Elucidating Multiple Negative Differential Resistance and Rectification Ratio Through L-Aspartic Acid at Nanometre Scale Using Symmetrical Metal Electrodes


 Protein-based electronics is one of the growing areas of bio-nanoelectronics, where novel electronic devices possessing distinctive properties, are being fabricated using specific proteins. Furthermore, if the bio-molecule is analysed amidst different electrodes, intriguing properties are elucidated. This research article investigates the electron transport properties of L-aspartic acid (i.e., L-amino acid) bound to symmetrical electrodes of gold, silver, copper, platinum and palladium employing NEGF-DFT approach using self-consistent function. The theoretical work function of different electrodes is calculated using local density approximation and generalized gradient approximation approach. The calculated work function correlates well with the hole tunnelling barrier and conductance of the molecular device, which further authenticate the coupling strength between molecule and electrode. Molecule under consideration also exhibits the multiple negative differential resistance and rectification ratio with all the different electrodes, due to its asymmetrical structure. The molecular device using platinum electrodes exhibits the highest peak to valley ratio of 1.38 and rectification ratio of 3.20, at finite bias. The switching characteristics of different molecular device are justified with detailed transmission spectra and MPSH. These results indicate that L-aspartic acid and similar biomolecule can be vital to the growth of Proteotronics.


Introduction
Biomolecules have evoked substantial attention among researchers due to their immense applications in nanoelectronic devices [1][2][3][4][5][6][7][8][9][10]. Such biomolecules exhibit the redox process and optical functionality in biological environment. Electrical charge in such biomolecules is generally transported by ions. The research is inclined towards the biomolecules acting as bridge between donor and acceptor moieties to form bio-nanoelectronic devices [11]. Proteins (from the Greek word Protos, i.e. of primary importance) are the bio-molecules that offer the distinctive optical and electronic properties. Due to biological existence, intense research has been focussed on charge transfer in proteins. In order to design practical bionanoelectronic devices, investigation of their electron transport properties is highly imperative. Electronic recti cation in protein-based devices has evolved into a challenge for the researchers working in the eld of bio-nanoelectronic [12]. Proteotronics has emerged as an essential branch to study the electron transport properties of proteins for new bio-nanoelectronic devices [13]. Although, there is signi cant connection between electron transfer (ET) and electron transport (ETp) properties [14,15], yet there is a sense of ambiguity to predict the exact mechanism of electron transport through proteins [16,17]. The emphatic potency of proteins can be predicted, if the building blocks of proteins (i.e., amino acids) are intrigued individually.
Among 20 amino acids, only two (i.e., L-glutamic acid and L-aspartic acid) are negatively charged. Different L-amino acids are distinguished by their distinct side chain structures [18]. Charged amino acids are the major determinants of the recti cation of gap junctional channel [19] and short-range ET and ETp [20]. Current recti cation is observed in asymmetric molecule structures [21][22][23][24] and due to the moleculeelectrode coupling [25].
In our previous work, we examined the transport properties of L-glutamic acid (i.e. C 5 H 9 NO 4 ) [26]. In this research work, L-aspartic acid (i.e., L-amino acid) C 4 H 7 NO 4 , is molecule of choice due to the presence of asymmetrical alkane carbon chain [27,28]. L-amino acid acts as a transmitter for central nervous system of mammals and is being exceedingly used in biosynthesis of proteins [29]. Asymmetric structure of the L-aspartic acid crystal has been observed using atomic force microscopy [30]. Carboxylic acid side-chain has an important role to play in the conductivity of the amino acids [20]. This side chain can also in uence the long-distance electron transfer in peptides [31].
These molecules are rigidly attached to atomic scale electrodes to form molecular junctions [37].
Furthermore, nite bias is applied across electrodes to investigate electronic transport behaviour of such molecules. The distinctive electronic behaviour con rms the candidature of such molecules for future electronic devices [24].
Biomolecules show different current-voltage (I-V) characteristics with different electrodes [43][44][45]. In our previous work, we elucidated electronic transport properties of L-glutamic acid stringed to gold, silver and copper electrodes [26]. We move a step forward towards investigating negatively charged L-amino acid (i.e. L-aspartic acid) with two additional metallic electrodes of platinum and palladium. We also focus on the correlation of metal work function and molecule-electrode coupling in this research work.

Theory And Simulations
Presently, lot of focus is on developing molecular devices particularly containing bio-molecule. Speci cally, amino acids are getting utmost attention among researchers to develop distinct bionanoelectronic devices [24]. We have assembled ve different device con gurations with central scattering region comprising of L-aspartic molecule attached to semi-in nite metallic electrodes. The metallic electrodes are assumed to be ballistic conductors having unity probability of transmission.
