Length-Dependent Electronic Transport Properties of the ZnO ... - MDPI

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Length-Dependent Electronic Transport Properties of the ZnO Nanorod Baorui Huang 1,2 , Fuchun Zhang 2 , Yanning Yang 2 and Zhiyong Zhang 1, * 1 2

*

School of Information Science Technology, Northwest University, Xi’an 710127, China; [email protected] School of Physics and Electronic Information, Yan’an University, Yan’an 716000, China; [email protected] (F.Z.); [email protected] (Y.Y.) Correspondence: [email protected]; Tel.: +86-135-7296-6755

Received: 23 November 2018; Accepted: 27 December 2018; Published: 31 December 2018

Abstract: The two-probe device of nanorod-coupled gold electrodes is constructed based on the triangular zinc oxide (ZnO) nanorod. The length-dependent electronic transport properties of the ZnO nanorod was studied by density functional theory (DFT) with the non-equilibrium Green’s function (NEGF). Our results show that the current of devices decreases with increasing length of the ZnO nanorod at the same bias voltage. Metal-like behavior for the short nanorod was observed under small bias voltage due to the interface state between gold and the ZnO nanorod. However, the influence of the interface on the device was negligible under the condition that the length of the ZnO nanorod increases. Moreover, the rectification behavior was observed for the longer ZnO nanorod, which was analyzed from the transmission spectra and molecular-projected self-consistent Hamiltonian (MPSH) states. Our results indicate that the ZnO nanorod would have potential applications in electronic-integrated devices. Keywords: zinc oxide (ZnO) nanorod; transmission spectrum; transport properties; molecular-projected self-consistent Hamiltonian (MPSH); current–voltage (I–V) curves

1. Introduction In the past decade, the research on ZnO materials has received sustained and high attention owing to its unique electrical properties, which include a wide band gap (3.37 eV), high excitation binding energy (60 meV), and large piezoelectric coefficient at room temperature [1–4]. ZnO has been demonstrated as the most promising application for electric devices. Among these ZnO nanostructures, ZnO nanorods (NRs) are the most important nanostructures. Its high surface-to-volume ratio [5], easy to fabricate [6–8], and one-dimensional carrier transport make it suitable for developing high performance nanoelectronic and optoelectronic devices [9–11], such as piezoelectric nanogenerators [12], solar cells [13,14], light emitting diodes (LED) [15], Schottky diodes [16], field effect transistors (FET) [17,18], ultraviolet sensors [19,20], and spintronics devices [21]. Moreover, the movement of electrons in a nanorod is confined to two directions, thus allowing the electron motion in one direction, leading to quantum effect. Therefore, a nanorod also shows dramatic quantum size effect, which results in large variation in electrical, chemical, and mechanical properties of the nanorod as compared to its bulk materials. Quantum effects are closely related to the axis orientation, diameter, and length of the material. The length dependence of transport properties is also widely discussed [22–24]. Zhou et al. [25] studied the quantum length dependence of conductance in oligomers and declared that Ohm’s law is not valid for the molecular conductance anymore. Lang et al. [26] performed first principle calculations of transport properties of carbon atom wires and found a conductance oscillation with respect to the number of carbon atoms. Garcia and Lambert [27] studied molecular wire with density functional theory (DFT) combined with the Micromachines 2019, 10, 26; doi:10.3390/mi10010026

