Nanoindenter

1. Theory

• Definition: A nanoindenter presses a calibrated diamond tip into a surface while recording load and depth with micronewton and nanometre resolution, and extracts hardness and elastic modulus from the load-depth curve (Abernathy et al.; Randall).
• Elastic recovery: The initial unloading slope, the contact stiffness, is set by the reduced modulus of tip and sample and the contact area, $E^{\ast }=\frac{\sqrt{\pi }}{2}S/\sqrt{A}$ (Abernathy et al.; Prou et al.).
• Contact area: The Oliver-Pharr method infers contact depth from the curve and converts it to area through a calibrated area function, near $24.5h_c^2$ for a Berkovich tip (Abernathy et al.; Prou et al.; Sousa et al.).
• Hardness: Mean contact pressure at peak load, H = P/A (Randall).

2. Working Principle

• Indenter: A three-sided Berkovich diamond pyramid with 65.3 degree semi-angle, equivalent to a 70.3 degree cone (Prou et al.).
• Load cycle: Loading to a peak force, an optional hold, and unloading; the upper unloading curve is fitted with a power law (Abernathy et al.; Prou et al.).
• Calibration: Area function and frame compliance from a reference such as fused quartz; drift is measured or compensated (Abernathy et al.; Randall).
• Thin films: Depths are kept small relative to film thickness, or film-substrate models are used (Abernathy et al.; Prou et al.).

3. Applications

• Thin-film mechanics: Modulus and hardness of dielectric, metal and optical coatings such as Ti-doped tantala and TiW (Abernathy et al.; Randall).
• Silicon phase transformation: Pressure-induced metallic phases and amorphization under the tip, linked to SSRM contacts (Mylvaganam et al.).
• Coating adhesion and cracking: Residual imprint area and volume analysis on coated substrates (Randall).

Elastic Unloading Analysis

Name	Formula	Related Formulae	Variables/Constants
Reduced modulus from unloading stiffness	$E^{\ast }=\frac{\sqrt{\pi }}{2}\frac{S}{\sqrt{A}},S={\frac{dP}{dh}|}_{h_{max}}$	$\frac{1}{E^{\ast }}=\frac{1-{\nu }_i^2}{E_i}+\frac{1-{\nu }_s^2}{E_s}$	$E^{\ast }:reduced(effective)modulus$ $S:unloadingstiffness$ $A:projectedcontactarea$ $P:load$ $h:depth$ $E_i,{\nu }_i:indentermodulusandPoissonratio$ $\begin{array}{r}{E}_s,{\nu }_s:samplevalues;Abernathyetal.\\ andProuetal.:theserelations(Pro{u}^{\prime }s\\ firstformprintedwith1/A_c,readas\\ 1/\sqrt{A_c});Sousaetal.:diamond{E}_i=1140\\ \mathrm{GPa}and{\nu }_i=0.07;Yanetal.:geometry\\ factor\beta =1.05recommendedbyOliverand\\ Pharr\end{array}$ $\begin{array}{r}(computed:thediamondtermis8.7\times 10^{-4}\\ \mathrm{GP}{\mathrm{a}}^{-1},12percentofthe7.1\times 10^{-3}\mathrm{GP}{\mathrm{a}}^{-1}term\\ forSiwithE=130\mathrm{GPa}and\nu =0.28)\end{array}$
Unloading curve fit	$P=\alpha {\left(h-h_f\right)}^m$	$S=\alpha m{\left(h_{max}-h_f\right)}^{m-1}$	$\alpha ,m:fitconstants$ $\begin{array}{r}{h}_f:finaldepth;Abernathyetal.andProu\\ etal.:power-lawunloadingfit;\\ derivative(computed);Sousaetal.:m=1\\ foraflatpunch,1.5foraparaboloidand\\ 2foracone\end{array}$ $\begin{array}{r}(computed:m=1.5makesSequalto1.5\\ P_{m}ax/(h_{m}ax-h_f))\end{array}$
Contact depth	$h_c=h_{max}-\epsilon \frac{P_{max}}{S}$	$\epsilon =0.72(\text{cone}),0.75(\text{paraboloid}),1(\text{flat punch})$	$h_c:contactdepth$ $\begin{array}{r}\epsilon :geometryconstant;Prouetal.:\epsilon =\\ 0.72forBerkovich,Berkovich65.3degree\\ semi-anglemodelledasa70.3degreecone;\\ Sousaetal.:thesegeometryvalues(see\\ theQ/A)\end{array}$ $\begin{array}{r}(computed:withP/S=9.3\mathrm{nm},0.72and\\ 0.75give{h}_{c}differingby0.28\mathrm{nm})\end{array}$