These electrodes accept all the carrier ow from the channel and avoid backscattering into the channel [46].
In order to achieve non-equilibrium, a nite bias is applied across the junctions using Landauer's approach [47]. The metallic electrodes for this research work are prepared using (1, 1, 1) miller indices. We observe that copper, platinum and palladium electrodes exhibit 6 layers in comparison to 3 layers in gold and silver electrodes. Such increase in layers is due to smaller inter-atomic distance of the respective electrodes. For the sake of comparing some signi cant parameters, we have used the xed size simulation box of such electrodes and considered only 3 layers for all the electrodes as shown in Fig.1 (ae).
Though numerous fabrication techniques have been listed in literature for fabricating molecular junctions, but we have theoretically employed mechanically control break junction (MCBJ) approach for its simplicity and effective results [48]. This technique is based on the stretching the wire, until the junction breaks and gives two separate electrodes. Relaxing the force on the elastic substrate by backbending allows the junction to be closed again [49]. This technique also offers the possibility to vary the contact geometry and contact resistance between molecule and electrodes [50].
The transport properties of proposed molecular devices are investigated employing a combination of DFT and non-equilibrium Green's function (DFT-NEGF), which has emerged as workhorse for many mathematical modelling calculations in last two decades [51,52]. This study has been carried out using Atomistic Tool Kit-Virtual Nano Lab (ATK-VNL) software [53] which is based on Gaussian basis set and TranSiesta-C.
The electron exchange correlation has been described employing the Perdew-Burke-Ernzerhof (PBE) [54] version of the generalized gradient approximation (GGA) that foremost ful ls the several mathematical requirements of DFT [55]. PBE suggests good trade-off between computational efforts and precision in amino acids and oligopeptides [56]. A combination of Double-Zeta Plus polarization (DZP) basis set and PBE-GGA has been excessively studied for environmental stability [57] and bio-sensing [58] of amino acids. However, we have employed Double-Zeta Double Polarized basis sets for the purpose of extending wave functions [59]. The atomic calculations are performed using norm-conserving Troullier-Martins pseudo-potentials [60]. The Monkhorst-Pack k-point sampling of 1x1x100 points along with mesh cutoff energy of 75 Hartree is employed for our mathematical calculations.

Results And Discussions
Firstly, we focus on the theoretical work function of the different metal electrodes. Theoretical prediction of work function offers a convenient and complementary tool to cumbersome experiment. Nevertheless, these predictions are not perfect due to approximations that are meant to make theory tractable [61]. Work function is the minimum energy required to remove an electron from the Fermi level to a state where it is at rest, without interacting with the solid. It is the type of binding energy which is equal to energy difference between the vacuum level and the Fermi level. Chemically, it is de ned as the difference between ionization potential and HOMO energy [62]. We initiated our research with local density approximation (LDA) and GGA for predicting work functions of the different electrodes using 9x9x1 kpoint sampling given in Table 1. Experimental as well as theoretical values of work function reported by other researchers are also given in Table 1 If we scrutinize the electrodes on the basis of work function, we found that Au(111) and Pt(111) offers the maximum and Cu(111) offers the minimum work function in both LDA and GGA. We extend our further research using GGA as it gives balanced descriptions of structures and energies with overall improvement over LDA [67,74].
Next, we focus on the energy offset between dominant molecular orbital and Fermi energy (E f ), which is used to predict the tunnelling barrier. In our theoretical modelling of Aspartic acid with different electrodes, the Highest Occupied Molecular Orbital (HOMO) lies closer to Fermi energy, providing the Hole tunnelling barrier. The Hole tunnelling barrier (HTB) can be given as where is the HOMO energy level of the molecular device. The HTB of l-Aspartic acid within different electrodes is given in g 1(f). There is signi cant correlation between work function and tunnelling barrier of the molecular junctions. The Electrodes with higher work function result in lower tunnelling barriers [79]. This is clearly acceptable in our case as Pt (111) and Au (111) offers the maximum work function and Au-Aspartic-Au and Pt-Aspartic-Pt offers the minimum HTB. The lower tunnelling barrier of molecular device offers the stronger coupling between molecule and the electrode [80].
Next, we measure the conductance across the proposed molecular devices, which is expressed as , where is the signi cant quantum conductance unit and is the transmission coe cient of the channel. The value of i.e., , where is the elementary charge and is the Planck constant [81]. We notice that the conductance dip is visible in Ag-Aspartic-Ag and Cu-Aspartic-Cu devices as shown in Fig. 1(h) and (i). This is due to weak coupling of molecule to the speci c electrode [82].
