Gate voltage-dependent magnetoresistance of Zn_0.8Co_0.2O:H

Abstract

The magnetoresistance of a hydrogenated Zn_0.8Co_0.2O film with an inverted thin film transistor structure was measured at 7 K, in magnetic fields up to 3 T in order to verify the magnetoresistance dependency on carrier density. The gate voltage-dependent magnetoresistance was measured between −15 V and 15 V. A large positive magnetoresistance was identified at all gate biases. Changes in positive gate voltage did not result in significant changes in the magnetoresistance; however, an increase in negative gate voltage resulted in an increase in magnetoresistance and zero field resistivity. The magnetoresistance comprises a positive component, as a result of quantum conductivity correction due to the s–d exchange interaction, and a negative component induced by weak localization. The gate voltage-dependence of the positive and negative magnetoresistances was described by the density of states for ZnCoO:H.

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Introduction

ZnO is a promising material for use in semiconductor devices due to its wide band gap (3.4 eV) in the near-ultraviolet (UV) region and its large free-exciton binding energy (60 meV). Many researchers have attempted to measure room-temperature ferromagnetism (RTFM) in transition metal (TM)-doped wide band gap semiconductors, such as ZnO and GaN.^1–4 An abundance of hydrogen impurities is unavoidable in ZnO samples, which influences its electronic and magnetic properties. Hydrogen is thought to be responsible for the n-type conductivity of ZnO.^5,6 Theoretical calculations show that H is a shallow donor in ZnO,⁷ and experimental results indicate that the conductivity of ZnO increases in an H₂ atmosphere.^5–8 The role of hydrogen in enhancing the ferromagnetism of 3d-TM-doped ZnO has been studied experimentally^9,10 and theoretically.^11–13 Although there is much experimental evidence of RTFM in TM-doped ZnO, its origin is unclear; various theories have been suggested.^11,14,15

Magnetoresistance in ZnO systems comprises both positive and negative components, with or without TM-doping.^13,16–18 Negative magnetoresistance (nMR) results from suppression of weak localization, even in strongly localized systems,^19,20 or 3rd order expansion of the spin-exchange Hamiltonian between localized moments and itinerant electrons.^13,21 Positive magnetoresistance (pMR) in TM-doped ZnO and TiO₂ has been attributed to the spin-splitting effect of the conduction band, owing to the strong s–d exchange interaction between carriers and doped TM atoms.^18,22,23 Others have suggested that the pMR is developed in a two band model from the action of Lorentz force on the mobile carriers.^13,24,25

Understanding the origins of MR in TM-doped oxide semiconductors is necessary when solving theoretical issues and designing spintronic devices. In this study, we examined the MR and electrical properties of Co-doped ZnO with various carrier densities.

Carrier density can be controlled through chemical doping methods, such as chemical substitution and intercalation. However, it is difficult to synthesize a variety of samples with precisely controlled doping ratios. Doped elements inherently introduce disorder and may, therefore, introduce an increase in resistivity. Carrier density can also be controlled by an electric field introduced by an applied gate voltage.^26,27 This method is free from disorder. The application of a gate voltage changes the density of carriers; i.e., changes the position of the Fermi energy, and induces carrier accumulation or depletion as a function of the bias. This significant carrier accumulation has led to various achievements in condensed matter physics, such as metal–insulator transitions in ZnO.²⁸

In this work, we report the magnetoresistance of hydrogenated Co-doped ZnO thin films of varying carrier density, by changing the bottom gate at low temperatures. We discuss the transverse magnetoresistance of ZnCoO:H, in which the magnetic field is applied perpendicular to the input current.

Experimental

Using radio frequency sputtering, a 100 nm-thick Co (20 mol%)-doped ZnO film was deposited on a p-type silicon substrate, which was covered with a 100 nm-thick insulating layer of Si₃N₄ (provided by Crystal Bank-NRF2015M3A9B8047340 in Pusan National University). The p-Si substrate and Si₃N₄ layer act as the bottom electrode and the insulating layer of the inverted transistor structure, respectively. During the sputtering process, the substrate temperature was maintained at 300 °C in a high purity (99.99%) Ar atmosphere. To measure magnetotransport, a Hall bar with a 400 μm × 1000 μm channel was fabricated using conventional UV-lithography (Fig. 1), and etched in an NH₄Cl aqueous solution. After defining the Hall bar, the sample was plasma-treated for 1 min in an Ar–H₂ (20 wt%) gas mixture at room temperature to implant hydrogen into the surface of the film (ZnCoO:H).

Fig. 1 (a) A schematic diagram of the Hall bar used in magnetotransport measurements. The Zn_0.8Co_0.2O Hall bars were fabricated on a p-type silicon substrate with a 100 nm-thick layer of Si₃N₄. V_xx was measured with a 1.0 μA channel current and a magnetic field applied perpendicular to the thin film at 7 K. (b) Schematic diagram of the density of states (DOS) of ZnCoO with H captured by the two nearest Co ions. The left (right) curves denote the majority (minority) spin states.

A schematic illustration of the Hall bar used in magnetotransport measurements is shown in Fig. 1(a). The magnetotransport properties of the sample at 7 K were measured using a Physical Properties Measurement System (PPMS-9, Quantum Design), two source meters (Keithley 2425C, 2635A), a nanovoltmeter (Keithley 2182A), and a switcher (Keithley 7001). During the magnetotransport measurements, the magnetic field was swept between −3 T and 3 T, perpendicular to both the sample surface and the direction of the current, with a fixed gate voltage. To eliminate spurious voltages, the magnetoresistance voltage V_xx(H) was calculated by V_xx(H) = ½[V_xx(H) + V_xx(−H)]. The voltage was averaged as the direction of the current was changed for each magnetic field strength. The longitudinal resistivity ρ_xx is defined as , where w, a, and t are the channel width, the distance between the contacts, and the film thickness, respectively. The leakage current was less than 2 nA when the gate voltage was swept, which is much less than the 1 μA that was applied during the measurements.

Fig. 1(b) shows the density of states (DOS) of the hydrogenated ZnCoO. The red and blue colors represent the occupied majority and minority spin states, respectively, and the white color represents the empty states. The localized states that originate from the hybridization of H-s and Co-t_2g orbitals are in the conduction band. The electron mobility can be reduced significantly by the presence of hydrogen, and electrons can be transported by hopping between the localized states.²⁹

Results and discussion

Fig. 2(a) shows the resistivity of the ZnCoO:H Hall bar when the perpendicular magnetic field is swept from −3 T to 3 T. Across this range, the resistivity increased for increasingly negative gate voltages, and decreased slightly when a positive gate voltage was applied. The gate voltage-dependence of the resistivity at 0 T and 3 T is shown in Fig. 2(b). When no magnetic field was applied (0 T), the resistivity decreased by 8.35% from 4.648 Ω cm to 4.260 Ω cm as the gate voltage increased from 0 V to 15 V. The resistivity increased by 37.3% from 4.648 Ω cm to 6.383 Ω cm as the gate voltage decreased from 0 V to −15 V. The Fermi energy is located above the conduction band minimum when V_g = 0, as shown in Fig. 1(b). A positive gate voltage increases the Fermi energy into the region of localized states with lower mobility. Therefore, the resistivity does not increase when the carrier density increases with a positive gate voltage. When a negative gate voltage is applied, the Fermi level is lowered into the delocalized states. The decrease in carrier density is greater than the increase in mobility; thus, the resistivity increases. The resistivity at 3 T shows similar behavior as that at 0 T.

Fig. 2 (a) Resistivity of Zn_0.8Co_0.2O:H as a function of the magnetic field and various gate voltages. The magnetic fields were applied perpendicular to the Zn_0.8Co_0.2O:H film. The solid curves are the result of fitting with eqn (5). (b) Gate voltage-dependence of the resistivity at 0 T and 3 T. The resistivity increased with increase of the absolute value of the negative gate voltage.

The magnetoresistance is defined as where ρ(H) and ρ(0) are the resistivity with and without an applied magnetic field, respectively. A large positive magnetoresistance is shown at each gate voltage, as shown in Fig. 3(a).

Fig. 3 (a) Measured (symbol) and simulated (solid curves) transverse magnetoresistance of Zn_0.8Co_0.2O:H with zero gate voltage. The solid curves are the fitted results using eqn (5). The experimental data for the other gate voltages fitted well to eqn (5), which suggests that there is excellent agreement between the theoretical and experimental MR. The red and blue curves are the pMR and nMR, respectively. (b) Gate voltage-dependence of the magnetoresistance as 3 T. The positive and negative magnetoresistance were calculated using eqn (5), and the fitting parameters in Fig. 4.

The magnetoresistance of ZnCoO:H was studied through the use of a model that considers both negative and positive components. Several groups have observed negative magnetoresistance in ZnO systems, and the mechanism was ascribed to the weak-localization effect.^16,18,20 The field suppression of the constructive interference in weak localization is one possible source of the small negative MR. Owing to the thickness, the film is expected to exhibit three-dimensional (3-D) transport. The negative MR due to the field-suppressed weak localization in 3-D systems can be expressed as follows:^19,20

where L_Th is the dephasing length, and

Fig. 4 (a) Gate voltage dependence of the dephasing length L_TH, (b) the effective mole fraction x_eff, and (c) screening parameter F_σ. The dephasing length L_TH decreased slightly from 3.66 nm to 3.58 nm as the gate voltage decreased from 15 V to 0 V, and then decreased rapidly to 2.19 nm at −15 V. The effective mole fraction x_eff increased slightly with the negative gate voltage. The error bars are calculated for 90% confidence bounds.

An exchange interaction between the s-orbit and d-orbit has been proposed for a large pMR.^16,30 In this model, the pMR arises from the quantum correction of the conductivity on the disorder-modified electron–electron interaction due to the s–d exchange interaction.

The change of conductivity in a 3-D system can be modeled as follows:

where F_σ is a Coulomb interaction screening parameter between 0 and 1, and μ is the electron mobility.

The analytical expression

was introduced by Ousset et al.³¹

The parameter β = [gμ_BH + x_effαN₀SB_S(T, H)]/kT represents the spin-splitting of the conduction band comprising the Zeeman energy gμ_BH and the s–d contribution x_effαN₀SB_S(T, H). Here, the g-factor is given by g = 2, and the s–d exchange energy is αN₀ = 0.2 eV;³² x_eff is the effective magnetic ion mole fraction, and B_S(T, H) is the Brillouin function, in which S = 3/2 for Co²⁺.

The total magnetoresistance is the sum of the negative and positive components, as given by

In the simulation, the fitting parameters were L_Th for nMR, and F_σ and x_eff for pMR.

Eqn (5) well fit the experimental data, as shown in Fig. 2, which suggests excellent agreement between the theoretical and experimental MR behaviors. The fitting parameters for the least square fit are shown in Fig. 4.

The magnetoresistance for each magnetic field with zero gate bias is shown in Fig. 3(a); the red curve is the calculated pMR, which is a product of the quantum correction of the s–d spin splitting on the disorder-modified electron–electron interaction. The blue curve is the nMR due to the suppression of weak localization. The green curve is the magnetoresistance, specifically, the sum of pMR and nMR.

The calculated pMR did not change with gate voltage, as shown in Fig. 3(b). However, the calculated nMR decreased as the gate voltage decreases to −15 V. Because pMR remains constant and nMR decreases, MR also decreases as the gate voltage decreases to −15 V. The fact that pMR stays constant indicates that the gate voltages that were applied were insufficient to change the s–d spin splitting which results pMR.

The gate voltage-dependence of MR at 3 T is shown in Fig. 3(b). The positive and negative MR were calculated from eqn (5), and the fitting parameters in Fig. 4. The magnitude of MR at 3 T increased by 22.9% from 0.310 to 0.381 as the gate voltage was lowered from 0 V to −15 V. The changes in resistivity and MR at 0 T and 3 T are summarized in Table 1. For positive gate voltages, the MR did not change significantly. The gate voltage-dependence of the resistivity and MR were similar, but the change in MR was less significant. When the magnitude of the negative gate voltage increased, nMR was reduced to zero due to electron depletion, and pMR did not change. It was found that metallic Co-doped ZnO showed a negative MR, and insulating Co-doped ZnO samples showed a positive MR. The increase in pMR with decreasing carrier density may be the result of the larger s-d spin splitting effect at lower conduction electron concentrations.¹⁷ This study shows that pMR does not depend on the carrier concentration and an increase in MR is not caused by an increase in pMR, but by a decrease in nMR.

Table 1 Change in resistivity and MR at 0 T and 3 T with respect to zero gate voltage

	ρ (Ω·cm)@0 T	ρ (Ω·cm)@3 T	MR@3 T	pMR@3 T	nMR@3 T
−15 V	6.383 (+37.3%)	8.876 (+45.6%)	0.381 (+22.9%)	0.421 (−2.10%)	−0.04 (−66.3%)
0 V	4.648	6.096	0.310	0.429	−0.118
15 V	4.260 (−8.35%)	5.583 (−8.42%)	0.309 (−0.326%)	0.425 (−0.93%)	−0.116 (−1.69%)

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Conclusions

The magnetoresistance of hydrogenated ZnCoO with different gate voltages at 7 K was studied. It was found that MR increased with negative gate voltage. This increase in MR as the carrier density decreases may be thought as a result of an increase in spin-polarized current at lower conduction electron concentrations which causes positive MR. But, this study shows that an increase in MR is not caused by an increase in pMR, but by a decrease in nMR. The gate voltage dependence of the observed decrease in nMR indicates that the dephasing length decreases, such that the localization effect reduces to zero as the carrier density decreases. This study suggests the possibility of the gate control of MR in the ZnCoO system.

Acknowledgements

This work was supported by the Converging Research Center Program (NRF-2014M3C1A8048820) through the Ministry of Science, ICT and Future Planning (MSIP) and a research program (NRF-2015R1D1A3A01018611) through the Ministry of Education of Korea. C. H. Park acknowledge the support of the research by the National Research Foundation Grant (NRF-2013R1A1A2065742) of the Basic Science Research Program of Korea.

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