Contact Area and Hardness

Name	Formula	Related Formulae	Variables/Constants
Berkovich area function	$A\left(h_c\right)=C_1{h}_c^2+C_2{h}_c+C_3{h}_c^{1/2}+C_4{h}_c^{1/4}+\dots$	$C_1\approx 24.5,E^{\ast }=\frac{1}{2h_c}\sqrt{\frac{\pi }{24.5}}\frac{dP}{dh}$	$\begin{array}{r}{C}_i:calibrationconstantsfortiprounding;\\ Abernathyetal.:series(third\\ coefficientprintedas{C}_2)with{C}_{1}closeto\\ 24.5,calibrationonfusedquartz;Prouet\\ al.:ideal-Berkovichformof{E}^{\ast };Randall:\\ tipcalibrationdiscrepanciesinflating\\ low-loadhardness\end{array}$ $\begin{array}{r}(computed:h_c=40\mathrm{nm}givesA=39200\mathrm{n}{\mathrm{m}}^2,\\ anequivalentcontactradiusof112\mathrm{nm})\end{array}$
Hardness	$H=\frac{P_{max}}{A\left(h_c\right)}$	$V_p\approx \frac{1}{3}{A}_p{h}_f(\text{residual-volume method})$	$H:indentationhardness$ $V_p:plasticvolume$ $\begin{array}{r}{A}_p:residualplasticarea;Randall:H=\\ P/A,residualareaandvolumealternative\\ (equationgarbled,pyramid-volumeform\\ background),Sisubstrateabout9\mathrm{GPa},\\ low-loadoverestimationfromroughness,\\ oxideandtipcalibration,differential\\ measurementcompensatingdrift\end{array}$ $\begin{array}{r}(assumed:H=7\mathrm{GPa}atA=39200\mathrm{n}{\mathrm{m}}^2;\\ computed:P_{m}ax=274\mu \mathrm{N})\end{array}$
Worked Oliver-Pharr example	$S=\frac{2}{\sqrt{\pi }}\beta E^{\ast }\sqrt{A}$	$h_{max}=h_c+\epsilon \frac{P_{max}}{S}$	$\begin{array}{r}\beta :geometrycorrection;inverseuseofthe\\ relationsabove(computed);Yanetal.:\beta \\ =1.05;Abernathyetal.:500\mathrm{nm}films,\\ 500to10000\mu \mathrm{N}loads,\nu =0.25assumed,\\ tantalamoduli132to177\mathrm{GPa}\end{array}$ $\begin{array}{r}(assumed:E=140\mathrm{GPa},\nu =0.25,\beta =1,h_c\\ =40\mathrm{nm};computed:E^{\ast }=132\mathrm{GPa},S=29.5\\ \mu N/nm,h_{m}ax=47\mathrm{nm},below10percentof\\ 500\mathrm{nm})\end{array}$

