Temperature Dependent Intrinsic Carrier Mobility and Carrier Concentration in Individual ZnO Nanowire with Metal Contacts

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1 Journal of the Korean Physical Society, Vol. 58, No. 2, February 2011, pp Temperature Dependent Intrinsic Carrier Mobility and Carrier Concentration in Individual ZnO Nanowire with Metal Contacts Hwangyou Oh and Ju-Jin Kim Department of Physics and Institute of Physics and Chemistry, Chonbuk National University, Jeonju , Korea Jeong-O Lee Advanced Material Division, Korea Research Institute of Chemical Engineering, Daejeon , Korea Sang Sub Kim Department of Materials Science and Engineering, Inha University, Incheon , Korea (Received 14 December 2010, in final form 20 December 2010) We studied the temperature-dependent electrical transport properties of individual ZnO nanowires with metal contacts. We used temperature dependent gate response curves to obtain the carrier mobility and the carrier concentration of ZnO nanowires as function of temperature; these were estimated from the modified transconductance equation to subtract the unavoidable contact resistance effect. As the temperature was lowered from 300 K, the carrier concentration decreased and the carrier mobility increased until it reached a maximum at 150 K. An increase in the carrier mobility upon cooling occurred due to a decrease in the electron-phonon scattering rate; the scatterings from defects and impurities became dominant at temperatures below 150 K. The intrinsic conduction of the ZnO nanowire itself, neglecting the contact effect, followed the thermal activation process related to zinc interstitials, Zn I, rather than a variable range hopping behavior. PACS numbers: i Keywords: ZnO, Mobility, Nanowire DOI: /jkps I. INTRODUCTION With the progress in analytical technology and device fabrication, the realization of devices with semiconducting nano-materials become popular due to their unique electrical properties and potential to be integrated into nanoscale devices [1 3]. Among those, ZnO nanowires have been receiving much attention because ZnO has a wide and direct band gap of 3.37 ev at room temperature [4]. ZnO is known to have a wurtzite structure with lattice constants of a = Å and c = Å [5]. Its large exciton binding energy (about 60 mev), which is greater than the thermal energy at room temperature, makes it a promising candidate for applications in blue- UV light emission and room temperature UV lasing [6]. Furthermore, its high piezoelectric constant makes it a highly valuable material for fabricating mechanical devices, such as acoustic transducers, sensors, and actuators [7]. The n-type semiconducting property of bulk ZnO is jujinkim@chonbuk.ac.kr known to originate from the non-stoichiometric composition of the crystal Zn 1+δ O (δ < 10 3 ). The Zn excess can be described in terms of a point-defect model as zinc interstitials, Zn I (Frenkel defect), or as oxygen vacancies, V O (Schottky defect). Schottky defect theory, which states that oxygen vacancies V O, as well as zinc vacancies, V Zn, appear and can be doubly ionized in the ZnO lattice, is more established than the Frenkel defect hypothesis [8]. According to the schematic band diagram of vacancy levels in ZnO, proposed by Kröger [9], the first-ionized zinc vacancy forms an acceptor level at 0.7 ev above the valence band while the first-ionized oxygen vacancy makes up a donor level at only 0.05 ev below the conduction band. Based on the point-defect model, the dominant donors for n-type ZnO are usually shallow, with activation energies between 30 and 60 mev [10], and are almost always identified as either V O or Zn I due to crystal growth under a Zn-rich environment [9]. Still, there is much debate regarding the transport mechanism in n-type ZnO because vacancies in ZnO are deep donors [11 13] or because the formation energy of donors is too high to participate in observed conductivity. There are reports that background donors can be

