JOURNAL OF APPLIED PHYSICS 102, 113706 共2007兲 Electrical conduction in undoped ultrananocrystalline diamond thin films and its dependence on chemical composition and crystalline structure Eric J. Correa and Yan Wu Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, Illinois 61801, USA Jian-Guo Wen Center for Microanalysis of Materials, Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, 104 South Goodwin Avenue, Urbana, Illinois 61801, USA Ramesh Chandrasekharan and Mark A. Shannona兲 Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, Illinois 61801, USA 共Received 17 July 2007; accepted 23 September 2007; published online 6 December 2007兲 The electrical conduction behavior of undoped ultrananocrystalline diamond 共UNCD兲 and its dependence on deposition temperature and chemical structure are presented. UNCD films were grown using a microwave plasma-enhanced chemical vapor deposition technique at deposition temperatures of 400 ° C and 800 ° C. The chemical structure of the UNCD films is characterized with several tools including: Elastic recoil detection analysis, Fourier transform infrared spectroscopy, electron energy loss spectroscopy, Raman spectroscopy, and environmental scanning electron microscope. The results show a higher content of sp2-bonded carbon for the 800 ° C deposition samples 共⬃65%兲 in comparison with the 400 ° C samples 共⬃38%兲. In both kinds of films, the hydrocarbon bonds have the saturated sp3 structures, while there is lower hydrogen content in the 800 ° C samples 共⬃8%兲 than in the 400 ° C samples 共⬃10%兲. For conduction properties, experiments are conducted using a probe station and conductive-atomic force microscopy. Experimental data show that the samples deposited at 800 ° C are several orders of magnitude more conductive than the 400 ° C samples. The conduction occurs primarily along the grain boundary for both types of samples. The conductivity of both types of films also shows field dependent nonlinear behavior. Both the Poole–Frenkel models and single and overlapping Coulombic potential models show that the conduction is directly correlated with the sp2 bond carbon density, and the role of the hydrocarbon bonds in the conduction path is formed by the network of the sp2 bonded carbon. © 2007 American Institute of Physics. 关DOI: 10.1063/1.2816214兴 I. INTRODUCTION The ultrananocrystalline diamond 共UNCD兲 is a thin film form of diamond developed by the Argonne National Laboratory researchers. The UNCD film is grown through a patented microwave plasma-enhanced chemical vapor deposition 共MPCVD兲 technique1 using a mixture of CH4 共⬃1%兲 with inert gases 共e.g., Ar, Kr, or Xe兲. In contrast to conventional CVD microcrystalline diamond films prepared by atomic hydrogen-rich microwave plasma, the UNCD films are grown with less than 5% molecular hydrogen in gas mixtures and consist of equiaxial nanograins of less than 10 nm diameter and elongated twinned dendritic grains around 100 nm in length.2 The high surface smoothness offered by the nanometer scale grain sizes, the diamondlike mechanical and tribological properties, the thermal stability, and the chemical inertness make the UNCD an attractive material for microscale microelectromechanical systems 共MEMS兲 devices and a兲 Electronic mail: mshannon@uiuc.edu 0021-8979/2007/102共11兲/113706/10/$23.00 applications.3 It is known that the electrical properties of the UNCD can be conducting or insulating by controlling the nitrogen content 共doping兲 during the deposition process. In particular, we are interested in undoped UNCD as a dielectric in the MEMS applications. A better understanding of the electrical conduction behavior of the UNCD as a function of chemical bonding and nanostructure will provide a basis for the use of the UNCD in the MEMS and other devices in need of a low-surface energy hard tribological material. Experimental work has also shown that the deposition temperature has an impact on the hydrogen content in the UNCD film as well as the grain size of the CVD diamond and the sp2 / sp3-bonded carbon ratio.4,5 The hydrogen abstraction is lower for lower deposition temperatures, leading to lower secondary nucleation density and larger grains.4 Three parameters, the sp2 / sp3-bonded carbon ratio, the hydrogen content, and the grain size, are not only each dependent on the film growing process, together they also determine the many physical properties of the CVD diamond films,6 such as density and hardness. With respect to electrical properties, sp2-bonded carbon within the CVD diamond 102, 113706-1 © 2007 American Institute of Physics Downloaded 14 Jul 2010 to 130.126.102.222. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp 113706-2 Correa et al. films can be thought of as a conduction promoter, particularly if the sp2 forms interconnected networks of ␲ bonds along which electrons are free to move. Most of the sp2 structure has been detected in the grain boundaries in the UNCD.7 Hydrogen is also thought to be located at the grain boundaries since atomic hydrogen can easily react with carbon atoms having dangling bonds in the grain boundaries during the film growing process, which can then saturate these dangling bonds. However, the role of hydrogen in the conduction path is not clear. The purpose of this paper is to report the conduction behavior of undoped UNCD films grown at 400 ° C and 800 ° C and its dependence in chemical composition and crystalline structure. The deposition temperature affects the ratio of sp2 and sp3 bonding, the hydrogen content, as well as the crystalline structure. For macroscopic conduction properties, current-voltage 共I − V兲 curves for samples with electrical contact pad sizes from 50 to 125 ␮m2 are collected using an electrical I − V probe station. For microscopic properties, conductive-atomic