Study of Potential Change, Charge Distribution, Voltage Drop, Band

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Study of Potential Change, Charge Distribution, Voltage Drop, Band Lineup and Transmission Spectrum of Molecular Break Junction Under Low Bias Abhisek Kole, and K Radhakrishnan J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 22 May 2017 Downloaded from http://pubs.acs.org on May 28, 2017

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The Journal of Physical Chemistry

Study of Potential Change, Charge Distribution, Voltage Drop, Band Lineup and Transmission Spectrum of Molecular Break Junction Under Low Bias Abhisek Kole and K Radhakrishnan† Centre for Micro-/Nano-electronics (NOVITAS), School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Drive, Singapore 639798. †

E-mail: [email protected]; Fax: +6567933318.

KEYWORDS: DFT, NEGF, Molecular Break Junction, DNA, Charge Distribution.

ABSTRACT: Using the Density Functional Theory (DFT), combined with Non-Equilibrium Green’s Function (NEGF) method, the effect of potential change, charge distribution, voltage drop, band lineup and evolution of the transmission spectrum under small applied bias for memantine-functionalized gold nanogap device for DNA detection have been studied in this report. We have investigated the potential perturbation and charge distribution introduced by the electrodes and the nucleobases separately, which helps to understand the development of the potential profile throughout the molecular break junction and the effect on the transmission

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spectrum. The presence of electrodes is found to modify the energy levels and band lineup of the device. We have also investigated the local density of states to understand the contact- and nucleobase-modified charge distributions in the molecular states. The electronic wave functions for HOMO transmission peak at various applied voltages are also examined to understand the physics behind the evolution of the transmission peaks. The potential drop and the charge distribution at 1 V were analyzed for the extended molecular region, and the potential drop was found to be almost uniform. The current voltage (I-V) and the differential conductance characteristics for both the nucleobases of cytosine and adenine indicate that the device will operate normally up to a maximum bias of 1 V. Beyond this voltage, the resonant peaks will become very broad, and they will start to overlap with each other (from other nucleobases), in addition to the transmission peaks becoming weak.

INTRODUCTION Recently, it has been proposed that nanopores in a material can be used to develop fast and cheap DNA sequencing technology [1-4]. As the DNA bases translate through the nanopore, the electron resonance tunneling can identify individual nucleobases in single-stranded DNA (ssDNA) without any amplification. These kinds of devices involve a nanopore including brake junction electrode, which measures the tunneling current during the translation of DNA nucleobases [5-7]. Every single nucleobase gives different tunneling current signature, and hence the DNA nucleobases can be easily identified by observing the resonant tunneling current. This method of sensing can be very efficient, but achieving good coupling between the molecule and electrode is not easy. In our previous work

[8]

, modified diamondoid structure called memantine

[9,10]

was

used to functionalize gold nanogap to detect the nucleobases (4 Natural and 2 Mutated, 5mC and


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8oG). These functionalizing molecules provide hydrogen bond bridge with the nucleobases. Consequently, the coupling between the nucleobases and the electrode improves, which leads to better tunneling current and sensitivity. The nucleobases studied were adenine (A), cytosine (C), guanine (G) and thymine (T), and the two epigenetic makers, 5mC and 8oG. The device proposed was able to detect all the natural and mutated nucleobases with the sensitivity ranging from 103 to 107. The resonance peaks in the transmission spectra of the nucleobases, by calculating the projected density of states, were identified to be due to the translation of the nucleobases.

Figure 1. Functionalized gold electrode device configuration for quantum mechanical transport property calculation.

In this work, we have investigated the potential change, charge distribution, voltage drop, band lineup and transmission spectrum [11-27] of molecular break junction under low bias. The charge transfer and the potential perturbation introduced by the gold electrode and nucleobases in the break junction were also investigated. Cytosine (C) and adenine (A) nucleobases were only considered for analysis in this report, but similar analysis is applicable to other nucleobases also. The device configuration used is shown in Figure 1 [8]. We started our exploration with the gold electrode and nucleobase induced charge distribution and potential perturbation in the molecular


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break junction. Then, the contact induced modification of the molecular states and the band lineup of metal-molecule-metal junction were analyzed. To understand the physics behind the charge distribution in the molecular states and the potential distribution, the local density of states (LDOS) related to various energy levels were studied, followed by the analysis of the evolution of transmission spectrum under small bias applied between the source and drain contacts. Then, the transmission eigenchannels and related electronic wave functions were investigated to understand the behavior of the transmission spectrum. To understand the underlying physics behind these phenomena, the potential drop and charge distribution of the device with a small applied bias were studied. The critical normal operating range of the device for the maximum applied voltage was determined. Finally, the I-V characteristics and the differential conductance,

, with respect to applied voltage were also examined, and the results

are reported.