2 -292- Journal of the Korean Physical Society, Vol. 58, No. 2, February 2011 formed by exposure to hydrogen during the growth process [14] and that they can contribute significantly to the conductivity. On the other hand, Zn I can form a complex with nitrogen to form a shallow donor level as well [15]. We studied the detailed temperature dependent transport properties of ZnO nanowire devices. We obtained the net intrinsic values of the carrier mobility and the carrier concentration in ZnO nanowires via the modified conductance equation with contact resistances considered. Finally, we studied the intrinsic transport mechanism of ZnO nanowires by retrieving four-probe resistance data. II. EXPERIMENTAL ZnO nanowire arrays grown on bare Al 2 O 3 (0001) substrates at an O/Zn precursor ratio of 102 were scratched with a sharp experimental tool and ultra-sonicated in vials containing ethanol [16]. A droplet of the nanowire solution was dispersed with a micropipet on a prefabricated chip and blown dry, and this process was repeated until a sufficient density of nanowires had been deposited on the surface. A single appropriate ZnO nanowire was selected with reference to a pre-defined coordinate system by using a scanning electron microscope (SEM). Contact electrodes were patterned via e-beam lithography, followed by evaporation and lift-off. The electrodes were composed of Ni metal, and their thickness was 100 nm. A 50-nm-thick Au metal layer was then deposited successively as a passivation layer. The heavily-doped Si substrate was used as a back gate to control source-drain current. III. CARRIER MOBILITY AND CARRIER CONCENTRATION To investigate the temperature dependent transport properties of a single ZnO nanowire, we fabricated field effect transistors (FETs) with metal electrodes, as shown in inset of Fig. 1(a). When an appropriate voltage V g is applied between the source and gate, majority carriers accumulate at the insulator-semiconductor interface, leading to the formation of a conducting channel between the source and the drain [17]. The standard MOSFET (metal oxide field effect transistor) model can be improved by accounting for the series resistance or the contact resistance at the source and the drain. For this, the voltage drop through the series resistance R s is introduced: I d Z L C iµ (V g V T ) (V d I d R s ) Fig. 1. (Color online) (a) I V characteristics as a function of gate voltage and (b) I-V g transfer characteristics as a function of bias voltage at 280 K under 10 3 Torr. Upper inset: schematic energy band model when a gate voltage V g is applied. Lower inset: SEM image of the ZnO nanowire FET. where Z and L are the channel width and length, respectively, C i is the gate insulator capacitance per unit area and µ is the field-effect mobility. V T is the threshold voltage, which can be deduced from the linearly extrapolated value at the V g axis in the plot of I d versus V g. We used the method described by Jain [18] to remove the series resistance from a device. First, the drain conductance (g d ) and the transconductance (g m ) are estimated as and g d = I d V d = I d = V d (Z/L)C i µ (V g V T ) V d 1 + (Z/L)C i µr s (V g V T ), (2) g m = I d V g (Z/L)C i µv d = [1 + (Z/L)C i µr s (V g V T )] 2. (3) The division of Eq. (2) by the square root of Eq. (3) and some manipulations result in = (Z/L)C i µ (V g V T ) V d 1 + (Z/L)C i µr s (V g V T ), (1) g d L V d = µ(v g V T ) 2. (4) gm Z C i

