Weak Localization and Weak Antilocalization in Double-Gate a-InGaZnO Thin-Film Transistors
Wei-Hsiang Wang, Elica Heredia, Syue-Ru Lyu, Shu-Hao Liu, Po-Yung Liao, Ting-Chang Chang, Pei-hsun Jiang
WWeak Localization and Weak Antilocalization in Double-Gate a-InGaZnO Thin-FilmTransistors
Wei-Hsiang Wang, Elica Heredia, Syue-Ru Lyu, Shu-Hao Liu, and Pei-hsun Jiang ∗ Department of Physics, National Taiwan Normal University, Taipei 116, Taiwan
Po-Yung Liao and Ting-Chang Chang
Department of Physics, National Sun Yat-Sen University, Kaohsiung 804, Taiwan
We demonstrate manipulation of quantum interference by controlling the competitions betweenweak localization (WL) and weak antilocalization (WAL) via variation of the gate voltages of double-gate amorphous InGaZnO thin-film transistors. Our study unveils the full profile of an intriguinguniversal dependence of the respective WL and WAL contributions on the channel conductivity.This universality is discovered to be robust against interface disorder.
Measurements of magnetoconductivity are known tobe a powerful tool to study spin effects.
Weak localiza-tion (WL) refers to constructive quantum interferenceof coherently back-scattered conduction electrons, whichleads to a suppressed conductivity [1].
Weak antilocal-ization (WAL), on the other hand, refers to destructiveinterference due to rotated spins of the waves in the op-posite direction in the presence of spin–orbit coupling(SOC), leading to an enhanced conductivity [2]. WL andWAL have recently been explored in doped ZnO filmsand nanowires because of potential applications in nano-electronics and spintronics [3–10]. Crossovers from WLto WAL have been observed in magnetoconductivity ofInZnO films via temperature variation [7, 9]. However,gate-controlled quantum interference in ZnO or its dopedform was not reported until very recently, when compe-titions between WL and WAL were discovered in single-gate a-IGZO TFTs via electric gating in our previousresearch [11], and an intriguing universal dependence ofthe respective WL and WAL contributions on the chan-nel conductivity was observed [12]. In this paper, moreinformation about this universal dependence is revealedby quantum magnetotransport measurements on double-gate a-IGZO TFTs with higher conductivity. This uni-versal dependence is found to be robust against interfacedisorder, and therefore the conductivity can reliably re-veal the strength of the SOC effect tuned by variation ofa single or multiple gate voltages of spintronic devices.The a-IGZO TFTs with an inverted staggered via-contact structure are fabricated on glass as shown inFig. 1. First, a Mo film was sputtered as bottom gateelectrodes, followed by a SiO x gate insulating layer de-posited by plasma-enhanced chemical vapor deposition(PECVD). Next, a 40-nm-thick a-IGZO channel layerwas sputtered at room temperature with a targetedIn O :Ga O :ZnO atomic ratio of 1:1:1. A SiO x etchingstop layer was then deposited by PECVD at 200 ◦ C. Thevia-contact-type source and drain electrodes were formedby sputtering Mo. A SiO x /SiN x film was deposited as the ∗ E-mail: [email protected]
Glass SubstrateMo (Bottom Gate)Mo (Source) Mo (Drain)IGZOITO top-gateeffective region
SiO x (b)(a) Mo 95 nm
ITO 43 nm
SiO x
360 nm
IGZO 40 nm
SiO x
250 nm
Mo 160 nmSiO x
120 nm
SiN x
100 nm
FIG. 1. (a) Schematic drawing and (b) the TEM image ofthe cross-sectional view of the double-gate a-IGZO thin-filmtransistor. passivation layer using PECVD. Indium-tin-oxide (ITO)electrodes were then formed as the top gates. Finally, thedevice was annealed at 240 ◦ C in an atmospheric oven.Electrical measurements were performed on severaldouble-gate a-IGZO TFTs. Low-temperature measure-ments were conducted with the device mounted in acryogenic system equipped with a superconducting mag-net. Connections to the electrodes are made via wirebonding. The data presented in this paper are collectedfrom a representative sample with a channel width ( W )of 20 µ m and a channel length ( L ) of 10 µ m. Fig. 2ashows I D under a bottom-gate voltage ( V BG ) sweep witha grounded top gate, a top-gate voltage ( V TG ) sweepwith a grounded bottom gate, and a double-gate voltagesweep with V BG = V TG , respectively. Their respectivefield-effect mobilities ( µ ) are displayed in Fig. 2b. Thethree curves on the left in Fig. 2a are taken at roomtemperature with V D = 0 . V BG sweep with V TG = 0, the threshold gate voltage is 1.9 V, the sub-threshold swing is 0.18 V/decade, and µ ∼ . /Vsand I D ∼ . µ A when entering the linear regime. Forthe double-gate voltage sweep, I D behaves similarly tothat under the V BG sweep, but I D and µ at the be-ginning of the linear regime increase to ∼ µ A and ∼ /Vs, respectively. If instead V TG is swept with V BG = 0, I D is much smaller than the other two sweeps,and stays almost constant for V TG >
