driftLX =	22b	u_driftMY =
23a	u_linearLX =	23b	u_linearMY =
24a	u_platLX =	24b	u_platMY =

Note 4: platLX = cal_z AVE(platLXa, platLXb, platLXc) - platLr
Note 5: s_platLX = cal_z STDEV(platLXa, platLXb, platLXc)
Note 6: σ_platLXave = cal_z AVE(σ_platLXa, σ_platLXb, σ_platLXc)
Note 7: u_LplatLX = σ_platLXave - cal_z σ_roughLX
Note 8: u_WplatLX = SQRT(s_platLX²+s_platLr²)
Note 9: u_certLX = |σ_cert platLX / cert|
Note 10: u_{repeat(shs)LX}= |z_repeat(shs) platLX / [2(1.732) z₆]|
Note 11: u_driftLX = |(z_drift cal_z) platLX / [2(1.732)cert]|
Note 12: u_linearLX= |z_perc platLX / (1.732)|
Note 13: u_platLX = SQRT(u_LplatLX²+u_WplatLX²+u_certLX²+u_{repeat(shs)LX}²+u_driftLX²+u_linearLX²)
(Each of the standard uncertainty components is obtained using a Type B analysis,
except for u_WplatLX, which uses a Type A analysis.)
Note 14: The calculations for the second test structure are similar to the calculations for the first
test structure given in Notes 4 through 13, inclusive.

Table 4 - Calibrated OUTPUTS (in μm)
	*stepL_XM_Y*	*u_cSH*
25

Note 15: stepL_XM_Y= platMY-platLX
Note 16: u_cSH= SQRT(u_platLX²+u_platMY²)
Note 17: The numerical values of the sample platform inputs in Data Sheet SH.1 are identical to the numerical values of the sample 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_cSH in this data sheet is larger than the u_cSH value in Data Sheet SH.1. This implies that step height measurements from one step height test structure (as calculated in Data Sheet SH.1) are preferred to step height measurements from two step height test structures (as calculated in this data sheet).

Report the results as follows: Since it can be assumed that the estimated values of the uncertainty
components are approximately uniformly or Gaussianly distributed with approximate combined standard
uncertainty u_cSH, the step height is believed to lie in the interval stepL_XM_Y ± u_cSH (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.		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 step height test structure.
3b.		Alignment has not been ensured for the second step height test structure.
4a.		Data has not been leveled for the first step height test structure.
4b.		Data has not been leveled for the second step height test structure.
5.		The value for cert should be between 0.000 μm and 15.000 μm.
6.		The value for σ_cert should be between 0.000 μm and 0.100 μm.
7.		The value for z_repeat(shs) 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, inclusive.
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 values for σ_roughLX and σ_roughMY should be greater than 0.0 μm and less than or equal to the smallest measured value for σ_platLXt and σ_platMYt, respectively.
13.		All the reference platform inputs have not been provided.
14.		More reference platform inputs are required for standard deviation calculations.
15.		The reference platform inputs should be between -0.010 μm and 0.010 μm.
16.		The values for platLr and platMr should be between -0.007 μm and 0.007 μm.
17.		The values for s_platLr and s_platMr should be less than 0.010 μm.
18.		All the platform inputs have not been provided.
19.		More platform inputs are required for standard deviation calculations.
20.		The values for platLXt and platMYt should be between -2.500 μm and 2.500 μm.
21.		The values for σ_platLXt and σ_platMYt should be between 0.0 μm and 0.02 μm, inclusive.
22.		The values for platLX and platMY should be between -2.500 μm and 2.500 μm.
23.		The values for s_platLX and s_platMY should be less than 0.010 μm.
24.		The value for stepL_XM_Y should be between -2.500 μm and 2.500 μm.
25.		The value for u_cSH should be less than 0.030 μm.

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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: 3/4/2006
Last updated: 4/26/2013