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IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 61, NO. 6, DECEMBER 2014
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Single Event Effects in Carbon Nanotube-Based Field Effect Transistors Under Energetic Particle Radiation Adam W. Bushmaker, Don Walker, Colin J. Mann, Vanessa Oklejas, Alan R. Hopkins, Moh. R. Amer, and Stephen B. Cronin
Abstract—We present results from proton radiation experiments with carbon nanotube field effect transistors. Single event effects were observed consisting of drops in current, with very long durations (100 s of ms), and sudden, discrete switching events between quantized current levels. These studies are important for the development and understanding of advanced nano-electronic devices operating in the space radiation environment. Index Terms—Carbon nanotube, field effect transistor (FET), proton radiation, single event effects (SEEs).
I. INTRODUCTION
P
ROGRESS in device-level research has matured carbon nanotube field effect transistors (CNT FETs), and they are now being considered as a promising new technology for nextgeneration micro- and nano-electronic devices and circuitry. They offer potential performance advantages such as high carrier mobility [1], tunable band gap, high-linearity in analog RF amplifiers [2], high surface-to-volume ratio for chemical sensors [3], high frequency mechanical oscillations for RF NEMs devices [4], pliability for flexible electronics and display driver applications [5], and high cutoff frequencies in the THz region [6]. Single-walled CNTs also provide an excellent system for studying one-dimensional physics, such as exceptionally strong electron-phonon coupling [7]–[9], ballistic electron transport [10], and strongly correlated electrons [11]–[14]. Single event effects (SEE) caused by energetic particles are generally believed to be the greatest radiation-related threat to modern microelectronic circuits operating in the space environment. This is mainly due to scaling, which results in lower capacitance of individual nodes in microelectronics, and higher sensitivity to charge deposition and transport. Conversely, scaling has simultaneously resulted in some mitigation of total ionizing dose (TID) effects, which increases the attention
focused by the community on SEE. Radiation hardness by design (RHBD) techniques have been developed to mitigate this sensitivity to SEE; however, such techniques often rely on redundant architectures, which can adversely affect semiconductor real-estate usage and performance. Several important radiation studies on CNT based field effect transistor (FET) devices have shown marginal to minimal [15]–[18] sensitivity to TID; however, to the authors’ knowledge, no reports have been made concerning the observation of SEE in CNT FET devices. In this study, isolated, suspended, single-walled carbon nanotube FETs were electrically probed in-situ during exposure to proton radiation fluxes. Single event effects and threshold voltage shifts were observed. The CNT material was grown by using Chemical Vapor Deposition (CVD) at temperatures between , argon hosted ethanol as the carbon source, and lithographically defined catalyst islands consisting of Fe-Mo mix on an oxide support [8], [19], [20]. After CVD, no further processing is performed on the devices, which leaves nearly defect-free, as-grown CNTs, as evidenced by Raman spectroscopy [21]. CNTs span 500 nm deep trench structures formed in a silicon substrate with m SiO nm low stress . Trench width is nm m. Fig. 1 illustrates the device layout. 50 MeV protons and 10 MeV/Nucleon Xe ions from the 88” cyclotron facility at Lawrence Berkeley National Lab and 100 keV protons from the Low Energy Ion Accelerator Facility at The Aerospace Corporation were directed onto the samples, while the electrical properties of the devices were characterized in-situ with an Agilent 4155 semiconductor parameter analyzer. All measurements are conducted at room temperature. II. RESULTS A. TID Effects During 50 MeV Proton Irradiation
Manuscript received July 09, 2014; revised October 01, 2014; accepted November 02, 2014. Date of publication November 25, 2014; date of current version December 11, 2014. This work was supported in part by The Aerospace Corporation which was funded by the Independent Research And Development Program at The Aerospace Corporation and in part by the UCSB nanofabrication facility, part of the NSF funded NNIN network. A. W. Bushmaker. D. Walker, C. J. Mann, V. Oklejas, and A. R. Hopkins are with the Physical Sciences Laboratories, The Aerospace Corporation, El Segundo, CA 90245 USA (e-mail: [email protected]). M. R. Amer and S. B. Cronin are with the Electrical Engineering Department, The University of Southern California, Los Angeles, CA 90089 USA. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TNS.2014.2367519
Fig. 2 plots the drain current versus gate voltage for the CNT FET before and after exposure to protons/cm , which gives an equivalent dose of 326 krad(Si). The devices are p-type, turning ON for negative gate voltages, and the curves are hysteresis free. After exposure to the proton radiation, there is a positive threshold voltage shift of less than 200 mV. This is attributed to negative charge traps in the underlying on the edges of the trench (100 nm thickness). This positive threshold voltage shift causes a net increase in current levels on the device for all gate voltages below 0.7 V. The suspended nature
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Fig. 3. Drain current versus time with and without proton radiation. Proton flux protons/cm . While the proton radiation is on, large drops are was observed in the drain current, which are attributed to proton induced single event effects.
Fig. 1. Scanning electron microscope image (a) and schematic representation (b) of suspended carbon nanotube field effect transistor. Suspended portion is m in length, with 500 nm of air between the gate and CNT. 500 nm to
Fig. 2. Drain current versus gate voltage before (blue) and after (green) expoprotons/cm . The corresponding dose is 326 krads(Si). A small sure to threshold voltage shift of less than 200 mV is observed.
of these devices results in minimal gate-dielectric total ionizing dose (TID) effects. B. Major SEEs During 50 MeV Proton Irradiation Fig. 3 plots the drain current versus time for a CNT FET, showing the observed SEE. This data is characteristic of the devices which showed SEEs. While the devices were exposed to proton radiation, large and small drops in drain current were observed, and are attributed to proton irradiation induced SEE. The black curve represents the drain current in the absence of
proton radiation, and the red and blue curves represent two different data collection runs with the same proton flux of protons/cm directed onto the device in air. The drainsource voltage applied to the device was 0.1 V, and the gate voltage was held at 0 V. The drops in current appear to take on a bi-modal magnitude distribution; there is one set of reductions in current by only (minor), and there is another set of reductions in current by factors of over two orders of magnitude (major). The observed count rate can be used with the measured beam flux to calculate a device cross section. The observed count rate for major single event effects was 0.067 counts per second during exposure to an average high energy proton radiation flux of protons/cm , giving a cross section of cm . The CNT used in this experiment was m long, with an assumed diameter of 1 nm, giving a physical cross section of cm . This observed radiation cross section is x larger than the physical cross section of the carbon nanotube. The measured cross sections for several CNT FET devices are plotted in Table I above. Major SEEs were observed in 8 devices. The cross section varied by a large amount in the devices, 5 devices having relatively large cross sections ( cm to cm ), three devices having relatively small cross sections ( cm to cm ). A very small number of SEEs were observed in the devices after the radiation was turned off. These are attributed to nuclear decay of atoms in the substrate activated by exposure to the high energy proton beam. The average duration of the SEEs varies, being as high as 660 ms in one device, but as low as 8 ms (instrument limited) in another device. The longest SEEs observed lasted for multiple seconds. The chips with three-digit serial numbers are older samples, which had been stored for a longer period of time before use in the experiment. The chips with four-digit serial numbers were newer, having been fabricated only weeks before the experiment. The older, m length chips exhibited the highest cross sections for SEEs and also have longer average SEE durations, when compared to the newer, m chips. Thus, it is possible that either the sample age and/or the channel length has an effect on the SEE cross section and duration.
