date (optional) = / /
identifying words (optional)   = 
instrument used (optional)   = 
fabrication facility/process (optional)   =   
test chip name (optional)   =   
test chip number (optional)   =   
filename of 3D data set (optional)   = 
filename of 2D data trace (optional) =
comments (optional) =
 

Table 1 - Preliminary ESTIMATES			Description
1	temp	°C	temperature during measurement (should be held constant)
2	relative humidity	%	relative humidity during measurement (if not known, enter -1)
3	material	Poly1 Poly2  stacked Poly1 and Poly2  Metal1 Metal2 SiC-2  SiC-3    other	material
4	type	Loo Lii   Lio   Loi	type of measurement: Loo= outside edge-to-outside edge length measurement, Lii = inside edge-to-inside edge length measurement Lio= inside edge-to-outside edge length measurement Loi = outside edge-to-inside edge length measurement
5	design length	μm	design length
6	which?	first      second third     other	indicates which iteration of the test structure where "first" corresponds to the topmost or leftmost test structure in the column or array of the same material that has the specified length?
7	magnification	×	magnification
8	orientation	0°        90°      other	orientation on the chip
9	calx		x-calibration factor (for the given magnification)
10	rulerx	μm	maximum field of view in the x-direction for the given magnification (as measured on the screen of the interferometric microscope)
11	σxcal	μm	one sigma uncertainty in a ruler measurement (for the given magnification)
12	xres	μm	uncalibrated resolution of the interferometric microscope in the x-direction (for the given magnification)
13	caly		y-calibration factor (for the given magnification)
14	calz		z-calibration factor (for the given magnification)
15	Loffset	μm	in-plane length correction term for the given magnification of the given interferometric microscope and associated with a given type of in-plane length measurement taken on similar structures when using similar calculations (If the transitional edges face the same direction, Loffset=0 μm.)
16	srepeat(samp)'	μm	in-plane length repeatability standard deviation (for the given magnification) as obtained from test structures fabricated in a process similar to that used to fabricate the sample and for the same or a similar type of measurement
17	aligned?	Yes       No	alignment ensured?
18	leveled?	Yes       No	data leveled?

 

Table 2 - INPUTS (uncalibrated values)					Notes*,**,***,****,*****
Trace a' inputs:
19	x1uppera' =	μm	n1a' =		1 < n1a' < 4
20	x2uppera' =	μm	n2a' =		1 < n2a' < 4 (x2uppera' > x1uppera')
21	ya' =	μm			an outermost data trace (used in misalignment angle, α, calculations)
Trace a inputs:
22	x1uppera =	μm	n1a =		1 < n1a < 4
23	x2uppera =	μm	n2a =		1 < n2a < 4 (x2uppera > x1uppera)
Trace e inputs:
24	x1uppere =	μm	n1e =		1 < n1e < 4
25	x2uppere =	μm	n2e =		1 < n2e < 4 (x2uppere > x1uppere)
Trace e' inputs:
26	x1uppere' =	μm	n1e' =		1 < n1e' < 4
27	x2uppere' =	μm	n2e' =		1 < n2e' < 4 (x2uppere' > x1uppere')
28	ye' =	μm			an outermost data trace (used in misalignment angle, α, calculations) ya' > ye'

^*Where x_uppert is the uncalibrated x-value that most appropriately locates the upper corner of the
transitional edge (Edge 1 or Edge 2) using Trace "t"
^**The values for n1_t and n2_t indicate the data point uncertainties associated with the chosen value for x_uppert
with the subscript "t" referring to the data trace.  In other words, if it is easy to identify one point that
accurately locates the upper corner of transitional Edge 1, the maximum  uncertainty associated with the
identification of this point is n1_tx_rescal_x, where n1_t=1.
^***Where y_a' and y_e' are the uncalibrated y-values associated with Traces a' and e', respectively.
^****Four 2D data traces are typically used to obtain an in-plane length measurement such that each trace
can be used for both Edge 1 and Edge 2.  However, if the measurement is such that eight 2D data traces
are required (four for Edge 1 and four for Edge 2), call the data traces associated with Edge 1 a', a, e, and e'
and the data traces associated with Edge 2 aa', aa, ee, and ee'.  Therefore, throughout this data sheet, replace
x2_uppera' with x2_upperaa', x2_uppera with x2_upperaa, x2_uppere with x2_upperee, x2_uppere' with x2_upperee', n2_a'
with n2_aa', n2_a with n2_aa, n2_e with n2_ee, and n2_e' with n2_ee'. And, if n1_a' + n1_e' > n2_aa' + n2_ee', also enter
y_aa' and y_ee' in the above table instead of y_a' and y_e', respectively.
^*****If the transitional edges face the same direction and have similar slopes and magnitudes, the values locating
the lower corner of each transitional edge are entered instead of the upper values, if the uncertainties associated
with the lower corner are typically less than the uncertainties associated with the upper corner. If this is the case,
throughout this data sheet, replace all occurrences of "upper" with "lower."