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non-equilibrium Green’s function (NEGF) calculation method, and reported that the conductance is almost independent of molecular length and exhibits negative differential resistance. Hu et al. [28] reveal length dependences of the rectification ratio in organic co-oligomer. The length dependence of characteristics shows us wonderful physical phenomena, such as conductance oscillation, negative differential resistance, rectification, and so on. We are curious about the length-dependent electronic transport properties of the ZnO nanorod. Furthermore, the physical properties of a device based on the ZnO nanorod are closely related to the electron transport of the ZnO nanorod. Understanding the length-dependent transport properties of the ZnO nanorod is of great significance for the preparation of electronic devices based on the ZnO nanorod. In this paper, we concentrated on the transport behaviors of Au-ZnONR-Au nanodevice by the DFT combined with the NEFG method. We investigate the electronic and transport properties of the triangle ZnO nanorod, which is rigidly coupled between two semi-infinite linear Au atoms. Similarly, the two-probe systems have been successfully used for the description of nanotubes [29]. The current–voltage (I–V) curve of the Au-ZnONR-Au device under the bias voltages from −1.50 V to 1.50 V is obtained. The obvious metal-like behavior and rectification characteristics are observed and analyzed. 2. Structure Model and Theoretical Method Here we present an Au-ZnONR-Au nanodevice model, as shown in Figure 1. The system we studied was a typical two-probe open system, which was divided into three parts: left electrode, scattering region, and right electrode. Our central region consisted of the triangle ZnO (0001) nanorod and an electrode extension that ensured a smooth transition between the potential of the central region and electrodes. The length of the ZnO nanorod was labeled by the number of unit cells, and the length and diameter of the unit cells were 5.21 Å and 7.70 Å, respectively. The Au-ZnONR-Au nanodevice with n unit cells was named as n-ZnONR. In Figure 1, the left electrode directly couples the zinc atoms at the terminal of the nanorod form Au-Zn contact and the right electrode directly couples the oxygen atoms at the terminal of the nanorod form Au-O contact. The distance between the nanorod and the electrode was fixed to be a constant for all the n-ZnONR devices. The coupling surface distances of Au-Zn and Au-O were set to be 2.4 Å and 1.9 Å, respectively. The values were obtained from total energy optimization, and the binding energy between the ZnO nanorod and Au surface could be defined as: Ebinding = Etotal [ZnONR + Au] − Etotal [ZnONR] − Etotal [Au] (1) The coupling surface distances of Au-Zn and Au-O were varied from 1.5 Å to 3.5 Å with a minimal step of 0.2 Å, respectively. Then, according to the lowest energy principle, it could determine the value of the coupling surface distance. This method is widely used to fix the electrode contact distance of one-dimensional nanodevices, including boron nitride nanotubes [30], ZnO nanotubes [31], and phenylene vinylene oligomere molecule systems [32]. All our calculations were carried out using the Virtual Nanolab Atomistix ToolKit (VNL-ATK, 2015.1, Synopsys, Inc., Mountain View, CA, USA) calculation package [33], which is based on the basis of the first-principles DFT combined with the NEGF formalism. Within the NEGF formalism, the current that passes through the central region at a finite bias voltage can be computed using the Landauer–Büttiker formula [34–36]: 2e I(V) = h

Z µR

dE[ f L ( E − Vb ) − f R ( E − Vb )] T ( E, Vb )

(2)

µL

where µL and µR are the electrochemical potentials of the two electrodes, and T(E, Vb ) is the transmission coefficient at energy E and bias voltage Vb . The transmission coefficient determines


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the probability of electrons transferring between the two semi-infinite electrodes. The transmission spectrum is calculated by the standard equation: T ( E, Vb ) = T r [Γ L ( E, Vb ) G ( E, Vb )Γ R G † ( E, Vb )

i


(3) 3 of 9

where G is the retarded Green’s function of the contact region, ΓL/R is the coupling matrix. Theequilibrium equilibriumconductance conductance(G) (G)ofofthe thetwo-probe two-probedevice devicewas wasevaluated evaluatedbybythe thetransmission transmission The coefficients [37]. coefficients [37]. 2 2e2𝑒 2 G= T E , V = 0 V (4) f b (4) 𝐺 =h 𝑇 (𝐸𝑓 , 𝑉𝑏 = 0 V) ℎ InIn our the ofofallallthe ourcalculations, calculations, thewave wavefunctions functions theatoms atomswere wereexpanded expandedbybydouble-zeta double-zetapolarized polarized (DZP) (DZP)basis basisset. set.The Theelectrostatic electrostaticpotentials potentialswere werecomputed computedon ona areal realspace spacegrid gridwith witha amesh meshcutoff cutoff energy of 75 hartree. The exchange correlation potential was approximated by the Perdew–Zunger energy of 75 hartree. The exchange correlation potential was approximated by the Perdew–Zunger parameterization 100 k-point was used in the parameterizationofoflocal localdensity densityapproximation approximation (LDA). (LDA). The The 11 ××11×× 100 k-point was used in the x, y, x,and y, and z direction, respectively. Note that the z direction is the direction of electron transport. z direction, respectively. Note that the z direction is the direction of electron transport. The The temperature of the electrodes to 300 K.vacuum A vacuum region ofleast at least Å was added to temperature of the electrodes waswas set set to 300 K. A region of at 10 Å10was added to void void interaction of adjacent nanorods. the the interaction of adjacent nanorods.

