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Keysight Technologies
Quantitative Mechanical Measurements
at the Nano-Scale Using the DCM II
Application Note
Introduction respectively. The range and resolution
in force are 30mN and 3nN, respectively.
Feature miniaturization, especially in the Because the DCM II has a resonant fre-
electronics industry, demands knowledge quency of about 120Hz, measurements
of mechanical properties on the scale of force and displacement are insensitive
of nanometers. Instrumented indenta- to environmental noise which occurs at
tion facilitates such testing, because the lower frequencies. The DCM II can be
area of the contact impression does not used in combination with a variety of
have to be measured visually, but can indenter tips including Berkovich,
be inferred solely from the relationship cube-corner, and sphero-conical.
between applied force and consequen- Changing from one tip to another
tial penetration of the indenter into the takes just a few minutes. Figure 1. The Keysight DCM II.
testing surface 1. Instrumented indenta-
tion has been used since the 1980's to
make measurements at the sub-micron Experimental Method
scale, but recent developments allow Prior to testing, the shape of the diamond
quantitative determination of mechani- indenter was "calibrated" by performing
cal properties using indents of just a few 55 indents on a reference material, fused
nanometers deep. This article addresses silica. Then seven different materials,
special considerations for such testing, including the fused silica, were tested
and reports results for seven different using the force-time algorithm shown in
materials tested with the DCM II. Figure 2. All materials were tested to the
same peak force of 50N. The materials
The DCM II, shown in Figure 1, is an tested were polycarbonate, Pyrex, fused
optional high-resolution actuating silica, single-crystal aluminum, silicon Figure 2. Force-time algorithm for
transducer for the Keysight Technologies, (111), nickel, and sapphire. Because indentation tests.
Inc. G200 Nano Indenter. The DCM II these materials are of varying hardness,
may be used in addition to or instead of the indentation depths resulting from
the standard indentation head. If both the applied force of 50N varied. The
heads are included on a single system, deepest indents of about 100nm were
transition from one head to the other is achieved on the polycarbonate, while
entirely software controlled; the user the shallowest indents of less than 7nm
doesn't have to make any adjustments were achieved on the sapphire. Fifteen
to hardware, controllers, or calibrations. indents were performed on each sample
The range and resolution in displace- using the DCM II itted with a diamond
ment (travel) are 70m and 0.0002nm, Berkovich indenter. Force and displace-
02 | Keysight | Quantitative Mechanical Measurements at the Nano-Scale Using the DCM II - Application Note
ment measurements were acquired at Results and Discussion relationship between the distance from the
a rate of 12.5kHz, averaged in a buffer apex of the diamond, d, and the cross-sec-
and reported at a rate of 100Hz. Data Calibration tional area at that distance, A, is called the
were analyzed according to the method The process for determining the precise "area function". For a perfect Berkovich
prescribed by an international standard shape of the indenter is automated within indenter, the area function is
for instrumented indentation testing, ISO the NanoSuite software. The following dis-
14577 2, which in turn draws heavily upon cussion should not intimidate new users;
the landmark article by Warren Oliver However, when making nanometer-scale
it is only intended to explain what is done
and George Pharr 1. Average modulus and indents, imperfections at the apex of the
and why.
standard deviation were computed using diamond demand that the area function
all 15 tests. If a particular test yielded a be determined more precisely. We do this
The data used to "calibrate" the shape of
measure of modulus that was different by calculating contact depth and contact
the tip are shown in Figure 3 in the form of
from the average value by more than two area, assuming a value for the reduced
stiffness squared divided by applied force
standard deviations, the result for that test modulus of the material. Therefore, each
(S2/P) as a function of displacement into
was discarded, and the remaining results indent on fused silica yields an ordered
the test surface, h. We begin by looking
were averaged again. pair (hc, A) with contact depth (hc) calcu-
at the data in this way, because S2/P is
lated as
directly proportional to reduced modulus
The main focus of this work was the deter- squared divided by hardness (Er2/H), but is
mination of quantitative mechanical prop- ,
independent of contact area (A):
erties at the scale of nanometers. How- and A calculated as
ever, when used in combination with the
NanoVision option, the DCM II becomes a .
proilometer, capable of generating topo-
logical images with excellent dimensional
accuracy. In this work, a grid for verifying If the machine is working well, then we Figure 4 shows these (hc, A) data. To
the dimensional accuracy of atomic-force expect S2/P to be constant with increas- determine the reined area function, we
microscopes was scanned. The grid has ing penetration, having a value of 700GPa curve it this data to the functional form
periodic steps; the steps have a height of 6 50GPa. (As the displacement into the suggested by Oliver and Pharr 1:
19nm and a period of 3 microns. A square surface decreases to zero, the contact
area of 6.5m on a side was scanned using becomes increasingly Hertzian, and we
a scanning force of 1.0N; the result- expect S2/P to increase exponentially, be-
ing scan was used to select a site for an cause for a Hertzian contact, the param- If we only use the irst two terms of this
indentation test. Following this test, the eter S2/P goes as h-1/2.) Since the trace of expression to it the data, the best-it
same area was scanned again to reveal the S2/P meets our expectations, we proceed coeficient of the second term can be used
residual indentation impression. to use this data to determine the pre- to determine the radius of the tip. By this
cise shape of the diamond indenter. The analysis, the radius of the diamond tip was
Figure 3. Stiffness squared divided by force (S2 /P) vs. displacement Figure 4. Fused silica data (hc, A) together with 5-term area function.
(h). For fully plastic contacts, acceptable range for fused silica is
700GPa 6 50GPa.
03 | Keysight | Quantitative Mechanical Measurements at the Nano-Scale Using the DCM II - Application Note
Figure 5. Young's modulus measured using DCM II at 50 N. Error bars Figure 6. Three consecutive indents on sapphire (E = 400 GPa). Loading
represent 1son n/15 measurements. Solid line indicates unity; i.e. per- and unloading curves coincide, indicating that the indents are completely
fect agreement between measured and nominal. elastic.
determined to be 52nm. However, two from crystalline elastic constants for the to the test method that was employed. As
terms rarely provide a it that is suficiently direction normal to the testing surface a polymer, polycarbonate manifests some
good for making nanometer-scale mea- [4-7]. For polycarbonate, the nominal value viscoelasticity. Thus, obtaining the contact
surements. The it shown in Figure 4 is a is that reported on the website "engineer- stiffness from the slope of the unloading
ive-term it. For hc < 100nm, the maxi- ingtoolbox.com". curve likely results in a stiffness that is too
mum difference between this it and the high, because the indenter continues to
data is about 4%. Overall, the agreement between nominal move into the material even as the force
and measured values is excellent, espe- is reduced. It would be better to measure
Young's modulus cially given the scale of testing. For the the modulus of this material with our
The results for Young's modulus are sum- Pyrex, fused silica, nickel, and sapphire, continuous stiffness measurement option
marized in Table 1. The fourth column measured values for Young's modulus were (CSM). For the single-crystal aluminum,
of this table gives the number of tests within 1 standard deviation of the nomi- the measured value of 59.866.9 GPa is low
(out of 15) that were used in the calcula- nal value. Two sets of 15 indents were relative to the nominal value of 70.0 GPa.
tion of results. On all but three materials, performed on the fused silica, because it However, we have no reason to question
all 15 tests were used. In Figure 5, the is standard practice to test this reference the accuracy of the measured value. One
measured values for Young's modulus material before and after the materials of possible explanation for the discrep-
are plotted against nominal values, with interest. The average maximum inden- ancy between the measured and nominal
the ideal plotted as a solid line. For fused tation depths achieved for both sets of values may be a surface oxide layer. For
silica and Pyrex, the nominal values are indents on fused silica agreed to 0.005nm! the (111) silicon, the measured value of
what we measured sonically in-house 3. 186.3611.6 GPa was slightly high, rela-
For sapphire, aluminum, silicon (111), and For polycarbonate, the measured value of tive to the nominal value of 168.9 GPa. We
sapphire, the nominal values for Young's 3.3560.08 GPa is high relative to the nomi- chose (111) silicon for this testing, because
modulus are theoretical values calculated nal value of 2.6 GPa. This is probably due it has the same Young's modulus perpen-
Material Poisson's ratio hmax n valid tests EIT s(E IT ) Nominal E Ref. for nominal E
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