                                       

                                     

 

Table 3 - OUTPUTS (calibrated values)			Equation
29	Lmeasa' =	μm	Lmeasa' =  (x2uppera' – x1uppera' ) calx
30	Lmeasa =	μm	Lmeasa =  (x2uppera – x1uppera ) calx
31	Lmease =	μm	Lmease =  (x2uppere – x1uppere ) calx
32	Lmease' =	μm	Lmease' =  (x2uppere' – x1uppere' ) calx
33	Lmeas =	μm	Lmeas = (Lmeasa' + Lmeasa + Lmease + Lmease')/4
34	α =	radians °	α = tan–1[Δx calx / (Δy caly )] where Δy = ya' – ye'  and if  (n1a' + n1e' ) < (n2a' + n2e' ) then Δx = Δx1 = x1uppera' - x1uppere' if  (n1a' + n1e' ) > (n2a' + n2e' ) then Δx = Δx2 = x2uppera' - x2uppere'
35	Lalign =	μm	Lalign =  Lmeas cos α
36	L =	μm	in plane length L =  Lalign + Loffset
Uncertainty calculations:
37	uL =	μm	uL = ( LmaxL − LminL ) / 6 LminL= Lmeasmin cos(α)+Loffset Lmeasmin = (Lmeasmina'+Lmeasmina                        +Lmeasmine+Lmeasmine') / 4 Lmeasmint = Lmeast− (n1t+n2t) xres calx LmaxL= Lmeasmax cos(α)+Loffset Lmeasmax = (Lmeasmaxa'+Lmeasmaxa                        +Lmeasmaxe+Lmeasmaxe') / 4 Lmeasmaxt = Lmeast+ (n1t+n2t) xres calx
38	urepeat(L) =	μm	urepeat(L) = σrepeat(L) cos(α)                 =STDEV(Lmeasa', Lmeasa, Lmease,                                                Lmease') cos(α)
39	uxcal =	μm	uxcal = (σxcal / rulerx) Lmeas cos(α)
40	ualign =	μm	ualign = |(Lmaxalign – Lminalign)/(2SQRT(3))| , with Lminalign= Lmeas cos(αmin) + Loffset, Lmaxalign= Lmeas cos(αmax) + Loffset, αmin = tan–1[Δx calx / (Δy caly )                    – 2xres calx / (Δy caly )] , αmax = tan–1[Δx calx / (Δy caly )                    + 2xres calx / (Δy caly )]
41	uoffset =	μm	uoffset = |Loffset | / 3
42	urepeat(samp) =	μm	urepeat(samp) = srepeat(samp)'
43	ucL =	μm	combined standard uncertainty ucL = SQRT [uL2 + urepeat(L)2 + uxcal2       + ualign2 + uoffset2 + urepeat(samp)2] where each of the standard uncertainty components is obtained using a Type B analysis, except for urepeat(L) and urepeat(samp), which use a statistical Type A analysis
44	2ucL = UL	μm	expanded uncertainty
45	3ucL =	μm	three times the combined standard uncertainty
46	L – UL =	μm	a lower bound for L
47	L + UL =	μm	an upper bound for L

Report the results as follows:  If it is assumed that the estimated values of the uncertainty
components are approximately Gaussianly distributed with approximate combined standard
uncertainty u_cL, the in-plane length is believed to lie in the interval L ± u_cL (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 fill out the entire form.
2.		The value for temp should be between 19.4 °C and 21.6 °C, inclusive.
3.		The value for relative humidity (if known) should be between 0 % and 60 %, inclusive.
4.		The design length should be between 0 μm and 1050 μm.
5.		The measured value for L is more than 3ucL from the design length.
6.		Is the magnification appropriate given the design length ?
7.		Magnifications at or less than 2.5× shall not be used.
8.		Is 0.95 < calx < 1.05 but not equal to "1" ?  If not, recheck your x-calibration. Is 0.95 < caly < 1.05 but not equal to "1" ?  If not, recheck your y-calibration.
9.		The value for rulerx should be between 0 μm and 1500 μm.
10.		The value for σxcal should be between 0 μm and 4 μm.
11.		The value for xres should be between 0 μm and 2.00 μm.
12.		Is 0.95 < calz < 1.05 but not equal to "1" ?  If not, recheck your z-calibration.
13.		The value for Loffset should be between –9.0 μm and 9.0 μm, inclusive.
14.		The value for srepeat(samp)' should be between 0 μm and 5 μm, inclusive.
15.		Alignment has not been ensured.
16.		Data has not been leveled.
17.		x2uppert should be greater than x1uppert.
18.		The measured values for x1uppert should be within 5 μm of their average.
19.		The measured values for x2uppert should be within 5 μm of their average.
20.		ya' should be greater than ye'.
21.		n1t and n2t should be between 1 and 4, inclusive.
22.		α should be between –2° and 2°.

---

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: 12/4/2000
Last updated: 4/26/2013