Graphene quantum point contact transistor for DNA sensing
Anuj Girdhara,b, Chaitanya Satheb,c, Klaus Schultena,b, and Jean-Pierre Leburtona,b,c,1
Departments of aPhysics and cElectrical and Computer Engineering, and bBeckman Institute for Advanced Science and Technology, University of Illinois at Urbana–Champaign, Urbana, IL 61801
Edited* by Karl Hess, University of Illinois at Urbana–Champaign, Urbana, IL, and approved September 3, 2013 (received for review May 11, 2013)
By using the nonequilibrium Green’s function technique, we show the GNR-edge boundary condition on the nanopore sensitivity, that the shape of the edge, the carrier concentration, and the or a self-consistent treatment of screening due to charged ions position and size of a nanopore in graphene nanoribbons can in solution. strongly affect its electronic conductance as well as its sensitivity GNRs are strips of graphene with a finite width that quantizes to external charges. This technique, combined with a self-consis- the energy states of the conduction electrons (23–26). Unlike tent Poisson–Boltzmann formalism to account for ion charge traditional quantum wells, the boundary conditions of GNRs are screening in solution, is able to detect the rotational and positional complicated functions of position and momentum resulting from conformation of a DNA strand inside the nanopore. In particular, the dual sublattice symmetry of graphene, giving rise to a unique we show that a graphene membrane with quantum point contact band structure. Because of this, the shape of the boundary as well geometry exhibits greater electrical sensitivity than a uniform as the presence of nanopores profoundly affects the electronic armchair geometry provided that the carrier concentration is states of GNRs (27–30), for example, leading to a difference in tuned to enhance charge detection. We propose a membrane de- band structure for zigzag and armchair-edged GNRs (31). sign that contains an electrical gate in a configuration similar to The edge of a GNR can be patterned with near-atomic pre- a field-effect transistor for a graphene-based DNA sensing device. cision, opening up the possibility to investigate many different geometries (32). In the case of complicated edge shapes, the solid-state membrane | transport | bio-molecule | simulation current displays an extremely nonlinear and not strictly increasing dependence on carrier concentration. The graphene quantum ENGINEERING ver the past few years the need has grown for low-cost, high- point contact (g-QPC) is a perfect example in this regard, as its speed, and accurate biomolecule sensing, propelling the so- irregular edge yields a complex band structure and rich conduc- O tance spectrum with many regions of high sensitivity and negative called third generation of genome sequencing devices (1–4). differential transconductance (NDTC) as shown below. In addi- Many associated technologies have been developed, but recent tion, the g-QPC electronic properties are not limited by stringent advances in the fabrication of solid-state nanopores have shown GNR uniformity (armchair or zigzag) in the boundary conditions. that the translocation of biomolecules such as DNA through Moreover, the carrier concentration itself, which can be con-
such pores is a promising alternative to traditional sensing BIOPHYSICS AND trolled by the presence of a back gate embedded within a g-QPC methods (5–9). Some of these methods include measuring (i) device as in a field-effect transistor (FET), can profoundly af- COMPUTATIONAL BIOLOGY ionic blockade current fluctuations through nanopores in the fect the sensitivity and nonlinearity of the current. As a result, presence of nucleotides (10), (ii) tunneling currents across nano- fi iii changes in external electric elds, including changes due to ro- pores containing biomolecules (11), and ( ) direct transverse- tation and translation of external molecular charges, alter the current measurements (12). Graphene is a prime candidate for local carrier concentration and can dramatically influence the g- such measurements. Theoretical studies suggest that function- QPC conductance. In the following we demonstrate the complex alized graphene nanopores can be used to differentiate passing and nonlinear effects of altering boundary shapes, graphene car- ions, demonstrating the potential use of graphene membranes in fl rier concentrations, and electric potentials due to DNA trans- nano uidics and molecular sensing (13). In addition, its atomic- location on the conductance of such a device. We propose scale thickness allows a molecule passing through it