10 V. The smallconstant I D can be interpreted as the electron-injection-induced diffusion current due to the screening of top-gateelectric field by the redundant source and drain electrodes a r X i v : . [ c ond - m a t . m e s - h a ll ] D ec m ( c m / V s ) V G (V) m ( c m / V s )
297 K V D = V 3.7 K V D = V double doublebottombottomtop -11 -10 -9 -8 -7 I D ( A ) V G (V) -8 -7 -6 -5 -4 s ( e / h )
297 K V D = V 3.7 K V D = V Gate double bottom top 10 -8 -6 -4 s ( e / h ) V BG (V)
34 V V TG = -8 -6 -4 s ( e / h ) V TG (V)
34 V V BG =
15 V (a)(b) (c)(d)
FIG. 2. (a) Drain currents ( I D ) as functions of the bottom-, top-, or double-gate voltages. Room-temperature data aretaken with a drain voltage ( V D ) of 0.1 V, whereas 3.7-K dataare taken with V D = 10 V. The corresponding 2D conductivity( σ ) is appended on the right axis. (b) Respective field-effectmobilities ( µ ) as functions of the gate voltages. µ = dI D /dV G · L/ ( W C ins V D ), where C ins is the insulating-layer capacitancemeasured as functions of the bottom-, top-, or double-gatevoltages, respectively. µ curves at 3.7 K are appended to theright axis. (c) σ at 3.7 K with V D = 10 V as functions of thebottom-gate voltage ( V BG ) at various top-gate voltages ( V TG )of 0, 10, 20, 25, 30, and 34 V, respectively from bottom totop. (d) σ at 3.7 K with V D = 10 V as functions of V TG atvarious V BG of 15, 20, 25, 30, and 34 V, respectively frombottom to top. [13], as illustrated in Fig. 1, leading to an effective lengthof only ∼ T ) of 3.7 K, the threshold gatevoltage is seriously enhanced, and I D is not detectablewith V D = 0 . V D of 10 V is supplied for all 3.7-K measurements to give detectable I D [15]. At 3.7 K, I D increases much more slowly with the gate voltages,as shown in Fig. 2a, and is not even detectable at any V TG below 35 V when V BG = 0 because of the extremelylow diffusion rate of the carriers. µ is only ∼ /Vswhen V TG = V BG = 34 V, and remains higher under thedouble-gate voltage sweep than under the V BG sweep.The seriously suppressed µ at low T can be interpretedin the percolation model for amorphous oxide semicon-ductor TFTs [16, 17]. Shown on the right axis of Fig. 2ais the 2D conductivity ( σ ) given by I D /V D · L/W , and isexpressed in unit of e /h , where h is the Planck’s con-stant.The conductivity ( σ ) at 3.7 K was further measuredunder various combinations of gate voltages. Fig. 2cpresents σ vs V BG at various fixed V TG , whereas Fig. 2dshows σ vs V TG at various fixed V BG . It can be seenthat the two gates control the carriers in the channel invery different manners. In Fig. 2c, all σ curves of differ- (a) (b) B (T) V BG = 20V V BG = 25V ∆ σ V BG = 30V V TG =
10 V 34 V 0.20.10 V TG = 30 V V BG =
20 V
34 V 0.20.10 V TG = 20 V V TG =10V (c)(d) (e) (f) ( x - e / h ) FIG. 3. ∆ σ at 3.7 K as functions of the magnetic field ( B )(a)–(c) at fixed V BG (30, 25, or 20 V) with various V TG of 10,20, 30, and 34 V, respectively from top to bottom, and (d)–(f)at fixed V TG (30, 20, or 10 V) with various V BG of 20, 25, 30,and 34 V, respectively from top to bottom. Theoretical fits(Eq. 1) are shown as solid smooth lines. ent V TG approach an “asymptote” that passes through ∼ − e /h at V BG = 34 V. However, V TG = 34 V,as shown in Fig. 2d, gives much smaller values of σ at various smaller V BG until V BG reaches 34 V to give σ ∼ − e /h . These results reflect the limited effective-ness of V TG .The quantum magnetotransport are investigated at 3.7K with magnetic field ( B ) perpendicular to the channelplane. The representative curves of ∆ σ ( B )( ≡ σ ( B ) − σ (0)) are shown in Fig. 3. Figs. 3a–3c display ∆ σ ( B )at respective fixed V BG with various V TG from 10 V to34 V, whereas Figs. 3e–3f display ∆ σ at respective fixed V TG with various V BG from 20 V to 34 V. In general, ∆ σ curves with higher gate voltages increase with B up to B ∼ .