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TABLE I SUMMARY OF OBSERVED MAJOR SEES
Fig. 5. Overlay of drain current versus gate voltage sweeps taken during exposure to 50 MeV protons. During a “major” single event effect, the current level drops down to a lower level that is dependent on gate voltage.
Fig. 6. Drain current versus time (a) during exposure to 50 MeV protons, and resulting current distribution (b) for a larger data set including the data plotted in (a). The current level distribution shows clear quantization of current levels.
Fig. 4. Drain current versus time with normalized SEE start times (a) and distribution of SEE durations for many SEEs (b). SEE durations of up to several seconds were observed during 50 MeV proton radiation. The distribution of SEE ms. durations takes an exponential form with an average duration of
The drain currents for 17 observed SEEs on chip 418, device 17 are plotted versus time in Fig. 4(a), with the start times lined up. The events were automatically characterized by a computer algorithm, which measured the total time the current for each event spent below a detection threshold (noted in Fig. 4(a)). The SEE duration distribution for a large number of SEEs observed on this device is shown in Fig. 4(b). The number of observations for a given SEE duration decays exponentially, with an average duration ms. The initial drop in current observed in the major SEEs was investigated with greater time resolution
using an oscilloscope. The transition of the current level from the pristine state to the low-current state took the form of an exponential decay with a time constant of s. This figure corresponds well to the estimated RC time constant of the measurement circuit. Thus, we can place an upper limit of s on the transition time for the major SEEs. The major SEEs observed in the drain current are dependent on gate voltage, as is illustrated in Fig. 5, which plots an overlay of many gate voltage sweeps measured during proton irradiation. The pristine IV curves group in an upper manifold, while the currents during the major SEEs group in a lower manifold that is dependent on gate voltage. C. Minor SEEs During 50 MeV Proton Irradiation The minor single event effects were also analyzed. Fig. 6(a) shows drain current versus time, plotted alongside a current distribution plot (Fig. 6(b)) for a larger data set which included the data in Fig. 6(a). The bias conditions for this test were V, V. The current distribution plot shows groupings of the current into five distinct peaks with equal spacing. As many as six peaks were observed. The peaks indicate quantization of the current into quasi-stable states. The finite width of each peak takes a Gaussian distribution, and is attributed to general noise sources. When the radiation is removed, the current distribution takes a single approximate Gaussian distribution with similar
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Fig. 7. Fourier analysis of current noise for a period 0.5hrs before (a), 3 hrs during (b), and 1.5 hrs after (c) proton radiation exposure. Before the radiation exposure, there is a small 1/f tail in the noise spectra, with white noise over most of the device. During radiation exposure, the noise level rises, taking a 1/f form. After exposure, the noise decreases, but remains higher than before the radiation exposure, with a more noticeable 1/f signature at low frequencies.
line-width to the individual peaks in the Fig. 6(b), with the same average current level as the highest current peak in Fig. 6(b). Counting for determination of a cross section for the minor SEEs is more difficult than for the major SEEs, due to the smaller drain current step size, as well as the level of noise present in the data. A computer algorithm was developed to detect minor SEEs by counting events where the current abruptly changes by an amount larger than a threshold value, which was determined by analysis of the Gaussian peak widths of the entire data set. The algorithm then categorized each counted event according to one of several distinct Gaussian distributions by comparison of the event current value relative to the average current value within the individual current trace. This resulted in a count rate of 2.71 Hz, which, for an average beam flux of protons/cm corresponds to a cross section of cm . This method may over-count minor SEEs, however, due to the noise in the system. Visual inspection of the data in Fig. 6(a) gives a count rate of Hz, with a smaller corresponding cross section of cm . Both methods for estimation of minor SEE cross section result in cross sections larger than any of the measured cross sections for major SEEs. These two estimates for the cross section are and larger than the physical cross sectional area of the CNT, respectively. D. Fourier Analysis of the Drain Current Noise The current versus time data for chip 418, device 17 were also investigated by Fourier analysis. This data is shown in Fig. 7. Before radiation exposure, there was a small amount of 1/f noise in the noise spectra, but it was mostly dominated by white noise. During radiation the noise rose significantly, taking on a 1/f spectral profile. After the radiation was turned off, the noise went down, but didn’t return to its pre-irradiation levels, exhibiting higher 1/f noise than before the irradiation. 1/f noise is also referred to as flicker noise, and is associated with carrier density or mobility fluctuations [22]–[24] caused by traps in the oxide or defects on the CNT surface [25], [26]. Experiments with CNTs in air versus vacuum suggest that charge fluctuations of adsorbed atmospheric contaminants on the surface of the CNT cause 1/f noise [23].
Fig. 8. Drain current versus time during exposure to 100 keV protons. Beam protons/cm . The bias conditions were V, flux was V. Significant degradation in device performance was observed, but no single event effects.
