IDENTIFYING INFORMATION:

date data taken (optional) = / /
identifying words (optional) =
instrument used (optional) =
fabrication facility/process (optional) =
test chip name (optional) =
test chip number (optional) =
root filename (optional) =
 

Table 1 - Preliminary INPUTS			Description
1	mag=	×	magnification
2	mat=	poly1 poly2 SiO2   other	composition of the thin film layer
3*	ρ=	g/cm3	density of the thin film layer
4	σρ=	g/cm3	one sigma uncertainty of the value of ρ
5*	μ=	×10-5 Ns/m2	viscosity of the ambient surrounding the cantilever
6	σμ=	×10-5 Ns/m2	one sigma uncertainty of the value of μ
7	temp=	°C	temperature during measurement (should be held constant)
8*	W=	μm	suspended beam width
9	σW=	μm	one sigma uncertainty of the value of W
10*	t=	μm	thickness of the thin film layer
11	σthick=	μm	one sigma uncertainty of the value of t
12	dgap=	μm	gap depth (distance between the bottom of the suspended beam and the underlying layer)
13*	Einit=	GPa	initial estimate for the Young's modulus value of the thin film layer
14	finstrument=	Hz	for calibrating the time base of the instrument:  the frequency setting for the calibration measurements (or the manufacturer's specification for the clock frequency)
15	fmeter=	Hz	for calibrating the time base of the instrument:  the calibrated average frequency of the calibration measurements (or the calibrated average clock frequency) taken with a frequency meter
16	ucmeter=	Hz	for calibrating the time base of the instrument:  the uncertainty of the frequency measurements taken with the frequency meter

* The five starred entries in this table are required inputs for the calculations in the Preliminary Estimates Table.

 

Table 2 - Cantilever INPUTS			Description
17	name=		cantilever name (optional)
18	orient=	0°      90°    180°  270°  other	orientation of the cantilever
19*	Lcan=	μm	suspended cantilever length
20	whichcan=	first      second third     fourth   fifth      sixth     other	which cantilever on the test chip, where "first" corresponds to the topmost cantilever in the column or array that has the specified length?
21	σL=	μm	one sigma uncertainty of the value of Lcan
22	fresol=	Hz	uncalibrated frequency resolution for the given set of measurement conditions
23	fmeas1=	kHz	first uncalibrated, damped resonance frequency measurement (or first uncalibrated, undamped resonance frequency measurement, for example, if the measurements were performed in a vacuum)
24	fmeas2=	kHz	second uncalibrated, damped resonance frequency measurement (or second uncalibrated, undamped resonance frequency measurement, for example, if the measurements were performed in a vacuum)
25	fmeas3=	kHz	third uncalibrated, damped resonance frequency measurement (or third uncalibrated, undamped resonance frequency measurement, for example, if the measurements were performed in a vacuum)

* The starred entry in this table is a required input for the calculations in the Preliminary Estimates Table.

 

Table 3 - Fixed-Fixed Beam INPUTS (if cantilever not available)			Description
26	name2=		fixed-fixed beam name (optional)
27	orient2=	0°        90°      other	orientation of the fixed-fixed beam
28*	Lffb=	μm	suspended fixed-fixed beam length
29	whichffb=	first      second third     fourth   fifth      other	which fixed-fixed beam on the test chip, where "first" corresponds to the topmost fixed-fixed beam in the column or array that has the specified length?
30	fffb=	kHz	average uncalibrated resonance frequency of the fixed-fixed beam

* The starred entry in this table is a required input for the calculations in the Preliminary Estimates Table.

 

Table 4 - Optional INPUTS
For residual stress calculations:			Description
31	εr=	×10-6	residual strain of the thin film layer (Compressive residual strain can be found using ASTM E 2245 and Data Sheet RS.1 or RS.2.)
32	ucεr=	×10-6	combined standard uncertainty value for residual strain (For compressive residual strain, ucεr can be found using Data Sheet RS.1 or RS.2.)
For stress gradient calculations:
33	sg=	m-1	strain gradient of the thin film layer (can be found using ASTM E 2246 and Data Sheet SG.1 or SG.2)
34	ucsg=	m-1	combined standard uncertainty value for strain gradient (can be found using Data Sheet SG.1 or SG.2)

2.  Young's modulus calculation (as obtained from a fixed-fixed beam...not recommended):
           a.  E_simple  =  4.864 ρ ( f_ffb cal_f )² L_ffb⁴ / t²  = GPa
                            (as obtained from the fixed-fixed beam assuming simply-
                             supported boundary conditions for both supports)

           b.  E_clamped = 0.946 ρ ( f_ffb cal_f )² L_ffb⁴ / t² = GPa
                            (as obtained from the fixed-fixed beam assuming
                             clamped-clamped boundary conditions)

           c.  E = (E_simple + E_clamped) / 2 = GPa       (use this value, if must)

           d.  u_E = (E_simple - E_clamped) / 6 = GPa      (as obtained from a Type B analysis)

           e.   Report the results as follows:  Since it can be assumed that the estimated value of the standard
                 uncertainty, u_E, is approximately Gaussianly distributed, the Young's modulus value is believed
                 to lie in the interval E ± u_E (expansion factor k=1) representing a level of confidence of
                 approximately 68 %.  
 