Films, Substrates and Silicon

Name	Formula	Related Formulae	Variables/Constants
Substrate effect on films	$h_{max}<0.1t_c$	$\frac{1}{E^{\prime }}=\frac{1}{E_s}+\left(\frac{1}{E_c}-\frac{1}{E_s}\right)I_0\left(\frac{t}{a}\right)$	$\begin{array}{r}{t}_c:coatingthickness,E^{\prime }:measured\\ film-substratemodulus\end{array}$ $E_c:coatingmodulus$ $I_0:weightfunction$ $\begin{array}{r}a:contactradius;Abernathyetal.:10\\ percentrule,impracticalforthin\\ coatings,Song-Pharrmodel,silica\\ substrateloweringmodulibyupto5per\\ cent;Prouetal.:10percentrule,\\ inversemethodsreaching10and20per\\ centaccuracyatabout20and30percent\\ depth,Oliver-Pharrfailing20percent\\ forlargemismatch\end{array}$ $\begin{array}{r}(computed:a500\mathrm{nm}filmallows50\mathrm{nm}\\ depth;a50\mathrm{nm}gatedielectriconly5\mathrm{nm})\end{array}$
Poisson-ratio sensitivity	$E_s=\frac{1-{\nu }_s^2}{1/E^{\ast }-\left(1-{\nu }_i^2\right)/E_i}$	$\frac{E_s\left(\nu =0.2\right)}{E_s\left(\nu =0.3\right)}=\frac{0.96}{0.91}$	$\begin{array}{r}Abernathyetal.:\nu =0.25assumed,0.20\\ to0.30changingmodulibylessthan3per\\ cent;rearrangedrelation(computed)\end{array}$ $\begin{array}{r}(computed:ratio1.055,thatis+2.4and\\ -2.9percentabout\nu =0.25,consistent\\ withthesource)\end{array}$
Phase transformation in silicon	$\text{Si-I}\stackrel{\text{load}}{\to }\beta \text{-Sn}\stackrel{\text{unload}}{\to }\text{a-Si},\text{Si-I}$	$\Delta V/V\approx -20\text{per cent}$	$\begin{array}{r}Mylvaganametal.:beta-tinmetallic,20\\ percentvolumereduction,amorphouson\\ unloadingwithsomereturntoSi-I,MD\\ loads2.5,3.4and4.1\mu \mathrm{N}at4\mathrm{nm}depth\\ for5,7.5and10\mathrm{nm}tipradii,\\ SSRM-detectedresistancedrop,5N/m\\ diamondprobe;Randall:Siabout9\mathrm{GPa}\\ hardnessand130\mathrm{GPa}modulus,TiW155\mathrm{GPa}\end{array}$ $\begin{array}{r}(computed:a10\mathrm{nm}sphereat4\mathrm{nm}depth\\ has8\mathrm{nm}contactradius,so4.1\mu \mathrm{N}isa\\ meanpressureof20\mathrm{GPa})\end{array}$

Important Questions

Ques: How does nanoindentation measure elastic modulus?

From the slope at the start of unloading. Abernathy et al. give $E^{\ast }=\frac{\sqrt{\pi }}{2}\frac{dP}{dh}\frac{1}{\sqrt{A}}$ and $1/E^{\ast }=(1-{\nu }_i^2)/E_i+(1-{\nu }_s^2)/E_s$, so the sample modulus follows once the diamond terms are removed. With diamond at 1140 $\mathrm{GPa}$ and 0.07 (Sousa et al.), the indenter term is $8.7\times 10^{-4}$ $\mathrm{GP}{\mathrm{a}}^{-1}$, 12 per cent of the $7.1\times 10^{-3}$ $\mathrm{GP}{\mathrm{a}}^{-1}$ term for silicon at 130 $\mathrm{GPa}$ (computed), so ignoring it underestimates stiff samples. The unloading curve is fitted as $P=\alpha (h-h_f{)}^m$ (Abernathy et al.; Prou et al.), and differentiating at peak load gives the stiffness S. Abernathy et al. note a Poisson ratio from 0.20 to 0.30 changes results by under 3 per cent, which the ratio 0.96/0.91 confirms (computed). Reference: M. R. Abernathy, J. Hough, I. W. Martin, S. Rowan, M. Oyen, C. Linn and J. E. Faller, ‘Investigation of the Young’s modulus and thermal expansion of amorphous titania-doped tantala films’, arXiv:1401.7061 (2014) (fetch-tool summary); J. Prou, K. Kishimoto, K. Inaba and A. Constantinescu, ‘Inverse Analysis of Multiple Indentation Unloading Curves for Thin Film Young’s Modulus Evaluation’ (fetch-tool summary); B. C. Sousa, J. Hay and D. L. Cote, ‘Toward an Instrumented Strength Microprobe: Origins of the Oliver-Pharr Method and Continued Advancements in Nanoindentation: Part 1’, in Elasticity of Materials, IntechOpen 2023: diamond E_i = 1140 GPa and nu_i = 0.07, epsilon = 0.72 cone, 0.75 paraboloid, 1 flat punch, unloading exponents 1, 1.5 and 2 for flat punch, paraboloid and cone, ideal Berkovich area 24.5 hc^2, pile-up underestimating area by up to 60 per cent (Bolshakov and Pharr) (fetch-tool summary).

Ques: How is the contact area found without imaging the indent?