(a)

(b)

Left electrode

Right electrode Central region

Scattering region Right electrode extension

Left electrode extension (c)

Figure Schematic the two-probe device structure model. The x–y plane unit cell. The Figure 1. 1. Schematic ofof the two-probe device structure model. (a)(a) The x–y plane of of thethe unit cell. (b)(b) The z–y plane the unit cell.(c)(c)The Theshadow shadowareas areasatatthe theends endsofof the model indicatethe the left and right z–y plane ofof the unit cell. the model indicate left and right electrodes, channel length is indicated by the number of unit ofZnO the ZnO (ZnOand O atoms electrodes, thethe channel length is indicated by the number of unit cellscells of the (Zn and atoms are are denoted withand grayred, andrespectively). red, respectively). denoted with gray

3.3.Results Resultsand andDiscussions Discussions 3.1. Transport Properties under Zero Bias Voltage 3.1. Transport Properties under Zero Bias Voltage We firstly discuss the transport properties of the length-dependent ZnO nanorod at equilibrium. We firstly discuss the transport properties of the length-dependent ZnO nanorod at equilibrium. Taking the n-ZnONR (n = 4, 6, 8, 10) device as an example, we calculated the transmission spectrum Taking the n-ZnONR (n = 4, 6, 8, 10) device as an example, we calculated the transmission spectrum of the device with different channel lengths, as shown in Figure 2. It can be observed that there of the device with different channel lengths, as shown in Figure 2. It can be observed that there were were many transmission peaks in the energy range, which means multiple intrinsic transmission many transmission peaks in the energy range, which means multiple intrinsic transmission channels channels existed in this energy region. However, there was a different phenomenon near the Fermi existed in this energy region. However, there was a different phenomenon near the Fermi level; the level; the transmission spectrum near the Fermi level was not equal to zero in Figure 2a,b and was transmission spectrum near the Fermi level was not equal to zero in Figure 2a,b and was zero in zero in Figure 2c,d. To explain this phenomenon, we consider that the transmission value near the Figure c,d. To explain this phenomenon, we consider that the transmission value near the Fermi level Fermi level may be formed by direct tunneling from one electrode to the other. So we removed the may be formed by direct tunneling from one electrode to the other. So we removed the ZnO nanorod ZnO nanorod from the two-probe system model and calculated the direct tunneling between the two from the two-probe system model and calculated the direct tunneling between the two electrodes at electrodes at varying distances. When the distance between the two electrodes was equal to the length varying distances. When the distance between the two electrodes was equal to the length of one unit cell, the equilibrium conductance was 0.0324 G0 (G0 = 2e2/h). For two unit cells, the value of the transmission coefficient was zero in the range from −4 V to 4 V. So the direct tunneling could be ignored for the n-ZnONR device (n ≥ 2) .


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of one unit cell, the equilibrium conductance was 0.0324 G0 (G0 = 2e2 /h). For two unit cells, the value of the transmission coefficient was zero in the range from −4 V to 4 V. So the direct tunneling could be ignored for the device (n ≥ 2). Micromachines 2019,n-ZnONR 10, 26 4 of 9

Figure 2. Transmission Transmission spectrum spectrumof ofthe then-ZnONR n-ZnONR((a): ((a):nn==4,4,(b): (b):nn== 6, 6, (c): (c): nn == 8, 8, (d): (d): n == 10) device at and the the zero zero of of the the energy energy is is set set to to Fermi Fermi level. level. equilibrium, and

