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Formation of nano-pores in nano-crystalline diamond films Armin Kriele , Oliver A. Williams, Marco Wolfer, Jakob J. Hees, Waldemar Smirnov, Christoph E. Nebel Fraunhofer-Institute for Applied Solid State Physics (IAF), Freiburg 79108, Germany article info Article history: Received 17 February 2011 In final form 30 March 2011 Available online 2 April 2011 abstract Various nano-pores in nano-crystalline diamond (NCD) thin films have been fabricated and characterized. Therefore in this work two aspects of NCD thin films synthesized by microwave assisted chemical- vapour-deposition (MWCVD) have been investigated. Firstly, the influence of CVD-growth conditions on the film morphology and chemical grain boundary composition and their impact on the mechanical properties. Second, the formation of nano-pores by selective etching of the non-diamond phase. Free- standing NCD membranes were fabricated and bulged to calculate the Young’s modulus which can reach surprisingly high values (1100 GPa) close to single crystal diamond. The presence of nano-pores was ver- ified by electrochemical experiments where ions have been used to detect the porosity. Ó 2011 Elsevier B.V. All rights reserved. 1. Introduction Nano-porous materials are of interest for molecular filter appli- cations as water purification, for sequencing and chromatography in biology and chemistry as well as for membranes in energy stor- age systems as batteries. The requirements on material properties are defined by purpose. Diamond has many extraordinary attrac- tive technological properties as exceptional hardness and elastic modulus [1], wear-resistance [2], chemical stability, high thermal conductivity [3] and dopant controlled variable electrical resistiv- ity usable for sensor applications [4]. Diamond surfaces can be chemically modified for electrodes, gas sensors [5] and bio attach- ment [6–9], Its wettability [10], and negative electron affinity [11] can be adjusted over a wide range. Since diamond can be grown cost-effective on large scale as nano-crystalline thin films achiev- ing a very low surface roughness on various materials either on sil- icon wafers or on sacrificial layers (even conformal on structured sacrificial layers like SiO 2 and Si 3 N 4 ), and as very thin extreme insulating layer [12], these films are also ideal for MEMS and NEMS fabrication. Nano-diamond films synthesized by MWCVD consist of dia- mond crystals surrounded by few atomic layers of non-diamond carbon compounds as amorphous carbon, trans-poly acetylene and graphite. The diamond crystal morphology (crystal size and orientation) as well as the non-diamond matrix (volume ratio and composition) is defined by the growth conditions as seeding density, gas mixture, pressure and temperature. By this the mechanical as well as the morphological properties of such films can be adjusted and optimized. Especially the possibility to remove the non-diamond matrix by selective etching changes the mechan- ical properties and will transform the initial dense material to a nano-porous material. In this Letter we show that for optimized growth parameters, nano-crystalline diamond films with properties like micro-crystal- line diamond can be achieved but with much lower surface rough- ness. The effect of morphology and chemical composition of these NCD films on its elastic moduli will be discussed in detail. Finally, we will show for the first time that by removal of non-diamond carbon components due to oxidation NCD films get softer which is attributed to the formation of nano-pores. 2. Materials and methods Overall, nano crystalline diamond films have been grown under various CVD growth conditions and have been investigated sys- tematically with respect to film morphology and chemical compo- sition. Circular membranes from NCD films have been fabricated and used to (a) investigate the mechanical properties performing bulging experiments and (b) creating nano-pores by selective etch- ing of the non-diamond phase. The presence of nano-pores was verified by electrochemical experiments where K + and Cl ions have been used to detect the porosity. In detail, NCD films of 150 nm thickness were grown on 3 inch (100) silicon wafers where the silicon surface was ultra-sonificated for 30 min with a water based suspension of ultra dispersed (0.1 wt.%) nano-diamond (UDD) particles of typically 5–10 nm in size in order to achieve a high nucleation density (>10 11 cm 2 ) [13]. Then samples were rinsed with de-ionized water, dried under nitrogen flow and subsequently exposed to micro wave chemical vapour deposition (MWCVD 2.45 GHz) plasma with CH 4 /H 2 gas 0009-2614/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2011.03.089 Corresponding author. E-mail addresses: [email protected] (A. Kriele), oliver.williams@iaf. fraunhofer.de (O.A. Williams), [email protected] (M. Wolfer), jan. [email protected] (J.J. Hees), [email protected]. de (W. Smirnov), [email protected] (C.E. Nebel). Chemical Physics Letters 507 (2011) 253–259 Contents lists available at ScienceDirect Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
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Page 1: Formation of nano-pores in nano-crystalline diamond films