to be scan- to sense DNA by performing transport measurements in a g- ned at the highest possible resolution, and the feasibility of using QPC device and demonstrate that the sensitivity of the con- graphene nanopores for DNA detection has been demonstrated ductance can be geometrically and electronically tuned to experimentally (14–17). Lastly, electrically active graphene can, in principle, both control and probe translocating molecules, acting Significance as a gate as well as a charge sensor, which passive, oxide-based nanopore devices are incapable of doing. Molecular dynamics studies describing the electrophoresis of Rapidly sequencing the human genome in a cost-effective man- DNA translocation through graphene nanopores demonstrated ner will revolutionize modern medicine. This article describes a that DNA sequencing by measuring ionic current blockades is unique paradigm for sensing DNA molecules by threading them possible in principle (18, 19). Additionally, several groups have through an electrically active solid-state nanopore device con- reported first-principles–based studies to identify base pairs using taining a constricted graphene layer. We show that the electrical tunneling currents or transverse conductance-based approaches sensitivity of the graphene layer can be easily tuned by both (12, 20, 21). Saha et al. reported transverse edge current variations shaping its geometry and modulating its conductance by means of the order of 1 μA through graphene nanoribbons (GNRs) of an electric gate integrated in the membrane. caused by the presence of isolated nucleotides in a nanopore, and reported base pair specific edge currents (12). These studies, Author contributions: A.G., C.S., K.S., and J.-P.L. designed research; A.G. and C.S. per- however, do not account for solvent or screening effects; the formed research; J.-P.L. contributed new reagents/analytic tools; A.G. and C.S. analyzed latter effects are due to the presence of ions in the solution and data; and A.G., C.S., K.S., and J.-P.L. wrote the paper. can reduce the ability of the nanoribbon to discern individual The authors declare no conflict of interest. nucleotides. Very recently, Avdoshenko et al. investigated the *This Direct Submission article had a prearranged editor. influence of single-stranded DNA on sheet currents in GNRs 1To whom correspondence should be addressed. E-mail: [email protected]. with nanopores (22). However, their study does not consider the This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. carrier concentration modulation of the current, the influence of 1073/pnas.1308885110/-/DCSupplemental.
www.pnas.org/cgi/doi/10.1073/pnas.1308885110 PNAS Early Edition | 1of6 Downloaded by guest on September 26, 2021 detect small differences in the charge geometry of biomolecules A B such as DNA. Structure Description Fig. 1 shows a monolayer g-QPC device in an ionic water solu- tion, containing a single layer of patterned graphene connected to source and drain leads and sandwiched between two oxide layers to isolate the graphene from the aqueous environment. The graphene and oxide layers have coaxial nanopores ranging from 2 to 4 nm, allowing charges, molecules, or polymers to pass through. Critical to the device shown is a back gate underneath the lower oxide substrate made of a metal or heavily doped CD semiconductor or another graphene layer to control the charge carrier concentration in graphene as in a FET configuration (the gate layer could in practice be capped by an oxide layer to avoid unwanted electrochemistry); the back gate enhances its electrical sensitivity to DNA translocation. The diameter of the nanopore is small enough to attain the required sensitivity, but is wide enough to let the biomolecules translocate. Results In this study, we investigate four edge geometries, namely a 5-nm-wide (Fig. 2A) and a 15-nm-wide (Fig. 2B) pure armchair- Fig. 2. Transmission functions for various edge geometries and pore con- edge GNR (Fig. 2A, Inset) as well as an 8-nm-wide (Fig. 2C) and figurations: (A) 5-nm (5-GNR)- and (B) 15-nm (15-GNR)-wide GNR-edged a 23-nm-wide (Fig. 2D) QPC edge (Fig. 2C, Inset). These ge- devices, (C) 8-nm (8-QPC)- and (D) 23-nm (23-QPC)-wide QPC-edged devices. ometries will herein be referred to as 5-GNR, 15-GNR, 8-QPC, Pristine (solid), a 2-nm pore at point P (long dash), a 2-nm pore at point Q and 23-QPC. The QPC geometries have pinch widths of 5 and (short dash), and a 4-nm pore at point P (dot–dash). 