Table 7 - Optional OUTPUTS (using E and ucE from the cantilever and assuming fmeas1, fmeas2, and fmeas3 in the second table are damped resonance frequencies)
For residual stress:			Description
47	σr=	MPa	= E εr (residual stress of the thin film layer)
48	ucσr=	MPa	= SQRT[uE(σr)2 + uεr(σr)2] (combined standard uncertainty value for residual stress where each of the standard uncertainty components is obtained using a Type B analysis)
49	uE(σr)=	MPa	= [ (E+3ucE)|εr| - (E-3ucE)|εr| ] / 6 = ucE|εr| (component in the combined standard uncertainty calculation for residual stress that is due to the measurement uncertainty of E)
50	uεr(σr)=	MPa	= [ E(|εr|+3ucεr) - E(|εr|-3ucεr) ] / 6 = ucεrE (component in the combined standard uncertainty calculation for residual stress that is due to the measurement uncertainty of εr)
For stress gradient:
51	σg=	GPa/m	= E sg (stress gradient of the thin film layer)
52	ucσg=	GPa/m	= SQRT[uE(σg)2 + usg(σg)2] (combined standard uncertainty value for stress gradient where each of the standard uncertainty components is obtained using a Type B analysis)
53	uE(σg)=	GPa/m	= [ (E+3ucE)sg - (E-3ucE)sg ] / 6 =  ucE sg (component in the combined standard uncertainty calculation for stress gradient that is due to the measurement uncertainty of E)
54	usg(σg)=	GPa/m	= [ E(sg+3ucsg) - E(sg-3ucsg) ] / 6 = ucsgE (component in the combined standard uncertainty calculation for stress gradient that is due to the measurement uncertainty of sg)

Modify the input data, given the information supplied in any flagged statement below, if applicable, then recalculate:
 

1.		Please provide inputs to Tables 1 and 2 for calculations using data from a cantilever.
2.		Please provide inputs to Table 3, ρ, W, t, and Einit for calculations using data from a fixed-fixed beam, if applicable.
3.		The value for mag should be greater than or equal to 20×.
4.		The value for ρ should be between 1.00 g/cm3 and 5.00 g/cm3.
5.		The value for σρ should be between 0.0 g/cm3 and 0.10 g/cm3.
6.		The value for μ should be between 0.70×10-5 Ns/m2 and 3.0×10-5 Ns/m2.
7.		The value for σμ should be between 0.0 Ns/m2 and 0.05×10-5 Ns/m2.
8.		The value for temp should be between 15 °C and 30 °C.
9.		The value for W should be greater than t and less than Lcan.
10.		The value for W should be greater than t and less than Lffb, if inputted.
11.		The value for σW should be between 0.0 μm and 2.0 μm.
12.		The value for t should be between 0.000 μm and 10.000 μm.
13.		The value for σthick should be between 0.0 μm and 0.3 μm.
14.		Squeeze film damping expected for the cantilever since dgap < W / 3.
15.		The value for Einit should be between 10 GPa and 300 GPa.
16.		The value for ucmeter should be between 0.0 Hz and 25.0 Hz.
17.		The value for Lcan should be between 0 μm and 1000 μm.
18.		The value for σL should be between 0.0 μm and 2.0 μm.
19.		The value for fresol should be between 0 Hz and 50 Hz.
20.		The values for fmeas1, fmeas2, and fmeas3 should be between 5.00 kHz and 300.0 kHz.
21.		If inputted, the value for Lffb should be between 0 μm and 1000 μm.
22.		If inputted, the value for fffb should be between 5.0 kHz and 1200 kHz.
23.		If inputted, the value for εr should be between -100×10-6 and 100×10-6 and not equal to 0.0.
24.		If inputted, the value for ucεr should be between 0.0 and 4.0×10-6.
25.		If inputted, the value for sg should be between 0.0 m-1 and 20.0 m-1.
26.		If inputted, the value for ucsg should be between 0.0 m-1 and 2.0 m-1.
27.		The values for fmeas1, fmeas2, and fmeas3 are not within 20 kHz of fcaninit.
28.		If inputted, the value for fffb should be between fffbinitlo and fffbinithi.
29.		The value for pdiff should be between 0 % and 2 %.
30.		The value for calf should be between 0.9990 and 1.0010.
31.		The value for σfreq should be between 0.0 kHz and 0.5 kHz, inclusive.
32.		The value of E obtained from the cantilever should be within 20 GPa of Einit.
33.		The values for uthick, uρ, uL, ufreq, ufresol, udamp, and ufreqcal should be between 0 GPa and 5 GPa, inclusive.
34.		The value of ucE obtained from the cantilever should be between 0 GPa and 10 GPa.
35.		If applicable, the value of E obtained from the fixed-fixed beam should be within 30 GPa of Einit.
36.		If applicable, the value of uE obtained from the fixed-fixed beam should be between 0 GPa and 20 GPa.