force microscopy AFM 共C-AFM兲 measurements are performed within 1 ␮m2 scans to study the local conduction behavior of the UNCD film as a function of surface morphology. Raman spectroscopy and electron energy loss spectroscopy 共EELS兲 are used to analyze the chemical composition and bonding structure of the UNCD films. The hydrogen content of the films is obtained by through elastic recoil detection 共ERD兲. Fourier transform infrared spectroscopy 共FTIR兲 spectra are used to characterize the bonding structure of the hydrocarbon bonds. Film thickness and grain size are characterized by using environmental scanning electron microscopy 共ESEM兲 and transmission electron microscopy 共TEM兲, respectively. The results show that the I − V characteristics are consistent with changes observed in sp2 / sp3-bonded carbon ratios, hydrogen content, and crystalline structures of the UNCD films. Similar to the microcrystalline CVD diamond, the conductivity of both types of UNCD films shows field dependent nonlinear behavior. Poole–Frenkel 共P-F兲 models with single and overlapping Coulombic potentials8–13 show that the conduction is directly correlated with the sp2-bond carbon density and the role of hydrocarbon bonds in the conduction path formed by the sp2-bonded carbon, both of which act on the formation of extended networks of ␲ bonds. II. EXPERIMENTS Thin films of tungsten 共10 nm thick兲 were deposited on commercial n-type Si wafers 共using magnetron sputtering兲 in order to enhance the nucleation and growth of the UNCD film. The UNCD thin films were grown at Argonne National Laboratory using the MPCVD at two deposition temperatures: 400 ° C. and 800 ° C. No nitrogen or hydrogen was added during the deposition process. For electrical conduction property measurements, an Ohmic contact was created on the back side of the sample by depositing chrome-gold films and annealing the sample at 375 ° C in a furnace tube with a nitrogen atmosphere. Chrome/gold thin films 共250 nm thick兲 were deposited on the topside of the sample to form electrical contacts of different sizes 共50− 125 ␮m sq兲. J. Appl. Phys. 102, 113706 共2007兲 The hydrogen content of the UNCD thin films was determined by elastic recoil detection analysis 共ERDA兲 using a Van de Graaff accelerator. A 2 MeV He2+ ion beam was incident on the UNCD film with an angle of 50° or 55° with respect to the surface normal. The hydrogen atoms recoiled by the ion beam are detected at 45° with respect to the incident beam direction by a Si surface barrier 共SSB兲 detector. The detector was covered with a 1 ␮m thick Mylar foil to trap the recoiled carbon atoms from the films. High density polyethylene 共关CH2兴n兲 was used as a standard to determine the hydrogen concentration against the number of carbon atoms. To characterize the bonding configuration of hydrocarbon in the UNCD film, a Nicolet IR-750 FTIR spectrometer was used to record the C–H stretching modes in the 2880– 3300 cm−1 range. All measurements were done using the mercury–cadmium–telluride 共MCT兲 detector with a 2 cm−1 resolution. Raman spectroscopy and EELS were used to analyze the relative sp3 to sp2 bonding ratio of the UNCD films. For Raman spectroscopy, the radiation of an Ar+ laser 共␭ = 488 nm兲 was used for excitation. The laser spot size was 50 ␮m and the beam power used for the experiment was 100 mW. All the Raman spectra were collected by a SPEX Triplemate spectrometer with a back-illuminated liquidnitrogen-cooled charge coupled device 共CCD兲 detector. Two different samples were set and tested as standards; the first one is natural diamond corresponding to 100% sp3-bonded carbon, whereas highly ordered pyrolytic graphite 共HOPG兲 was used as a reference for graphite, which consists of 100% sp2-bonded carbon. Plan-view TEM samples were prepared by a mechanical polishing down to about 30 ␮m and then ion beam milling, at a low ion incidence angle 共6 ° – 10°兲 at room temperature with 5 kV argon ions, until reaching film perforation. The final thickness of the film where the TEM images were taken was less than 200 nm. The specimens were studied using a JEOL-2010F scanning transmission electron microscope operated at 200 kV. The instrument was equipped with a Gatan Image Filter to obtain EELS. As described by Wan and Egerton,14 the sp2 / sp3 ratio in the diamond film can be obtained by using a graphite standard with 100% sp2. However, edge intensity strongly depends on the orientation of a single-crystal sample,6,14 so crystalline graphite cannot serve as a standard. Thus, a lacey-carbon film 共100% sp2 amorphous carbon兲 supported by a 400 mesh copper grid was placed on top of the sample to create the standard for the EELS experiments. Figure 1 shows a TEM image of the UNCD sample with the lacey carbon grid. EELS spectra were measured over a 200 nm by 200 nm area randomly selected on the UNCD film and the lacey carbon film. To remove plural scattering, a zero-loss peak was recorded for each EELS spectrum. Both Raman and EELS data were analyzed using OriginLab Scientific Graphing and Analysis Software, in which multiple peak fitting routines are employed over the data through iterations to get the sp2 content for each sample. The cross-sectional area of the samples and its thickness at randomly selected locations were imaged using an ESEM 共Philips XL30 ESEM-FEG兲. An ESEM was calibrated using Downloaded 14 Jul 2010 to 130.126.102.222. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp 113706-3 Correa et al. FIG. 1. The TEM image of the UNCD sample with the lacey carbon grid prepared for the EELS experiments. a diffraction grating replica specimen from Ted Pella, Inc. that consists of a grid with 2160 lines/mm. The calibration was performed at different magnifications, beam voltages 共kV兲, and working distances 共WDs兲. An Alesi REL-2100 analytical probe station with a tungsten tip radius of 2.4 ␮m was used to perform the I − V measurements. A commercial power supply 共Bertan, Series 225, Spellman High Voltage Corporation, USA兲 was used as a power source with an operating range of 0–3 kV and 0–30 mA. Each sample was randomly selected in terms of pad size and location. Both the output current and the applied voltage were measured using digital multimeters 共HP 3457A and HP 3478A, respectively兲. To study the local electrical properties as a function of surface morphology and position, conductive atomic force microscopy 共C-AFM兲 measurements were performed using a commercial AFM 共MFP-3D™, Asylum Research, USA兲 in a setup shown in Fig. 2. In three scanning axes, the hysteresis and creep of the piezoactuators were corrected by a closed loop control system with a linear voltage differential transducer 共LVDT兲 as the feedback sensor. The AFM tip J. Appl. Phys. 102, 113706 共2007兲 共AC240™ Electri-Lever, Olympus, Germany兲 was coated with platinum iridium. When a dc bias was applied to the sample, the conduction current was collected by the conductive AFM probe. The current signal was amplified by a transimpedance amplifier with a gain of 5 ⫻ 108 V / A and sampled by a data acquisition system. The AFM can be operated in two modes: current imaging and the I − V spectrum. In the current imaging mode, the tip is scanned in contact with the sample surface, and a feedback loop maintains a constant cantilever deflection signal to image the surface topography. At the same time, a constant bias voltage is applied to the sample, and the current at each pixel is measured to generate the current image. In the I − V spectrum mode, the AFM probe is moved to a specified location within an acquired image and brought into contact with the sample. The sample bias voltage is ramped within a user specified range and rate while the current is measured to generate the I − V curve. III. RESULTS AND DISCUSSION A. Hydrogen content of the UNCD films and hydrocarbon bonding configuration The ERDA spectra of the two types of UNCD films are shown in Fig. 3共a兲. The spectrum of each type of sample is characterized by two height steps at 1148 and 544 eV. The height of the first step is determined by the frequency that a helium ion is forward scattered from a carbon atom at the top UNCD surface layer. The second height is determined by the frequency that a hydrogen atom at the top surface layer is recoiled from a helium ion. The hydrogen content of the films can be calculated from the ratio of the two height steps in each spectrum.15,16 The spectra in Fig. 3共a兲 are rescaled so that the two types of samples have the same height at 1148 eV. The slightly greater height at 544 eV for the 400 ° C sample indicates a higher hydrogen content. Repeated measurements give an atomic percentage of hydrogen of 8.1% ± 1.2% and 10.0% ± 1.5% for the 800 ° C and 400 ° C samples, respectively. Figure 3共b兲 shows the FTIR spectra of the two types of UNCD films. For both of the films, the primary dips are located at 2855 and 2920 cm−1, which are identified to be saturated sp3 hydrocarbon bonds as in CH2 and CH, respectively.6 It is possible that there is also a small amount of saturated sp3 hydrocarbon bonds as in CH3, which shows up faintly at 2955 cm−1 within the broadband dip of 2920 cm−1. B. Grain structure by TEM FIG. 2. The conductive-AFM experimental setup for the microscopic experiments. When a dc bias is applied to the sample, the conduction current is collected by the conductive AFM probe. The current signal is amplified by a transimpedance amplifier with a gain of 5 ⫻ 108 V / A and is sampled by a data acquisition system. Figure 4 shows TEM microstructure photographs for undoped UNCD for samples grown at 400 ° C 关Figs. 4共a兲 and 4共b兲兴 and 800 ° C 关Figs. 4共c兲 and 4共d兲兴, respectively. From the pictures, a variation in the grain shape for both samples can be seen. Figure 4共a兲 shows that for samples grown at 400 ° C, the grain arrays are better oriented in one direction, whereas Fig. 4共c兲 shows that for the samples grown at 800 ° C, the grains meet with each other more randomly. The samples grown at 400 ° C also show elongated twined dendritic grains that are approximately 100 nm in length and less than 5 nm in width, as depicted in Fig. 4共b兲. The UNCD Downloaded 14 Jul 2010 to 130.126.102.222. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp 113706-4 Correa et al. J. Appl. Phys. 102, 113706 共2007兲 FIG. 4. The TEM images of UNCD films deposited at 共a兲, 共b兲 400 ° C and 共c兲, 共d兲 800 ° C. The 400 ° C films show elongated twined dendritic grains around 100 nm in length and less that 5 nm in width as depicted in 共a兲. The UNCD grown at 800 ° C exhibits different grain structure; the nanocrystalline grain arrays are more uniform or equiaxed with an average diameter of 4 nm. FIG. 3. 共a兲 The ERD spectra of UNCD films grown at 400 ° C and 800 ° C. The 400 ° C sample has a slightly higher step height at 544 eV indicating higher hydrogen content than the 800 ° C sample. 