037 T, demonstrating a WL signature, but thenbend over to WAL and decrease substantially at higher B . The WL and WAL features are suppressed as eithergate voltage is decreased, but with different effectiveness.Fig. 3 shows that varying V BG substantially changes themagnetotransport of the device, whereas varying V TG only tunes it mildly.To assess the respective contributions of WL andWAL for each ∆ σ ( B ) curve, we use the two-componentHikami–Larkin–Nagaoka (HLN) theory for the magneto-conductivity of a 2D system in the limit of strong SOC[2, 18, 19]:∆ σ ( B ) = A (cid:88) i =0 , α i e πh (cid:34) Ψ (cid:32) (cid:96) B (cid:96) φi + 12 (cid:33) − ln (cid:32) (cid:96) B (cid:96) φi (cid:33)(cid:35) , (1)where Ψ is the digamma function, (cid:96) B ≡ (cid:112) (cid:126) / (4 e | B | ) ishalf the magnetic length, the prefactors α and α standfor the weights of WL and WAL, respectively, and (cid:96) φi isthe corresponding phase coherence length. The originaltwo-component HLN equation was proposed for topologi- -8-6-4-20 ∆ σ ( . T ) ( x - e / h ) V TG =34 V30 V20 V10 V0 V–5 V 8004000 σ (0) ( x10 -6 e / h ) -0.4-0.3-0.2-0.10.0 α σ (0) ( x10 -6 e / h ) α (a) (b) V BG = 34 V 30 V 25 V 20 V (c) (d) FIG. 4. ∆ σ (0 . σ (0) (a) at various fixed V TG , and(b) at various fixed V BG . There are duplicate data points in(a) and (b); for example, “+” at σ (0) = 637 × − e /h in(a) and “ (cid:3) ” at the same σ (0) in (b) are the same data pointat V TG = 0 and V BG = 34 V. α (the prefactor for WL) and α (the prefactor for WAL) obtained from the theoretical fits(Eq. 1) at various gate voltages used in (a) and (b) are shownin (c) and (d), respectively. Eye-guiding lines of the universalcurves are shown as solid smooth lines. cal insulator thin films [18, 19]. Owing to the percolationconduction in a-IGZO [16], it is believed that the effec-tive L is much larger and the effective W is much smallerthan the values of the channel dimensions[20, 21]. Thisimplies that the real conductivity is much larger than σ ≡ I D /V D · L/W . Therefore, we add a small coefficient A to the original equation [18, 19] to address this issue.The magnitudes of σ of the double-gate a-IGZO TFTs arefound to be ∼ A is set to 3 × − in this work to roughly compen-sate the difference in sample quality [22]. Eq. 1 providesexcellent fits to all the curves in Fig. 3, which are shownas solid smooth lines.Measurements on the double-gate a-IGZO TFTs withhigher σ (0) ( σ at zero B ) allow us to investigate the evo-lution of the WL and WAL competitions from zero- tohigh-conductivity regimes. In our previous experimenton single-gate a-IGZO TFTs [12], only low-conductivitytransport ( σ (0) (cid:46) × − e /h ) could be studied.Figs. 4a and 4b display ∆ σ (0 . σ (0) to demon-strate that different gate operations may give differ-ent ∆ σ at the same σ (0) and B when σ (0) is large( > × − e /h for the case of B = 0 . σ (0 . V TG as functions of σ (0) achieved by varying V BG , whereas Fig. 4b shows∆ σ (0 . V BG as functions of σ (0)achieved by varying V TG . The values of α and α ob-tained by fitting experimental ∆ σ ( B ) curves at respec-tive gate voltages to Eq. 1 are plotted against σ (0) inFigs. 4c and 4d [23], and each of them surprisingly col- lapses onto a universal curve despite the distinct patternsof ∆ σ (0 . σ (0) obtained from different gate opera-tions shown in Figs. 4a and 4b. α increases rapidly from0 to ∼ σ (0), but then stays around0.1 after the transport passes the threshold. | α | growssubstantially with increasing σ (0), and then slows downto approach ∼ σ (0) gets close to ∼ − e /h .It is noticed that the shape of the universal curve mayvary among devices with different structure fabrications.The single-gate a-IGZO TFTs in our previous experiment[12], for example, never entered the linear regime withinthe V G range studied, and