The conductance remains quantized within the nite bias range of -0.2 to +0.2V, -0.6 to +0.4V and -0.6 to +0.6V in case of Au-Aspartic-Au, Ag-Aspartic-Ag and Cu-Aspartic-Cu devices, shown in Fig.1(g, h and i) respectively. This quantized conductance implies insensitivity of the respective devices at speci c bias range [83,84]. Further, this insensitivity can lead to almost I-V characteristics of such devices within the same bias region.
The highest conductance peak appears at +0.2 V in case of Pt-Aspartic-Pt device. The molecule exhibits the least conductance with Cu-Aspartic-Cu device within the nite bias range of -2 to +2V. In case of Pd-Aspartic-Pd device, the conductance shows uctuations of varying magnitude. The zero bias conductance of the proposed molecular devices follow the order as Pt-Aspartic-Pt (0.1184 G0) > Pd-Aspartic-Pd (0.0751 G0) > Au-Aspartic-Au (0.0650 G0) > Ag-Aspartic-Ag (0.0114 G0) >Cu-Aspartic-Cu (0.0034 G0). Different amino acids including l-aspartic acid, offers very less conductance even in experimental MCBJ techniques [32].
The coupling strength and the HTB between the electrodes and the molecule signi cantly in uence the conductance of the molecular junction [85]. The zero bias conductance of different molecular devices correlates well with the work function of the metal electrodes based on GGA. The zero bias conductance is maximum in Pt-Aspartic-Pt and minimum in Cu-Aspartic-Cu.
Next, we observe the I-V characteristics and calculate the recti cation ratios (RR) of all the proposed molecular devices in nite bias range of -2 to +2V. The current is approximately equal to integration of transmission coe cient within the bias window ranging from to , where is the magnitude of the bias voltage. The three-dimensional transmission spectra of the proposed molecular devices within the bias range of -2 to +2V is shown in the Fig.1 (l-p). The dotted black lines indicate the bias window. The molecule exhibits nite negative differential resistance (NDR) and RR with all the ve electrodes.
In case of Au-Aspartic-Au device, the current changes almost linearly in the bias range of -0.8 to +0.8V as depicted in Fig. 2 (a). Three different NDR regions are observed in the different bias ranges. We noticed peak to valley ratio, ηg1= 1.  Fig. 2 (e).
The at conductance observed in both Ag-Aspartic-Ag device (i.e. from -0.6 to +0.4V) and Cu-Aspartic-Cu device (i.e. from -0.6 to +0.6V) (shown in Fig. 1 (h) and (i)) has insightful effect on their IV characteristics, (shown in Fig. 2 (b) and (c)) as the current does not show any signi cant rise within this speci c bias range.
In case of Au-Aspartic-Au device, the molecule exhibits the highest recti cation ratio of 1.89 at ±1.4 V as shown in inset of Fig 2 (a). As the bias voltage sweeps from 0.6 to 1.4 V, the recti cation ratio increases with increase in bias voltage and then decreases with increase in bias voltage from 1.4 to 1.8V. This is due to the shifting of transmission peaks within the bias window with respect to change in bias voltage as shown in Fig.1 (l).
The NDR and rectifying behaviour of the device can be pointed by transmission spectra, which is the most signi cant representation of quantum transport behaviour. The appearance of transmission peaks within the bias window (shown in Fig. 1(l-p)) can be attributed to the enhancement of current.
The I-V range for molecular devices at nite bias range of -2 to +2V, increases as the electrode work function increases. The Cu-Aspartic-Cu has minimum I-V range but Pt-Aspartic-Pt has maximum I-V range. Junctions with higher contact resistance have smaller coupling strength [86]. The higher the work function, the closer is the HOMO to the Fermi level, smaller is the offset between HOMO and Fermi energy (i.e. HTB) and the stronger is the molecule-electrode coupling [80].
We now focus on the cause of the highest NDR and RR of respective devices. In Fig. 2(f), (g), (i) and (j) the area under the curve decreases with increase in bias voltage, which causes the existence of NDR behaviour. In Fig. 2(h), the HOMO shifts away from the vicinity of Fermi level with increase in bias voltage from 1.8 to 2.0V. This shift causes the destruction of HOMO to split into HOMO and HOMO-1 resonances, which causes the NDR behaviour.
In case of Au-Aspartic-Au device, the area covered under HOMO and HOMO-1 resonant peaks at -1.4V is more as compared to +1.4V, re ecting the cause of recti cation ratio as shown in Fig. 2 (k). In case of Ag-Aspartic-Ag device, though HOMO of +1.8V is near to the Fermi level, yet the combination of HOMO and HOMO-1 of -1.8V is more effective to show more current shown in Fig. 2 (l).