共b兲 The FTIR spectra of the UNCD films grown at 400 ° C and 800 ° C. The primary dips at 2855 and 2920 cm−1 are identified to be hydrocarbon bonds with saturated sp3 structure. two features, a peak at 285 eV due to excitation to p␲ⴱ states of sp2- bonded carbon and a step at 290 eV due to excitation to p␴ⴱ states of sp3 and sp2 sites.6 Thus, pure 100% sp2 carbon phase such as the lacey-carbon reference possess well resolved 285 and 290 eV peaks, whereas pure 100% sp3 carbon 共diamond兲 has no peak at 285 eV. The sp2 fraction of the UNCD film is found by taking the ratio of the area of the 285 eV peak to the area of the 290 eV step within the energy window from of 270–570 eV, and comparing it to the ratio of the 100% sp2 lacey-carbon reference.14 As seen in Fig. 5, the sp2 peak has greater intensity for the sample grown at grown at 800 ° C shows a different grain structure; the nanocrystalline grain arrays are more uniform or equiaxial with an average diameter of 4 nm 关Fig. 4共d兲兴. Both grain structures for the two deposition temperatures are comparable with those in the UNCD literature.4,5 It is important to note that all variables, save temperature, are kept constant during the deposition of the films. Thus, the change in grain structure is primarily due to the difference in deposition temperature. The TEM pictures also show that the 800 ° C samples exhibit a larger amount of grain boundaries per unit volume than the 400 ° C samples. C. sp2 vs sp3 ratio by EELS and Raman spectrum analysis The EELS spectra are shown in Fig. 5 for UNCD films deposited at 400 ° C and 800 ° C. The spectrum consists of FIG. 5. The EELS spectra for UNCD films deposited at 400 and 800 ° C. The reference peak takes place near 285 eV corresponding to sp2-bonded carbon. The higher intensity peak shows a higher concentration of sp2-bonded carbon for the 800 than the 400 ° C samples. Downloaded 14 Jul 2010 to 130.126.102.222. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp 113706-5 Correa et al. J. Appl. Phys. 102, 113706 共2007兲 TABLE I. The chemical composition and bonding structure of tested UNCD films. EELS & ERDA Raman & ERDA 400 800 400 800 °C °C °C °C sp2 C% sp2 C% H% 39.6± 11.6 65.2± 13.2 36.9± 19.7 65.2± 4.4 50.4± 11.6 26.7± 13.2 53.1± 19.7 26.7± 4.4 10.0± 1.5 8.1± 1.2 10.0± 1.5 8.1± 1.2 800 ° C when compared to the 400 ° C sample, indicating a higher sp2 content. Calculated results show the 800 ° C sample has an average sp2 content of 65.2% ± 13.2% whereas the 400 ° C sample showed a content of 39.6% ± 11.6% of sp2 carbon, as listed in Table I. Raman spectra are shown in Fig. 6 for the UNCD films deposited at 400 ° C. and 800 ° C. A reference line for pure diamond 共100% sp3兲 is also shown. Three modes 共peaks兲 can be identified at 1332, 1355, and 1550 cm−1. The sp3 mode is found to be near to 1332 cm−1, which agrees with the reference line and the literature for natural diamond.17,18 The other two broadband modes are approximately at 1355 and 1550 cm−1. These modes represent disordered sp2-bonded carbon within the UNCD films and are observed for both deposition temperatures. The HOPG reference line at 1580 cm−1 corresponding to single crystalline graphite is also shown in Fig. 6.18 None of the samples showed a significant intensity near 1580 cm−1, but rather a shifted peak closer to 1500 cm−1. This shift supports the assumption that the sp2-bonded carbon within the UNCD is not the same as in single crystalline graphite. Also, since Raman scattering in the visible range is about 100 times more sensitive to sp2-bonded carbon 共which is thought to reside almost exclu- FIG. 7. Characteristic macroscopic I − V response curves for the UNCD. The I − V curve for the 400 ° C sample exhibits a dielectric material behavior, with a sharp transition from linear to exponential growth in conductivity with applied electric field. The UNCD sample grown at 800 ° C shows a semiconductorlike behavior. By inspection, the 800 ° C sample is more conductive by 1 to nearly 4 orders of magnitude than the 400 ° C sample. sively in the grain boundary兲 than the sp3-bonded carbon, the change in the sp2 peaks at 1355 and 1550 cm−1 shows that the 800 ° C samples contain ⬃1.7 times more 共from Table I兲 sp2-bonded carbon in the grain boundaries than the 400 ° C samples. Furthermore, the samples grown at 400 ° C show a greater intensity at 1332 cm−1 in the Raman plot than the 800 ° C samples. The 1332 cm−1 peak is usually associated with microcrystalline diamond grains and not nanocrystalline diamond.5 Therefore, the 400 ° C sample has greater sp3 carbon-carbon bond content in the microcrystalline phase than does the 800 ° C sample. Hence, there is a lower concentration of grain boundaries per unit volume in the 400 ° C vs 800 ° C samples. Thus, the likelihood of extended interconnected networks of sp2-bonded carbon within the 800 ° C grown samples is greater than the 400 ° C samples. The sp3 vs sp2 ratio can be extracted from the Raman plot by integrating the intensity of each mode with respect to the wavelength18 and is listed in Table I. Since Raman scattering in the visible range does not see C–H bonds,6 the results from the Raman spectrum analysis show the sp3 bonded carbon ratio in all types of carbon-to-carbon bonds. The EELS results are consistent with the Raman results for the 800 ° C and 400 ° C samples within 3% and 12%, respectively. D. UNCD macroscopic and microscopic I − V curves FIG. 6. The Raman spectra for UNCD at different growing temperatures. Three modes can be identified from the plot: 1332, 1355, and 1550 cm−1. They correspond to sp3 and sp2 carbon bonding. A natural diamond reference 共100% sp3兲 and a HOPG 共100% sp2兲 reference are also shown. The sample grown at 400 ° C shows a greater intensity at 1332 cm−1 in the Raman spectra than the 800 ° C, showing a higher sp3-bonded carbon content in the 400 ° C samples. Figure 7 shows a characteristic I − V curve for UNCD as a macroscopic property measurement for each deposition temperature: 400 ° C and 800 ° C. Both samples have a 50 ␮m pad size length and 1.50 ␮m 共approximately兲 film thickness as measured by the ESEM. The I − V curve for the 400 ° C sample shows two different behaviors: linear before and exponential after a critical voltage is reached, which is typical for a dielectric material. When the applied voltage is under 60 V for the 400 ° C sample, a linear change in current Downloaded 14 Jul 2010 to 130.126.102.222. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp 113706-6 Correa et al. J. Appl. Phys. 102, 113706 共2007兲 FIG. 8. 