RESEARCH ARTICLE www.acsami.org
Asymmetric Contacts on a Single SnO2 Nanowire Device: An Investigation Using an Equivalent Circuit Model Junghwan Huh,†,§ Junhong Na,†,§ Jeong Sook Ha,‡ Sangtae Kim,*,§ and Gyu Tae Kim*,† †
School of Electrical Engineering and ‡Department of Chemical and Biological Engineering, Korea University, Seoul 136-701, South Korea § Department of Chemical Engineering and Materials Science, University of California, Davis, California 95616, United States
bS Supporting Information ABSTRACT: Electrical contacts between the nanomaterial and metal electrodes are of crucial importance both from fundamental and practical points of view. We have systematically compared the influence of contact properties by dc and EIS (Electrochemical impedance spectroscopy) techniques at various temperatures and environmental atmospheres (N2 and 1% O2). Electrical behaviors are sensitive to the variation of Schottky barriers, while the activation energy (Ea) depends on the donor states in the nanowire rather than on the Schottky contact. Equivalent circuits in terms of dc and EIS analyses could be modeled by Schottky diodes connected with a series resistance and parallel RC circuits, respectively. These results can facilitate the electrical analysis for evaluating the nanowire electronic devices with Schottky contacts. KEYWORDS: Schottky contact, asymmetric contact, equivalent circuit, nanowire, electrochemical impedance spectroscopy (EIS), activation energy
1. INTRODUCTION Over the past decade, nanometer-scale one-dimensional functional materials (hereafter nanomaterials) have been of particular interest mainly because these materials often present unique characteristics suitable for a wide variety of advanced device applications, ranging from biomedical/chemical sensors1,2 to optoelectronic devices.3,4 To fabricate such devices, however, nanomaterials should be interconnected with the external circuits so that the inclusion of various junctions and/or contacts in the devices is inevitable. This fact implies that the actual performance of the fabricated devices may not necessarily be determined solely by the characteristics of the nanomaterials. In fact, it has been reported that extra complications (e.g. Schottky barriers) caused by the contacts between the nanomaterial and metal electrodes often becomes substantial, leading to the device performance rather inconsistent with the intrinsic property of the materials.5 On the other hand, because of this reason, it may provide one opportunity to further improve the device performance by manipulating, e.g., the Schottky contacts as recently demonstrated for photovoltaic and sensor devices.69 It is thus critically important to have a precise knowledge of the nature of such contacts and the corresponding electrical behaviors at a fundamental level to better understand the actual device performance and thus to eventually develop nano-scale devices that are more reliable for practical uses. To date, electrical behavior of conventional Si-based electronic devices has been characterized by employing dc-measurement r 2011 American Chemical Society
techniques almost exclusively, whereas analyses using ac-impedance measurements have been rarely reported. One of the advantages of using an electrochemical impedance spectroscopy (EIS) technique over the dc-characterization methods for electrical characterizations is that, in principle, EIS allows for deconvolution of dc resistance into the local resistances that compose the dc resistance, if an appropriate fitting model (i.e., an equivalent circuit model) is available for the analysis.10,11 This means that one can possibly investigate electric characteristics of Schottky contacts in a device directly as well as exclusively using the EIS technique. On the other hand, it is also true that the equivalent circuit models which can accurately represent electrical behavior of the device are rarely available. We previously proposed an equivalent circuit model to describe the change in conduction mechanism at the contact between a Ti/Au electrode and a single individual ZnO nanowire from tunneling to thermionic emission as temperature increases.12,13 In this contribution, we report the results of our investigation on electrical nature of the Schottky contacts which we deliberately fabricated on a single SnO2 nanowire device by using combined dc and EIS analysis. As discussed below, we first developed an advanced equivalent circuit model which precisely reproduces the dc current-voltage(IV) characteristics measured Received: May 16, 2011 Accepted: July 20, 2011 Published: July 20, 2011 3097
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Figure 1. (a) Representative FESEM image of an asymmetric device. A forward bias denotes a positive bias at the gold electrode and a negative voltage applied to Ti/Au contacts. (b) Currentvoltage characteristics of the SnO2 nanowire device with an asymmetric contact. Inset: Energy band diagram of the Schottky contact, indicating that the contact barrier height (0.2 eV) is attributed to the difference between the ΦAu (5.1 eV) and χSnO2(4.9 eV). (c) Room-temperature dV/dI versus 1/I plot for the series resistance model with a forward bias. The linear slope (red solid line) indicates the validity of the equivalent circuit model with a contact barrier. Inset: The equivalent circuit of the device with a contact barrier. (d) IV plots corresponding to the experimental data (black dot) and the simulation data using an equivalent model (red solid line) and the conventional resistance model (black dash line). Inset: The suggested equivalent circuit.