3 Temperature Dependent Intrinsic Carrier Mobility and Carrier Concentration Hwangyou Oh et al In contrast, at high V d above pinch-off, the drain current is saturated and given by I dsat mz L C iµ(v g V T ) 2, (5) where m is a function of the doping concentration [17]. Therefore, in the saturation region, g m is obtained as follows: g m = I d V g = 2mZ L C iµ(v g V T ). (6) Figure 1 shows the I V characteristics and the I- V g transfer characteristics from Ni/Au contacted device at 280 K, which indicate that ZnO nanowires had n- type semiconductor behavior. As shown in the upper inset of Fig. 1(a), as the gate voltage V g applied to the device becomes increasingly negative, higher contact barriers are established at the interfaces, leading to channel off. The lower right inset of Fig. 1 shows an SEM image of the ZnO nanowire FET used in this experiment. To determine the various temperature-dependent characteristics for a ZnO nanowire FET composed of Ni/Au contact electrodes, we measured the device at temperaturesfrom 1.3 K to 280 K in steps of 10 K. The bias range was -500 mv +500 mv, and the gate voltage range was -10 V +10 V. Figures 2(a) and (b) show the temperature-dependent I V characteristics at V g = 10 V in the bias range of mv and the I- V g transfer characteristics at V d = 500 mv in the gate voltage range of -10 V 10 V to get the characteristic values of the device, such as g d, g m, and V T, at the respective temperatures. Although the lowering of the Schottky barrier made contact barriers less significant at temperatures near room temperature, they were not negligible at low temperatures. As the temperature was lowered to 1.3 K, carriers from the source electrode to the ZnO nanowire experienced the contact barrier due to decreases in their thermal energy. Figure 3 shows the characteristic values obtained from Fig. 2, and the corresponding carrier mobility (µ) and carrier concentration (n) are calculated. As described above, contact barriers were not negligible, so parasitic contact resistances should be taken into consideration. Therefore, Eq. (4) was used to determine the carrier mobilities at the respective temperatures, which can be approximated as g d L gm Vd C = µ(v g V T ) (7) for Z d and C i C/dL. Here, d is the diameter of the ZnO nanowire channel and L is its length. The carrier concentration n is defined as n = C(V g V T ) eπr 2 L, (8) where e is the electronic charge and R is the radius of the ZnO nanowire channel [19]. For cylinders using an Fig. 2. (Color online) (a) I V characteristics at V g = 10 V in the bias range of mv and (b) I-V g transfer characteristics at V d = 500 mv in the gate voltage range of V for temperatures from 280 K to 1.3 K. Inset: semi-log plot of the I-V g transfer characteristics at the corresponding temperatures. infinite plate model, the gate insulator capacitance C is given as C = 2πε 0εL ln(2h/r), (9) where ɛ 0 is the permittivity in vacuum, ɛ is the dielectric constant of the gate insulator, and h is its thickness. Figure 4 shows the carrier mobilities and the carrier concentrations of the device, as obtained from Eqs. (7) and (8). Here, the parametric values of the device were ɛ = 3.9, L = 1.1 µm, d = 130 nm, and h = 300 nm. The carrier concentration decreased upon cooling, as is expected for semiconductor materials. Also, the mobility of the device increased upon cooling until it reached a maximum at 150 K. This increase upon cooling is expected in semiconductors due to a lower electron-phonon scattering rate, caused by the freezing out of phonons and a lower electron-electron scattering rate caused by a decrease in the carrier concentration [17]. Additionally, the semiconductor mobility is expected to decrease, when approaching 0 K as carrier scattering due to the presence of ionized impurities predominates. Yet, the measured val-

4 -294- Journal of the Korean Physical Society, Vol. 58, No. 2, February 2011 Fig. 5. (Color online) Plot of the conductance as a function of temperature. Inset: ln(g d /T ) versus T 1. IV. INTRINSIC TRANSPORT MECHANISM IN ZNO NANOWIRE FET In the case when the transport mechanism follows thermionic emission, the current density is given by [ ( J n = A T 2 exp qφ )] [ ( ) ] Bn qv exp 1. (10) kt kt Fig. 3. (Color online) (a) Conductances at V g = +10 V, along with transconductances at V d = 500 mv. (b) Threshold voltages at V d = 500 mv as a function of temperature. Fig. 4. (Color online) Linear