ME 495
Lab 6
Micro/Nano Science and Engineering
Nanoindentation of Quartz, Aluminum Single
Crystals and UNCD Thin Films
1. Introduction
With the development of micro/nano science and engineering, mechanical properties of
thin films at the micro scale have attracted more and more interest. For example, thin
films can decrease wear and friction. Thin films are also building blocks of MEMS
devices. Recently, techniques have been developed to interrogate the mechanical
properties of materials at submicron scales. For example, a nanoindenter system can
continuously control and monitor the loads and displacements of an indenter as it is
driven into and withdrawn from a material.
In Professor Espinosa’s laboratory, a
combined MTS Nanoindenter - Digital
Instrument 3100 AFM (Atomic Force
Microscope) microscope with loading
fixture will be used for this lab session. By
imaging the sample surface using the AFM
optics, you will choose some places you are
interested to test. Then the sample will be
sent to under the nanoindenter to run the
tests. After the tests are finished, your
sample will be sent back to the AFM.
Fig.1 instruments setup
The most common tip geometry used for nanoindentation is the Berkovich diamond tip. It
is a three-sided pyramid-shaped indenter
with an area function (projected area as a
function of depth) similar to that of the
Vickers indenter. The centerline to face
angle
is
65.35.
Because
of
manufacturing limitations, the tip is not
perfectly sharp. Its radius of curvature is
typically between 100 and 200 nm. This
tip geometry has been used as the
standard for nanoindentation. It is used
primarily for Bulk materials and thin
films of thickness greater than 100 nm.
The Berkovich tip is also widely used
for scratch measurements.
Fig.2 Berkovich tip
ME 495
Micro/Nano Science and Engineering
In this lab session, we will study how to operate the nanoindenter instrument, how to
properly interpret the load-displacement data and extract the material’s mechanical
properties (Young’s modulus and Hardness).
2. Nanoindentation Theory
Nanoindentation tests are performed by nanoindenters that can continuously record the
load and displacements. When a nanoindenter tip penetrates into the sample surface, the
sample deforms both elastically and plastically. When the tip is withdrawn, the initial
unloading is elastic. The key is how to determine the plastic depth hp at which the
deformation still conforms to the indenter tip. Projected area can be obtained from hp
with the knowledge of tip geometry. The stiffness of the system is given by:
S
dP
dh

max P , max h
2

Er A
(1)
Where P is the load, h is the penetration depth, A is the projected contact surface area at
maximum depth and Er is the reduced modulus. The hardness is given by:
P
H  max
(2)
A
A reduced modulus was used in (1). This takes in account the effects of non-rigid
indenters on the load- displacement behavior:
1   i2
1 1


(3)
Er
E
Ei
where E and  are Young's modulus and Poisson's ratio for the specimen and E i and  i
are the same parameters for the indenter.
2
During the initial unloading, Nix (1986)
assumed that the elastic behavior of the
indentation contact is similar to that of a flat
cylindrical punch, that is, the area in contact
with the indenter remains constant. A line fit
tangent to the unloading curve at the
maximum load has a slope S, and its
intercept with the x axis gives hp. The
deviation from the line implies the loss of
contact with the indenter, as a result of the
change in shape of the indentation that
occurs when the elastic displacements are
recovered.
Fig.3 a schematic representation of load versus displacement showing quantities used
in the analysis as well as a graphical interpretation of the contact depth
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Micro/Nano Science and Engineering
Oliver (1992) shows that linear unloading is not true for most materials. He suggests that
the unloading curve can be better described by power laws. Dynamic techniques
confirmed that unloading contact stiffnesses change immediately and continuously as the
indenter is withdrawn, as would be expected from continuous changes in contact area,
thus, the flat punch approximation is not entirely adequate. However, the stiffness values
at maximum load obtained by linear unloading and power laws unloading are very close
mathematically.
Sneddon derived closed form analytical solutions for punches of several geometries such
as flat punch, conical punch and
paraboloids of revolution.
P
(4)
hs   max
S
h p  hmax  hs
(5)
For flat punch,  = 1, for paraboloids of
revolution,  = 0.75, for conical punch,
2
  (  2)