THEORETICAL BACKGROUND AND MODEL The quantum transport calculations were carried out using the Atomistix Toolkit package (ATK) based on non-equilibrium Green’s function (NEGF)

[28,29]

combined with density functional

theory (DFT) [30-32]. The generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE)

[33-37]

was used for the exchange-correlation (XC) functional. The mesh cutoff energy of

150 Ry and 5 × 5 × 100 k point mesh with Monkhorst-Pack scheme were used to obtain better match between the Fermi level of the electrodes and central region of the device. While double- polarized (DZP) basis set were used for nitrogen, hydrogen, carbon, oxygen and sulphur atoms, single- polarized (SZP) basis set was employed for gold atoms. The geometry optimization and


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structural relaxations of the central region were performed with sufficient vacuum spacing (minimum of 12 Å ) to prevent interaction between the periodic images. The relaxation procedure was carried out to ensure that the Hellmann-Feynman force acting on the atoms become less than 0.02 eV/Å. A molecular device consists of a molecule and two contacts, with the molecule sandwiched between the source (left electrode) and drain (right electrode) contacts. As can be seen in Figure 1, some part of the contact is included into the central region, which is called the extended molecule (EM). The and are the chemical potentials of the source and drain contacts, respectively. At equilibrium, the chemical potentials are equal to each other, = , and also the system is completely charge neutral. As soon as we apply voltage across the source and the drain contacts, the potential profile and the charge distribution will start to modify. It is critically important that the potential profile of the EM must match the potential profile of the electrode at the boundary. The scattering will generate at the boundary, if the discontinuity appears. Consequently, the coupling between the EM and the contacts will become poor. In order to prevent these problems, we needed to introduce the concept of extended molecule (EM). The Hamiltonian of the whole system can be written as, ℋ, Hˆ = HˆSS + HˆS- Mol + Hˆ Mol - Mol + HˆMol - D + HˆDD It must be noticed that ℋ (calligraphic) is an infinite matrix, and is a finite matrix. Similar to the Hamiltonian, we also have the overlap matrix , which can be written as,

Sαβ = ϕα ϕ β = ∫ ϕα (r )*ϕ β (r )d 3 r

After dividing the whole device into three parts and by using the localized basis set, we can write the Green’s function matrix as,


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∑ [ε 0+ Sβα − H βα ]GαβR (ε ) = δ αβ α

where,

ε

0+

=

(ε lim δ →0

+ iδ

).

As we have used the localized basis, the overlap between the two

localized functions Φ ( − ) and Φ ( − ) will be zero if they are separated far away from each other. In other words, when | − | > certain distance, the overlapping matrix,

ϕα ϕ β = 0 . Hence, the H S-Mol and HMol-D become finite. So, after neglecting the direct tunneling from the source to drain, from the above matrix equation, the retarded green’s function for the EM region can be easily written as, R GMol - Mol

= [ε

0+

S Mol - Mol - H Mol - Mol

− Σ S (ε ) − Σ D (ε )]

−1

where Σ S (ε ) and Σ D (ε ) are the self-energy terms of the source and drain contacts, respectively. In general, in the mean field electronic structure theory, such as DFT method, the matrix elements of the Hamiltonian of the system are not known initially. The only term which is known to us is their functional dependency, which is given by the charge density[38,39] !. Hence, the Hamiltonian can be described as H = H[ ρ ] , which can be calculated by DFT method. Consequently, the Hamiltonian of the EM can also be written as,

H Mol - Mol = H Mol - Mol [ ρ (r )] So, the new Hamiltonian can be written as, H Mol - Mol [ ρ (r )] = ϕα H K − S (r ) ϕ β

where H K − S (r ) is the Khon Sham Hamiltonian from the DFT loop. The steady state current through the central region can be written as,


6

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2e 2 ∞ I =− ∫ T( ε ,v )[ f (ε − µ s ) − f (ε − µ D )]dε h −∞

where T( ε ,v ) is the total transmission probability of the eigenchannel, and is given as, R A T( ε , v) = Trace[ΓS GMol - Mol ΓD GMol - Mol ]

ΓS , D describes the broadening due to the coupling between the central region and the source to

drain, which can be written as, ΓS , D = i[Σ S , D (ε ) − Σ †S , D (ε )] . The projected density of states (PDOS) of any molecule is: DOS molecule (ε ) = −

1

π

R Im{Trace molecule [GMol - Mol (ε + iδ ) S Mol - Mol ]}

Tracemolecule means that the trace has been performed only on the selected part of the molecule.

RESULTS AND DISCUSSION The charge transfer, and hence the potential change through the electrode-molecule-electrode system is one of the most important parameters for the device at equilibrium since the transport property of the device in equilibrium completely depends on this phenomenon. In the break junction system, two kinds of perturbations are introduced. The first one is coming from the coupling between the electrode and functionalized molecules, and the second is due to the coupling between the functionalized molecules and DNA nucleobases. In this study, both the perturbations were analyzed for adenine and cytosine separately. In Figures 2 (a) and (e), we have plotted the differences between the self-consistent charge distribution in the electrodemolecule-electrode system and the isolated molecule plus the isolated metallic electrode for the


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cytosine and adenine, respectively. The plots show the charge redistribution and the effect of binding the metallic electrode to the molecular system. From the figures, it can be seen that the charge redistribution is greatly localized to the anchor atom (sulphur) and the neighboring carbon and gold atoms for both the cases. As the bonding configuration across the metal-molecule through the sulphur atom is almost identical for both the cases, a similar distribution is completely expected. The spatial distribution (not shown here) of the transferred charges also confirms that most of the charge transfer process involves the sulphur atom and neighboring atoms. It can also be noticed that the charge perturbation introduced by the two electrodes does not interfere with each other as the perturbation decays very rapidly as we go away from the molecule-metal junction towards inside the molecule. The increment of electrons in the sulphur atom is due to rehybridization of the sulphur "# orbital with the gold atoms. As the sulphur atoms are more electronegative than gold atoms, the charge is transferred from the gold to sulphur atoms. It can be also noticed that the electron density decreases in the sulphur-carbon $ bond, which is indicated in blue color. This is because of the charge transfer to the "% orbital as the gold-sulphur bond is formed, which weakens the sulphur-carbon bond. As there is charge redistribution across the metal-molecule junction, it is natural to have potential perturbation across the metal-molecule junction. In Figures 2 (b) and (f), the differences between the electrostatic potential of the junction and the isolated molecule plus the isolated electrode are plotted for the cytosine and adenine, respectively, which is equivalent to the potential perturbation introduced by the formation of metal-molecule junction corresponding to the charge transfer. As the electrons are transferred to the sulphur atoms from gold atoms after the junction formation, the electron density increases in the sulphur and the neighboring atoms, which create a potential barrier between the metal surface


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and sulphur atom. The potential barrier reduces rapidly as we go away from the metal-sulphur junction and becomes almost negligible at the central molecular region. As the charge redistribution configuration is almost identical in both the cases (adenine and cytosine), the potential barrier profile is also almost the same.

Figure 2. a), e) Isosurface plots of charge redistribution after the formation of the gold-moleculegold contact for Cytosine and Adenine, respectively. b), f) Potential perturbations upon formation of the gold-molecule-gold contact for Cytosine and Adenine, respectively. c), g) Isosurface plots of charge redistribution in the break junction after the introduction of cytosine and adenine, respectively. d), h) Potential perturbations after the introduction of cytosine and adenine, respectively, in the break junction.


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In Figures 2 (c) and (g), the differences between the self-consistent charge distribution in the electrode-molecule-electrode system and the isolated nucleobase plus the isolated functionalized metallic electrode are plotted for the cytosine and adenine, respectively. They show the charge redistribution and the effect of coupling between the functionalized electrode and the nucleobases. As we can clearly see, the charge redistribution looks very much different for the two nucleobases. As the nucleobases are coupled to the functionalized electrode through the hydrogen bond, the relaxed geometry of the functionalized molecule-nucleobasefunctionalized molecule system becomes different for different nucleobases. Consequently, after coupling, the charge redistribution also becomes different for different nucleobases. In the case of cytosine, the spatial distribution of redistributed charges confirms that there is more charge redistribution in the left-hand side making it asymmetric. But, in the case of adenine, the charge redistribution is almost symmetric. In Figures 2 (d) and (h), the potential perturbations introduced by the nucleobases for cytosine and adenine, respectively, are plotted corresponding to the charge redistribution. In the case of cytosine, it can be noticed that a potential barrier is being created, which is related to the increment of electron density corresponding to the hydrogen bond between the functionalized molecule and cytosine. It can also be noticed that there is a shallow potential well followed by the barrier. In the case of adenine, a potential barrier can be noticed at the middle of the nucleobase. Also, there are two potential wells situated on both sides of the barrier, corresponding to the reduced electron density at both the junctions. Thus, it can be said that the introduction of different nucleobases will perturb the potential profile differently. Since the potential barrier controls the flow of tunneling electrons, the tunneling current will be different for different potential profiles, which ultimately leads us to the detection of various nucleobases.


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The coupling between the gold electrodes and the molecular region perturbs the whole potential profile throughout the gold-molecule-gold system. Consequently, the charge distribution and the energy level also modify with respect to the Fermi level. To understand the band-lineup and the modification of the molecular states due to various perturbation, the case of cytosine only has been analyzed. Similar results are also applicable to other nucleobases. In Figures 3 (a) and (b), the transmission spectrum and PDOS projected on the molecular region have been plotted, respectively, for cytosine. Only the HOMO states are shown. From the molecular energy spectrums obtained, it can be confirmed that the HOMO-1, HOMO, LUMO, LUMO+1 molecular states correspond to the energy level of -1.33, -1.27, 2.55 and 3.76 eV, respectively. Under a small applied voltage, the conductance is dominated by the HOMO state, which is the closest energy level relative to the Fermi level. The coupling between the electrodes and the molecule will modify the molecular orbital of the isolated molecule through rehybridization. To understand the modified molecular orbitals and the related energy levels, the MPSH (molecular projected self-consistent Hamiltonian) eigenstates projected on the molecular part in the presence of electrodes were analyzed. The eigenstate of the MPSH can be referred to the renormalized molecular orbital, which includes the modification of the electronic structure of the molecule due to the electrodes. In Figures 3 (c) and (d), the various MPSH eigenstates without and with the presence of electrode projected on the molecule are shown, respectively, for comparison. It can be seen that the energy levels of the eigenstates of the isolated molecule shifts by some amount due to the presence of the electrodes. For example, the HOMO (E = −1.27 eV) and LUMO (E = 2.55 eV) states of the electrodemolecule-electrode system are actually related to the isolated molecular orbital situated at E = −0.612 eV and E = −0.43 eV, correspondingly.


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c)

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d)

Figure 3. a) Plot of transmission spectrum with respect to energy, b) Plot of PDOS with respect to energy. (Dominant HOMO peak is only shown). c) Plot of energy eigenstates corresponding to LUMO and HOMO energy levels for an isolated molecule. d) Plot of MPSH eigenstates corresponding to LUMO and HOMO energy levels projected on the molecular region for the electrode-molecule-electrode system. e) Isosurface plot of LDOS corresponding to HOMO state. f) Isosurface plot of LDOS corresponding to LUMO state. g) Isosurface plot of LDOS corresponding to HOMO state with respect to the potential profile. h) Isosurface plot of LDOS corresponding to LUMO state with respect to the potential profile.

The contact also modifies the charge distribution of the molecular state of the electrodemolecule-electrode system. This can be understood by investigating the LDOS at energy levels corresponding to the peak position of PDOS. Here, we have only analyzed the HOMO and LUMO states. In Figures 3 (e) and (f), we have plotted the (3D) LDOS corresponding to HOMO and LUMO molecular states. The charge distribution in the molecular region is closely related to its potential profile. As mentioned earlier, there are mainly two kinds of perturbations, which


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deform the potential profile of the molecular region. The first one is from the potential barrier close to the sulphur atom due to the charge transfer from the contact, and the second barrier is due to the introduction of the cytosine. These potential barriers affect the LDOS of both HOMO and LUMO states. In Figures 3 (g) and (h), the LDOS along with the potential profiles are plotted to understand this effect. It can be seen in Figure 3 (g) that the LDOS of the HOMO state is completely deformed by the potential barrier followed by a shallow well introduced by the cytosine in the break junction. The potential barrier pushes the LDOS into the molecule towards the well creating higher LDOS inside some part of the cytosine. Figure 3 (h) illustrates that LDOS of the LUMO is also deformed by the potential barrier introduced mainly by the electrodes. It is clear that the potential barrier near sulphur atoms pushes the electrons into the molecular region and put the LDOS inside the molecular region, consequently increasing the LDOS. In this section, the evolution of transmission spectrum with the small voltage applied between the contacts is discussed. Figures 4(a) and (b) show the transmission spectrums for the cytosine and adenine, respectively, with the applied voltage of −1 ≤ () ≤ 1. The resonant peaks occur at E = −1.2733 eV with T(E) = 0.65 at the zero-bias condition for cytosine. From the previous section, we know that the dominant resonant peak was corresponding to the HOMO state of cytosine. As the applied voltage is increased, the transmission peaks (HOMO) start to shift for both cytosine and adenine. From Figure 4 (c), one can clearly observe that the transmission spectrum has shifted by almost ±0.05 eV. The transmission peaks start shifting away from the Fermi level when positive voltage is applied, and they shift towards the Fermi level in the case of negative bias. It can also be observed that the magnitude of the transmission spectrum decreases significantly under the biasing. The spectrum drops below 0(1) = ±0.05


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with the applied voltage of () = ±1.0 V. The applied voltage across the source and drain terminal modifies the transport property in two ways, 1) it changes the molecular level relative to the Fermi level, and 2) it modifies the charge distribution across the molecular region, and hence the capability of carrying current. As the molecular energy level shifts with the applied electric field, the coupling between the molecular state (HOMO) and the electrode becomes weaker. The eigen channel electronic wave functions related to HOMO states are plotted at various applied voltages for cytosine in Figure. 4 (e). It can be observed that the coupling between the electrodemolecule-electrode decreases significantly with the applied voltage. Further increase in the applied voltage brings the HOMO-1 state towards the equilibrium Fermi level and it becomes the dominant state beyond ± 1 ( . In the low bias regime, the LDOS of the system does not change much, but the charge distribution becomes significant at the high field (> 1.6 V). A clear shift in the charge distribution for both the HOMO and HOMO-1 states can be noticed in Figure 5.

e)

Figure 4. The transmission spectrum plots with the applied voltage between source and drain for (a) Cytosine and (b) Adenine. (c) and (d) The shift of Dominant Transmission peak (HOMO) with the applied voltage for Cytosine and Adenine, respectively. e) The electronic wave function for HOMO transmission peak at various applied voltages for Cytosine.


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Figure 5. (a) The HOMO state at 0 V (b) The HOMO-1 state at 0 V (c) The HOMO state at 2 V. (d) The HOMO-1 state at 2 V.

The electrostatic potential of EM is related to the Poisson’s equation. If the electrostatic non− Equlilibrium (r) at equilibrium (r) and VES

Equlilibrium

potentials of the device are given as VES

(zero bias) and non-equilibrium (with bias), respectively, Equlilibrium

∇ 2 VES

Equlilibrium (r ) = ρMol (r ) - Mol

non− Equlilibrium

∇2VES Equlilibri um

where ρMol-Mol

non−Equlilibrium

and ρMol -Mol

non− Equlilibrium (r) = ρMol (r) - Mol

are the corresponding charge densities. Thus, the

potential drop across the molecule δV and the transferred charge δρ , respectively, under the applied bias can be written as, non− Equlilibrium Equlilibrium Mol δVES −VES - drop = VES


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non−Equlilibrium Equlilibrium − ρMol δρMol = ρMol - Mol - Mol

Therefore, Mol Mol (r ) ∇2δVES- drop(r ) = δρ

The boundary conditions of the potential drop in the molecular region can be written as, Mol δVES - drop

Mol δVES - drop

Source

= V Source

Drain

= V Drain

where V Source and V Drain are the applied voltages at the source and drain contacts, respectively, and the total applied voltage V b = V Source − V Drain . It may be noted that the difference between the chemical potential of the source and drain contact is,

µSource− µDrain= eVb .