Chemical Physics Letters 507 (2011) 253–259

Contents lists available at ScienceDirect

Chemical Physics Letters

journal homepage: www.elsevier .com/ locate /cplet t

Formation of nano-pores in nano-crystalline diamond films

Armin Kriele ⇑, Oliver A. Williams, Marco Wolfer, Jakob J. Hees, Waldemar Smirnov, Christoph E. NebelFraunhofer-Institute for Applied Solid State Physics (IAF), Freiburg 79108, Germany

a r t i c l e i n f o a b s t r a c t

Article history:Received 17 February 2011In final form 30 March 2011Available online 2 April 2011

0009-2614/$ - see front matter � 2011 Elsevier B.V. Adoi:10.1016/j.cplett.2011.03.089

⇑ Corresponding author.E-mail addresses: [email protected] (A.

fraunhofer.de (O.A. Williams), [email protected]@iaf-extern.fraunhofer.de (J.J. Hees), waldede (W. Smirnov), [email protected] (C

Various nano-pores in nano-crystalline diamond (NCD) thin films have been fabricated and characterized.Therefore in this work two aspects of NCD thin films synthesized by microwave assisted chemical-vapour-deposition (MWCVD) have been investigated. Firstly, the influence of CVD-growth conditionson the film morphology and chemical grain boundary composition and their impact on the mechanicalproperties. Second, the formation of nano-pores by selective etching of the non-diamond phase. Free-standing NCD membranes were fabricated and bulged to calculate the Young’s modulus which can reachsurprisingly high values (1100 GPa) close to single crystal diamond. The presence of nano-pores was ver-ified by electrochemical experiments where ions have been used to detect the porosity.

� 2011 Elsevier B.V. All rights reserved.

1. Introduction

Nano-porous materials are of interest for molecular filter appli-cations as water purification, for sequencing and chromatographyin biology and chemistry as well as for membranes in energy stor-age systems as batteries. The requirements on material propertiesare defined by purpose. Diamond has many extraordinary attrac-tive technological properties as exceptional hardness and elasticmodulus [1], wear-resistance [2], chemical stability, high thermalconductivity [3] and dopant controlled variable electrical resistiv-ity usable for sensor applications [4]. Diamond surfaces can bechemically modified for electrodes, gas sensors [5] and bio attach-ment [6–9], Its wettability [10], and negative electron affinity [11]can be adjusted over a wide range. Since diamond can be growncost-effective on large scale as nano-crystalline thin films achiev-ing a very low surface roughness on various materials either on sil-icon wafers or on sacrificial layers (even conformal on structuredsacrificial layers like SiO2 and Si3N4), and as very thin extremeinsulating layer [12], these films are also ideal for MEMS and NEMSfabrication.

Nano-diamond films synthesized by MWCVD consist of dia-mond crystals surrounded by few atomic layers of non-diamondcarbon compounds as amorphous carbon, trans-poly acetyleneand graphite. The diamond crystal morphology (crystal size andorientation) as well as the non-diamond matrix (volume ratioand composition) is defined by the growth conditions as seedingdensity, gas mixture, pressure and temperature. By this the

ll rights reserved.

Kriele), [email protected] (M. Wolfer), [email protected]. Nebel).

mechanical as well as the morphological properties of such filmscan be adjusted and optimized. Especially the possibility to removethe non-diamond matrix by selective etching changes the mechan-ical properties and will transform the initial dense material to anano-porous material.

In this Letter we show that for optimized growth parameters,nano-crystalline diamond films with properties like micro-crystal-line diamond can be achieved but with much lower surface rough-ness. The effect of morphology and chemical composition of theseNCD films on its elastic moduli will be discussed in detail. Finally,we will show for the first time that by removal of non-diamondcarbon components due to oxidation NCD films get softer whichis attributed to the formation of nano-pores.