共a兲 and 共b兲 1 ␮m2 topography scan, with 共c兲 and 共d兲 the corresponding current image, and 共e兲 and 共f兲 I − V response for the 400 ° C and 800 ° C grown UNCD samples, respectively. The specified locations of where the I − V curves are taken are indicated in 共c兲 and 共d兲 for 400 ° C and 800 ° C samples, respectively. The AFM topography pictures show that the films prepared at 400 ° C and 800 ° C are both continuous and dense with similar surface morphologies. Calculated rms roughness for the 400 ° C film is 12.0 nm whereas the 800 ° C film is 8.4 nm. is observed, and an exponential increase in current occurs above 60 V as observed in Fig. 7. The critical voltage of 60 V corresponds to a critical electrical field of 40 MV/m. The I − V curve for the 800 ° C data shows a different behavior. No linear-exponential transition is observed for the undoped UNCD sample grown at 800 ° C, but rather a semiconductorlike behavior is seen. In Fig. 7, the 800 ° C sample starts to show an immediate exponential increase in conductivity. Notice that the samples grown at 400 ° C and 800 ° C have the same pad size and thickness, so they are comparable. The I − V plot in Fig. 7 shows that the 800 ° C UNCD is more conductive than the 400 ° C UNCD by a minimum of an order of magnitude over the range tested and nearly 4 orders near 80 V. Figures 8共a兲 and 8共b兲 show 1 ␮m2 topography scans; Figs. 8共c兲 and 8共d兲 the corresponding current images; and Figs. 8共e兲 and 8共f兲 the I − V response for the UNCD 400 ° C and 800 ° C samples, respectively. The current image for the 400 ° C sample is acquired at a bias of 50 V, and for the 800 ° C sample is acquired at a 40 V bias. The specified locations of where the I − V curves are taken are indicated in Figs. 8共c兲 and 8共d兲 for the 400 ° C and 800 ° C samples, respectively. The AFM topography images in Figs. 8共a兲 and 8共b兲 show that the films prepared at 400 ° C and 800 ° C are both continuous and dense with similar surface morphologies. The calculated root-mean-square 共rms兲 roughness for the 400 ° C film is 12.0 nm, and for 800 ° C film it is 8.4 nm, which is consistent with the difference in the nanometer scale grain sizes as shown in the TEM images 共Fig. 5兲. Since the lateral resolution of the topography image is limited by the tip radius of the AFM probe 共15 nm in this case兲, the grain structure shown in Figs. 8共a兲 and 8共b兲 is attributed to a colony of nanocrystalline grains. The average thickness of the UNCD film used in the AFM experiments is 0.51 ␮m for the 400 ° C films and 1.24 ␮m for the 800 ° C films as measured by the ESEM. These values correspond to an averageapplied electrical field of 98 MV/m for the current images in Fig. 8共c兲, and 32 MV/m in Fig. 8共d兲. Figures 8共c兲 and 8共d兲 show that the 800 ° C sample is more conductive since the average current is 120 pA at 32 MV/m of the applied field, whereas the 400 ° C sample shows a smaller average current of 30 pA at a higher applied Downloaded 14 Jul 2010 to 130.126.102.222. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp 113706-7 Correa et al. field of 98 MV/m. Comparing the current images with the topography scans, no drastic change in conduction current is observed that correlates to the surface features for either type of sample, which implies that the conduction in these films is not dominated by extrinsic structural defects, such as voids or impurities in the films. The 800 ° C film does not behave as having extended graphitic or amorphous carbon domains, since the current response at every location behaves as a semiconductor, not metallic as graphite does, even though the sp2-bond fraction is high. On the other hand, most of the higher conduction current sites coincide with the boundaries of the colony of grains. The question arises as to whether the higher conduction current is due to the higher electric field for the same bias voltage at deeper surface valleys or comes from an increased conductivity at the grain boundary. The variation of the electrical field between surface valleys and peaks for the given bias is calculated from the measured roughness and thickness for each sample. Based on the I − V response, the variation of the electrical field due to the surface roughness leads to a maximum contrast of 14 pA for the samples grown at a 400 ° C sample and 42 pA for the samples grown at a 800 ° C sample. Both of these values are less than the contrast of the current images in Figs. 8共c兲 and 8共d兲, which is 30 and 120 pA for the 400 ° C and 800 ° C samples, respectively. We conclude that the higher conduction at the grain boundaries is indeed from an increased local conductivity due to intrinsic conduction promoter such as sp2-bonded carbon from the C-AFM measurements. The I − V response at three specified locations are measured for both UNCD samples, and the results are shown in Figs. 8共e兲 and 8共f兲. Although there is a slight difference within the three I − V curves for each sample, all the I − V curves in Fig. 8 show similar behavior as the macroscopic measurements shown in Fig. 7. For the 400 ° C sample, there is almost zero conduction below a critical voltage, and above the critical voltage, the conduction current increases exponentially. For the 800 ° C sample, the microscopic I − V curve again shows a semiconductorlike behavior. The critical field for the 400 ° C sample in the microscopic I − V measurement using the C-AFM is 71 MV/m, which is higher than the 40 MV/m critical field in the macroscopic I − V measurement using the probe station. The difference between the critical field measured by the C-AFM and the probe station indicates there is some degradation in the dielectric property with increasing area coverage due to the extrinsic defects for the samples grown at 400 ° C sample, which is consistent with a slight dependence of conduction behavior on pad sizes for the macroscopic I − V data, as shown in Fig. 9. The conduction behavior will be discussed in more detail in the next section. E. The dependence of conduction property on the structure of UNCD samples The CVD diamond thin films are often reported to have a nonlinear conductivity as a function of the applied field due to the presence of numerous defects and charge localization sites, or ionizable sites, within the material, as well as nondiamond structured carbon within grain boundaries.8–13 The UNCD samples we tested also exhibit nonlinear conductiv- J. Appl. Phys. 102, 113706 共2007兲 FIG. 9. 