. Oliver proceeds his
model on the assumption that one of
these geometries gives a better
description of elastic unloading of an indentation with a Berkovich indenter tip. The
conical indenter, like the Berkovich indenter, has a cross-sectional area varying with the
square of the depth of contact and the geometry is singular at the tip. Paraboloids of
revolution are also a potential in that no real indenter is perfectly sharp, i.e., at some scale
the tip exhibits some rounding. In addition, because of plasticity, an elastic singularity
cannot really exist at the indenter tip, the paraboloid geometry accounts for this. For both
geometries, the load-displacement relationships are nonlinear and the contact area
changes continuously during unloading. Experiments and FEM with Berkovich indenters
show that  = 0.75, paraboloid works well.
Another assumption is that the contact area at maximum load is same as that by
observation of the residual hardness impression when the elastic recovery is done. This is
confirmed by experiments.
Please note that Sneddon’s formulas are based
strictly on elastic contact where sink-in always
occurs. Sometimes pile-up happens, this
phenomenon implies that plastic component is
playing a significant role in nanoindentation
and its consequences cannot be explained by
elastic models. So indentations should be
imaged to examine the true area of contact in
this case.
Fig.5 a schematic representation of pile-up
and sink-in effects
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Micro/Nano Science and Engineering
To account for elastic displacements of the load
frame of the instrument, the machine compliance Cm ,
must be added to the contact compliance Cc , to
obtain the overall or total compliance of the testing
system.
 1 1
Ctotal  Cm  Cc  Cm 
(6)
2 Er A
The linear relationship between and for indentations
of several depths is used to determine the machine
compliance, which is simply the intercept of this
curve. The contact compliance is then the difference
between the measured total compliance and the
experimentally determined machine compliance.
Once the contact compliance is known, the
indentation modulus can be calculated.
Fig.6 schematic representation of the basic
components of an indentation testing system
The next question is how to get the indenter area function. Oliver's method is based on
the assumption that the elastic modulus is independent of indentation depth. The initial
guess at the area function is
A(hc )  24.5hc2  C1hc1  C 2 hc1 / 2  C3 hc1 / 4    C8 hc1 / 128
(7)
where C1 through C8 are constants. The lead term is a perfect Berkovich indenter. The
others describe deviations due to blunting at the tip. The calibration procedure involves
making a series of indentations in two standard materials, aluminum and fused quartz,
and relies on the facts that both these materials are elastically isotropic, their moduli are
well known and their moduli are independent of indentation depth. Indentation contact
stiffnesses are measured accurately and precisely over a wide range of indentation depths.
Use the new area function (7) and compliance-area function and iterate several times
until convergence was achieved. The procedure is simpler because Er is known in this
case. In this way, the machine compliance is obtained and area function is determined.
The last important point is thermal drift calibration. This calibration is to account for
small amounts of thermal expansion or contraction in the test material and/or indentation
equipment. For materials exhibiting little or no time-dependent deformation behavior
(metals and ceramics tested at room temperature), we can include a period near the end of
the test, during which the load is held constant for a fixed period of time while the
displacements are monitored to measure the thermal drift rate. If the test material exhibits
significant time-dependent deformation, thermal drift correction should not be used
because we cannot distinguish the thermal displacement from time-dependent
deformation in the specimen.
Our Nanoindenter XP system software uses Oliver model to extract reduced modulus and
hardness and monolithic method, Eq. (3), to get the material’s Young’s modulus.
ME 495
Micro/Nano Science and Engineering
3. UNCD (ultra-nanocrystalline diamond)
Diamond is the hardest substance and has the highest thermal conductivity and sound
velocity. Diamond was difficult to fabricate until chemical vapor deposition (CVD)
techniques were developed. Conventional CVD method of synthesizing diamond films
( MCD, microcrystalline diamond ) relies on hydrocarbon precursors (CH3) in the
presence of a large excess of hydrogen. However, atomic hydrogen etches the diamond
phase, resulting in the formation of intergranular voids and a columnar morphology with
grain size and RMS surface roughness typically ~10% of the film thickness. The grain
morphology is therefore not suitable for the fabrication of components requiring
resolution on the order of several microns. Also there are amorphous diamond-like
carbon ( DLC ) films with C as growth species. The novel UNCD ( ultra-nanocrystalline
diamond ) coating technology using microwave CVD, invented in Argonne National
Laboratory, uses carbon dimers (C2) as growth species, result in ultra fine grain size of 3
~ 5 nm and RMS roughness of 10-20 nm. Most excitingly, when nitrogen gas is added
during the deposition, UNCD films become conductive. UNCD can be conformally
coated on a wide variety of materials. It can be used as an etch-stop layer and UNCD
patterns can be achieved by selective area UNCD growth or RIE. These superior
mechanical and microfabrication-compatible properties show that UNCD is a potential
MEMS material.
Fig.7 Photolithographic and etching procedures used to fabricate UNCD MEMS devices. One takes
advantage of the drastically different chemistries of diamond and silicon to produce freestanding
micrometer- and submicrometer-sized diamond structures.
Fig.8 UNCD scanning electron micrograph
Fig.9 Freestanding UNCD cantilever, ~2um
thick, ~4um wide,~ 150um long, attached to
the substrate at one end. The slight liftoff
from the Si base indicates a very small
internal stress and the apparent absence of stiction.
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Micro/Nano Science and Engineering
4. Consideration of Substrate Effects
The measurement of films is more difficult than monolithic materials because the loaddisplacement data depend in complex ways on the properties of the thin film and the
substrate. Thus, obtaining absolute measurements of film properties is often difficult and
requires careful analysis.
An often-used guideline is to make measurements at depths that are a small fraction of
the film thickness. It is recommended for the indentation depth to be less than 10% of the
film thickness.
There are many measurement cases in which the film is so thin that the influences of the
substrate cannot be avoided at depths at which useful load-displacement data can be
obtained. Under such circumstances, we must estimate the film properties from
measurement of composite structure. There are some empirical and analytic expressions
for the composite hardness and elastic modulus that model the depth dependence of the
composite film-substrate properties so as to allow extrapolation to the small depth limit.
Gao Model
It works well in predicting the depth dependence of the composite elastic modulus Ec of
a film-substrate system with film thickness t f . In his model, Ec is related to modulus of
film, E f , and modulus of substrate, E s , in this way,
Ec  ( E f  E s )  E s
(8)
 is a weighting function that depends on the ratio of contact radius to film thickness
( x  a / t f ) and Poisson's ratio (assumed to be same for film and substrate),
1
1
1
x
(9)