Then, influence of the between the Authe electrode and the and ZnO the nanorod. Then, we weconsidered consideredthethe influence of interface the interface between Au electrode ZnO Figure 3 shows densitythe of states (DOS) of the(DOS) scattering regions, including theincluding ZnO nanorod and nanorod. Figurethe 3 shows density of states of the scattering regions, the ZnO 96 Au atoms were evenly distributed both endsatofboth the nanorod, and the projected of nanorod and that 96 Au atoms that were evenlyat distributed ends of the nanorod, and thedensity projected states of(PDOS) the ZnO includingincluding only O and n-ZnONR (n = 4, (n 6, =8,4,10) density(PDOS) of states ofnanorod, the ZnO nanorod, onlyZn O atoms and Znfor atoms for n-ZnONR 6, devices at equilibrium. It can be observed that the shapes of the DOS of the scattering regions were 8, 10) devices at equilibrium. It can be observed that the shapes of the DOS of the scattering regions similar to theto PDOS of theof ZnO However, the DOS theof scattering regionregion near Fermi level were similar the PDOS the nanorod. ZnO nanorod. However, the of DOS the scattering near Fermi was than the PDOS of the ZnO nanorod, which means the that transmission spectrumspectrum near the levelhigher was higher than the PDOS of the ZnO nanorod, whichthat means the transmission Fermi level of the device wasdevice mainly contributed to by the interface state rather than central near the Fermi level of the was mainly contributed to by the interface state the rather thanZnO the nanorod. Fornanorod. the 4-ZnONR device, the interface of the two terminals of the ZnO nanorod will central ZnO For the 4-ZnONR device, states the interface states of the two terminals of the ZnO overlap a transmission near Fermi level. can Electrons travel from the left electrode nanorodand willform overlap and form a channel transmission channel nearElectrons Fermi level. can travel from the to right electrode along the transmission channel. So channel. the 4-ZnONR indicates leftthe electrode to the right electrode along the transmission So thedevice 4-ZnONR devicemetal-like indicates behavior Ferminear level. For the 10-ZnONR device, thedevice, scattering region had a longer metal-likenear behavior Fermi level. For the 10-ZnONR the scattering region had nanorod. a longer Although it had the same interface state as the 4-ZnONR device, the overlapping of the interface nanorod. Although it had the same interface state as the 4-ZnONR device, the overlapping ofstate the decreased rapidly with the increase ofthe theincrease ZnO nanorod length. The effect of interface can be interface state decreased rapidly with of the ZnO nanorod length. The effectstates of interface ignored inbe theignored n-ZnONR (n =n-ZnONR 8, 10) devices. states can in the (n = 8, 10) devices. In order to further understand properties of electronic transport, the transmission eigenstates near the Fermi level were calculated, as shown in Figure 4. The transmission eigenstate corresponds to the scattering state from the left electrode to the right electrode. In Figure 4a, the eigenstates have larger amplitudes on the left side. The eigenstates corresponding to the higher transmission eigenvalue also had larger amplitude on the right side of the scattering region, which indicates that the incident state on the left side had a greater transmission probability through the intermediate region into the right electrode. The transmission eigenstates on the left side of the scattering region include the incident state and the reflective state, and the two portions have a certain superimposed interference effect. The amplitude of the eigenstate on the leftmost Zn atoms, in Figure 4a, was small due to the destructive interference of the incident state and the reflected state. In Figure 4b, the amplitude of the eigenstates almost disappearred to zero in the middle to the right of the scattering region, that is, only the scattering eigenstate was not transmitted. So the results show that the transmission eigenstates gradually changed from delocalized, throughout the channel region, to localized, at the one electrode, when the channel length increased, which indicates the carriers transport is inhibited by the increases 3. Density of theFigure channel length.of states (DOS) of the scattering regions and projected density of states (PDOS) of the n-ZnONR ((a): 4-ZnONR, (b): 6-ZnONR, (c): 8-ZnONR, (d): 10-ZnONR) for different lengths at equilibrium, and the zero of the energy is set to Fermi level.