15 nm (2/3 total width), the same as the widths of the armchair- edged GNRs. For each edge geometry, we consider four pore configurations: pristine (no pore), a 2-nm pore in the center The resulting transmission probability varies largely within nar- (point P in Fig. 2), a 2-nm pore centered at 75% of the total row carrier energy ranges and exhibits resonances at particular (pinch) width for the GNR (QPC) (point Q in Fig. 2), and a carrier energies, revealing the strong dependence of transmission 4-nm pore at the center (point P in Fig. 2). probability on carrier energy. Increasing the pore diameter en- hances the scattering nature of the nanopore, thereby reducing Transmission Probability of Patterned GNRs. In Fig. 2, we demon- the transmission probability, as can be seen in Fig. 2A, where the strate the effects of the different edge geometries and pore 5-GNR with a 4-nm pore has an almost negligible transmission configurations previously described on the transmission spectra probability for most carrier energies in the represented range. By for suspended GNRs in vacuum. Here we choose a Fermi energy changing the nanopore positions, the particular wavelengths of range from 0 to (or smaller than) 0.5 eV, which corresponds to the electronic states that satisfy the boundary conditions vary, − − carrier concentrations varying from ∼1011 cm 2 to 5–7 × 1012 cm 2 which further affects the transmission probability. For instance, at a temperature of 300 K, easily achievable in a conventional the transmission of the GNR with the pore at Q is higher at graphene FET (g-FET). The transmission for the pristine (no lower energies compared with the GNR with the pore at P, be- pore) 5-GNR edge exhibits the classic staircase shape resulting cause the allowed electronic states at these lower energies have from the armchair-edge boundary conditions (Fig. 2A) (23). The larger wavelengths. presence of a nanopore introduces a scatterer in the GNR, which Similar trends can be seen for the transmission probability manifests itself as additional boundary conditions at the pore determined for the 15-GNR (Fig. 2B). Because of the larger edge, restricting the transmission in two ways: first, the number width compared with that of 5-GNR, there are significantly more of allowed electronic states becomes reduced due to the need of electronic states within a particular carrier energy range, in- satisfying more stringent boundary conditions; second, the elec- creasing the transmission probability for all pore configurations. tronic states that do satisfy these boundary conditions generally This results in more closely spaced transmission steps in the have smaller probability currents due to scattering off the nanopore. pristine GNR. As for 5-GNR with and without pore, pore edge boundary conditions destroy the staircase behavior of the transmission seen for pristine 15-GNR as well as reduce the magnitude of the transmission probability. In contrast, because of the larger width, the density of allowed electronic states in the 15-GNR is larger at high energies compared with the respective density in the 5-GNR. As a result, both pore configurations P and Q in the 15-GNR have a similar number of allowed elec- tronic states within a specific energy range, minimizing the differ- ence in transmission between the two configurations at higher carrier energies. Fig. 2C shows the transmission probability for the 8-QPC, which exhibits strong variations compared with that in the 5- or 15-GNR, because the nonuniform QPC edge introduces more stringent boundary conditions on the electronic states, especially Fig. 1. Schematic diagram of a prototypical solid-state, multilayer device when the QPC contains a nanopore. The transmission proba- containing a GNR layer (black) with a nanopore, sandwiched between two bility curves for the pristine 8-QPC and for the 8-QPC with
oxides (transparent) atop a heavily doped Si back gate, VG (green). The DNA a pore exhibit many resonance peaks throughout the Fermi en- is translocated through the pore, and the current is measured with the ergy range. It can be seen that the 4-nm pore (green curve)
source and drain leads, VS and VD (gold). (See SI Methods for a cross-sectional exhibits negligible transmission probability over the whole Fermi schematic diagram.) energy range, except around the band gap, which is reflected in
2of6 | www.pnas.org/cgi/doi/10.1073/pnas.1308885110 Girdhar et al. Downloaded by guest on September 26, 2021 two resonance peaks in both the conduction and valence bands. the electronic states with the edge and pore boundaries as seen Increasing the width in going from the 8- to 23-QPC increases in Fig. 2C. Even more remarkable is the appearance of a NDTC the density of states within an energy range, smoothing out the region in the conductance in the case of the 8-QPC with a 4-nm transmission at higher carrier energies as in the case of the 15-GNR hole, a feature unobserved for the GNR systems. Apparently, (Fig. 2D). The influence of the position and size of the nanopore tailoring the pore properties within a QPC geometry can result in on the transmission function follows the same trend as with the large changes in the conductance behavior. 15-GNR at high carrier energies as mentioned above. Fig. 3D shows the conductance properties of the four 15-QPC systems investigated. Comparison with the 8-QPC results shows Electronic Conductance of g-FET Devices. The electronic conduc- that the increased width renders the conductance less sensitive to tance as a function of the Fermi energy of charge carriers is pore geometry; in particular, NDTC regions are not recognized shown in Fig. 3. The conductance at a particular Fermi energy is in the 15-QPC with a 4-nm pore. However, conductance values the average of the transmission probability around that carrier at Fermi energies above 0.15 eV differ greatly for different pore energy weighted by the Fermi–Dirac distribution as described in sizes. Paradoxically, one notices that the conductance at low Eq. 4. In Fig. 3A we observe that the conductance of the 5-GNR Fermi energies of the 15-QPC with a 4-nm pore is larger than in as a function of carrier energy is strongly dependent on nanopore the case of the 15-QPC with a 2-nm pore at P. This behavior is size and position. As expected, the pristine 5-GNR has the due to enhanced transmission probability at low Fermi energies, largest conductance and increases relatively monotonically over caused by the particular shape of 4-nm nanopore. a wide range of carrier energies. Compared with the pristine Most of the conductance curves in Fig. 3 A–D exhibit different 5-GNR, the conductance curve of the 2-nm pore at P is much regions of high and low “sensitivity,” which we define as the slope lower over the range of Fermi energies up to 0.3 eV, whereas the of the conductance with Fermi energy. As a result, small changes curve with the pore at Q is at least 1 order of magnitude higher, in the Fermi energy can result in large variations in conductance exhibiting a plateau beyond 0.15 eV. The 4-nm pore in the similar to the transconductance in a FET (33). Because the local 5-GNR displays the lowest conductance values compared with all carrier potential energy will be influenced by a nearby charge, other 5-GNRs (pristine, 2-nm hole at P, 2-nm hole at Q) because which on our diagrams translates into Fermi energy changes, of its suppressed transmission probability as discussed earlier (Fig. deviations in such a charge’s position can significantly modify the 2).Fig.3B shows the conductance curves for the 15-GNR geom- device conductance. This behavior can be exploited to build an etries. All four systems (15-GNR: pristine, 2-nm hole at P, 2-nm ultrasensitive charge-sensing device. hole at Q, 4-nm hole at P) show a relatively monotonic increase in
conductance with Fermi energy. All conductance curves achieve Conductance Variations Due to External Charges. The influence of ENGINEERING values about 3 times larger than seen for the 5-GNR, exhibiting the the solvent is treated as a mean-field approximation based on expected scaling with GNR width. The positional effects are Boltzmann statistics in the electrolyte to determine the on-site mitigated as the 2-nm Q and P curves are almost identical. How- potentials on graphene as described in Methods. We also neglect ever, the pore size effects are retained, illustrated by a decrease electrochemical interactions between graphene and solution, in the conductance with increased (4-nm) pore size. because in practice the graphene will be capped by an insulator, Fig. 3C shows the conductance properties of the 8-QPC sys- preventing, for the most part, direct interaction between gra- tems investigated. The conductance changes at varying rates phene and the solvent. The effect of a test charge, placed within