From the contact depth and a calibrated area function. Contact depth is $h_c=h_{max}-\epsilon P_{max}/S$, because the surface around the indenter sinks in elastically (Prou et al.). The area then follows from $A(h_c)=C_1{h}_c^2+C_2{h}_c+\dots$ with $C_1$ close to 24.5 for a Berkovich tip, and the extra terms capture tip rounding, calibrated on fused quartz of known properties (Abernathy et al.). For $h_c$ = 40 $\mathrm{nm}$, the ideal area is 39200 $\mathrm{n}{\mathrm{m}}^2$, an equivalent radius of 112 $\mathrm{nm}$ (computed). Randall compares this with directly measured residual area and volume, noting that tip calibration errors, roughness and oxides inflate hardness at low loads. Pile-up makes the true area larger than this estimate; Sousa et al. quote underestimates of up to 60 per cent. Reference: J. Prou, K. Kishimoto, K. Inaba and A. Constantinescu, ‘Inverse Analysis of Multiple Indentation Unloading Curves for Thin Film Young’s Modulus Evaluation’ (fetch-tool summary); M. R. Abernathy, J. Hough, I. W. Martin, S. Rowan, M. Oyen, C. Linn and J. E. Faller, ‘Investigation of the Young’s modulus and thermal expansion of amorphous titania-doped tantala films’, arXiv:1401.7061 (2014) (fetch-tool summary); N. X. Randall, ‘Direct Measurement of Residual Contact Area and Volume During the Nanoindentation of Coated Materials as an Alternative Method of Calculating Hardness’, HARDMEKO 2004 (fetch-tool summary; equations OCR-garbled); B. C. Sousa, J. Hay and D. L. Cote, ‘Toward an Instrumented Strength Microprobe: Origins of the Oliver-Pharr Method and Continued Advancements in Nanoindentation: Part 1’, in Elasticity of Materials, IntechOpen 2023: diamond E_i = 1140 GPa and nu_i = 0.07, epsilon = 0.72 cone, 0.75 paraboloid, 1 flat punch, unloading exponents 1, 1.5 and 2 for flat punch, paraboloid and cone, ideal Berkovich area 24.5 hc^2, pile-up underestimating area by up to 60 per cent (Bolshakov and Pharr) (fetch-tool summary).

Ques: Should epsilon be 0.72 or 0.75 for a Berkovich tip?

Prou et al. use $\epsilon$ = 0.72 for a Berkovich indenter, whereas 0.75 is the Oliver-Pharr value for paraboloids (Sousa et al.). The values are not contradictory: 0.72 is the conical result, matching Prou’s model of the Berkovich as a 70.3 degree cone, while 0.75 goes with the paraboloid unloading exponent of 1.5 (Sousa et al.); real tips are slightly rounded and behave closer to paraboloids (my reading). For practical work with calibrated area functions, 0.75 is more likely to give consistent moduli, and 0.72 is appropriate in idealized cone simulations (my reading). The effect is small: with $P_{max}/S$ = 9.3 $\mathrm{nm}$ the two give contact depths differing by 0.28 $\mathrm{nm}$, under 1 per cent of a 40 $\mathrm{nm}$ contact depth (computed). Reference: J. Prou, K. Kishimoto, K. Inaba and A. Constantinescu, ‘Inverse Analysis of Multiple Indentation Unloading Curves for Thin Film Young’s Modulus Evaluation’ (fetch-tool summary); B. C. Sousa, J. Hay and D. L. Cote, ‘Toward an Instrumented Strength Microprobe: Origins of the Oliver-Pharr Method and Continued Advancements in Nanoindentation: Part 1’, in Elasticity of Materials, IntechOpen 2023: diamond E_i = 1140 GPa and nu_i = 0.07, epsilon = 0.72 cone, 0.75 paraboloid, 1 flat punch, unloading exponents 1, 1.5 and 2 for flat punch, paraboloid and cone, ideal Berkovich area 24.5 hc^2, pile-up underestimating area by up to 60 per cent (Bolshakov and Pharr) (fetch-tool summary); W. Yan, C. L. Pun, Z. Wu and G. P. Simon, ‘Some issues on nanoindentation method to measure the elastic modulus of particles in composites’, Composites Part B 42, 2093 (2011): correction factor 1.05 recommended by Oliver and Pharr, e = 0.72 for cones, pile-up causing underestimated area (fetch-tool summary).

Ques: How deep can you indent a thin film before the substrate matters?