In order to further understand properties of electronic transport, the transmission eigenstates near the Fermi level were calculated, as shown in Figure 4. The transmission eigenstate corresponds to the scattering state from the left electrode to the right electrode. In Figure 4a, the eigenstates have

nanorod will overlap and form a transmission channel near Fermi level. Electrons can travel from the left electrode to the right electrode along the transmission channel. So the 4-ZnONR device indicates metal-like behavior near Fermi level. For the 10-ZnONR device, the scattering region had a longer nanorod. Although it had the same interface state as the 4-ZnONR device, the overlapping of the Micromachines 2019, 10, 26 5 of 9 interface state decreased rapidly with the increase of the ZnO nanorod length. The effect of interface states can be ignored in the n-ZnONR (n = 8, 10) devices.


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eigenvalue also had larger amplitude on the right side of the scattering region, which indicates that the incident state on the left side had a greater transmission probability through the intermediate region into the right electrode. The transmission eigenstates on the left side of the scattering region include the incident state and the reflective state, and the two portions have a certain superimposed interference effect. The amplitude of the eigenstate on the leftmost Zn atoms, in Figure 4a, was small due to the destructive interference of the incident state and the reflected state. In Figure 4b, the amplitude of the eigenstates almost disappearred to zero in the middle to the right of the scattering region, that is, only the scattering eigenstate was not transmitted. So the results show that the transmission eigenstates gradually changed from delocalized, throughout the channel region, to Figureat 3. Density states ofofthe scattering regions and projected density of states (PDOS) of Density states(DOS) (DOS) the scattering regions and projected density of states (PDOS) localized, the oneofof electrode, when the channel length increased, which indicates the carriers of the ((a) 4-ZnONR, (b)6-ZnONR, 6-ZnONR,(c): (c)8-ZnONR, 8-ZnONR,(d): 10-ZnONR) for for different lengths at the n-ZnONR ((a): 4-ZnONR, (b): transport isn-ZnONR inhibited by the increases of the channel length. (d) 10-ZnONR) equilibrium, and the zero of the energy is set to Fermi level.

In order to further understand properties of electronic transport, the transmission eigenstates near the Fermi level were calculated, as shown in Figure 4. The transmission eigenstate corresponds to the scattering state from the left electrode to the right electrode. In Figure 4a, the eigenstates have larger amplitudes on the left side. The eigenstates corresponding to the higher transmission (a)

(b) Figure 4. 4. The The transmission transmissioneigenstates eigenstatesofofthe then-ZnONR n-ZnONRdevice deviceatatE f𝐸with isovalue of 0.2. = Figure an an isovalue of 0.2. (a) (a) (n =(n4), 𝑓 with 4), (b) = 10), of the energy is to setFermi to Fermi level. (b) (n =(n10), andand thethe zerozero of the energy is set level.

3.2. 3.2. Transport Transport Properties Properties under under Bias Bias Voltage Voltage The spectrum is is not not sufficient The transmission transmission spectrum sufficient to to describe describe the the transport transport properties properties of of the the device device under zero bias voltage. It is necessary to investigate the current–voltage (I–V) curve, which under zero bias voltage. It is necessary to investigate the current–voltage (I–V) curve, which can can intuitively properties under finite biasbias voltage. For For a further insight into intuitivelydescribe describethe theelectron electrontransport transport properties under finite voltage. a further insight the transport properties of the of n-ZnONR devices, we presented the I–V the curve n-ZnONR intoelectronic the electronic transport properties the n-ZnONR devices, we presented I–Vfor curve for n(n = 4, 6, 8, 10) devices, as shown in Figure 5. The n-ZnONR devices showed a strong nonlinearity and ZnONR (n = 4, 6, 8, 10) devices, as shown in Figure 5. The n-ZnONR devices showed a strong reflected the Schottky-type electronic structure. The I–V curve was highly symmetric within a bias nonlinearity and reflected the Schottky-type electronic structure. The I–V curve was highly range of −1.5 V toa1.5 V.range At theofsame voltage, thesame current decreased withvalue the increase of symmetric within bias −1.5 Vbias to 1.5 V. At the biasvalue voltage, the current decreased the length of the ZnO nanorod. For the 4-ZnONR device, it displayed linear features and exhibited a with the increase of the length of the ZnO nanorod. For the 4-ZnONR device, it displayed linear metal-like behavior in the low bias range ( − 0.75 V, 0.75 V). Comparing the I–V curves of 4-ZnONR features and exhibited a metal-like behavior in the low bias range (−0.75 V, 0.75 V). Comparing the I– with n-ZnONR (n = 6, 8,with 10), n-ZnONR we also found offound n-ZnONR 6, 8, 10)of increased slowly V curves of 4-ZnONR (n = that 6, 8,the 10),current we also that (n the=current n-ZnONR (n = in the beginning and then increased exponentially, which is similar to a Schottky diode. 6-ZnONR 6, 8, 10) increased slowly in the beginning and then increased exponentially, which is similar to a had the best rectification characteristics in n-ZnONR (n =characteristics 6, 8, 10). However, there were(ntwo orders of Schottky diode. 6-ZnONR had the best rectification in n-ZnONR = 6, 8, 10). magnitude difference compared with experiment results [38]. We think that the significant differences However, there were two orders of magnitude difference compared with experiment results [38]. We mainly come two aspects. First,mainly their size is quite TheFirst, diameter of the in the think that thefrom significant differences come from different. two aspects. their size is nanorod quite different. experiment was while in thethe theoretical calculation 0.77the nm.theoretical Second, there is quantum The diameter of130 thenm, nanorod experiment was 130was nm,only while calculation was size effect, Li et al. [39] reported that there is a significant quantum size effect when the diameter of the only 0.77 nm. Second, there is quantum size effect, Li et al. [39] reported that there is a significant ZnO nanowire is lesswhen than the 2.8 nm. quantum size effect diameter of the ZnO nanowire is less than 2.8 nm.

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Figure 5. Current–voltage (I–V) curves of the n-ZnONR (n = 4, 6, 8, 10) devices. Figure 5. Current–voltage (I–V) curves of the n-ZnONR (n = 4, 6, 8, 10) devices.

In order to better understand the rectification characteristics caused by dependence length for to understand the characteristics caused dependence length for the In order to better better understand therectification rectification characteristics caused by dependence length for the ZnOorder nanorod device, it is necessary to investigate the change of thebytransmission spectra under ZnO nanorod device, it is necessary to investigate the change of the transmission spectra under the the ZnO nanorod device, it is necessary to n-ZnONR investigate(nthe change of theattransmission under applied bias. Transmission spectra of = 4, 6) devices different biasspectra voltages are applied bias. Transmission spectra of n-ZnONR (n =current 4,(n6)=devices at different bias voltages areintegral shown the applied bias. Transmission of n-ZnONR 4,was 6) devices at different voltages are shown in Figure 6. According tospectra Equation (2), the contributed from thebias energy in According to Equation (2),Fermi the(2), current wasiscontributed from energy integral the shown in 6. Figure 6. According to Equation the current wasaverage contributed the energy in Figure the bias window region. Here, the level that the of μthe Lfrom and μR was set integral asinzero. bias window region. Here, the Fermi level is that the average of µL and µ was as zero. in the bias window Here, the Fermiathat level is of thetransmission average of μ LR and μset R observed was set asFirstly, Firstly, in the case ofregion. the 4-ZnONR device, small value peak was atzero. 0.08 in the case of the 4-ZnONR device, a small value of transmission peak was observed at 0.08 eV in Firstly, in the case of the 4-ZnONR device, a small value of transmission peak was observed at 0.08 eV in the bias window from −0.2 eV to 0.2 eV, in Figure 6a, which resulted in current. With the the bias window from − 0.2 eV to 0.2 eV, in Figure 6a, which resulted in current. With the increase eV in theofbias eV to 0.2 peaks eV, in were Figurelocated 6a, which resulted in current. With the increase biaswindow voltage,from more−0.2 transmission on the bias window, as shown in of bias 6b,c, voltage, more peakslinearly. were located onlocated the bias window, shown inasFigure increase of bias voltage, moreincreased transmission peaks were on the voltage biasaswindow, shown in Figure hence thetransmission current In Figure 6d,e, the bias was greater than6b,c, 1.6 hence the current increased linearly. Figure the bias voltage was than eV, which Figure 6b,c, hence the current increased linearly. Figure 6d,e, biasgreater voltage was1.6 greater than 1.6 eV, which was mainly because of theInfact that6d,e, theIn large value of the transmission peaks appearred inwas the mainly because of the fact that the large value of transmission peaks appearred in the bias window, eV, waswhich mainly becauseinofthe themarked fact thatincrease the large of transmission appearred in the biaswhich window, resulted of value the current. In Figure peaks 6f,g, the bias voltage is which resulted in theresulted marked the current. In Figure the window bias voltage is 0.4 V and bias which inincrease the is marked increase ofspectrum the current. In bias Figure 6f,g, the voltage is 0.4 Vwindow, and 0.8 V, respectively. There noof transmission in 6f,g, the forbias the 6-ZnONR 0.8 V,and respectively. There is no transmission spectrum in the bias window for the 6-ZnONR device. 0.4 V V, respectively. There is nospectrum transmission in the the bias window for 6-ZnONR device. In0.8 Figure 6h, the transmission was spectrum located on window andthe generated a In Figure 6h, the transmission spectrum was above located onFermi the bias window and a current. device. In Figure 6h,many the transmission spectrum wasthe located on the and generated a current. There were transmission peaks level atbias 2.0 Vwindow and generated a transmission peak There were many transmission peakslevel, above Fermi level at V and a transmission peak waspeak also current. There were manythe transmission peaks above the Fermi level atwas 2.0 V a transmission was also observed below Fermi asthe shown Figure 6k,2.0 which anand exponential increase in observed below the Fermi level, as shown Figure 6k, which was an exponential increase in current. was also observed below the Fermi level, as shown Figure 6k, which was an exponential increase in current. current.

Figure 6. Transmission (a–e) and 6-ZnONR (f–k) devices under bias bias voltage. The Transmissionspectra spectraofof4-ZnONR 4-ZnONR (a–e) and 6-ZnONR (f–k) devices under voltage. Figure 6. Transmission spectra of 4-ZnONR (a–e) and 6-ZnONR (f–k) devices under bias voltage. The dotted lineslines represent biasbias windows and and the zero of the is set level. The dotted represent windows the zero of energy the energy is to setFermi to Fermi level. dotted lines represent bias windows and the zero of the energy is set to Fermi level.

The electron cancan alsoalso be analyzed usingusing the spatial distribution of the frontier electrontransport transportproperties properties be analyzed the spatial distribution of the Themolecular electron transport properties cantoalso be to analyzed the below spatial distribution molecular orbital. The orbitThe corresponding the first transmission peak the Fermi is the frontier orbital. orbit corresponding the firstusing transmission peak belowlevel the of Fermi frontier molecular orbital. The orbit corresponding to the first transmission peak below the Fermi highest occupied molecular orbital (HOMO). Similarly, the orbit corresponding to the first transmission level is the highest occupied molecular orbital (HOMO). Similarly, the orbit corresponding to the first level is the highest occupied molecular orbital (HOMO). Similarly,orbital themolecular orbit corresponding to the peak above the Fermi level the lowest unoccupied (LUMO). The (LUMO). nature offirst the transmission peak above theis Fermi level is the lowestmolecular unoccupied orbital The transmission above Fermioflevel the lowest unoccupied molecular Hamiltonian orbital (LUMO). The nature of thepeak HOMO andthe LUMO the is molecular-projected self-consistent (MPSH) nature of the HOMO and LUMO of the molecular-projected self-consistent Hamiltonian (MPSH)