2. Materials and methods

Overall, nano crystalline diamond films have been grown undervarious CVD growth conditions and have been investigated sys-tematically with respect to film morphology and chemical compo-sition. Circular membranes from NCD films have been fabricatedand used to (a) investigate the mechanical properties performingbulging experiments and (b) creating nano-pores by selective etch-ing of the non-diamond phase. The presence of nano-pores wasverified by electrochemical experiments where K+ and Cl� ionshave been used to detect the porosity.

In detail, NCD films of 150 nm thickness were grown on 3 inch(100) silicon wafers where the silicon surface was ultra-sonificatedfor 30 min with a water based suspension of ultra dispersed(0.1 wt.%) nano-diamond (UDD) particles of typically 5–10 nm insize in order to achieve a high nucleation density (>1011 cm�2)[13]. Then samples were rinsed with de-ionized water, dried undernitrogen flow and subsequently exposed to micro wave chemicalvapour deposition (MWCVD 2.45 GHz) plasma with CH4/H2 gas

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254 A. Kriele et al. / Chemical Physics Letters 507 (2011) 253–259

mixtures varying from 0.3% to 20% methane in hydrogen at a pres-sure of 60 mbar using a bell jar reactor [14]. The gas flow rate was300 sccm. The microwave power was kept constant at 3 kW andthe typical deposition temperature was 800 �C. The depositiontime decreases with increasing CH4 admixture and was 30 min at0.3% CH4 and 7 min at 20% CH4. The thickness of films was mea-sured to be in the range of 150 nm as was determined by usingin situ laser interferometry and has been confirmed by SEM crosssection images and elipsometry.

To remove selectively the silicon substrate we applied photoli-thographic patterning using a Si3N4 mask material and HF andHNO3 (2:1) wet-chemical etching thereby generating circularmembranes 1–2 mm in diameter from NCD.

The sp3/sp2 ratio of the as grown NCD films was calculated fromRaman spectroscopy measurements whereas the crystal size andgrain boundary was measured using atomic force microscopy(AFM, Veeco Inst. Multimode V) and transmission electron micros-copy (TEM, FEI Tecnai F30 G2 300 kV). For high resolution TEM,NCD films were thinned with argon plasma (Gatan PIPS, Ar2.5 kV) from the nucleation side.

SEM micrographs with magnification 100.000�were made withZeiss DSM 962 FE-SEM at 5 kV acceleration voltage and working

Figure 1. SEM micrographs and 1 � 1 lm AFM phase images obtained from NCD films ophase images appear as black lines.

distance 4 mm using the intense secondary electron detector. Toavoid charging of the NCD films a very low e-beam current of50 nA was chosen. AFM images 1 � 1 lm in size were made innon-contact mode at 150 kHz in air, using a Nanosensors NCLR sili-con tip 5 nm in diameter and a cantilever spring constant of 50 N/m.

Nano-pores have been created by decomposing the non-dia-mond phase located at grain boundaries. Therefore the NCD-mem-branes were annealed in air for various times and at varioustemperatures using a temperature controlled quartz-tube oven.Samples were loaded into the centre of the 40 mm long quartz tubeafter temperature has reached the desired setpoint. After annealingthe non-diamond content was calculated from Raman spectroscopymeasurements and has been compared with the as grown films.

Bulging experiments on as grown and annealed membraneswere carried out using a home build over-pressure setup. The threedimensional shape of the bulged membranes and the maximumheight was measured by white light interferometry (WLI, Wyco,NT 1100).

Conductivity measurements in aqueous solutions were carriedout using a commercial (Mettler–Toledo) temperature compen-sated two electrode conductivity sensor with a sensitivity of±0.01 lS.

f 150 nm in thickness grown with various CH4 admixtures. Grain boundaries in the

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Table 1Youngs moduli (E) and roughness (RMS) results for NCD films 150 nm in thicknessgrown with various CH4 admixtures.