[(1  2 ) ln( 1  x 2 ) 
]

x 2 (1   )
x
1  x2
The conclusion that the model works well is based only on a comparison of the
experimental data with the mathematical form of Eq. (8)(9). The model is yet to be fully
evaluated using systems for which the modulus of the film and substrate are known
independently of the indentation measurements.

2
arctan
King Model
King modified the solution presented by Doerner and Nix and made it applicable to all
film/substrate systems. He used numerical methods to study the problem and defined the
reduced modulus as
2
 (t  h )
 (t  h)

1 1  i2 1   f
1  s2  a
a
(10)


(1  e
)
(e
)
Er
Ei
Ef
Es
where a is the square root of the projected contact area, t is the thickness of the film, h
is the total indenter displacement,  is a numerically determined scaling parameter that is
a function of a /( t  h) ,
a
a 0.5
a 0.25
  0.37828  0.0056092 
 0.34744  (
)  1.197  (
)     (11)
(t  h)
(t  h)
(t  h)
Another promising and merits further development technique for extracting film
properties combines finite element simulations with experimental load - displacement
data.
ME 495
Micro/Nano Science and Engineering
5. Activities
In this lab session, we will calibrate the system using an aluminum sample and do
nanoindentation tests on quartz, and do some calculations on data previously obtained
from 2 m thick UNCD thin film on silicon substrate. The UNCD thin film has a surface
roughness of 20nm.
Activity 1: Sample loading
The standard sample tray can accept up to five samples on standard metallographic
mounting disks (1.25” diameter, 1” height). To load the samples, insert the sample disk
into the bored sample hole and tighten
the set screw in place against the sample
disk. Once the samples are loaded, and
all are tightened in place, turn the sample
mount tray upside down so that the
leveling arms are facing downward, and
set the sample mount tray on a flat,
smooth and lint-free surface. Loosen all
of the sample disks, so that the sample
tray rests entirely on the sample leveling
arms. Once all of the samples are loose
and resting against the “flat surface”,
retighten the set screw until each sample
disk is fixed firmly in place. Turn over
the sample tray back. The sample tray is
then ready to mount into the rails.
Fig.10 sample tray with loaded samples
If the samples are mounted too low in the sample tray, the indenter will not be able to
reach the surfaces, causing the experiment run to abort, but no damage to the system will
ensue. If the samples are mounted at a height higher than the levelling arms, the indenter
head will be damaged when the sample tray is sent to under indenter head! You are asked
to load aluminum and quartz samples.
Activity 2: Calibration of the system
Upon each start-up the AFM/Nanoindenter will need a distance microscope to indenter
calibration – the vector position between the two units must be determined periodically
due to back-lash in the motion stage. Prepare a soft material (metallic), in most cases,
aluminum, and choose “AFM to Nanoindenter Distance Calibration” from the menu. The
program will make three indents to determine the calibration vector. When the indents are
finished, the program will ask you to select the calibration indent. This will be the indent
to the far right and is always the largest of the three. You will also be certain of which tip
you are using. Select the indent furthest to the right by moving the crosshair over it and
save the results.
ME 495
Micro/Nano Science and Engineering
Activity 3: Running nanoindentation tests on Quartz
Now the system is ready to launch nanoindentation tests. Use the joystick to move the
quartz sample to under the AFM head. Focus the AFM optics and get a clear image of
quartz surface. Design a set of nanoindentation tests at maximum depth of 1000 nm.