共a兲 The P-F plot with single Coulombic potentials and 共b兲 the P-F plot with overlapping Coulombic potentials for UNCD samples grown at 400 ° C and 800 ° C. The standard error 共SE兲 at the 95% Confidence Interval 共CI兲 of the fit for the P-F model with single Coulombic potential is found to be 0.83 for the 400 ° C samples and 0.98 for the 800 ° C whereas the SE for P-F with overlapping Coulombic potentials is found to be 0.63 and 0.80 for 400 ° C and 800 ° C, respectively. For clarity, the 95% CI limit lines are omitted for the 800 ° C curves. ity, as observed during the I − V experiments and shown in Fig. 7. Raman, TEM, and EELS showed that UNCD, like the other types of diamondlike films, has a high degree of grain boundaries and fraction of sp2 to the total number of bonds. Amorphous, graphitic, and extended networks of ␲-bonded carbon are well known to be highly conductive 共≫1000/ ⍀ cm兲. However, hydrogen remaining within the structure after diamond growth can also play a strong role in conductivity, potentially to increase or decrease conductivity of the resulting structure. Hydrogen can act to interrupt sp3 diamond networks, creating unsaturated defects that could act as charge localization sites, thereby increasing nonlinear Downloaded 14 Jul 2010 to 130.126.102.222. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp 113706-8 Correa et al. J. Appl. Phys. 102, 113706 共2007兲 conductivity at high fields. Hydrogen can also act to terminate sp2-bonded carbon, thereby interrupting ␲-bonded networks and reducing both linear 共Ohmic兲 and nonlinear conduction. Since the ERDA spectra show there is around 10% hydrogen in both types of the tested UNCD films, hydrogen could play a strong role in the conductivity of these films, which needs further elucidation. Non-Ohmic conductivity in dielectrics and semiconductors, such as that observed for these UNCD films, is most often phenomenologically characterized with basic constitutive relationships that are based on low-dimensional conduction models. Nonlinear conductivity resulting from charge hopping along the ionizable sites is often modeled for diamond films using a P-F type response model. Therefore, a question arises as to whether the exponential increase in conductivity with applied field that is observed for these films correlates with discrete ionizable sites, and if so, what are these sites with respect to the films chemical composition and crystalline structures. P-F type responses, modeled as charges being excited from Coulombic potential wells as detailed in Hill,20 differ depending on the type of interactions of the ionizable sites. Sparse ionization sites and single Coulombic wells leads to a function of the form 冉 冊 − ⌽i + ␤冑E , Jsparse = AE exp kT 共1兲 where A can be considered as a constant parameter, E is the electrical field, ⌽i is the ionization energy of a localized site, and ␤ is the P-F coefficient ␤= TABLE II. The fittings parameters, ln共a兲, b, ln共c兲, d, obtained from the data in Fig. 9. Statistical parameter ln共a兲 400 800 400 800 400 800 400 800 b ln共c兲 d °C °C °C °C °C °C °C °C Mean Standard deviation Relative error −30.35 −14.541 1.64⫻ 10−3 8.19⫻ 10−4 −3.896 5.384 8.05⫻ 10−8 6.83⫻ 10−8 1.040 0.2490 1.27⫻ 10−4 1.58⫻ 10−5 0.535 0.322 6.81⫻ 10−9 2.83⫻ 10−9 3.43⫻ 10−2 1.71⫻ 10−2 7.75⫻ 10−2 1.93⫻ 10−2 13.7⫻ 10−2 5.98⫻ 10−2 8.46⫻ 10−2 4.15⫻ 10−2 site. Therefore, after Hill20 and heeding the admonition of Ongaro and Pillonnet,19 the use of two parameter fits of J to E based on different types of charge motion and material structure is proposed to relate gross material structure and composition to the macroscopic conductivity properties observed, regardless of the attribution to global material properties such as permittivity, mobility, and activation energy. Thus, Eqs. 共1兲 and 共2兲 take the simple form of Jsparse = a E exp共b冑E兲, 共2兲 冑␥ ␲ ␧ o ␧ d , where e is the electronic charge, ␧o is the permittivity of free space, ␥ is a factor relating to geometry, and ␧o is the local dielectric function. For idealized one-dimensional wells without additional barriers in the bulk, ␥ is unity, but in real materials with complex aggregated three-dimensional 共3D兲 sites with interacting barriers, ␥ can vary by an order of magnitude. Similarly, the local fields and dielectric function also vary from the bulk values as Hill noted.20 Thus, ␤ can be expected to vary with material structure, composition, and defect density. In contrast to the case of sparse sites for charges to occupy, dense ionization sites with overlapping Coulombic potentials and interacting sites leads to a function of the form 冉 Jdense = C exp 冊 − ⌽i + ␤2/es + es E , kT 共3兲 where s is the ionization site spacing, which is thought to be inversely proportional to N1/3 i , where Ni is the number density of ionization sites. Classic and semiclassic P-F models utilize numerous simplifications that make it difficult to directly link structure of the material to a generalized conductivity property.19 The concern is that the conduction of charge along defects and ionizable sites is fully 3D in terms of material structure and Coulombic potentials, which in turn affects the local susceptibility and fields at each interacting 共4兲 where a and b are fitting constants. Notice that b relates to ␤ as b= ␤ . kT 共5兲 Similarly Eq. 