To

Mol understand the physical meaning of the δVES- dropin the extended molecular region, one can

write, Mol δVES - drop = V b ( r ) + ∫ dr2

δρ Mol (r2 ) r − r2

Hence, the potential profile at the non-equilibrium condition (bias applied) is:

δρ Mol (r2 ) non− Equlilibrium Equlilibrium Equlilibrium Mol + δVES- drop = VES + V b (r ) + dr2 VES = VES r − r2

∫


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Here, δρ Mol is the charge redistribution in the extended molecule due to the applied voltage. If 0 due to the charge redistribution inside the the external electrostatic potential of the contacts V Ext

contacts is included, Equlilibrium 0 = VExt + V n (r ) + dr2 VES

∫

Equlilibrium ρ Mol (r2 ) - Mol

r − r2

where V n (r ) is the potential for the positive background charge density. Similarly, non − Equlilibri um 0 = VExt + V n (r ) + V b (r ) + dr2 VES

∫

non − Equlilibri um ρ Mol ( r2 ) - Mol

r − r2

Since sufficient amount of contact region is included in the extended molecular region, the effect 0 of the external electrostatic potential of the contacts V Ext is almost negligible. Hence, the

Hamiltonian of the device at non-zero bias can be written as, non − Equlilibrium ρ Mol (r2 ) 1 2 0 - Mol H = − ∇ + VExt + V n ( r ) + V b (r ) + ∫ dr2 + V xc (r ) 2 r − r2

where V xc (r ) is the exchange correlation potential. The charge response under an applied bias can be understood in terms of charge injection and their distribution into the molecules. The charge redistribution in the equilibrium state is explained by balancing out the charge injection through the source contact and extraction through the drain contact. In Figure 6 (b), the charge accumulation through the molecular region is plotted for the applied voltage of 1 V. It can be noticed that the electron accumulation is very small. The fractional electron occupation in the molecular orbital is due to the coupling of the molecule with the gold contacts, which broadens the molecular level. Although the injected


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charge due to the applied voltage is very small, the charge redistribution within the molecule is very significant, as it will ultimately affect the potential drop across the molecular region. The potential drop can be calculated as the difference between the potential profiles with and without the applied biasing (2() = (() ) − (() ) = 1 eV ) conditions. The chemical potentials of the

source and the drain electrodes are given by (() ) = (0) 3 2 4 5 7 and (() ) = (0) − 6

2 4 5 7 , respectively. From Figure 6 (a), it can be clearly observed that the potential does not 6 drop abruptly at any point, rather drops uniformly along the length of the molecular region. Inside the contact, the potential profile becomes flat to match the boundary conditions of the contact regions. Similar charge distribution and potential drop can be found at other biasing voltages. Although the molecular region shows different conductances for various applied biases, the charge distribution and the potential drop do not change much. They show almost similar characteristics.

Figure 6. At an applied voltage of 1 V, (a) Contour plot of induced potential, (b) Plot of induced charge density, (c) Plot of charge evolution from an applied voltage of 0.2 V (Pink and Magenta) to 1 V (Blue and Red). (d) 3d-plot of the potential drop and charge density in the device.


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The charge evolution with the applied bias is plotted in Figure 6 (c). The pink and magenta colors describe the charge density at the extended molecule at an applied bias of 0.2 V. The blue and red colors describe the charge density induced at the EM when the applied voltage is 1.0 V. As the bias is applied between the two electrodes, the electrons move from the source side sulphur atom to the drain side sulphur atom. When the voltage (1 V) is applied, it can be clearly seen that more charges accumulate at the drain side, as shown in red color in Figure 6 (d). After the shifting of the electrons with the applied bias, it can be noticed that most of the charges are accumulated at the drain side sulphur and the neighboring atoms. This is due to the presence of the potential barrier at the metal-sulphur junction at the drain contact, which controls the charges from flowing into the drain. Similar reason is also applicable for the source junction. This phenomenon leads to the creation of a dipole with the accumulation of electrons in the drain side and depletion of electrons in the source side. The current voltage (I-V) characteristics for cytosine and adenine are plotted in Figure 7 (a). As the transmission spectrum does not overlap at the Fermi level, both the nucleobases can be clearly detected by analyzing the I-V curve. In Figure 7 (b), the differential conductance is plotted for both the nucleobases. At low bias, the current changes linearly with the voltage corresponding to the tunneling transport of HOMO-LUMO gap. It is interesting that the functionalized molecules and adenine create much more symmetric structure than that of cytosine in the relaxed structure state, and hence the I-V and conductance curves for adenine are found more symmetric than that for cytosine.