plots of the carrier mobility and the carrier concentration as functions of temperature. Differentiating Eq. (10) with respect to the bias voltage, V, yields [ g d T exp q(φ ] Bn V ), (11) kt where ϕ Bn, k, and q are the bias-voltage-independent barrier height, the Boltzmann constant, and the electric charge of carrier, respectively. The inset of Fig. 6(b) shows the temperaturedependent I V characteristics at V g = 0 V in the ZnO nanowire FET. The conductance was estimated from this plot for qv > 3kT [17]. Figure 5 shows that the conductance decreased exponentially with decreasing temperatures and that the transport mechanism followed thermionic emission at temperatures between 280 K and 160 K. For this thermionic range, plotting the natural logarithm of (g d /T ) against (1/T ) and taking a linear fit to be compared with Eq. (11) yields q(φ Bn V ) k For q = e and k = ev/k, = (12) (φ Bn V ) = mv. (13) ues of n c and µ depended not only on the fundamental semiconductor mobility but also on the device geometry and the contact resistance, making deductions about the relative concentrations of electronic scattering due to phonons and ionized impurities difficult [20]. Consequently, by setting V = 0 V, φ Bn is found to be φ Bn = mv. (14) This value is similar to the value of mv reported for Ga Zn and/or Al Zn, levels which act as surface states

5 Temperature Dependent Intrinsic Carrier Mobility and Carrier Concentration Hwangyou Oh et al Fig. 6. (Color online) Semi-log plots of (a) the contact resistances along with the four-probe resistances and (b) the resistivity of a ZnO nanowire FET as functions of temperature. Inset: I V characteristics at V g = 0 V for temperatures from 280 K to 1.3 K for the ZnO nanowire FET. in ZnO [21]. Also, in the case when there are surface states on a semiconductor, the Fermi level at the interface is pinned to the surface states. Therefore, it can be inferred that there are surface states related to Ga Zn and/or Al Zn levels on the ZnO nanowire FET. On the other hand, in a disordered system, the electrons undergo a variable-range hopping (VRH) process, which gives the following relation between the resistivity ρ(t ) and the temperature T [22]: ρ(t) = ρ 0 exp(t 0 /T ) 1/p, (15) where ρ 0 and T 0 denote material parameters that do not strongly depend on temperature and T 0 is determined by the density of localized states N(E) near the Fermi energy E F. The parameter p depends on the dimensionality of the system: p = 2 for one-dimensional (1D), p = 3 for 2D, and p = 4 for 3D systems. For the case of the thermal activation resistivity, however, the low temperature functional form is ρ(t ) = ρ 0 exp( E/2kT ), (16) where E is the activation energy. Fig. 7. (Color online) Linear plots of (a) ln(ρ NW ) versus T 1 and (b) ln(ρ NW ) versus T 1/2. The insets show the temperature range between 20 K and 140 K. To investigate the relationship between the resistivity of ZnO nanowires and the temperature, we calculated the contact resistances were calculated from the estimated mobilities. The contact resistance R s can be directly derived from Eq. (2) [23], R s = 1 g d L ZµC i (V g V T ). (17) In addition, the two-probe resistance (R 2p ) of any semiconductor device is described as follows: R 2p = R 4p + 2R s = R NW + 2R s, (18) where R 4p = R NW is the four-probe resistance or resistance of the semiconductor device. However, the contact resistance obtained from Eq. (14) includes all parasitic series resistances except for R 4p, the following equation is satisfied, R 4p = R NW = R 2p R s. (19) Accordingly, the resistivity of a ZnO nanowire is approximated from the following equation, along with Eq. (16): R NW = ρ NW L A, (20)

6 -296- Journal of the Korean Physical Society, Vol. 58, No. 2, February 2011 where A is its cross-section. R s, R NW, and ρ NW are plotted as a function of temperature in Fig. 6, which reconfirms that the contact resistance cannot be ignored during estimating the carrier mobility with temperatures. To figure out whether the conduction process of a ZnO nanowire itself is a VRH or a thermal activation process, we used an algebraic method was used on its estimated resistivities and temperatures. In other words, the logarithm of its resistivity and the power of the temperature were determined and then graphed in Fig. 7. Figure 7 shows plots of ln(r NW ) versus T 1 and ln(r NW ) versus T 1/2, respectively. The insets represent the temperature range between 20 K and 140 K, along with a linear fit. The linear fit of Fig. 7(a) reveals that the ZnO NW FET followed the thermal activation process in this range of these temperatures rather than VRH. Comparing Eq. (13) with the slope of the linear fit yields E = mev. This value is similar to the activation energy of 30 mev reported for Zn I, which resides on and in a ZnO NW. Therefore, this thermal activation energy is believed to be related to zinc interstitials, Zn I. V. SUMMARY In summary, we have studied the electrical transport properties of an individual ZnO nanowire with metal contacts. As the temperature was lowered from 300 K, the carrier concentration decreased and the carrier mobility increased until it reached a maximum at 150 K. The increase in the carrier mobility upon cooling was caused by a decrease in the electron-phonon scattering rate; the scatterings from defects and impurities became dominant at temperatures below 150 K. The intrinsic transport of the ZnO nanowire itself, neglecting contact effect, followed the thermal activation process, with an activation energy E = mev, related to the energy level of zinc interstitials, Zn I. ACKNOWLEDGMENTS This work was supported by the Chonbuk National University Research Fund in 2009 and the National Science Foundation of Korea (grant No. R ). REFERENCES [1] Y. Xia, P. Yang, Y. Wu, B. Mayer, B. Gates, Y. Yin, F. Kim and H. Yan, Adv. Mater. 15, 353 (2003). [2] X. Chen, J. Xu, R. M. Wang and D. Yu, Adv. Mater. 15, 419 (2003). [3] J. H. Choy, E. S. Jang, J. H. Won, J. H. Chung, D. J. Jang and Y. W. Kim, Adv. Mater. 15, 1911 (2003). [4] E. Mollwo, Semiconductors: Landolt-Börnstein New Series, edited by O. Madelung, M. Schulz and H. Weiss (Springer, Berlin, 1982), Vol. 17, p. 35. [5] T. Makino, T. Yasuda, Y. Segawa, A. Ohtomo, K. Tamura, M. Kawasaki and H. Koinuma, Appl. Phys. Lett. 79, 1282 (2001). [6] M. H. Huang, S. Mao, H. Feick, H. Yan, Y. Wu, H. Kind, E. Weber, R. Russo and P. Yang, Science 292, 1897 (2001). [7] P. M. Verghese and D. R. Clarke, J. Appl. Phys. 87, 4430 (2000). [8] G. D. Mahan, J. Appl. Phys. 54, 3825 (1983). [9] F. A. Kröger, Chemistry of Imperfect Crystals (Wiley, New York, 1974), Vol. 2, p [10] D. C. Look, D. C. Reynolds, J. R. Sizelove, R. L. Jones, C. W. Litton, G. Cantwell and W. C. Harsch, Solid State Commun. 105, 399 (1998). [11] A. F. Kohan, G. Ceder, D. Morgan and C. G. Van de Walle, Phys. Rev. B 61, (2000). [12] F. Oba, S. R. Nishitani, S. Isotani and H. Adachi, J. Appl. Phys. 90, 824 (2001). [13] S. B. Zhang, S.-H. Wei and A. Zunger, Phys. Rev. B 63, (2001). [14] C. G. Van de Walle, Phys. Rev. Lett. 85, 1012 (2000). [15] Y. V. Gorelkinskii and G. D. Watkins, Phys. Rev. B 69, (2004). [16] J. Y. Park, Y. S. Yun, Y. S. Hong, H. Oh, J. J. Kim and S. S. Kim, Appl. Phys. Lett. 87, (2005). [17] S. M. Sze, Physics of Semiconductor Devices, 2nd ed. (John Wiley & Sons, New York, 1981). [18] S. Jain, IEE Proc. Solid-State Electron Dev. 135, 162 (1988). [19] Z. Fan and J. G. Lu, Appl. Phys. Lett. 86, (2005). [20] J. Goldberger, D. J. Sirbuly, M. Law and P. Yang, J. Phys. Chem. B 109, 9 (2005). [21] H. V. Wenckstern, E. M. Kaidashev, M. Lorenz, H. Hochmuth, G. Biehne, J. Lenzner, V. Gottschalch, R. Pickenhain and M. Grundmann, Appl. Phys. Lett. 84, 79 (2004). [22] N. F. Mott and E. A. Davis, Electronic Process in Noncrystalline Materials, 2nd ed. (Clarendon, Oxford, 1979). [23] G. Horowitz, R. Hajlaoui, D. Fichou and A. E. Kassmi, J. Appl. Phys. 85, 3202 (1999).