There are several possible causes of the residual 1/f in the current noise spectra after irradiation. First, the radiation may have caused damage to the device. Second, there may be some residual major or minor SEEs occurring due to radioactive decay of radiation-induced unstable nuclear isotopes, as is mentioned above. E. Effects During 100 keV Proton Irradiation and 10 MeV/Nucleon Xe Irradiation One CNT FET device was also characterized during exposure to 100 keV protons in the LEAF (Low Energy ion Accelerator Facility) at The Aerospace Corporation. The drain current during this measurement is plotted versus time in Fig. 8. The bias conditions were V, V, and the testing was carried out in vacuum. The initial drain current of 60 nA gradually degraded to 25 nA during exposure to the 100 keV proton radiation. The drain current was significantly reduced from levels during operation in air, due to the removal of adsorbed oxygen at the CNT-Pt metal contact [27]. No large drops in drain current were observed. Small spikes in the current were observed, however these are comparable in size and attributed
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to the noise in the system. The conductance of the device eventually recovered several hours after the beam was shut off. Testing was also carried out during 10 MeV/nucleon heavy ion (Xe) irradiation at the LBNL 88” cyclotron facility. This testing was also carried out in vacuum. Two major SEE events were observed. The small number of events observed is due to the lower flux limit for the heavy ion experiment at the 88” cyclotron facility. III. DISCUSSION The attributes of the single event effects observed here suggest that they are caused by quantized switching events, rather than bulk charge collection, as is usually the case with SEEs in microelectronic circuits. In traditional SEEs, energetic particles deposit large amounts of ionized charge which is driven by electric fields in the device to the electrodes, resulting in a surge of current. The SEEs observed here are drops in current, rather than the surges, indicating a decrease in conductance as opposed to an increase. It is possible that an equal but opposite surge in current is responsible for the observed decrease in the drain current; this has been ruled out based on the lack of electric fields in the device with proper polarity to drive such a surge in current. In addition, the observed SEEs take the form of a step function, rather than an exponential decay which is what one would expect for a traditional SEE dominated by charge collection. Also, the SEEs switch between quasi-stable, evenly spaced, discrete current levels, as opposed to a broad, Gaussian distribution of current levels. This behavior suggests switching between discrete states with different associated current levels. Furthermore, the long observed lifetimes of the quasi-stable discrete current levels (100’s of ms to seconds) were much longer than SEEs observed in traditional single event effects (ps). These long delays cast doubt on charge collection as a possible mechanism. The major SEEs have a gate voltage dependence that is not consistent with charge collection. First, the polarity of the change in drain current associated with the SEE does not switch when the gate voltage polarity switches. Secondly, the change in drain current associated with the SEE gets smaller with increasing gate voltage magnitude, which is the opposite behavior one would expect if charge collection was driven by the electric field associated with the gate voltage. Also, the devices tested in this experiment were suspended, and all dielectrics and the silicon in the substrate are separated from the CNT by 30 nm thick Pt/W metal electrodes connected to low impedance voltage supplies or electrical ground. Any charge generated in the underlying substrate should be screened out very rapidly (fs-ps) by the free carriers in these metal electrodes. One possible hypothesis for the root cause of the observed single event effects during radiation exposure is that surface defects on the CNT are being ionized or switched by the radiation to create the drops in current and observed 1/f noise. Oxygen [27] and water molecules [28], [29] have been known for over a decade to readily adsorb onto the surface of CNTs and their contacts, and additional candidates include , , and other
Fig. 9. Drain current versus time from Liu et al.[33] showing random telegraph interface. This behavior is very signal switching due to defects at the CNT/ similar to the SEEs observed in CNT FETs during radiation exposure.
trace atmospheric gasses. In addition to this source of possible surface contaminants, more complex molecules such as volatile organic compounds or plasticizers outgassing from the plastic storage boxes [30] used to store the CNT FETs may be the source for surface contamination responsible for the observed single event effects. Finally, topological defects in the carbon atom lattice, may be present, such as 5-7 pairs [31]. This hypothesis explains the observed variation in radiation cross section for SEEs by including the possibility of differing levels of surface contamination. Indeed, the older samples, which had been stored for longer period of time before use in the experiment (chips with three-digit serial numbers) exhibited the highest cross sections for SEEs and also longer average SEE durations. Newer chips (those with four digit serial numbers) were fabricated only weeks before use in the experiment. This observation is consistent with the hypothesis that surface contamination occurs during storage. The maximum current that can pass through a single-walled CNT is set by the quantum conductance , where is the charge on an electron and is Planck’s constant. The actual current passing through a CNT is reduced due to scattering and charge depletion [32]. The devices used in this experiment were partially depleted, and long enough to exhibit diffusive transport, thus the measured conductance is far below the quantum conductance. Defect sites can introduce both additional scattering and charge depletion. Following Liu et al. [33], the change of current resulting from defect charging/discharging can be expressed as (1) where is the charge density and is the mobility. In order for surface defects on the CNT to cause the observed current fluctuations, the energy in the radiation field needs to be coupled to the CNT somehow. The largest radiation cross sections observed in the CNT devices are x x larger than the physical cross section of the CNTs (found by multiplying the length of the CNT by an approximate diameter of 1 nm). Furthermore, the probability of interaction for a high energy
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Fig. 10. Normalized drain current distribution histogram at various points during proton irradiation. The data (black curves) was fit with the model for radiation induced defect switching (red curves) described in the text. The defect switching probability/number product, Gaussian line width, and pristine current level were the only fitting parameters. Defect state current level spacing was held constant for all fits at 5.8 nA.