CH4

admixture[%]

Averagecrystal size[nm] atgrowth side

RMS[nm]

Nondiamondcontent[arb. units]

E [GPa] asgrowndensefilms

E [GPa]annealedporousfilms

0.5 130 ± 20 8.9 ± 0.9 2.0 1099 ± 75 1079 ± 741 100 ± 15 6.7 ± 0.7 2.6 1081 ± 62 –3 56 ± 9 5.6 ± 0.6 3.9 1020 ± 49 951 ± 475 40 ± 7 5.3 ± 0.5 5.0 971 ± 44 –7 30 ± 6 5.0 ± 0.5 6.2 881 ± 35 782 ± 3010 23 ± 5 5.3 ± 0.5 6.8 807 ± 30 679 ± 2715 18 ± 5 6.0 ± 0.6 8.2 735 ± 27 516 ± 2320 15 ± 5 7.0 ± 0.7 9.3 687 ± 22 420 ± 20

Figure 2. (A) Overview (1 � 1 lm2) TEM image of a rolled freestanding sheet of aNCD film which has been thinned from the nucleation side by plasma etching toapproximately 20 nm thickness. Such thinned NCD-films were used for the TEMimages (B) and (D). (B) TEM micrograph of NCD-film grown at 20% methaneadmixture. The randomly black lines in the micrographs indicate grain boundaries.One of these is highlighted by the arrow. (C) The electron diffraction pattern of filmB shows that the nano-crystals are randomly orientated in the film. The HRTEMimage (D) shows a single diamond crystal with a lattice constant of 1.4 Å.

A. Kriele et al. / Chemical Physics Letters 507 (2011) 253–259 255

3. Results and discussion

Amongst MWCVD diamond growth parameters as temperature,pressure and microwave power, the gas composition has a strongimpact on the formation of film morphology in terms of grain sizeand sp2/sp3 bonding ratios. Commonly, CVD diamond deposition iscarried out using hydrogen plasma with an admixture of a few per-centage of methane. The influence of the CH4 admixture on grainsize distribution has been measured by SEM and AFM and is shownin Figure 1. Because of a better contrast of the grain boundaries, thephase signal was chosen from the AFM measurements.

These results reveal a decrease of the crystal size with increas-ing CH4 admixture from typical 130 nm at 0.3% CH4 to 15 nm at20% CH4, respectively, at the growth side of the film. The valuesfor all films are summarized in Table 1. TEM and High ResolutionTEM analysis as shown in Figure 2 reveal a homogeneous distribu-tion of nano-crystals. The electron diffraction pattern (Figure 2C)indicates a random orientation of the diamond crystals.

Diamond crystals are generated by homoepitaxial growth onthe seed layer, whereat non-diamond carbon will be incorporatedin the grain boundaries. NCD films grown with low methaneadmixture still exhibit a columnar structure even when grownon very high nucleation density [15]. The decrease of crystal sizewith increasing methane content is due to a more and more dom-inant secondary nucleation process [16]. Correspondingly the sur-face roughness is changed by the decrease of crystal size. By AFM

Figure 3. Raman spectra of 150 nm thin NCD films grown with various methaneadmixtures before (A) and after (B) annealing in air for 1 h at 550 �C.

Page 4: Formation of nano-pores in nano-crystalline diamond films

Figure 4. (A) Increase of the non diamond content within 150 nm thin NCD filmsgrown with various methane admixtures for as grown and annealed NCD films withrespect to a low (0.3%) CH4 admixture film obtained from Raman measurements. (B)Calculation of the non diamond content by integration of the area beneath theRaman spectra. (C) Cross section scheme of the formation of pores in NCD filmsgrown with various CH4 admixtures due to thermal annealing.

256 A. Kriele et al. / Chemical Physics Letters 507 (2011) 253–259

height analysis a surface root mean square roughness minimum ofRMS = 6 nm for NCD films grown with 7% methane content wasfound [17]. The roughness increases with lower and higher meth-ane content (9 nm at 0.5% CH4 and 7 nm at 20% CH4). The increaseof roughness for higher CH4 admixtures is attributed to the forma-tion of a cauliflower structure while for lower CH4 admixtures theroughness is dominated by variations of the crystal growth relatedto (111) or (100) orientation.