by using a dc technique even at relatively high levels of applied bias (( 200 mV) where the conventional circuit model with which a single diode often fails. More importantly, on the basis of bias-dependent EIS analysis employing the advanced equivalent circuit model newly developed, we for the first time were able to determine the resistance at the Schottky contact separately from the total resistance in the device and thus to gain deeper understanding of the electrical characteristics of such contacts at a fundamental level.
2. EXPERIMENTAL DETAILS Device Fabrication. A detailed method for synthesis of SnO2 nanowires can be found elsewhere.14 The synthesized SnO2 nanowires were suspended in isopropyl alcohol (IPA) by sonication, and then the dispersed nanowire in the solution was dropped onto a Si/Si3N4 substrate with pre-defined probe pads. The probe pads were fabricated by using a photo lithography technique followed by an electron beam evaporation (Cr/Au) process. For the fabrication of the individual nanowire devices, an electron beam lithography technique was applied using an Elphy Quantum, Raith. To make the Ohmic and the Schottky contact on the nanowire device, Ti (20 nm)/Au (100 nm) and Au (120 nm) were deposited on the SnO2 nanowire devices, respectively, using an electron beam evaporation technique followed by a lift-off process. Nanowire and Device Characterizations. The morphology of the nanowire devices was characterized by using a field emission scanning electron microscope (FE-SEM, Philips XL 30). The acceleration voltage was either 5 or 10 kV. The dc current-voltage characteristics were recorded by a source-measure unit (Keithley 236). The EIS analyses were obtained by employing an impedance analyzer (Novocontrol).
3. RESULTS AND DISCUSSIONS Figure 1(a) shows a representative SEM image of a single SnO2 nanowire device with the asymmetric contacts (i.e., one with Ti/Au and the other with Au electrodes) we fabricated (hereafter the device). As clearly demonstrated in Figure S1 in the Supporting Information, the IV characteristics are indeed asymmetric to present more typical rectifying behavior of the device upon applying forward bias when compared with the behavior observed at the reverse bias. It should be noted that the forward bias is defined as a positive voltage applied to the Au and a negative voltage to the Ti/Au contacts. The asymmetric IV characteristics observed are attributed to the dc-bias dependence of the Schottky barrier formed at the Au contact. It is well conceived that a Schottky barrier forms at the contact between a semiconductor and metal to compensate the difference between the electron affinity of the semiconductor (e.g., χSnO2 = 4.9 eV) and the work function of metal (e.g., ΦAu =5.1 eV) as illustrated in the inset of Figure 1b. The IV characteristics in Figure 1b show weak rectifying behaviors. Unlike other significant asymmetric device characteristics, less attention has been paid to the weak rectifying behavior. In fact, the observation of various electrical characteristics in seemingly identical one-dimensional nanostructures is not rare. Although it is essential to deal with the case of different behaviors to elucidate the nature of electrical contacts, the weak rectifying behavior of the asymmetric contact has been rarely reported. Herein, we report a combined study of dc and EIS on asymmetric contacts fabricated on a single nanowire device with the weak rectifying behavior. It is realized from Figure 1b that the current level measured at the reverse bias is relatively higher compared with those previously reported for such asymmetric contacts,15,16 implying that the doping concentration in the SnO2 nanowire used in the device is 3098
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relatively higher: According to the thermionic emission (TE) theory in the reverse direction and the image force lowering effect for Schottky barriers, the correlation between the current density (J), and the doping concentration (ND) can be described by the following equation8,17 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3ffi! 4 q7 ND ðV þ Φbi kB T=qÞ=8π2 εS Jreverse ¼ JS, TE exp kB T ð1Þ qΦEB JS, TE ¼ AT 2 exp kB T
ΦEB
rffiffiffiffiffiffiffiffiffiffi qE ¼ ΦIB 4πεS
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! u u2qND kB T t V þ Φbi E¼ q εS
ð2Þ
ð3Þ
ð4Þ
where A* is the effective Richardson constant, ΦEB the effective barrier height, ΦIB the ideal barrier height without the image force lowering effect, E the maximum electric field at the Schottky junction, εS the dielectric constant of the SnO2 nanowire, ND the doping concentration of the tin oxide nanowire, V the bias voltage, and Φbi the built-in potential. According to above equations, J should be in proportion to ND so that the current flow at the reverse bias is expected to increase with the increase of ND in the SnO2 nanowires. ND in the SnO2 is estimated to be 4.61018/cm3 (see the Supporting Information for details) and indeed higher than the typical values of 1.5 1014/cm3 previously reported, as we suspected.18 A device with a Schottky barrier at the contact exhibits rectifying characteristics which have typically been modeled using a single diode circuit (Figure 1b). The current, I, through a diode can be given by eq 5 qV ID ¼ ID0 exp ð5Þ ηkB T where ID0 and η denote the saturation current and the ideality factor, respectively. On the other hand, it is worth pointing out that the results of the fits using eq 5 are often dissatisfactory at relatively higher biases, leading to substantial errors in η. We speculate that such inconsistency at the high biases may result from the fact that the conventional diode model focuses only on the rectifying behavior of the junction, neglecting additional invariant (i.e., bias-independent) resistance which may exist at the contact as well as in the channel of the device. To verify such a hypothesis, we construct an alternative circuit model which includes a resistor connected to a diode in series that concerns such resistance.19 According to this model, the applied voltage to the circuit is now shared between the resistor and the diode. Equation 5 should then be modified to yield eq 6. ηkB T I ln V ¼ IR þ q I0
ð6Þ
By differentiating eq 6, one can yield dV ηkB T ¼R þ dI qI
ð7Þ
In view of eq 7, dV/dI should be linearly proportional to I1, and the expected linear behavior is indeed confirmed by Figure 1c. Although such a relationship is also expected from the conventional diode model (see eq 2), eq 7 results in a much better fit (see fitting errors indicated in Figure 1d) and thus these results clearly verify our hypothesis. The ideality factor, ηD1 and the serial resistance, RS1, determined from the linear fit of Figure 1c using eq 7 are 2.71 and 190 kΩ, respectively. It is noted that the value of the ηD1 (2.71) now is reduced from that (3.03) determined using the conventional diode model. It is realized from Figure 1d that the IV curve measured at the reverse bias also presents a rectifying behavior. Hence for the complete fitting, it is necessary to construct a back-to-back circuit model (see the inset in Figure 1d). From the best fit using eq 7, the ηD2 and the RS2 on the reverse bias were determined to be 2.67 and 424 kΩ, respectively. The ηD2 is nearly identical to ηD1, whereas RS2 is found to be greater than RS1. As mentioned above, EIS allows for deconvolution of dcresistance into the local resistances that comprise the dc-resistance. The total resistance (in the circuit model we proposed (Figure 1d) consists of the resistance at the contact and that in the channel. To investigate the local electrical properties exclusively and to check the applicability of our equivalent circuit model of the asymmetric contact device, we analyzed impedance spectra (Nyquist plot or ColeCole plot) of the device measured at a frequency range of 1 to 1 106 Hz with an ac amplitude of 0.03 V under both nitrogen (N2) and 1% oxygen (1% O2, balanced N2) ambient atmospheres as a function of temperatures (20100 °C). Figure 2a exhibits the Nyquist plots of the SnO2 nanowire device under both the 1% O2 and the N2 environments, respectively. The diameter of each semicircular arc that corresponds to the total impedance of the Nyquist plot reduces as the temperature increases, implying that the conductance in the semiconducting nanowire increases with increasing temperature. It should be noted that the impedance in the device depends on not only the temperature but also the oxygen partial pressure of ambient gas. In the oxygen-rich environment, the width of the Schottky barriers in the SnO2 nanowire becomes wider since the oxygen molecules absorbed on the surface of the nanowire can trap the electrons in the vicinity of the surface1,20 (see below for the details). As a result, the impedance of the nanowire becomes higher under the 1% O2 compared with that in N2. The thermal activation energy can be determined from the slope of the Arrhenius plot of the impedance measured as a function of temperature, as shown in Figure 2b.10 The functional form of the thermal activation energy is given by Ea RðTÞ ¼ R0 exp ð8Þ kB T where kB denotes the Boltzmann constant, and Ea the activation energy. The Ea of the conduction in the SnO2 nanowire under N2 environment was determined to be about 46.3 meV, which is consistent with the value previously reported.1 On the other hand, the value of the Ea estimated under the 1% O2 was found to be greater (79.3 meV). Such high Ea may be attributed to the interactions between the oxygen molecules and the surface of the nanowire. The adsorbed oxygen leads to take electrons from 3099
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Figure 2. (a) Impedance spectra of the SnO2 nanowire device with an asymmetric contact at various temperatures (20100 °C) under the nitrogen or the 1% oxygen (inset) ambient. Numbers (0, 4, and 6) indicate the index of the frequencies in a logarithmic scale. (b) Arrhenius plot of the resistance at different temperatures under the nitrogen (black square dot) and the 1% oxygen (red circle dot) ambient. The slopes with a linear fit denote the activation energy (Ea) of the device under the different ambient.
the nanowire, so the shallow donor states are depleted by the oxygen chemisorptions while the oxygen gas is absorbed into the sample.20 The increasing tendency of Ea is similar to the result for the individual SnO2 nanowire device without the Schottky contact.1 Note that Ea of the asymmetric contact device shows the same value or the similar tendency although our devices have the Schottky contact. This result suggests that the activation energy depends on the donor states in the nanowire rather than on the contact barrier. To determine the effect of the Schottky contact in terms of the EIS analysis, we measured the impedance spectra of the device under identical conditions with different dc biases. Figure 3a shows the representative ColeCole plots of the device with different dc biases (from 0.3 to 0.3 V) under 1% O2 environment at T = 20 °C. A dc bias induces the change in the impedance
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Figure 3. (a) Nyquist plots of the device with a DC bias from -0.3 to 0.3 V under the 1% oxygen ambient. Numbers (0, 4, and 6) denote the index of the measured frequencies in a logarithmic scale. Inset: 1/C2 versus DC bias voltage (V) for the device in nitrogen and 1% oxygen at room temperature. (b) Impedance spectra corresponding to the experimental data (black square dot) and the simulation data (red solid line) obtained from the suggested equivalent circuit model in the nitrogen ambient at room temperature. Upper inset: The plots of the best fit of the capacitance as a function of the bias voltage. The connected solid lines are only for guidance. Lower inset: The equivalent electrical circuit model composed of the two serially connected R//Cs.
by modulating the height or the width of the Schottky barrier at the contact. As analyzed before, the Schottky barrier is subject to the thermionic emission theory so that the barrier height, in terms of the bias voltage, can be explained by the image force lowering effect.17,21 The effective Schottky barrier height (ΦEB) is lowered with the increase of the bias voltage, so that the current density 3100
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Table 1. Equivalent Circuit with the Best Fitting Values (R1, R2, C1, and C2) from the Impedance Spectra and dV/dI in Terms of DC Analysis Under the N2 Ambient Condition Vbias (V) R1 (kΩ) C1 (pF)
R2
C2 (pF)
R1 + R2
Table 2. Equivalent Circuit with the Best Fitting Values (R1, R2, C1, And C2) from the Impedance Spectra and dV/dI in Terms of DC Analysis under the 1% O2 Ambient Condition
dV/dI
Vbias (V)
R1
C1 (pF)
R2
C2 (pF)
R1 + R2
dV/dI
0
464
86.3
1.61 MΩ
88.7
2.07 MΩ
0
1.69 MΩ
6.90
1.00 MΩ
87.8
2.69 MΩ
0.1
456
78.6
914 kΩ
83.8
1.37 MΩ 1.39 MΩ
0.1
1.52 MΩ
6.81
664 kΩ
83.1
2.18 MΩ 2.17 MΩ
0.1
424
72.3
1.01 MΩ
127
1.43 MΩ 1.49 MΩ
0.1
1.51 MΩ
6.57
737 kΩ
149
2.25 MΩ 2.31 MΩ
0.2
307
53.2
231 kΩ
235
538 kΩ
585 kΩ
0.2
1.16 MΩ
6.43
366 kΩ
298
1.53 MΩ 1.46 MΩ
0.2 0.3
334 221
56.9 46.4
485 kΩ 101 kΩ
192 617
819 kΩ 322 kΩ
820 kΩ 315 kΩ
0.2 0.3
957 kΩ 782 kΩ
8.02 6.88
713 kΩ 325 kΩ
81.9 97.3
1.67 MΩ 1.67 MΩ 1.11 MΩ 1.11 MΩ
0.3
280
46.7
319 kΩ
371
599 kΩ
586 kΩ
0.3
1.1 MΩ
6.19
372 kΩ
266.3
1.47 MΩ 1.34 MΩ
increases in accordance with the above eqs 24. Therefore, the impedance has the largest value at a zero bias, as shown in Figure 3a. On the other hand, the impedance at the applied reverse bias has a larger value than that of the forward bias, which can be attributed to an asymmetric contact configuration and to an increase of the depletion width. When a reverse bias is applied to the Au electrode, the width of the depletion layer will increase, whereas it is suppressed at the forward junction (Ti/Au electrode).22 The widening of the depletion layer at the Au electrode will impede the conductance of the SnO2 nanowire, leading to an asymmetric behavior. For the same reason the ColeCole plots under the N2 ambient condition also show the bias dependence. It is well-known that the relationship between the capacitance depending on the depletion layer and the bias voltage in a Schottky diode is as follows ! 1 2 kB T Vbi V ¼ ð9Þ C2 ðqεS ε0 A2 ND Þ q where εS is the dielectric constant of tin oxide, εo the permittivity of the vacuum, A the area of the metal contacts, ND the carrier concentration, Vbi the built-in potential, kB the Boltzmann constant, and V the applied external bias.17 The inset of Figure 3a exhibits a linear correlation between 1/C2 and V, which follows eq 9 well. As shown in this figure, the capacitance of the device is varied by two variable factors: one is the width of depletion layer at the Schottky junction depending on the bias voltage and the other is that of the channel which can be affected by ambient gas (N2 and 1% O2). Note that the variation of the capacitance caused by the gas is greater than that caused by the external bias. This result strongly suggests that the electrical equivalent circuit has to include two capacitors to explain the impedance in the nanowire electronic devices. As discussed earlier, the equivalent circuit used for the AC analysis can be modeled by a scheme considering two series of RC parallel circuits, as depicted in Figure 3b. Each impedance spectrum of the device can be well-fitted on the basis of the equivalent circuit model. The values of the variable parameters were determined by the best fit (see Tables 1 and 2, including the dV/dI terms). In view of the fact that the ac signal is superimposed on the dc level, the total resistance (R1 + R2) has to be identical to the inverse of the slope of the tangent in the IV characteristics at a certain dc bias. It should be noted that the values of the total resistance of the AC analysis are consistent with those of the dV/dI determined by the DC analysis. Interestingly, C2 depends on the applied bias, whereas C1 is less sensitive to it. To better understand this observation, we assumed
that C1 corresponds to the capacitance of the channel and C2 corresponds to the Schottky junction of the SnO2 nanowire. If this is correct, then the values of C1 measured under the N2 ambient should be larger than that measured under the 1% O2, because of the depletion region being enhanced by adsorption of oxygen molecules on the nanowire surface. The C1 value in Table 1 is about 10 times greater than that in Table 2. On the other hand, the C2 values do vary much regardless of the ambient gas. Therefore, the decrease in C1 values under 1% oxygen environment confirms the widening of the depletion layer due to the decrease in the carrier concentration in the channel. These results clearly demonstrate that indeed the equivalent circuit model should be composed of both the channel and the Schottky contact parts.
4. CONCLUSIONS Individual SnO2 nanowire devices with asymmetric contacts have been thoroughly studied through dc measurements and EIS analyses. Electrical behaviors at the Schottky contact vary sensitively owing to variations of the Schottky barrier height or width, which is demonstrated using dc measurements and EIS analyses at various temperatures and atmospheres (N2 and 1%O2). Through the atmospheres experiments, on the other hand, it is found that Ea of the SnO2 nanowire device depends on the donor states in the nanowire rather than on the Schottky contact. We found that the relevant equivalent circuits in terms of dc and EIS analyses can be equivalent to a back-to-back diode model connected with a series resistance and to two series of RC parallel circuits, respectively. The model and the analysis can be utilized for the evaluation and the simulation on the potential performance of an asymmetric contact device at the fundamental device level. ’ ASSOCIATED CONTENT
bS
Supporting Information. Representative IV characteristics of a single SnO2 nanowire device with the asymmetric contact; Determination of dopant concentration (ND); output and transfer characteristics of a SnO2 nanowire FET with a symmetric contact device. This material is available free of charge via the Internet at http://pubs.acs.org/.