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HOMO and LUMO of the molecular-projected self-consistent Hamiltonian (MPSH) provides some provides some phenomenon of the rectification characteristics. The eigenstate of MPSH determines phenomenon of the rectification characteristics. The eigenstate of MPSH determines the transmission the transmission peak, which are linked to the poles of the Green’s function [40]. These are relevant peak, which are linked to the poles of the Green’s function [40]. These are relevant to the transmission to the transmission spectra within the bias window [41]. In general, the molecular energy orbit levels spectra within the bias window [41]. In general, the molecular energy orbit levels determine the determine the position of the transmission peak, and the height of the transmission peak is correlated position of the transmission peak, and the height of the transmission peak is correlated with the with the delocalization of the molecular orbitals. As shown in Figure 7, it clearly shows that the spatial delocalization of the molecular orbitals. As shown in Figure 7, it clearly shows that the spatial distribution of MPSH states corresponding to LUMO+1, LUMO, HOMO, and HOMO−1 of the 6distribution of MPSH states corresponding to LUMO + 1, LUMO, HOMO, and HOMO − 1 of the ZnONR device was at 0.8 V, and 1.6 V. At the bias voltage of 0.8 V, the orbitals were all localized near 6-ZnONR device was at 0.8 V, and 1.6 V. At the bias voltage of 0.8 V, the orbitals were all localized the right electrode, which was difficult to form a transmissive channel, resulting in a zero circuit. near the right electrode, which was difficult to form a transmissive channel, resulting in a zero circuit. However, at the bias voltage of 1.6 V, the orbitals were fully delocalized, which was easy to form a However, at the bias voltage of 1.6 V, the orbitals were fully delocalized, which was easy to form a transmission channel, resulting in a large circuit. transmission channel, resulting in a large circuit.

HOMO-1

HOMO

LUMO

LUMO+1

LUMO

LUMO+1

(a)

HOMO-1

HOMO (b)

(MPSH) states of of 6Figure 7. Spatial Spatial distribution distributionofofmolecular-projected molecular-projectedself-consistent self-consistentHamiltonian Hamiltonian (MPSH) states ZnONR, (a)(a) 0.8 6-ZnONR, 0.8V,V,(b) (b)1.6 1.6V,V,and andthe thezero zeroofofthe theenergy energyisisset settotoFermi Fermilevel. level.

4. 4. Conclusions Conclusions In DOS, and In conclusion, conclusion, we we computed computed transmission transmission spectra, spectra, DOS, and I–V I–V curve curve of of n-ZNONR n-ZNONR devices devices by by using the DFT method coupled with the NEGF. It was found that the contact interfaces between using the DFT method coupled with the NEGF. It was found that the contact interfaces between Au Au electrodes nanorod play essential rolesroles in theincurrent–voltage behaviors. For the For 4-ZnONR electrodesand andthe theZnO ZnO nanorod play essential the current–voltage behaviors. the 4device, the metal–nanorod interface states overlap to form a transmission channel, and results the ZnONR device, the metal–nanorod interface states overlap to form a transmission channel,inand linear behavior of the electrical transport at the low bias voltage. As the ZnO nanorod length is results in the linear behavior of the electrical transport at the low bias voltage. As the ZnO nanorod increased, the central region determines the transport characteristics of theofdevice and length is increased, thescattering central scattering region determines the transport characteristics the device exhibits excellent rectification characteristics. The rectification characteristics were analyzed using and exhibits excellent rectification characteristics. The rectification characteristics were analyzed transmission spectraspectra at different bias voltages and MPSH. results have theoretical guidance using transmission at different bias voltages andOur MPSH. Ourwould results would have theoretical for the preparation of field effect transistors based on the ZnO nanorod. guidance for the preparation of field effect transistors based on the ZnO nanorod. Author Contributions: B.H. and Z.Z. conceived and designed the calculation model; F.Z. performed the Author Contributions: B.H. and Z.Z.the conceived designed the wrote calculation model;allF.Z. performed the computational study; Y.Y. performed analysis and of the data; B.H. the paper; authors discussed computational study; Y.Y. performed the analysis of the data; B.H. wrote the paper; all authors discussed the the results and commented on the manuscript. results and commented on the manuscript. Funding: This work is funded by National Natural Science Foundation of China (Grant No. 61664008), the Special Research for Discipline Construction of Natural High-Level University Projectof (Grant No. 2015SXTS02) and Yan’an Funding:Funds This work is funded by National Science Foundation China (Grant No. 61664008), the Science and Technology Innovation Team Construction Project (Grant No. 2017CXTD-01). Special Research Funds for Discipline Construction of High-Level University Project (Grant No. 2015SXTS02) Conflicts of Science Interest:and TheTechnology authors declare no conflict interest. and Yan’an Innovation TeamofConstruction Project (Grant No. 2017CXTD-01).

Conflicts of Interest: The authors declare no conflicts of interest.

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