The chemical bonding structure of the carbon atoms have beeninvestigated by Raman scattering experiments. Raman spectra-recorded at an excitation wavelength of 457.94 nm are shown inFigure 3A. The NCD films show peaks at 1332 cm�1, which corre-sponds to sp3-bonded carbon (diamond). The D-band at1350 cm�1 is induced by disordered carbon atoms. It causes broad-ening of the diamond peak with increasing CH4 admixture. There isa substantial graphite band (G band) at 1585 cm�1, which corre-sponds to sp2-bonded carbon and two trans-polyacetylene bandsat 1150 and 1460 cm�1.

All non-diamond bands increase significantly with increasingCH4 admixture. By increasing the CH4 gas admixture from 0.3%to 20% the sum of graphite and trans-polyacetylene contents risesby a factor of 9 as shown in Figure 4A. Please note, that the valuesof non-diamond contents were calculated by using Lorentz fits andrelated integration calculations, as shown in Figure 4B. All Ramanspectra were normalized to their diamond peak. The non diamondcontent of a NCD film grown with 0.3% CH4 admixture was normal-ized to 1. All other data is plotted with respect to this film. For aquantitative discussion in terms of atomic percentage or volumepercentage for further experiments are currently performed andwill be presented in the near future.

The possibility to decompose and remove non-diamond frac-tions by thermal treatment of the NCD films in air in the tempera-ture regime ranging from 530 �C to 560 �C has been studied andwill be discussed in the following. Usually for decomposing sp/sp2 or hydrogenated carbon by annealing in UHV (absence of oxy-gen), temperatures >1000 �C are required [18]. The time depen-dence on the removal of non-diamond components by annealingin air (presence of oxygen) is shown in Figure 5A for a NCD filmgrown with 20% CH4. The temperature dependence variation isshown in Figure 5C for a NCD film grown with 15% CH4. The higherthe temperature and the longer the annealing time, the more effi-cient is the removal of non diamond compounds. Figure 5B showsthe drop of the ratio of non diamond peak heights versus the dia-mond peak height (non diamond/diamond) for annealing times of0, 30, 50 and 90 min at 550 �C. It can be seen, that after 50 min ofannealing no further decomposing of the non diamond carbon con-tents can be detected. In contrast the influence of the temperaturewhich is shown in Figure 5D where the non diamond/diamondpeak ratio is plotted for the temperatures 20 �C, 530 �C, 540 �C,and 560 �C is different. The peak heights decrease with increasingthe annealing temperature up to 560 �C. Obviously non-diamondphases can not be removed completely with temperatures at560 �C.

We found, that NCD-films can be exposed for one hour to a tem-perature of 550 �C without significant variation of crystal size(AFM) and diamond film thickness. Longer annealing time and/orhigher annealing temperature lead to graphitization and subse-quent oxidation (burning) of the diamond crystals. Especially smallcrystals of sizes <20 nm show this characteristic. Please note, thatthe diamond films have been annealed as membranes, thus the re-moval of the non-diamond phase occurred from both sides of thefilms. The reduction of non-diamond contents is due to oxidationof weakly bonded carbon and its removal by the formation of gas-eous carbon–oxygen compounds. A subsequent annealing of theNCD films in air at 550 �C for 60 min reduces the non-diamond Ra-man bands significantly as shown in Figure 3B. It is obvious that

films grown with high methane admixture (>7%) show a significantdrop of non-diamond content due to annealing. Films with lownon-diamond content (<3% CH4) show only weak annealing effectIn Figure 4A, the drop of the non-diamond content is shown com-pared to the as grown NCD films. To avoid Raman intensity varia-tions, the same normalization procedure has been applied asdescribed for the initial as grown films. The etching takes placethrough small voids and gaps (pores) between the grains whichcan limit its effectiveness if the voids become too small. Increasingthe annealing time to overcome this drawback will affect the dia-mond crystals itself as long as they are no longer protected by thesurrounding non diamond grain boundaries. To avoid this, we re-stricted the temperature to 550 �C and the annealing time to60 min for the following fabrication of the molecular filters.