About 10 per cent of the film thickness, as a rule of thumb. Abernathy et al. and Prou et al. both cite the 10 per cent rule, and Abernathy notes it is impractical on thin coatings: a 500 $\mathrm{nm}$ film permits 50 $\mathrm{nm}$, but a 50 $\mathrm{nm}$ dielectric only 5 $\mathrm{nm}$ (computed), close to tip-rounding scales. Abernathy et al. therefore apply the Song-Pharr model, $1/E^{\prime }=1/E_s+(1/E_c-1/E_s)I_0(t/a)$, and estimate that their softer silica substrate could reduce extracted moduli by up to 5 per cent. Prou et al. show that inverse analysis of multiple unloading curves reaches 10 and 20 per cent accuracy at depths of about 20 and 30 per cent of thickness, while plain Oliver-Pharr fails for large modulus mismatches. Reference: M. R. Abernathy, J. Hough, I. W. Martin, S. Rowan, M. Oyen, C. Linn and J. E. Faller, ‘Investigation of the Young’s modulus and thermal expansion of amorphous titania-doped tantala films’, arXiv:1401.7061 (2014) (fetch-tool summary); J. Prou, K. Kishimoto, K. Inaba and A. Constantinescu, ‘Inverse Analysis of Multiple Indentation Unloading Curves for Thin Film Young’s Modulus Evaluation’ (fetch-tool summary).

Ques: What would a typical thin-film indent look like numerically?

Tens of nanometres and a few hundred micronewtons. Taking a film with assumed E = 140 $\mathrm{GPa}$ and Poisson ratio 0.25, inside Abernathy’s 132 to 177 $\mathrm{GPa}$ tantala range, the reduced modulus with diamond is 132 $\mathrm{GPa}$ (computed). At a contact depth of 40 $\mathrm{nm}$ the area is 39200 $\mathrm{n}{\mathrm{m}}^2$, and $S=\frac{2}{\sqrt{\pi }}{E}^{\ast }\sqrt{A}$ gives 29.5 $\mu N/nm$ with $\beta$ = 1 (computed). With an assumed hardness of 7 $\mathrm{GPa}$, the peak load is 274 $\mu \mathrm{N}$, and $h_{max}=h_c+0.75P/S$ is 47 $\mathrm{nm}$ (computed), under 10 per cent of Abernathy’s 500 $\mathrm{nm}$ films. Their 500 to 10000 $\mu \mathrm{N}$ load range therefore spans shallow to substrate-affected indents. Including the factor $\beta$ = 1.05 recommended by Oliver and Pharr (Yan et al.) would lower the extracted modulus by about 5 per cent (computed). Reference: M. R. Abernathy, J. Hough, I. W. Martin, S. Rowan, M. Oyen, C. Linn and J. E. Faller, ‘Investigation of the Young’s modulus and thermal expansion of amorphous titania-doped tantala films’, arXiv:1401.7061 (2014) (fetch-tool summary); W. Yan, C. L. Pun, Z. Wu and G. P. Simon, ‘Some issues on nanoindentation method to measure the elastic modulus of particles in composites’, Composites Part B 42, 2093 (2011): correction factor 1.05 recommended by Oliver and Pharr, e = 0.72 for cones, pile-up causing underestimated area (fetch-tool summary).

Ques: Is the indentation modulus of silicon 130 GPa?

Not for an indentation measurement. Randall reports a separately measured modulus of 130 $\mathrm{GPa}$ and hardness of about 9 $\mathrm{GPa}$ for the silicon substrate. Ioffe lists 130 $\mathrm{GPa}$ as the Young’s modulus along [100] but 170 and 185 $\mathrm{GPa}$ along [110] and [111]. An indenter samples many directions, and a Hill average of Ioffe’s elastic constants gives an isotropic modulus of 163 $\mathrm{GPa}$ with Poisson ratio 0.22 (computed), so about 160 $\mathrm{GPa}$ is more likely for indentation (my reading). Ioffe’s Knoop microhardness of 1150 $kg/m{\mathrm{m}}^2$ is 11.3 $\mathrm{GPa}$ (computed), above Randall’s 9 $\mathrm{GPa}$, which may reflect calibration or load range. Silicon also transforms under the indenter, as the SSRM page discusses (Mylvaganam et al.). Reference: N. X. Randall, ‘Direct Measurement of Residual Contact Area and Volume During the Nanoindentation of Coated Materials as an Alternative Method of Calculating Hardness’, HARDMEKO 2004 (fetch-tool summary; equations OCR-garbled); Ioffe Institute, NSM archive, ‘Si - Silicon: Mechanical properties’: C11 = 16.60, C12 = 6.40, C44 = 7.96 (1e11 dyn/cm2), Young’s modulus [100] 13.0e11 dyn/cm2, Knoop microhardness 1150 kg/mm2 (fetch-tool summary); K. Mylvaganam, L. C. Zhang, P. Eyben, J. Mody and W. Vandervorst, ‘Evolution of metastable phases in silicon during nanoindentation’, Nanotechnology 20, 305705 (2009) (fetch-tool summary).