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:;

Figure 7. (a) I-V characteristics of cytosine and adenine at the applied voltage of ±8 9. (b) Plot of :9 for cytosine and adenine.

CONCLUSIONS Using DFT+NEGF method, the effect of potential change, charge distribution, voltage drop, band lineup and evolution of the transmission spectrum of memantine-functionalized gold nanogap molecular break junction device for DNA detection have been investigated. It is found that the electrodes and the nucleobases introduce potential perturbation and charge distribution, which deforms the potential profile and redistributes the charges of the equilibrium system. The presence of electrodes and nucleobases also modify the energy levels and band lineup resulting in modified charge distribution in the molecular states. The electronic wave functions under small applied bias were examined to understand the shifting and drop in the magnitude of the transmission spectrum. The LDOS of HOMO and HOMO-1 states were also analyzed to understand the high field charge distribution and their effect on the transmission spectrum. The


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potential drop and the charge distribution at 1 V were analyzed for the extended molecular region, and the potential drop was found to be almost uniform. The current voltage (I-V) and the differential conductance characteristics for both the nucleobases of cytosine and adenine indicate that the device will operate normally up to a maximum bias of 1 V. Beyond this voltage, the resonant peaks will become very broad, and they will start to overlap with each other (from other nucleobases), in addition to the transmission peaks becoming weak. This study will play an important role in the design and development of similar molecular devices in future. This investigation not only provides critical information about the device behavior but also shows the insight of some very complex physics, which may help to understand various phenomena in molecular electronics.

ACKNOWLEDGEMENTS The authors acknowledge Centre for Micro-/Nano-electronics (NOVITAS), School of Electrical and Electronic Engineering, Nanyang Technological University for the computational resources and help.

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Figure 1:

FIG. 1. Functionalized gold electrode device configuration for quantum mechanical transport property calculation.

Figure 2:


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FIG. 2. a), e) Isosurface plot of charge redistribution after the formation of the gold-molecule-gold contact for Cytosine and Adenine respectively. b), f) Potential perturbation upon formation of the gold-molecule-gold contact for Cytosine and

Adenine respectively. c), g) Isosurface plot of charge redistribution in the break junction after the introduction of cytosine and adenine respectively. d), h) Potential perturbation after the introduction of cytosine and adenine in the break junction.

Figure 3:


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C)


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d)


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FIG. 3. a) Plot of transmission spectrum with respect to energy, b) Plot of PDOS with respect to the energy for cytosine. (Dominant HOMO peak is only shown). c) Plot of energy eigenstates corresponding to LUMO and HOMO energy levels for isolated molecule. d) Plot of MPSH eigenstates corresponding to LUMO and HOMO energy levels projected on the molecular region for the electrode-molecule-electrode system. e) Isosurface plot of LDOS corresponding to HOMO state. f) Isosurface plot of LDOS corresponding to LUMO state. g) Isosurface plot of LDOS corresponding to HOMO state with respect to the potential profile. h) Isosurface plot of LDOS corresponding to LUMO state with respect to the potential profile.

Figure 4:


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e)


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FIG. 4. The transmission spectrum plots with the applied voltage between source and drain for (a) Cytosine and (b) Adenine. (c) and (d) The shift of Dominant Transmission peak (HOMO) with the applied voltage for Cytosine and Adenine, respectively. e) The electronic wave function for HOMO transmission peak with various applied voltages for Cytosine.



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Figure 5:


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FIG. 5. (a) The HOMO state at 0 V (b) The HOMO-1 state at 0 V (c) The HOMO state at 2 V. (d) The HOMO-1 state at 2 V.



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Figure 6:


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FIG. 6. At an applied voltage of 1 V, (a) Contour plot of induced potential, (b) Plot of induced charge density, (c) Plot of

charge evolution from an applied voltage of 0.2 V (Pink and Magenta) to 1 V (Blue and Red). (d) 3d-plot of the potential drop and charge density in the device.



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Figure 7:


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FIG.7. (a) I-V characteristics of cytosine and adenine at the applied voltage of ±1 𝑉. (b) Plot of !"!" for cytosine and adenine.



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Study of Potential Change, Charge Distribution, Voltage Drop, Band

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