To confirm the formation of the pores which are shown sche-matically in Figure 4C, electrochemical experiments have been ap-plied measuring the migration of ions from an aqueous KCLsolution (source) through the membrane to a buffer acting as drain.To perform these experiments, the silicon substrate has been re-moved by wet chemical etching in HF/HNO3 and the resultingNCD membranes were placed between two liquid reservoirs asshown in Figure 6A. One side was filled with saturated aqueousKCL solution (‘a’) and the other side with distilled water (solution‘b’), where the change in conductivity with time was measured.The conductivity of KCl solution is over a wide range proportionalto the number of ions in the liquid. The volume of the liquids onboth sides was 5 ml. Figure 6B shows the conductivity variationof solution ‘b’ for different membrane properties as function of

Page 5: Formation of nano-pores in nano-crystalline diamond films

Figure 5. Change of the of Raman spectra of NCD films 150 nm in thickness due to post annealing in air for various times at a fixed temperature of 550 �C (A) and at varioustemperatures for a fixed time of 60 min (C). Figure 5B shows the time dependence of the decline of non diamond Raman lines with respect to the diamond peak whereasFigure 5D shows the influence of temperature on the Raman lines.

Figure 6. (A) Scheme of the setup for conductivity measurements. (B) Change ofconductivity with time (pure water background conductivity subtracted). (C)Particle transport of K+ and Cl� ions through annealed NCD membranes 1 mm indiameter and grown with various CH4 admixture calculated from conductivitymeasurements (B).

A. Kriele et al. / Chemical Physics Letters 507 (2011) 253–259 257

time. A faster rise in conductivity for NCD membranes grown withhigher methane content is detected. This indicates that larger and/or more pores formed in the films. Less or even no change formembranes grown with low methane content is revealed. Pleasenote that the background conductivity of pure water is subtractedfrom this data. This confirms the results which have been obtainedfrom the pore volume estimation which will be discussed later. Thehigher the methane content, the larger the porosity after anneal-ing. It can be seen that after approximately 25 h the rise in conduc-tivity is linear with time which indicates a constant ion transferrate. For annealed NCD membranes grown with very low (0.5%)CH4 admixture the ion transfer rate is zero which indicates nochannels ranging through the whole film. The ion transfer throughNCD membranes grown with 20% CH4 is 3 times faster compare toNCD films grown with 10%, respectively as shown in Figure 6C.

Considering the huge concentration gradient between both liq-uids the transfer rate is very low. Even after 90 h just a smallamount of ions passed through the membrane. Considering a mo-lar conductance of 73.5 Scm2/mol for K+ ions and 76.4 Scm2/mol forCl� ions the concentration of KCl in the water ‘b’ is 44 and123 lmol/l after 90 h for annealed NCD membranes grown with10% and 20% CH4 admixture, respectively and is 6 orders of magni-tude smaller than the concentration of the saturated KCl solution.Therefore the concentration gradient has not changed significantlyand its impact on the transfer rate can be neglected for this exper-iment. In total, about 16 and 46 lg KCl was transferred through themembranes grown with 10% and 20% CH4 admixture, respectively.Depending on the crystalline structure, the pathways will be moreor less zig-zag shaped. Because of the robustness of the NCD filmswhich sustain overpressures of 2.5 bar (membranes 1 mm in diam-eter and 150 nm in thickness), these films are very promising formolecular filter applications. Using this technique, the size of thepores can be controlled by adjusting the CVD growth parameters

Page 6: Formation of nano-pores in nano-crystalline diamond films

Figure 7. Deviation curves (A) of circular NCD membranes 1 mm in diameter and150 nm in thickness grown with various CH4 admixture after applying gas overpressure from the backside obtained by white light interferometer (WLI) measure-ments (B). (C) compares the annealing effect on the pressure driven expansion ofNCD films grown with low (0.5%) and high (15%) CH4 admixture. The threedimensional spherical shape obtained by WLI measurements of a NCD membraneduring bulging is shown in (D).

Figure 8. (A) Young’s moduli of 150 nm thin NCD films grown with variousmethane admixture before and after annealing, calculated from bulging experi-ments. (B) Calculation of the range of porosity of NCD films after annealing usingPhani and Pabst-Gregorová equation.

258 A. Kriele et al. / Chemical Physics Letters 507 (2011) 253–259

which defines the film morphology and/or by setting the annealingconditions. Assuming a uniform removal of the non-diamond ma-trix the width of the pores can be estimated as below 1 nm whichwas the thickest grain boundary we had detected by HRTEManalysis.

As consequence on the removal of material the mechanicalproperties of the NCD films change whereby the change of elasticmoduli enables to calculate the porosity. Therefore the elasticproperties of the as grown and of the annealed NCD films werestudied, fabricating circular NCD membranes of 1 mm in diameterby partial removal of the silicon substrate. These membranes thenwere bulged applying a gas over pressure from one side. The threedimensional shape of the spherical expanded membranes (Figure7D) and the maximum height of deflection as a function of appliedpressure was measured with a white light interferometer [19]. Theresults given in Figure 7A, show that membranes grown with high-er methane content expand to the same deflection height at lowerpressures compared to low methane admixture films. All films be-come weaker after the post annealing step which causes largerexpansion at the same pressure (Figure 7C).

The load–deflection dynamics of the membranes show in gen-eral extreme flexibility, no hysteresis and no degradation up to

many cycles. Leak tests on inflated as grown membranes show,that there is no pressure drop within 48 hours which indicates thatthe as grown films are pinhole free.

The bulging variation was used to determine the Young’s mod-ulus of the NCD films. As the membrane deflection z is hemispher-ical in shape and the bulging is much larger than the film thickness,the following equation can be applied [20,21]:

p ¼ c0 þc1tr2 r0zþ c2f ðmÞt

r4 � E1� m

z3

where p is the uniform pressure applied to the membrane, z is themaximum deflection measured at the centre of the membrane, ris the membrane radius, t is the membrane thickness, r0 is theresidual stress, E is the Young’s modulus, and m is the Poisson’s ratio(0.069) [22]. The geometrical coefficients C1, C2, and f(v) for circularmembranes are 4, 2.67 and 1 respectively [21]. The residual stress(r0) and Young’s moduli (E) have been calculated by fitting thisequation to the experimental data. The constant term c0 is the ini-tial pressure which is needed to expand wrinkled membranes con-taining compressive stress until their wrinkles disappear.

As result the Young’s moduli for the as grown films decreasewith increasing CH4/H2 ratio from 1100 GPa at 0.5% to 687 GPa at20% and from 1080 GPa to 420 GPa for the annealed films respec-tively (Figure 8A). Please note that at low methane contents theYoung’s modulus for NCD films is closed to single crystal diamondwhich is 1200 GPa. The results show, that higher methane contentsresult in lower Young’s moduli of NCD films.

Page 7: Formation of nano-pores in nano-crystalline diamond films

A. Kriele et al. / Chemical Physics Letters 507 (2011) 253–259 259

The observed softening of NCD films with small grain sizes canbe attributed to the enhanced fraction of interfacial atoms as theaverage grain size becomes smaller in analogy with the reverseHall–Petch effect [23] observed in nano-crystalline materials[24]. C-atoms at grain faces and edges will naturally form twofold(sp1) or threefold (sp2) coordinated bonds which are weaker thanthose formed by the fourfold coordinated atom (sp3) in the bulk.These weaker bonds are easier to stretch and bend which resultsin a softer material which softens further as the grain boundaryto bulk volume ratio increases. The reason for the reduction ofthe stiffness is the higher amount of non-diamond content withinthe film. Post annealing of the films reduces the stiffness oncemore. This effect is enhanced with increasing methane admixture.It can be explained by a partial removal of the surrounding non-diamond carbon matrix due to annealing.

It has been reported that the Young’s modulus of porous brittlenano- and poly-crystalline materials decreases with increasingporosity. To obtain the exact prediction of Young’s modulus for aporous material at given porosity, various models, such as lineardependence, exponential dependence or quadratic equation, havebeen extensively used during the past years [25–27]. The theoret-ical relation E = E0 (1-aP)n between porosity and Young’s modulusintroduced by Phani has been derived semi-empirically and isinherent capable of treating isometric closed pores as well asnon-isometric interconnected pores. Here, P, E and E0 are theporosity (0 – 1), the Young’s modulus of porous material and densematerial, respectively. The parameter a is defined as a = 1/Pcrit,where Pcrit is the critical porosity (percolation threshold) at whichelastic modulus becomes zero or the maximum porosity where thematerial is still able to carry its weight. The second basic modelconsidering the percolation threshold is proposed by Pabst andGregorová [28]:

E ¼ E0ð1� aPÞ � 1� PPcrit

� �

They claimed that the coefficient a = 2 is always a reasonableapproximation for porous materials with isometric pores. Thisequation transforms into the Phani relation with n = 2 by settinga = 1/Pcrit. Due to the fact, that the critical porosity of NCD filmsis unknown and the crystallinity of these films change with themethane content used for the growth and considering, that NCDfilms consist of a multiphase material (diamond crystals sur-rounded by non-diamond carbon compound matrix), the range ofporosity was calculated using both equations with different set-tings for the parameters as a = 5–20, Pcrit = 0.05–0.2 and n = 2.14–4.12. Figure 8B shows the increase of the pore volume from closeto zero for NCD films grown with low methane content to only afew percent (1–4%) for NCD films grown with high methaneadmixture (20%) after annealing the films for 60 min at 550 �C.

4. Conclusions

As NCD films contain a variable fraction of non-diamond carbonphases at grain boundaries, their properties such as acoustic veloc-ity, Young’s modulus and internal friction can be affected adverselyif the NCD quality, indicated by the sp2/sp3 ratio, is not carefullycontrolled during the CVD growth. Film morphology, roughnessand mechanical properties can be adjusted over a wide rangeapplying different growth conditions. In this Letter we have shown,that by increasing the H2/CH4 ratio from 0.5% to 20% the grain sizeof the diamond crystals decreases from 130 ± 20 nm to 15 ± 5 nmwhereas as the non-diamond content located at the grain bound-aries increases by a factor of 9 as measured by Raman scattering.By this, the volume of non-diamond carbon compounds increases.Due to the weaker chemical bonds of the non-diamond compo-

nents compare to the sp3 bonds of the diamond crystals they canbe selectively etched. A thermal annealing in air at 550 �C for onehour removes partially non-diamond phase creating nano-pores.Raman spectra show a significant reduction of all non-diamondcompounds as trans-polyacetylene, sp2-carbon, graphite and disor-dered carbon. This removal affects the mechanical properties. Thechange in stiffness is used to calculate the porosity. To measurevariations of the Youngs modulus circular NCD membranes of150 nm thickness were fabricated and bulged. These experimentsreveal a Young’s modulus variation from 1100 GPa to 687 GPa byincreasing the CH4/H2 ratio from 0.5% to 20%. As higher the CH4

admixture as stronger the impact of a subsequent annealing onelastic moduli which is reduced by only 2 % for films grown with0.5% CH4 up to 40 % for films grown with 20% CH4 admixture.The calculated porosity varies from close to zero to about1% to 4%. Considering the grain morphology this depicts the forma-tion of very tinny pores. The porosity was confirmed by the trans-port of K+ and Cl� ions through annealed NCD membranes. Thetransfer rate is 3 times faster for NCD films grown with 20% CH4

compare to films grown with 10% and zero for films grown with0.5% CH4 admixture. This indicates the formation of larger and/ormore numerous pores as higher the non diamond carbon contentis. Table 1 shows the summary of the results obtained in this work.

Due to its robustness, chemical stability and biocompatibilitymembranes fabricated from NCD films can be used as nano-filtra-tion membranes for reverse osmosis, water purification, and wastewater treatment and for pressure-driven membrane separation. Asdiamond surface can be terminated with hydrogen, oxygen or fluo-rine the wettability and chemistry of the inner surface of the porescan be adjusted which would allow filtering certain species of ionsor molecules.

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