Ques: What happens to silicon under a sharp indenter?

It transforms to denser phases under load and becomes amorphous or recrystallizes on release. Mylvaganam et al. describe the transformation to metallic beta-tin with about 20 per cent volume reduction, its loss of crystalline order on unloading to amorphous silicon, and partial return to Si-I. Their molecular-dynamics loads at 4 $\mathrm{nm}$ depth were 2.5, 3.4 and 4.1 $\mu \mathrm{N}$ for tip radii of 5, 7.5 and 10 $\mathrm{nm}$. A 10 $\mathrm{nm}$ sphere at 4 $\mathrm{nm}$ depth has an 8 $\mathrm{nm}$ contact radius, so 4.1 $\mu \mathrm{N}$ is about 20 $\mathrm{GPa}$ mean pressure (computed), well above the transformation threshold. They verified the metallic phase by in-situ SSRM, detecting a resistance drop during loading with a 5 $N/m$ diamond probe. Reference: K. Mylvaganam, L. C. Zhang, P. Eyben, J. Mody and W. Vandervorst, ‘Evolution of metastable phases in silicon during nanoindentation’, Nanotechnology 20, 305705 (2009) (fetch-tool summary).

References

1. M. R. Abernathy, J. Hough, I. W. Martin, S. Rowan, M. Oyen, C. Linn and J. E. Faller, “Investigation of the Young’s modulus and thermal expansion of amorphous titania-doped tantala films,” Optical Society journal, preprint arXiv:1401.7061, 2014. Available: https://arxiv.org/pdf/1401.7061
2. J. Prou, K. Kishimoto, K. Inaba and A. Constantinescu, “Inverse Analysis of Multiple Indentation Unloading Curves for Thin Film Young’s Modulus Evaluation.” Available: https://ppi-lms.polytechnique.fr/andrei.constantinescu/PDF_Papers/JP_KK_KI_AC_identation_films_2012.pdf
3. B. C. Sousa, J. Hay and D. L. Cote, “Toward an instrumented strength microprobe: origins of the Oliver-Pharr method and continued advancements in nanoindentation: Part 1,” in Elasticity of Materials, G. A. Evinguer and O. Pekcan, Eds. IntechOpen, 2023. Available: https://intechopen.com/chapters/86301
4. W. Yan, C. L. Pun, Z. Wu and G. P. Simon, “Some issues on nanoindentation method to measure the elastic modulus of particles in composites,” Composites Part B, vol. 42, pp. 2093-2097, 2011. Available: https://users.monash.edu.au/~wyan/papers-pdf/Some%20issues%20on%20nanoindentation%20method%20to%20measure%20the%20elastic%20modulus-2011.pdf
5. Ioffe Physico-Technical Institute, “Si - Silicon: Mechanical properties,” New Semiconductor Materials. Available: https://www.ioffe.ru/SVA/NSM/Semicond/Si/mechanic.html
6. N. X. Randall, “Direct Measurement of Residual Contact Area and Volume During the Nanoindentation of Coated Materials as an Alternative Method of Calculating Hardness,” HARDMEKO 2004, Washington, D.C., 2004. Available: https://imeko.info/publications/tc5-2004/IMEKO-TC5-2004-019.pdf
7. K. Mylvaganam, L. C. Zhang, P. Eyben, J. Mody and W. Vandervorst, “Evolution of metastable phases in silicon during nanoindentation: mechanism analysis and experimental verification,” Nanotechnology, vol. 20, 305705, 2009. Available: https://www.unsw.edu.au/content/dam/pdfs/engineering/precision-and-nano/20250-05-evolution-of-the-metastable-phases-in-silicon-during-nanoindentation.pdf

Related pages in this vault: Scanning Spreading Resistance Microscope (SSRM), Atomic Force Microscope (AFM), Wire Capacitance and Low-k Dielectrics, Thermal Stress, Piezoresponse Force Microscope (PFM), Conductive AFM (C-AFM), Scanning Thermal Microscope (SThM), Stylus Profiler, Picosecond Ultrasonic Film Metrology, Wafer Curvature Stress Gauge.