therefore its partial universalcurve of α vs σ (0) did not show any changes in the slope.The values of (cid:96) φi obtained by fitting the experimental∆ σ ( B ) to Eq. 1 fluctuate mildly near 0.1 µ m as V BG or V TG is varied. A closer look at the dependence of (cid:96) φi on | V BG − V TG | reveals that (cid:96) φ decreases from ∼ µ mto ∼ µ m and (cid:96) φ decreases from ∼ µ m to ∼ µ m as | V BG − V TG | is increased from 0 to 54 V. Thisimplies that the transport suffers stronger disorder scat-tering at larger vertical electric fields. In a temperature-dependence measurement, on the other hand, (cid:96) φi is foundto decrease by more than a half when T is increased be-yond 50 K, which weakens the WL and WAL effects. Thedependence of α i on σ (0) also evolves with T [11]. To bet-ter observe WL and WAL, (cid:96) φi should be much larger thanthe elastic scattering length ( (cid:96) e ) and than the spin–orbitscattering length ( (cid:96) SO ) (i.e., the strong SOC limit). Anal-yses on our data at 3.7 K using the original HLN equationwithout the assumption of strong SOC [2, 24, 25] revealthat ( (cid:96) φi /(cid:96) SO ) ∼ ( (cid:96) φi /(cid:96) e ) ranges from ∼
50 to ∼ α and α were theoretically shownto be determined by the ratio of the gap opening at theDirac point to the Fermi energy [18, 19]. The univer-sal dependence of the competing WL and WAL on σ (0)observed in a-IGZO TFT may also find its explanationin the relation between the channel conductivity and thegate-controlled Fermi-level position relative to the bandstructure, but this is yet to be confirmed by theoreticalinvestigations. The a-IGZO TFTs can be used to tunethe SOC effect to a desired weight via electric gating bymonitoring σ (0) thanks to the universal dependence of α i on σ (0). More research is required for future realiza-tion of ZnO-based spin transistors [27] or other spintronicdevices.The double-gate structure offers a better control of thechannel potential [28, 29], and thus allows a more com-prehensive study. When V BG = V TG , the vertical elec-tric field becomes minimal, reducing the interface rough-ness scattering [30]. This explains why V BG = V TG givesthe highest µ as shown in Fig. 2b and the longest (cid:96) φi mentioned previously. However, the universal curves of α i vs σ (0) shown in Figs. 4c and 4d are robust at any | V BG − V TG | regardless of the existence of interface disor-der. This implies that, although WL, WAL, and σ (0) areall known to be affected by disorder [7, 9], the affected σ (0) alone is somehow sufficient to determine the weightsof WL and WAL in the system. More theoretical studiesare needed to fully understand the underlying physics.The resilience of the universal dependence to interfacedisorder should be a great advantage for future sophisti-cated multigate spintronic devices. Once the dependence of α i on σ is determined for a TFT structure with a con-stant a-IGZO channel quality at a constant T , the de-pendence should hold regardless of different strength ofinterface roughness scattering caused by different verticalelectric fields imposed by gate voltages.The work was supported by the Ministry of Scienceand Technology of the Republic of China under GrantNo. MOST 102-2112-M-003-009-MY3. [1] B. L. Altshuler and A. G. Aronov, in “Electron-electronInteractions in Disordered Systems,” edited by A. L.Efros and M. Pollak (Elsevier, Amsterdam, 1985).[2] S. Hikami, I. Larkin, and Y. Nagaoka, “Spin-Orbit Inter-action and Magnetoresistance in the Two DimensionalRandom System,” Prog. Theor. Phys. , vol. 63, no. 2, pp.707–710, Feb. 1980. DOI: 10.1143/PTP.63.707.[3] ¨U. ¨Ozg¨ur, Y. I. Alivov, C. Liu, A. Teke, M. A.Reshchikov, S. Do˘gan, V. Avrutin, S.-J. Cho, and H.Morko¸c, “A comprehensive review of ZnO materials anddevices,”
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