’ AUTHOR INFORMATION Corresponding Author
*Tel: +82-2-3290-3250 (G.-T.K.); +1-530-754-2254 (S.K.). E-mail:
[email protected] (G.-T.K.);
[email protected] (S.K.). 3101
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’ ACKNOWLEDGMENT This research was supported by the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0083380, 2005-2002369, R012008-000-20185-0 and WCU, R32-2008-000-10082-0). ’ REFERENCES (1) Kolmakov, A.; Zhang, Y. X.; Cheng, G. S.; Moskovits, M. Adv. Mater. 2003, 15, 997. (2) Kong, J.; Franklin, N. R.; Zhou, C. W.; Chapline, M. G.; Peng, S.; Cho, K. J.; Dai, H. J. Science 2000, 287, 622. (3) Chen, Z. H.; Appenzeller, J.; Lin, Y. M.; Sippel-Oakley, J.; Rinzler, A. G.; Tang, J. Y.; Wind, S. J.; Solomon, P. M.; Avouris, P. Science 2006, 311, 1735. (4) Duan, X. F.; Huang, Y.; Cui, Y.; Wang, J. F.; Lieber, C. M. Nature 2001, 409, 66. (5) Jeon, D. Y.; Kim, K. H.; Park, S. J.; Huh, J. H.; Kim, H. Y.; Yim, C. Y.; Kim, G. T. Appl. Phys. Lett. 2006, 89, 023108. (6) Chen, C. X.; Lu, Y.; Kong, E. S.; Zhang, Y. F.; Lee, S. T. Small 2008, 4, 1313. (7) Wei, T. Y.; Yeh, P. H.; Lu, S. Y.; Lin-Wang, Z. J. Am. Chem. Soc. 2009, 131, 17690. (8) Hu, Y.; Zhou, J.; Yeh, P. H.; Li, Z.; Wei, T. Y.; Wang, Z. L. Adv. Mater. 2010, 22, 3327. (9) Yeh, P. H.; Li, Z.; Wang, Z. L. Adv. Mater. 2009, 21, 4975. (10) Barsoukov, E.; Macdonald, J. R. Impedance Spectroscopy: Theory, Experiment, and Applications, 2nd ed.; John Wiley & Sons: Hoboken, NJ, 2005. (11) Huh, J.; Kim, G. T.; Lee, J. S.; Kim, S. Appl. Phys. Lett. 2008, 93, 042111. (12) Lee, S.; Yu, Y.; Hwang, S.; Ahn, D. International Conference on Nanoscience and Nanotechnology; Gwangju, South Korea; American Scientific Publishers: Stevenson Ranch, CA, 2006, p 4089. (13) Yim, C. Y.; Jeon, D. Y.; Kim, K. H.; Kim, G. T.; Woo, Y. S.; Roth, S.; Lee, J. S.; Kim, S. 4th International Conference on Advanced Materials and Devices/6th Symposium on the Nano-Technology and Plasma Application for Next Generation Processing; Jeju, South Korea; Korean Physical Society: Seoul, South Korea, 2005; p 1565. (14) Kim, D.; Kim, Y. K.; Park, S. C.; Ha, J. S.; Huh, J.; Na, J.; Kim, G. T. Appl. Phys. Lett. 2009, 95, 043107. (15) Lu, C. G.; An, L.; Fu, Q. A.; Liu, J.; Zhang, H.; Murduck, J. Appl. Phys. Lett. 2006, 88, 133501. (16) Yang, M. H.; Teo, K. B. K.; Milne, W. I.; Hasko, D. G. Appl. Phys. Lett. 2005, 87, 253116. (17) Sze, S. M. Physics of Semiconductor Devices, 2nd ed.; Wiley: New York, 1998. (18) Liu, Z. Q.; Zhang, D. H.; Han, S.; Li, C.; Tang, T.; Jin, W.; Liu, X. L.; Lei, B.; Zhou, C. W. Adv. Mater. 2003, 15, 1754. (19) Kim, G. T.; Muster, J.; Burghard, M.; Roth, S. Symposium on Nanophase and Nanocomposite Materials IV held at the 2001 MRS Fall Meeting; Boston; Komarneni, S., Parker, J. C., Vaia, R. A., Lu, G. Q., Matsushita, J. I., Eds.; Materials Research Society: Warrendale, PA, 2001; p 505. (20) Park, C. O.; Akbar, S. A. J. Mater. Sci. 2003, 38, 4611. (21) Nam, C. Y.; Tham, D.; Fischer, J. E. Nano Lett. 2005, 5, 2029. (22) Xu, J. H.; Wu, N. Q.; Jiang, C. B.; Zhao, M. H.; Li, J.; Wei, Y. G.; Mao, S. X. Small 2006, 2, 1458.
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