proton passing through a single-walled CNT is much less than unity. It is possible that secondary ionization could be a pathway for energy transfer to the CNT. Possible pathways for this secondary ionization include voltage pulses in the electrodes from charge collection elsewhere on the substrate, diffusion of ionized air particles in the vicinity of the chip, and scattered by-products from particle interaction with the substrate, such as scattered electrons (delta rays), nuclear fragments from nuclear spallation by the high energy protons, and secondary ion emission (sputtering). If the SEEs are indeed caused by switching or ionization of individual defects, the energy threshold for a switching event could be very low, possibly just a few eV. The ionized charge threshold for such a single defect to be excited by the secondary ionization might be as low as one electron; this is in contrast to a charge threshold of electrons for traditional single event effects through charge collection [34]. The extremely small threshold for ionization of an individual defect may compensate for the extremely small size of the CNT to result in a measureable SEE rate. Similar switching behavior has been observed before in CNT FETs without radiation exposure by Liu et al. [33] (Fig. 9). The observed switching behavior is known as random telegraph signal (RTS), is attributed to charge fluctuations in defects at the CNT/ interface or in the near the CNT, and is theoretically modeled by Wang et al. [26]. RTS behavior is in fact somewhat commonly observed in both CNT FET and conventional metal oxide semiconductor MOSFET devices [26]. The associated capture and emission times measured by Liu et al. take an exponential probability distribution (as do the SEE durations here), and are determined by the defect energy, Fermi energy, and the temperature [35]. In this context, the average major SEE duration (measured to be 200 ms in chip 418, device 17) can be interpreted as the emission time for a random telegraph-like system [33], where the emission corresponds to radiation-induced trapped charge being released from the defect. From data showing the emission time versus temperature, the activation energy for the defect can be determined [35]. This work is currently underway. The ability of a single charge to cause large changes in conductance in a single carbon nanotube device is rooted in the 1-di-
mensional nature of electrical transport in CNTs. Charge carriers are not free to route around scattering sites or potential barriers, and the conductance of the entire device is compromised, giving rise to the large changes in conductance of up to several orders of magnitude. This is in contrast with drain current fluctuations in bulk semiconductor devices which are typically less than 1% [35]–[37]. Thus, the CNT channel can be viewed as a series connection of many potential defect sites, with the resistances of each individual defect adding in series. The two types of conductance degradation observed here, “major” and “minor”, may represent two different types of defects being influenced by the radiation. In order to better understand the data presented in Fig. 6, the minor SEEs are modeled as independent, indistinguishable defects switching to a quasi-stable state with some radiationflux-dependent probability . The probability that exactly of defects have switched at any given time is given by (2) The binomial coefficient of possible combinations for
which expresses the number is given by (3)
Thus, we can model the relative peak heights for the quantized states observed in the drain current distribution histogram. Fig. 10 shows the drain current distribution histogram for the CNT shown in Fig. 6 measured at different points in time throughout a long exposure to 50 MeV proton radiation, plotted along with the fitting results from the model for minor SEEs. The time intervals are noted in the figure. The state intensities from the model were mapped to the peak height of Gaussian peaks. For large N (> 10), the distribution shape became dependent only on the product , and so we were unable to extract or independently. The fitting parameters were the product , Gaussian line width, and pristine current level. Defect state current level spacing was held constant for all fits at 5.8 nA. The mean value for the product was found to be 1.40. Throughout the experiment, the product varied
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(and thus also relative peak height and quantity). In general it rose from 0.63 at the beginning of the experiment to a maximum of 2.2 near the end of the experiment. This could be caused by an increasing number of defects N, or by an increasing switching probability . The proton beam was not very stable, and as a result, the flux varied somewhat over the course of the experiment. Consequently, the probability for radiation-induced defect switching also varied. Before the experiment was started, the current distribution was a single Gaussian-shaped peak centered near from the first data set during radiation exposure. During irradiation, shifts up due to the threshold voltage shift shown in Fig. 2, which increases the drain current level for all gate voltages. After irradiation, the current distribution returned to a nearly Gaussian-shaped peak centered near from the last data set during radiation exposure, however there was some residual RTS-like switching behavior with a small product of 0.04. If this hypothesis is further supported by additional experiments and analysis, the ramifications are that as electronic devices are scaled down to nanometer dimensions, they may become increasingly sensitive to radiation induced switching or charging of individual defects in sensitive areas. Understanding these defects may therefore be a key step in developing nano-electronics for use in the space environment. IV. CONCLUSION In conclusion, single event effects have been measured in isolated single CNT FETs exposed to high-energy proton radiation. The SEEs observed consist of large drops in device current of several orders of magnitude, and smaller, more frequent drops in device current of magnitude, which were quantized in evenly spaced levels up to 6 deep. The current distributions for these smaller SEEs were fit with a statistical model for radiation induced switching of many independent, identical defect states. The drops in current were sudden and discrete, and the degraded current persists much longer than traditional single event effects. Small accompanying threshold voltage shifts were also observed. A hypothesis for radiation induced defect state switching as the root cause of the observed SEE is outlined. ACKNOWLEDGMENT The authors gratefully acknowledge R. Koga, S. Bielat, and J. George for assistance with operation of the LBNL 88” cyclotron. The authors also acknowledge S. Moss, R. Lacoe, and J. Osborn for helpful discussions regarding interpretation of the data. REFERENCES [1] T. Durkop, S. A. Getty, E. Cobas, and M. S. Fuhrer, “Extraordinary mobility in semiconducting carbon nanotubes,” Nano Lett., vol. 4, pp. 35–39, 2004. [2] J. Baumgardner, A. Pesetski, J. Murduck, J. Przybysz, J. Adam, and H. Zhang, “Inherent linearity in carbon nanotube field-effect transistors,” Appl. Phys. Lett., vol. 91, p. 052107, 2007. [3] J. Li, Y. J. Lu, Q. Ye, M. Cinke, J. Han, and M. Meyyappan, “Carbon nanotube sensors for gas and organic vapor detection,” Nano Lett., vol. 3, pp. 929–933, Jul 2003.
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[25] P. Lim, W. Xinran, H. Dai, Y. Nishi, and J. Harris, “Threshold voltage and 1/f noise degradation in carbon nanotube field effect transistors under Hot-Carrier Stress,” in Proc. Device Res. Conf., 2008, pp. 109–110. [26] N.-P. Wang, S. Heinze, and J. Tersoff, “Random-telegraph-signal noise and device variability in ballistic nanotube transistors,” Nano Lett., vol. 7, pp. 910–913, Apr. 2007. [27] V. Derycke, R. Martel, J. Appenzeller, and P. Avouris, “Controlling doping and carrier injection in carbon nanotube transistors,” Appl. Phys. Lett., vol. 80, pp. 2773–2775, Apr. 2002. [28] W. Kim, A. Javey, O. Vermesh, Q. Wang, Y. Li, and H. Dai, “Hysteresis caused by water molecules in carbon nanotube field-effect transistors,” Nano Lett., vol. 3, pp. 193–198, Jan. 2003. [29] D. Sung, S. Hong, Y. H. Kim, N. Park, S. Kim, S. L. Maeng, and K. C. Kim, “Ab initio study of the effect of water adsorption on the carbon nanotube field-effect transistor,” Appl. Phys. Lett., vol. 89, Dec. 2006 [Online]. Available: http://dx.doi.org/10.1063/1.2397543 [30] S. K. Brown, M. R. Sim, M. J. Abramson, and C. N. Gray, “Concentrations of volatile organic compounds in indoor air–a review,” Indoor Air, vol. 4, pp. 123–134, 1994. [31] J. C. Charlier, T. W. Ebbesen, and P. Lambin, “Structural and electronic properties of pentagon-heptagon pair defects in carbon nanotubes,” Phys. Rev. B, vol. 53, pp. 11108–11113, Apr. 1996.