共3兲 can be simplified in a simple expression Jdense = c exp共d E兲, e3/2 ln共Jsparse/E兲 = ln a + b冑E, ln共Jdense兲 = ln c + d E, 共6兲 where c and d are fitting constants. Notice that d relates to s as d= es . kT 共7兲 The constants a, b, c, and d can be obtained experimentally from the I − V experiments by fitting the data to Eqs. 共4兲 and 共6兲, respectively. Figures 9共a兲 and 9共b兲 show P-F plots with single 关Eq. 共4兲兴 and overlapping Coulombic potentials 关Eq. 共6兲兴, respectively. Table II shows the parameters, a, b, c, and d obtained from the data in Fig. 9, along with the uncertainties. Both fits show that the 800 ° C films are of orders of magnitude more conductive than the 400 ° C films, which is consistent with the I − V plots. A linear curve fit is also shown for a representative sample in both figures, along with confidence limits. In both Figs. 9共a兲 and 9共b兲 the films grown at 400 ° C show a slight pad size dependence in the conduction behavior, whereas all the curves fall on one line for the films grown at 800 ° C films. Lower conductivity films should be more sensitive to extrinsic defects, such as submicron pinholes, and larger pads have a higher probability of being affected by any increased conductivity due to the extrinsic defects. The TEM data from the UNCD samples grown at 400 ° C 关Figs. 4共a兲 and 4共b兲兴 showed a larger grain size with higher alignment and orientation than the samples grown at Downloaded 14 Jul 2010 to 130.126.102.222. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp 113706-9 Correa et al. J. Appl. Phys. 102, 113706 共2007兲 800 ° C 共Figs. 4共c兲 and 4共d兲兴. Thus, the 800 ° C UNCD has a larger amount of grain boundaries, with grain boundary areas 1.4–1.8 times more than the 400 ° C films as estimated from the TEM photographs, and thus presumably higher intrinsic defect densities. From the C-AFM data in Fig. 8, the current conduction is several times higher along the valleys and presumed grain boundaries than over the peaks, which are assumed to be associated with diamond crystallites. As some researchers have suggested,7 the bulk of the sp2 bonds in diamondlike films exist in the grain boundaries, which if true, correlates with a fractional increase in sp2 versus total carbon of 1.6 times for the 800 ° C vs 400 ° C films. However, the difference in the sp2-bonded carbon percentage alone does not explain the orders of magnitude difference in the conductivity between these two types of films as shown in Table II. Hydrogen is also thought to be located at the grain boundaries since atomic hydrogen can easily react with carbon atoms having dangling bonds in the grain boundaries during the film growing process. The FTIR spectra show that in both types the UNCD films, hydrogen exists in the form of saturated sp3 hydrocarbon as in CH3, CH2, and CH, and with the remaining bonds to C. No unsaturated bond peaks, such • as 关−C-H兴, are observed in the spectra, suggesting that hy兩 drogen is not acting to increase the probability of charge carriers in the films. It is well known that saturated sp3 hydrocarbon bonds are the building blocks of highly insulating polymers, such as polyethylene 共关CH2兴n兲. Thus the role of hydrocarbon at the grain boundary can be thought as conduction inhibitor. It has been shown previously in macroscale composites, such as polyethylene/carbon black, that electrical conductivity is sensitive to small change in the ratio of polyethylene/carbon black.21 Carbon black is essentially sp2-bonded amorphous carbon.22 The conductivity of amorphous carbon separated by polyethylene can change 5 orders of magnitude when the percolation limit is reached. Thus, the proposed explanation of observed conductivity difference between the 400 ° Cand 800 ° C films lies in the ratio of hydrocarbon bonds over the sp2 carbon-carbon bonds at the grain boundary, which are 0.253 and 0.123 for UNCD films deposited at 400 ° C and at 800 ° C, respectively. The picture that emerges from these data is that the conductivity of these UNCD films is governed by networks of ␲-bonded and amorphous carbon6 resident in the grain boundaries. As depicted in Fig. 10, one might think of the grain boundaries as a 3D distribution of domains of ␲-bonded carbon that are bounded by hydrogen-saturated carbon and/or diamond nano- or microcrystalliltes. Each domain can receive, carry, and inject electrons to and from other domains. As such, these domains behave as ionizable sites in the P-F model. As in Fig. 10共a兲, if the network of these domains is sparse enough, the potential induced from charges within each domain decay by either 1 / r2 for 3D or 1 / r for two-dimensional 共2D兲 structures. The effective field will not sufficiently overlap an adjoining domain to superimpose fields. Conduction occurs when the transient local field becomes high enough to either tunnel through 共low-field conduction兲, or shift the intervening dielectric into the conduction band 共high-field conduction兲. Such conduction be- FIG. 10. Depiction of ␲-bonded carbon domains that provide a 3D conductive path for electrons through a dielectric matrix. The mode of conduction depends on the spacing of the domains. With nonoverlapping potentials shown in 共a兲 arising from a sparse network of domains shown in 共b兲, the UNCD behaves as a dielectric, until the field is high enough for current to increase exponentially, following a P-F response. With overlapping potentials shown in 共a兲 arising from a dense network of domains shown in 共b兲, the UNCD behaves as a semiconductor. havior is observed for the 400 ° C samples. As shown in Fig. 10共b兲, if the network is dense enough that the potential wells overlap, fields superimpose to shift the intervening dielectric into the conduction band at low fields, with conduction increasing exponentially with higher fields, which is described by the Coulombic interacting-wells P-F model. The degree of conduction depends on the applied field and conductivity, giving rise to semiconductor behavior observed for the 800 ° C samples. Changing sp2 to hydrocarbon ratio by two as measured for the 400 ° C and 800 ° C grown samples, if shifted from nonoverlapping to overlapping fields can therefore exponentially change the conductivity as we observed. Downloaded 14 Jul 2010 to 130.126.102.222. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp 113706-10 Correa et al. If the hydrogen to sp2 bond ratio drops further, it may be possible to create complete interconnected domains. Thus, a metallic conductive behavior may be possible in the UNCD films, although we have not yet observed this behavior. IV. CONCLUSION The ERDA measurements show that the atomic percentage of hydrogen in the film is 10.0% ± 1.5% and 8.1% ± 1.2% for the samples grown at 400 ° C and 800 ° C, respectively. The average sp2-bonded carbon content for the samples grown at 400 ° C according to the EELS and Raman spectra is found to be 39.6 and 36.9%, respectively. For the 800 ° C samples both Raman and EELS spectra gave an average sp2 content of approximately 65%. The TEM results showed nanocrystal elongated twined dendritic grains around 100 nm in length and less that 5 nm in width for the films grown at 400 ° C whereas the films grown at 800 ° C showed equiaxial nanograins with an average diameter of 4 nm. The I − V data from both the C-AFM and probe station measurements showed a dielectric behavior for films grown at 400 ° C whereas the film grown at 800 ° C showed a semiconductorlike behavior, with 1–4 orders of magnitude higher conductivity over 1 order of applied voltage. However, the 800 ° C film does not behave as having extended graphitic domains even though the sp2-bond fraction is high. The C-AFM measures show that the conduction in these films 共both deposition temperature兲 is not primarily governed by extrinsic structural defects. The conductivity of both types of films also shows field dependent nonlinear behavior similar to microcrystalline CVD diamond. The P-F models with single and overlapping Coulombic potentials are used to describe the conduction mechanism of the tested undoped UNCD films. Both the P-F models showed that the conduction is directly correlated with the sp2 bond density and the ratio of hydrocarbon bonds over sp2 bonded carbon in the conduction path at the gain boundary. ACKNOWLEDGMENTS This work was supported by the NSF Nano-CEMMS under Award No. DMI-0328162 and partially supported by the WaterCAMPWS under CTS-0120978. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessar- J. Appl. Phys. 102, 113706 共2007兲 ily reflect the views of the NSF. The ERDA, TEM, AFM, and Raman work is performed at the University of Illinois Center for Microanalysis of Materials, partially supported by the U.S. DOE under Grant No. DEFC02-91-ER45439. The authors would like to acknowledge Professor Ivan Petrov for helpful discussions on the ERDA data and Dr. Changhui Lei for the TEM sample preparation. 1 D. Zhou, T. G. McCauley, L. C. Qin, A. R. Krauss, and D. M. Gruen, J. Appl. Phys. 83, 540 共1998兲. 2 S. Jiao, A. Sumant, M. A. Kirk, D. M. Bruen, A. R. Krauss, and O. Auciello, J. Appl. Phys. 90, 118 共2001兲. 3 A. R. Krauss, O. Auciello, D. M. Gruen, A. Jayatissa, A. Sumant, J. Tucek, D. C. Mancini, N. Moldovan, A. Erdemir, D. Ersoy, M. N. Gardo, H. G. Busmann, E. M. Meyer, and M. Q. Ding, Diamond Relat. Mater. 10, 1952 共2001兲. 4 X. Xiao, J. Birrell, J. E. Gerbi, O. Auciello, and J. A. Carlisle, J. Appl. Phys. 96, 2232 共2004兲. 5 J. Birrell, J. E. Gerbi, O. Auciellob, J. M. Gibson, J. Johnson, and J. A. Carlisle, Diamond Relat. Mater. 14, 86 共2005兲. 6 J. Robertson, Mater. Sci. Eng., R. 37, 129 共2002兲. 7 F. Cleri, P. Keblinski, L. Colombo, D. Wolf, and S. R. Phillpot, Europhys. Lett. 46, 671 共1999兲. 8 P. W. May, S. Höhn, W. N. Wang, and N. A. Fox, Appl. Phys. Lett. 72, 2182 共1998兲. 9 B. Huang and D. K. Reinhard, Appl. Phys. Lett. 59, 1494 共1991兲. 10 Y. Muto, T. Sugino, and J. Shirafuji, Appl. Phys. Lett. 59, 843 共1991兲. 11 P. Gonon, Y. Boiko, S. Prawer, and D. Jamieson, J. Appl. Phys. 79, 3778 共1996兲. 12 A. Jauhiainen, S. Bengtsson, and O. Engstrom, J. Appl. Phys. 82, 4966 共1997兲. 13 P. Gonon, S. Prawer, Y. Boiko, and D. N. Jamieson, Diamond Relat. Mater. 6, 860 共1997兲. 14 L. Wan and R. F. Egerton, Thin Solid Films 279, 34 共1996兲. 15 W.-K. Chu, J. W. Mayer, and M. A. Nicolet, Backscattering Spectrometry 共Academic Press, New York, 1978兲, pp. 80–83. 16 J. R. Tesmer and M. Nastasi, Handbook of Modern Ion Beam Materials Analysis 共Materials Research Society, Pittsburgh, 1995兲, p. 85. 17 M. Yoshikawa, Y. Mori, H. Obata, M. Maegawa, G. Katagiri, H. Ishida, and A. Ishitani, Appl. Phys. Lett. 67, 694 共1995兲. 18 R. E. Shroder, R. J. Nemanich, and J. T. Glass, Phys. Rev. B 41, 3738 共1990兲. 19 R. Ongaro and A. Pillonnet, IEE Proc.-A: Sci., Meas. Technol. 138, 127 共1991兲. 20 R. M. Hill, Philos. Mag. 23, 59 共1971兲. 21 R. J. Ramos, R. F. Bianchi, and R. M. Faria, in The Tenth International Symposium on Electrets, Conference Series: ISE 10 共IEEE Service Center, Piscataway, NY, 1999兲, pp. 525–528. 22 F. Cataldo, in Astrobiology: Future Perspectives, edited by P. Ehrenfreund, W. Irvine, T. Owen, L. Becker, J. Blank, J. Brucato, L. Colangeli, S. Derenne, A. Dutrey, D. Despois, A. Lazcano, and F. Robert 共Kluwer Academic Publishers, Dordrecht, 2004兲, pp. 97–126. Downloaded 14 Jul 2010 to 130.126.102.222. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp