date (optional) = / /
identifying words (optional)  = 
instrument(s) used (optional)  = 
fabrication facility/process (optional)  = 
test chip name (optional)  = 
test chip number (optional)  = 
root filename of 3D data sets (optional)  = 
comments (optional) =
 
TABLE 1 - Calibrated Step Height MEASUREMENTS^*

#	Step #**	Step***	step height****	ucSH****	ures	ucstep*****
			(μm)	(μm)	(μm)	(μm)
1	1	H=step1AB
2	2	D=step2rA
3	3	F=step1EF
4	4	J=step1GH
5	5	E=step3AB(n)-
6	6	C=step3BC(0)

^* Supply inputs to the columns labeled "step height," "u_cSH," and "u_res."
^** The step number as labeled in Fig. T.1.1.
^*** The corresponding step for the test structures used with Data Sheet T.2.
^**** These inputs can be obtained from Data Sheet SH.1.a.
^***** Where u_cstep = (u_cSH² + u_res²)^1/2
         (where u_res is a Type B component that is typically set equal to 0)


TABLE 2 - Oxide Thickness Values From Capacitances^*,**
[with σ_ε = aF/μm]

#***	Thickness Designation	Ca	σCa	σresCa/rres	t	uctCa
		(aF/μm2)	(aF/μm2)		(μm)	(μm)
1	G=tfox(p1/sub)elec
2	I=tthin(p1/aan)elec
6	K=[tfox,m1(pmd/sub)+tpmd(m1/fox)]elec
7	L=tpmd(m1/aan)elec
10	M=[tfox,m2(pmd/sub)+tpmd(imd/fox)
	+timd(m2/pmd)]elec
11	A=[tpmd(imd/aan) +timd(m2/pmd)]elec

^* Supply inputs for "C_a," "σ_Ca," "σ_ε," and "σ_resCa/r_res."
^** Where t = ε_SiO2 / C_a with ε_SiO2 = 34.5 aF/μm
and u_ctCa = t [(σ_ε / ε_SiO2)² + (σ_Ca / C_a)² + (σ_resCa / r_res)²]^1/2
where each standard uncertainty component is obtained using a Type B analysis
with σ_resCa/r_res typically set equal to 0.
^*** The numbering in this table corresponds to the numbering for the corresponding thicknesses
in Table 2 of Data Sheet T.2.

 

TABLE 3 - Thickness Values For The Interconnects^*,**

#	Symbol	Rs	σRs	ρ	σρ	σresRs / rres	t	uctRs
		(Ω/□)	(Ω/□)	(Ω-μm)	(Ω-μm)		(μm)	(μm)
1	B=t(m2)elec

^* Supply inputs to the columns labeled "R_s," "σ_Rs," "ρ," "σ_ρ," and "σ_resRs / r_res."
^** Where t = ρ / R_s
and u_ctRs = t [(σ_ρ / ρ)² + (σ_Rs / R_s)² + (σ_resRs / r_res)²]^1/2
where each standard uncertainty component is obtained using a Type B analysis
with σ_resRs/r_res typically set equal to 0.

 

TABLE 4 - Oxide Thickness Calculation

#	Symbol	t	uc
		(μm)	(μm)
1	O=G-H+HI / (I-G)
2	X=B+C-D+E
3	Y1=M
4	Y2=A+K-L
5	Y3=A-J+O
6	Y4=A+F+O
7	Z1=X+Y1
8	Z2=X+Y2
9	Z3=X+Y3
10	Z4=X+Y4
11		toxide =	ucoxide =

U_oxide = 2u_coxide = μm     (expanded uncertainty)
3u_coxide = μm
t_oxide - U_oxide = μm  (a lower bound for t_oxide)
t_oxide + U_oxide = μm  (an upper bound for t_oxide)

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_coxide, the oxide beam thickness is believed to lie in the interval t_oxide ± u_coxide 
(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 values for the step heights in Table 1 should be between -2.500 μm and 2.500 μm.
3.		The ucSH input values in Table 1 should be between 0.0000 μm and 0.2000 μm.
4.		The values for ures in Table 1 should be between 0.0000 μm and 0.0500 μm, inclusive.
5.		The value of σε  for Table 2 should be between 0.0 aF/μm and 0.3 aF/μm, inclusive.
6.		The values for Ca in Table 2 should be between 1.0 aF/μm2 and 1300.0 aF/μm2.
7.		The values for σCa in Table 2 should be between 0.00 aF/μm2 and 10.00 aF/μm2.
8.		The values of σresCa/rres in Table 2 should be between 0 and 0.05, inclusive.
9.		The value of Rs in Table 3 should be between 0.0100 Ω/□ and 0.0700 Ω/ □.
10.		The value of σRs in Table 3 should be between 0.0001 Ω/□ and 0.0050 Ω/□.
11.		The value of ρ in Table 3 should be between 0.020 Ω-μm and 0.040 Ω-μm.
12.		The value of σρ in Table 3 should be between 0.000 Ω-μm and 0.005 Ω-μm, inclusive.
13.		The value of σresRs/rres in Table 3 should be between 0 and 0.05, inclusive.
14.		All of the thicknesses in Table 4 should be between 0.00 μm and 4.00 μm.
15.		All of the values for uc in Table 4 should be between 0.00 μm and 0.30 μm.

---

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: 1/12/2009
Last updated: 4/26/2013