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[32] A. W. Bushmaker, M. R. Amer, and S. B. Cronin, “Electrical transport and channel length modulation in semiconducting carbon nanotube field effect transistors,” IEEE Trans. Nanotechnol., vol. 13, no. 2, pp. 176–181, Mar. 2014. [33] F. Liu, K. L. Wang, C. Li, and C. Zhou, “Study of random telegraph signals in single-walled carbon nanotube field effect transistors,” IEEE Trans. Nanotechnol., vol. 5, pp. 441–445, 2006. [34] E. Petersen, “Soft errors due to protons in the radiation belt,” IEEE Trans. Nucl. Sci., vol. 28, no. 6, pp. 3981–3986, Jun. 1981. [35] K. S. Ralls, W. J. Skocpol, L. D. Jackel, R. E. Howard, L. A. Fetter, R. W. Epworth, and D. M. Tennant, “Discrete resistance switching in submicrometer silicon inversion layers: Individual interface traps and low-frequency 1/f noise,” Phys. Rev. Lett., vol. 52, pp. 228–231, 1984. [36] K. K. Hung, P. K. Ko, C. Hu, and Y. C. Cheng, “Random telegraph noise of deep-submicrometer MOSFETs,” IEEE Electron Device Lett., vol. 11, no. 2, pp. 90–92, Feb. 1990. [37] M. J. Uren, D. J. Day, and M. J. Kirton, “1/f and random telegraph noise in silicon metal-oxide-semiconductor field-effect transistors,” Appl. Phys. Lett., vol. 47, pp. 1195–1197, 1985.
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Single Event Effects in Carbon Nanotube-Based Field Effect Transistors Under Energetic Particle Radiation Adam W. Bushmaker, Don Walker, Colin J. Mann, Vanessa Oklejas, Alan R. Hopkins, Moh. R. Amer, and Stephen B. Cronin
Abstract—We present results from proton radiation experiments with carbon nanotube field effect transistors. Single event effects were observed consisting of drops in current, with very long durations (100 s of ms), and sudden, discrete switching events between quantized current levels. These studies are important for the development and understanding of advanced nano-electronic devices operating in the space radiation environment. Index Terms—Carbon nanotube, field effect transistor (FET), proton radiation, single event effects (SEEs).
I. INTRODUCTION
P
ROGRESS in device-level research has matured carbon nanotube field effect transistors (CNT FETs), and they are now being considered as a promising new technology for nextgeneration micro- and nano-electronic devices and circuitry. They offer potential performance advantages such as high carrier mobility [1], tunable band gap, high-linearity in analog RF amplifiers [2], high surface-to-volume ratio for chemical sensors [3], high frequency mechanical oscillations for RF NEMs devices [4], pliability for flexible electronics and display driver applications [5], and high cutoff frequencies in the THz region [6]. Single-walled CNTs also provide an excellent system for studying one-dimensional physics, such as exceptionally strong electron-phonon coupling [7]–[9], ballistic electron transport [10], and strongly correlated electrons [11]–[14]. Single event effects (SEE) caused by energetic particles are generally believed to be the greatest radiation-related threat to modern microelectronic circuits operating in the space environment. This is mainly due to scaling, which results in lower capacitance of individual nodes in microelectronics, and higher sensitivity to charge deposition and transport. Conversely, scaling has simultaneously resulted in some mitigation of total ionizing dose (TID) effects, which increases the attention
focused by the community on SEE. Radiation hardness by design (RHBD) techniques have been developed to mitigate this sensitivity to SEE; however, such techniques often rely on redundant architectures, which can adversely affect semiconductor real-estate usage and performance. Several important radiation studies on CNT based field effect transistor (FET) devices have shown marginal to minimal [15]–[18] sensitivity to TID; however, to the authors’ knowledge, no reports have been made concerning the observation of SEE in CNT FET devices. In this study, isolated, suspended, single-walled carbon nanotube FETs were electrically probed in-situ during exposure to proton radiation fluxes. Single event effects and threshold voltage shifts were observed. The CNT material was grown by using Chemical Vapor Deposition (CVD) at temperatures between , argon hosted ethanol as the carbon source, and lithographically defined catalyst islands consisting of Fe-Mo mix on an oxide support [8], [19], [20]. After CVD, no further processing is performed on the devices, which leaves nearly defect-free, as-grown CNTs, as evidenced by Raman spectroscopy [21]. CNTs span 500 nm deep trench structures formed in a silicon substrate with m SiO nm low stress . Trench width is nm m. Fig. 1 illustrates the device layout. 50 MeV protons and 10 MeV/Nucleon Xe ions from the 88” cyclotron facility at Lawrence Berkeley National Lab and 100 keV protons from the Low Energy Ion Accelerator Facility at The Aerospace Corporation were directed onto the samples, while the electrical properties of the devices were characterized in-situ with an Agilent 4155 semiconductor parameter analyzer. All measurements are conducted at room temperature. II. RESULTS A. TID Effects During 50 MeV Proton Irradiation
Manuscript received July 09, 2014; revised October 01, 2014; accepted November 02, 2014. Date of publication November 25, 2014; date of current version December 11, 2014. This work was supported in part by The Aerospace Corporation which was funded by the Independent Research And Development Program at The Aerospace Corporation and in part by the UCSB nanofabrication facility, part of the NSF funded NNIN network. A. W. Bushmaker. D. Walker, C. J. Mann, V. Oklejas, and A. R. Hopkins are with the Physical Sciences Laboratories, The Aerospace Corporation, El Segundo, CA 90245 USA (e-mail: [email protected]). M. R. Amer and S. B. Cronin are with the Electrical Engineering Department, The University of Southern California, Los Angeles, CA 90089 USA. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TNS.2014.2367519
Fig. 2 plots the drain current versus gate voltage for the CNT FET before and after exposure to protons/cm , which gives an equivalent dose of 326 krad(Si). The devices are p-type, turning ON for negative gate voltages, and the curves are hysteresis free. After exposure to the proton radiation, there is a positive threshold voltage shift of less than 200 mV. This is attributed to negative charge traps in the underlying on the edges of the trench (100 nm thickness). This positive threshold voltage shift causes a net increase in current levels on the device for all gate voltages below 0.7 V. The suspended nature
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Fig. 3. Drain current versus time with and without proton radiation. Proton flux protons/cm . While the proton radiation is on, large drops are was observed in the drain current, which are attributed to proton induced single event effects.