Choose a starting indent position on quartz where you are interested and make a 22
array indent positions with spacing of 25 m between each dimension. Please follow
Appendix A to setup your tests.
The tests will last about 30 minutes. Please follow Appendix B to convert data to text
files.
Activity 4: Calculation of nanoindentation data on UNCD/Silicon Composite
We will do some calculation to see how the soft substrate will affect the hard thin film.
Please download an excel file from https://*********. Preliminary nanoindentation
results were obtained at depths of 50nm, 75nm, 100nm, 125nm, 137.5nm, 150nm,
175nm, 200nm, 225nm, 250nm, 275nm and 300nm. At each depth, there are 25 tests and
the results are averaged at each depth in the excel tables. Please deduce formula carefully
based on Gao and King models and finish the blanks in excel. Should you have any
questions about excel functions, feel free to contact your TA.
6. Lab Report Questions
Read Part 1, 2, 3 and 4 carefully and answer the following questions in your lab report.
1) You have run 4 nanoindentation tests on quartz sample and obtained results both in
printed paper and in mh file ( You may read them in excel). What are your average
hardness and Young’s modulus results? What is the reduced modulus?
2) Theoretical models are always derived in conditions that can hardly be met in
experimental reality. For example, nanoindentation models are based on perfectly flat
surface, but actually any surface will have some roughness. Think about the
nanoindentation on UNCD/Si. List the factors that would cause experimental results to
deviate from UNCD’s true hardness and modulus. Explain why.
3) Open the UNCD excel file and fill the blanks in the tables. Esi=170Gpa.
a) Keep changing UNCD’s modulus until a value (call it Euncd-gao) in Gao model so
that Gao’s reduced modulus will fit the reduced modulus obtained from
experiment (Er-expt). Plot Er-expt, Euncd-gao, Euncd-gao  100Gpa curves with
displacement as X-axis and Modulus as Y-axis.
b) Calculate UNCD modulus in Gao model (Efuncd-gao) based on reduced modulus
obtained from experiment (Er-expt). Plot Efuncd-gao and Ef-mono (obtained from
monolithic model, already in excel table) curves with displacement as X-axis and
Modulus as Y-axis.
c) Keep changing the UNCD’s modulus until a value (call it Euncd-king) in King model
so that King’s reduced modulus will best close to the reduced modulus obtained
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Micro/Nano Science and Engineering
from experiment (Er-expt). Plot Er-expt, Euncd-king, Euncd-king  100Gpa curves with
displacement as X-axis and Modulus as Y-axis.
d) Calculate UNCD modulus in King model (Efuncd-king) based on reduced modulus
obtained from experiment (Er-expt). Plot Efuncd-king and Ef-mono (obtained from
monolithic model, already in excel table) curves with displacement as X-axis and
Modulus as Y-axis.
e) From the four plots, which model do you think is better to address the substrate
effects in UNCD/Si composite? Explain.
7. References
http://www.mts.com/nano/XP_specs.htm
http://clifton.mech.nwu.edu/~espinosa/micro-nano.html
M. F. Doerner and W. D. Nix, A Method for Interpreting the Data from Depth-Sensing
Indentation Instruments, J. Mater. Res. 1(4), Jul/Aug 1986, 601-609
K. W. McElhaney, J. J. Vlassak and W. D. Nix, Determination of Indenter Tip Geometry and
Indentation Contact Area for Depth-Sensing Indentation Experiments, J. Mater. Res., Vol.13,
No.5, May 1998, 1300-1306
G. M. Pharr, W. C. Oliver, and F. R. Brotzen, J. Mater. Res. 7, 613 (1992)
“Ultrananocrystalline Diamond in the Laboratory and the Cosmos”, Dieter Gruen, MRS Bulletin,
Oct. 2001, pp.771-775
“Fullerenes as precursors for diamond film growth without hydrogen or oxygen additions”, D.