In case of Cu-Aspartic-Cu device, the closeness of HOMO near the Fermi level at -2.0V depicts more current than +2.0 V as shown in Fig.2 (m). The area covered under the bias voltage of +0.2V and +0.4V is higher than -0.2V and -0.4 V in Pt-Aspartic-Pt and Pd-Aspartic-Pd devices, respectively shown in Fig. 2 (n) and (o). This clearly explains the cause of recti cation ratio.
In order to emphasize more on the cause of recti cation ratio, we need to focus on the Molecular Projected Self-consistent Hamiltonian (MPSH) states of proposed molecular devices. In Table 2, the bias voltage of -1.4 V shows more delocalization at HOMO-1 as compared to +1.4 V in Au-Aspartic-Au device, justifying the recti cation ratio.

Conclusions
It is imperative to study various parameters of molecular junction in order to predict the application of bio-molecule in Nano electronic devices. To gain a deeper insight, it is necessary to discern the transport properties of bio-molecule in conjunction with different electrodes.
The transport behavior of L-aspartic acid (i.e., L-amino acid) bound to gold, silver, copper, platinum and palladium electrodes is observed by evaluating numerous factors including work function, tunnelling barrier, molecule-electrode coupling, conductance, I-V characteristics, NDR, recti cation ratio, transmission spectra and MPSH. We perceive that the aspartic molecule offers the maximum coupling with platinum electrodes and minimum coupling with copper electrodes.
We observe the least conductance in Cu-Aspartic-Cu device at nite bias range of -2 to + 2V. This weak conductance con rms the weaker coupling of molecule with the electrode. Presences of conductance dip in Ag-Aspartic-Ag and Cu-Aspartic-Cu devices (shown in Fig. 2(b) and (c)) also con rm the weaker coupling of molecule with respective electrodes as compared to Pt-Aspartic-Pt devices. The conductance uctuations in Pd-Aspartic-Pd is due to the transmission probability, in which fraction of the transmitted electrons are scattered back [88].
This molecule in all the molecular con gurations exhibits remarkable NDR behaviour and reasonable recti cation. Such behaviour is corroborated by studying transmission spectra and MPSH in details. Laspartic molecule shows the highest recti cation ratio of 3.20 (at ± 0.2 V) with platinum electrode. Singlemolecule diode with recti cation ratio less than 10, have also been reported by other researchers [89][90][91][92].
The molecule depicts the multiple NDR behaviour with all electrodes at different bias voltages. Although, glutamic acid is a similar negatively charged amino acid, yet it does not offer NDR using silver electrodes [26]. Ag-Aspartic-Ag molecular device offers two NDR regions in positive bias range. Highest peak to valley ratio (i.e. 1.38) is observed in case of Pt-Aspartic-Pt device. We also nd the interesting behaviour of molecule that it offers equal number of NDR regions (i.e. 3 in each bias range) in Pd-Aspartic-Pd. Theoretically, NDR behaviour is also predicted in cysteine amino acid with Au (111), but detailed peak to valley ratio is not discussed [24]. Multiple NDR regions can also be observed in linear molecule by using nitro end groups [93]. Theoretical prediction of NDR behavior in single molecule is experimentally validated by using scanning tunnelling microscopy [94].
These ndings nally allow us to conclude the signi cance of molecule-electrode interface. Although the electrodes are symmetrical, yet there is visible NDR effects and signi cant recti cation ratio. This asymmetrical behaviour can hence be explained in two ways. Firstly, the molecule contains the alkane (-CH2) side chain, which leads to the nonlinear effects in I-V characteristics [25,26,95]. Secondly, the molecule shows spatial asymmetric structure i.e., mirror symmetry is absent, which can also manifest nonlinear effects [23,96].
The nonlinear effects can further be enhanced by asymmetrical molecule-electrode coupling which results into unequal shift of the Fermi levels of the electrodes [32,97]. The detection of NDR effect in the molecule witnesses the potential applications of it in random access memory devices, oscillators, and fast switching devices [98,99]. Finite recti cation ratio knocks the door to the future application in logic circuits and molecular memory [100]. We conclude from our theoretical ndings that such biomolecule must need various experimental prospects with different electrodes. Different experimental approaches further gives the seal of approval to such biomolecule for future protein based electronics.

Declarations
Funding: The authors did not receive support from any organizations for the submitted work.
Con icts of interests: The authors have no con icts of interest to declare that are relevant to the content of this article.
Availability of data and material: Not Applicable