Fig. 1. Scanning electron microscope image (a) and schematic representation (b) of suspended carbon nanotube field effect transistor. Suspended portion is m in length, with 500 nm of air between the gate and CNT. 500 nm to
Fig. 2. Drain current versus gate voltage before (blue) and after (green) expoprotons/cm . The corresponding dose is 326 krads(Si). A small sure to threshold voltage shift of less than 200 mV is observed.
of these devices results in minimal gate-dielectric total ionizing dose (TID) effects. B. Major SEEs During 50 MeV Proton Irradiation Fig. 3 plots the drain current versus time for a CNT FET, showing the observed SEE. This data is characteristic of the devices which showed SEEs. While the devices were exposed to proton radiation, large and small drops in drain current were observed, and are attributed to proton irradiation induced SEE. The black curve represents the drain current in the absence of
proton radiation, and the red and blue curves represent two different data collection runs with the same proton flux of protons/cm directed onto the device in air. The drainsource voltage applied to the device was 0.1 V, and the gate voltage was held at 0 V. The drops in current appear to take on a bi-modal magnitude distribution; there is one set of reductions in current by only (minor), and there is another set of reductions in current by factors of over two orders of magnitude (major). The observed count rate can be used with the measured beam flux to calculate a device cross section. The observed count rate for major single event effects was 0.067 counts per second during exposure to an average high energy proton radiation flux of protons/cm , giving a cross section of cm . The CNT used in this experiment was m long, with an assumed diameter of 1 nm, giving a physical cross section of cm . This observed radiation cross section is x larger than the physical cross section of the carbon nanotube. The measured cross sections for several CNT FET devices are plotted in Table I above. Major SEEs were observed in 8 devices. The cross section varied by a large amount in the devices, 5 devices having relatively large cross sections ( cm to cm ), three devices having relatively small cross sections ( cm to cm ). A very small number of SEEs were observed in the devices after the radiation was turned off. These are attributed to nuclear decay of atoms in the substrate activated by exposure to the high energy proton beam. The average duration of the SEEs varies, being as high as 660 ms in one device, but as low as 8 ms (instrument limited) in another device. The longest SEEs observed lasted for multiple seconds. The chips with three-digit serial numbers are older samples, which had been stored for a longer period of time before use in the experiment. The chips with four-digit serial numbers were newer, having been fabricated only weeks before the experiment. The older, m length chips exhibited the highest cross sections for SEEs and also have longer average SEE durations, when compared to the newer, m chips. Thus, it is possible that either the sample age and/or the channel length has an effect on the SEE cross section and duration.
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TABLE I SUMMARY OF OBSERVED MAJOR SEES
Fig. 5. Overlay of drain current versus gate voltage sweeps taken during exposure to 50 MeV protons. During a “major” single event effect, the current level drops down to a lower level that is dependent on gate voltage.
Fig. 6. Drain current versus time (a) during exposure to 50 MeV protons, and resulting current distribution (b) for a larger data set including the data plotted in (a). The current level distribution shows clear quantization of current levels.
Fig. 4. Drain current versus time with normalized SEE start times (a) and distribution of SEE durations for many SEEs (b). SEE durations of up to several seconds were observed during 50 MeV proton radiation. The distribution of SEE ms. durations takes an exponential form with an average duration of
The drain currents for 17 observed SEEs on chip 418, device 17 are plotted versus time in Fig. 4(a), with the start times lined up. The events were automatically characterized by a computer algorithm, which measured the total time the current for each event spent below a detection threshold (noted in Fig. 4(a)). The SEE duration distribution for a large number of SEEs observed on this device is shown in Fig. 4(b). The number of observations for a given SEE duration decays exponentially, with an average duration ms. The initial drop in current observed in the major SEEs was investigated with greater time resolution
using an oscilloscope. The transition of the current level from the pristine state to the low-current state took the form of an exponential decay with a time constant of s. This figure corresponds well to the estimated RC time constant of the measurement circuit. Thus, we can place an upper limit of s on the transition time for the major SEEs. The major SEEs observed in the drain current are dependent on gate voltage, as is illustrated in Fig. 5, which plots an overlay of many gate voltage sweeps measured during proton irradiation. The pristine IV curves group in an upper manifold, while the currents during the major SEEs group in a lower manifold that is dependent on gate voltage. C. Minor SEEs During 50 MeV Proton Irradiation The minor single event effects were also analyzed. Fig. 6(a) shows drain current versus time, plotted alongside a current distribution plot (Fig. 6(b)) for a larger data set which included the data in Fig. 6(a). The bias conditions for this test were V, V. The current distribution plot shows groupings of the current into five distinct peaks with equal spacing. As many as six peaks were observed. The peaks indicate quantization of the current into quasi-stable states. The finite width of each peak takes a Gaussian distribution, and is attributed to general noise sources. When the radiation is removed, the current distribution takes a single approximate Gaussian distribution with similar
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Fig. 7. Fourier analysis of current noise for a period 0.5hrs before (a), 3 hrs during (b), and 1.5 hrs after (c) proton radiation exposure. Before the radiation exposure, there is a small 1/f tail in the noise spectra, with white noise over most of the device. During radiation exposure, the noise level rises, taking a 1/f form. After exposure, the noise decreases, but remains higher than before the radiation exposure, with a more noticeable 1/f signature at low frequencies.
line-width to the individual peaks in the Fig. 6(b), with the same average current level as the highest current peak in Fig. 6(b). Counting for determination of a cross section for the minor SEEs is more difficult than for the major SEEs, due to the smaller drain current step size, as well as the level of noise present in the data. A computer algorithm was developed to detect minor SEEs by counting events where the current abruptly changes by an amount larger than a threshold value, which was determined by analysis of the Gaussian peak widths of the entire data set. The algorithm then categorized each counted event according to one of several distinct Gaussian distributions by comparison of the event current value relative to the average current value within the individual current trace. This resulted in a count rate of 2.71 Hz, which, for an average beam flux of protons/cm corresponds to a cross section of cm . This method may over-count minor SEEs, however, due to the noise in the system. Visual inspection of the data in Fig. 6(a) gives a count rate of Hz, with a smaller corresponding cross section of cm . Both methods for estimation of minor SEE cross section result in cross sections larger than any of the measured cross sections for major SEEs. These two estimates for the cross section are and larger than the physical cross sectional area of the CNT, respectively. D. Fourier Analysis of the Drain Current Noise The current versus time data for chip 418, device 17 were also investigated by Fourier analysis. This data is shown in Fig. 7. Before radiation exposure, there was a small amount of 1/f noise in the noise spectra, but it was mostly dominated by white noise. During radiation the noise rose significantly, taking on a 1/f spectral profile. After the radiation was turned off, the noise went down, but didn’t return to its pre-irradiation levels, exhibiting higher 1/f noise than before the irradiation. 1/f noise is also referred to as flicker noise, and is associated with carrier density or mobility fluctuations [22]–[24] caused by traps in the oxide or defects on the CNT surface [25], [26]. Experiments with CNTs in air versus vacuum suggest that charge fluctuations of adsorbed atmospheric contaminants on the surface of the CNT cause 1/f noise [23].