Gruen, S. Liu, et al, Appl. Phys. Lett. 64(12), 21 March 1994, pp.1502-1504
“Control of Diamond Film Microstructure by Ar Additions to CH4 /H2 Microwave Plasma”, D.
Zhou, D. Gruen, et al, Journal of Applied Physics, Vol.84, No.4, Aug.1998, pp.1981-1989
“Buckyball Microwave Plasma: Fragmentation and Diamond-film Growth”, D. Gruen, S. Liu,
A.Krauss, and X.Pan, “J. Appl. Phys. 75(3), Feb. 1994, pp.1758-1763
“Carbon Dimer, C2, as a Growth Species for Diamond Films from Methane/Hydrogen/Argon
Microwave Plasmas”, D.Gruen, C.Zuiker, A.Krauss, and X.Pan, J. Vac. Sci. Technol. A13(3),
May/Jun 1995, pp.1628-1632
“Synthesis and Characterization of Highly-conducting Nitrogen-doped Ultrananocrystalline
Diamond Films”, S.Bhattacharyya, O. Auciello, J. Birrel and et al, Appl. Phys. Lett., Vol.79,
No.10, Spet.2001, pp. 1441-1443
H. Gao, C.H. Chiu, and J. Lee, Elastic Contact Versus Indentation Modeling of Multi-Layered
Materials, Int. J. Solids Struct., Vol 29 (No.20), 1992, pp. 2471-2492
King, R. B., Int. J. Solids Struct., 1987 (23), 1657
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Micro/Nano Science and Engineering
Appendix A:
1) From the XP main menu choose “Design Custom Test”. The test design menu
will then come up. Work through each menu for each experiment.
2) Select “Working on specimen #” ex: “1”
3) Select “Specimen Name/comments” ex: “Quartz 1000nm depth”.
4) Select “Experiment to Perform”.
a) Choose a standard experiment. ex : “ test a maximum load” and input
“1000”.
b) Select “All Done, Continue On”.
5) Select “Array of positions”.
a) Move cross-hairs to first indent position.
b) Press “E” to exit.
c) If you chose more than 1 indent the program will then ask you “No. of
indents in the X dimension” and “No. of indents in the Y dimension”.
Input “2” in each case.
d) “Input the angle (0-360) between the X axis of the tables and the X-axis of
the array”. Input “0”.
e) “Spacing between indents in the X dimension” and “Spacing between
indents in the Y dimension”. Input “25” in each case.
f) When all the positions are selected the program will display a map and
prompt “Is this the shape you wanted?” Choose “Y” if it is.
6) If you have more than one experiment then continue from 2) above and create
experiments 2.
7) When all experiments are set choose “All Done, Continue On”. The program will
then ask what the final parameters are by displaying the “Menu of Execution
Parameters”
8) Select “All Done, Continue On”.
9) Input Operator’s name.
10) Be sure Printer has enough paper.
11) “Press F1” to continue.
12) The program will then perform the experiments. When it is finished it will return
the stage to the original position.
Appendix B:
1) After the tests are done, the program will ask you “Using spring constant? Y/N”
Choose “Y” and printer will print out result sheets.
2) From the XP main menu choose “Review Data”. The review data menu will then
come up.
3) Select “Re-format data to text“.
4) Select “Basename for input data files” and change the first two letters into “dh”
which means you want load-displacement files.
5) Select “ Add a contiguous series of files”.
a) “Starting file number of series” is always “1”, by default. This means the
first indenter number in the series.
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6)
7)
8)
9)
Micro/Nano Science and Engineering
b) Select “End files number of series”. Input “4” which is the last indent
number in the series.
Select “Accept this series”.
Select “Copy text files to floppy disk” and Select “All done continue on”.
The program will jump out “Please insert a blank floppy disk in drive A”. Insert a
floppy disk and press “F1”.
Repeat steps 2) to 8) to get “hardness and modulus data” but be careful that in
step 4) change the first two letters into “mh” and in step 5)b) “the end files
number of series” is “1”.