Fig. 8. Drain current versus time during exposure to 100 keV protons. Beam protons/cm . The bias conditions were V, flux was V. Significant degradation in device performance was observed, but no single event effects.
There are several possible causes of the residual 1/f in the current noise spectra after irradiation. First, the radiation may have caused damage to the device. Second, there may be some residual major or minor SEEs occurring due to radioactive decay of radiation-induced unstable nuclear isotopes, as is mentioned above. E. Effects During 100 keV Proton Irradiation and 10 MeV/Nucleon Xe Irradiation One CNT FET device was also characterized during exposure to 100 keV protons in the LEAF (Low Energy ion Accelerator Facility) at The Aerospace Corporation. The drain current during this measurement is plotted versus time in Fig. 8. The bias conditions were V, V, and the testing was carried out in vacuum. The initial drain current of 60 nA gradually degraded to 25 nA during exposure to the 100 keV proton radiation. The drain current was significantly reduced from levels during operation in air, due to the removal of adsorbed oxygen at the CNT-Pt metal contact [27]. No large drops in drain current were observed. Small spikes in the current were observed, however these are comparable in size and attributed
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to the noise in the system. The conductance of the device eventually recovered several hours after the beam was shut off. Testing was also carried out during 10 MeV/nucleon heavy ion (Xe) irradiation at the LBNL 88” cyclotron facility. This testing was also carried out in vacuum. Two major SEE events were observed. The small number of events observed is due to the lower flux limit for the heavy ion experiment at the 88” cyclotron facility. III. DISCUSSION The attributes of the single event effects observed here suggest that they are caused by quantized switching events, rather than bulk charge collection, as is usually the case with SEEs in microelectronic circuits. In traditional SEEs, energetic particles deposit large amounts of ionized charge which is driven by electric fields in the device to the electrodes, resulting in a surge of current. The SEEs observed here are drops in current, rather than the surges, indicating a decrease in conductance as opposed to an increase. It is possible that an equal but opposite surge in current is responsible for the observed decrease in the drain current; this has been ruled out based on the lack of electric fields in the device with proper polarity to drive such a surge in current. In addition, the observed SEEs take the form of a step function, rather than an exponential decay which is what one would expect for a traditional SEE dominated by charge collection. Also, the SEEs switch between quasi-stable, evenly spaced, discrete current levels, as opposed to a broad, Gaussian distribution of current levels. This behavior suggests switching between discrete states with different associated current levels. Furthermore, the long observed lifetimes of the quasi-stable discrete current levels (100’s of ms to seconds) were much longer than SEEs observed in traditional single event effects (ps). These long delays cast doubt on charge collection as a possible mechanism. The major SEEs have a gate voltage dependence that is not consistent with charge collection. First, the polarity of the change in drain current associated with the SEE does not switch when the gate voltage polarity switches. Secondly, the change in drain current associated with the SEE gets smaller with increasing gate voltage magnitude, which is the opposite behavior one would expect if charge collection was driven by the electric field associated with the gate voltage. Also, the devices tested in this experiment were suspended, and all dielectrics and the silicon in the substrate are separated from the CNT by 30 nm thick Pt/W metal electrodes connected to low impedance voltage supplies or electrical ground. Any charge generated in the underlying substrate should be screened out very rapidly (fs-ps) by the free carriers in these metal electrodes. One possible hypothesis for the root cause of the observed single event effects during radiation exposure is that surface defects on the CNT are being ionized or switched by the radiation to create the drops in current and observed 1/f noise. Oxygen [27] and water molecules [28], [29] have been known for over a decade to readily adsorb onto the surface of CNTs and their contacts, and additional candidates include , , and other
Fig. 9. Drain current versus time from Liu et al.[33] showing random telegraph interface. This behavior is very signal switching due to defects at the CNT/ similar to the SEEs observed in CNT FETs during radiation exposure.
trace atmospheric gasses. In addition to this source of possible surface contaminants, more complex molecules such as volatile organic compounds or plasticizers outgassing from the plastic storage boxes [30] used to store the CNT FETs may be the source for surface contamination responsible for the observed single event effects. Finally, topological defects in the carbon atom lattice, may be present, such as 5-7 pairs [31]. This hypothesis explains the observed variation in radiation cross section for SEEs by including the possibility of differing levels of surface contamination. Indeed, the older samples, which had been stored for longer period of time before use in the experiment (chips with three-digit serial numbers) exhibited the highest cross sections for SEEs and also longer average SEE durations. Newer chips (those with four digit serial numbers) were fabricated only weeks before use in the experiment. This observation is consistent with the hypothesis that surface contamination occurs during storage. The maximum current that can pass through a single-walled CNT is set by the quantum conductance , where is the charge on an electron and is Planck’s constant. The actual current passing through a CNT is reduced due to scattering and charge depletion [32]. The devices used in this experiment were partially depleted, and long enough to exhibit diffusive transport, thus the measured conductance is far below the quantum conductance. Defect sites can introduce both additional scattering and charge depletion. Following Liu et al. [33], the change of current resulting from defect charging/discharging can be expressed as (1) where is the charge density and is the mobility. In order for surface defects on the CNT to cause the observed current fluctuations, the energy in the radiation field needs to be coupled to the CNT somehow. The largest radiation cross sections observed in the CNT devices are x x larger than the physical cross section of the CNTs (found by multiplying the length of the CNT by an approximate diameter of 1 nm). Furthermore, the probability of interaction for a high energy
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Fig. 10. Normalized drain current distribution histogram at various points during proton irradiation. The data (black curves) was fit with the model for radiation induced defect switching (red curves) described in the text. The defect switching probability/number product, Gaussian line width, and pristine current level were the only fitting parameters. Defect state current level spacing was held constant for all fits at 5.8 nA.
proton passing through a single-walled CNT is much less than unity. It is possible that secondary ionization could be a pathway for energy transfer to the CNT. Possible pathways for this secondary ionization include voltage pulses in the electrodes from charge collection elsewhere on the substrate, diffusion of ionized air particles in the vicinity of the chip, and scattered by-products from particle interaction with the substrate, such as scattered electrons (delta rays), nuclear fragments from nuclear spallation by the high energy protons, and secondary ion emission (sputtering). If the SEEs are indeed caused by switching or ionization of individual defects, the energy threshold for a switching event could be very low, possibly just a few eV. The ionized charge threshold for such a single defect to be excited by the secondary ionization might be as low as one electron; this is in contrast to a charge threshold of electrons for traditional single event effects through charge collection [34]. The extremely small threshold for ionization of an individual defect may compensate for the extremely small size of the CNT to result in a measureable SEE rate. Similar switching behavior has been observed before in CNT FETs without radiation exposure by Liu et al. [33] (Fig. 9). The observed switching behavior is known as random telegraph signal (RTS), is attributed to charge fluctuations in defects at the CNT/ interface or in the near the CNT, and is theoretically modeled by Wang et al. [26]. RTS behavior is in fact somewhat commonly observed in both CNT FET and conventional metal oxide semiconductor MOSFET devices [26]. The associated capture and emission times measured by Liu et al. take an exponential probability distribution (as do the SEE durations here), and are determined by the defect energy, Fermi energy, and the temperature [35]. In this context, the average major SEE duration (measured to be 200 ms in chip 418, device 17) can be interpreted as the emission time for a random telegraph-like system [33], where the emission corresponds to radiation-induced trapped charge being released from the defect. From data showing the emission time versus temperature, the activation energy for the defect can be determined [35]. This work is currently underway. The ability of a single charge to cause large changes in conductance in a single carbon nanotube device is rooted in the 1-di-
mensional nature of electrical transport in CNTs. Charge carriers are not free to route around scattering sites or potential barriers, and the conductance of the entire device is compromised, giving rise to the large changes in conductance of up to several orders of magnitude. This is in contrast with drain current fluctuations in bulk semiconductor devices which are typically less than 1% [35]–[37]. Thus, the CNT channel can be viewed as a series connection of many potential defect sites, with the resistances of each individual defect adding in series. The two types of conductance degradation observed here, “major” and “minor”, may represent two different types of defects being influenced by the radiation. In order to better understand the data presented in Fig. 6, the minor SEEs are modeled as independent, indistinguishable defects switching to a quasi-stable state with some radiationflux-dependent probability . The probability that exactly of defects have switched at any given time is given by (2) The binomial coefficient of possible combinations for
which expresses the number is given by (3)
Thus, we can model the relative peak heights for the quantized states observed in the drain current distribution histogram. Fig. 10 shows the drain current distribution histogram for the CNT shown in Fig. 6 measured at different points in time throughout a long exposure to 50 MeV proton radiation, plotted along with the fitting results from the model for minor SEEs. The time intervals are noted in the figure. The state intensities from the model were mapped to the peak height of Gaussian peaks. For large N (> 10), the distribution shape became dependent only on the product , and so we were unable to extract or independently. The fitting parameters were the product , Gaussian line width, and pristine current level. Defect state current level spacing was held constant for all fits at 5.8 nA. The mean value for the product was found to be 1.40. Throughout the experiment, the product varied
BUSHMAKER et al.: SEEs IN CARBON NANOTUBE-BASED FETs UNDER ENERGETIC PARTICLE RADIATION
(and thus also relative peak height and quantity). In general it rose from 0.63 at the beginning of the experiment to a maximum of 2.2 near the end of the experiment. This could be caused by an increasing number of defects N, or by an increasing switching probability . The proton beam was not very stable, and as a result, the flux varied somewhat over the course of the experiment. Consequently, the probability for radiation-induced defect switching also varied. Before the experiment was started, the current distribution was a single Gaussian-shaped peak centered near from the first data set during radiation exposure. During irradiation, shifts up due to the threshold voltage shift shown in Fig. 2, which increases the drain current level for all gate voltages. After irradiation, the current distribution returned to a nearly Gaussian-shaped peak centered near from the last data set during radiation exposure, however there was some residual RTS-like switching behavior with a small product of 0.04. If this hypothesis is further supported by additional experiments and analysis, the ramifications are that as electronic devices are scaled down to nanometer dimensions, they may become increasingly sensitive to radiation induced switching or charging of individual defects in sensitive areas. Understanding these defects may therefore be a key step in developing nano-electronics for use in the space environment. IV. CONCLUSION In conclusion, single event effects have been measured in isolated single CNT FETs exposed to high-energy proton radiation. The SEEs observed consist of large drops in device current of several orders of magnitude, and smaller, more frequent drops in device current of magnitude, which were quantized in evenly spaced levels up to 6 deep. The current distributions for these smaller SEEs were fit with a statistical model for radiation induced switching of many independent, identical defect states. The drops in current were sudden and discrete, and the degraded current persists much longer than traditional single event effects. Small accompanying threshold voltage shifts were also observed. A hypothesis for radiation induced defect state switching as the root cause of the observed SEE is outlined. ACKNOWLEDGMENT The authors gratefully acknowledge R. Koga, S. Bielat, and J. George for assistance with operation of the LBNL 88” cyclotron. The authors also acknowledge S. Moss, R. Lacoe, and J. Osborn for helpful discussions regarding interpretation of the data. REFERENCES [1] T. Durkop, S. A. Getty, E. Cobas, and M. S. Fuhrer, “Extraordinary mobility in semiconducting carbon nanotubes,” Nano Lett., vol. 4, pp. 35–39, 2004. [2] J. Baumgardner, A. Pesetski, J. Murduck, J. Przybysz, J. Adam, and H. Zhang, “Inherent linearity in carbon nanotube field-effect transistors,” Appl. Phys. Lett., vol. 91, p. 052107, 2007. [3] J. Li, Y. J. Lu, Q. Ye, M. Cinke, J. Han, and M. Meyyappan, “Carbon nanotube sensors for gas and organic vapor detection,” Nano Lett., vol. 3, pp. 929–933, Jul 2003.
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