throughout the investigated range of Fermi energies. It is re- a pore, on electronic transport in graphene is illustrated in Fig. 4. BIOPHYSICS AND markable to see how the introduction of a 2-nm pore at either Shown are the conductance changes upon placing a single elec- P or Q actually enhances the magnitude of the conductance tron charge (e) at two positions within a 2-nm pore at P; one COMPUTATIONAL BIOLOGY dramatically compared with that of the pristine 8-QPC, contra- position is at 1/2 radius to the west of the pore center (W or dicting the intuitive notion that the pore acts as a scattering west) and the other at 1/2 radius south of the pore center (S or barrier. This behavior can be attributed to the rich interaction of south). Fig. 4 A and B displays the conductance response for the 5-GNR and 15-GNR, respectively, whereas Fig. 4 C and D dis- plays conductance responses for the 8-QPC and 23-QPC, re- spectively. The difference in conductance upon charge placement A B varies between 0 and 0.8 μS for all geometries, which is well within the sensing range of most current probes. Conductance changes for the 5-GNR (Fig. 4A) are negligible over most of the energy range for both angular charge (W and S) positions, due to the suppressed transmission probability at low carrier energies (blue curve of Fig. 2A); For the 15-GNR, 8-QPC, and 23-QPC cases (Fig. 4 B–D), the angular position of the charge within the pore has a significant effect on the conductance, causing not only large differences in conductance over the investigated energy range but also a different sensitivity of the conductance to the CD Fermi energy. In these cases, the maximum difference in con- ductance occurs for a test charge in the west (south) position at smaller (larger) Fermi energies. The conductance can be either enhanced or reduced by the test charge, depending on the valueoftheFermienergy.Inthecaseofthe15-GNR(Fig.4B), for example, when the Fermi energy lies between 0 and 0.18 eV, the conductance change for the electron test charge in the west position is positive, whereas the change is negative for Fermi energies above this range. Similar behavior is seen for the 8- QPC and 23-QPC, but over different Fermi energy ranges (Fig. 4 C and D). Fig. 3. Conductance versus Fermi energy (as a function of carrier concen- One also notes that in Fig. 4, for all cases, the differences in tration) for the four edge geometries with four pore configurations for each conductance are antisymmetric with respect to the Fermi energy. geometry. (A) 5-GNR, (B) 15-GNR, (C) 8-QPC, and (D) 23-QPC. Pristine (solid), This is a direct consequence of the symmetry between electrons 2-nm pore at point P (long dash), 2-nm pore at point Q (short dash), and and holes in graphene. Because of this symmetry, electrons and 4-nm pore at point P (dot–dash). holes tend to react to the same potential with opposite sign, such
Girdhar et al. PNAS Early Edition | 3of6 Downloaded by guest on September 26, 2021 A B initially placed such that the bottom of the strand is 3.5 Å above the graphene membrane, and the axis of the DNA passes through the center of the nanopore (Fig. 5A). The DNA is then rigidly translocated through the nanopore at a rate of 0.25 Å per time step (snapshot) until the DNA has passed through the pore completely. After the last (400th) snapshot the top of the DNA strand is 13.5 Å below the graphene membrane. The charge dis- tribution from the DNA at each time step (snapshot) is mapped into the Poisson solver, and the electric potential on the gra- phene membrane is calculated for each snapshot as the DNA CD rigidly translocates through the pore. Due to strong screening from ions and water near the gra- phene membrane, the on-site electric potential of the nanopore is dominated by charges contained within a slice coplanar with the graphene membrane and directly inside the nanopore. Hence, during the translocation of the biomolecule through the nano- pore, the graphene membrane will sense a succession of DNA slices, which appear as an in-place rotation of the double helix in the absence of translocation. Because it is only the charges in the pore that matter (due to the strong screening effects), the electric potentials around the pore due to the DNA being pulled through are virtually identical to the potential arising if the DNA slice Fig. 4. Change in the conductance due to adding an external charge within coplanar with the membrane was rotated without translocation. the 2-nm pore. “S” means the charge is placed 1/2 radius south of the center Fig. 5B shows the on-site potentials for eight successive positions of “ ” of the pore, and W means the charge is placed 1/2 radius west of the the DNA (A-B-C-D-E-D′-C′-B′) in the graphene plane, repre- center of the pore. (A) 5-GNR, (B) 15-GNR, (C) 8-QPC, and (D) 23-QPC . senting one half-cycle of this pseudorotational behavior. As mentioned above, the lattice including a nanopore may not be both x- and y-axis reflection symmetric with the pore at the that the conductance changes are an odd function of Fermi B center due to the discrete nature of the lattice. For example, the energy. For instance, in Fig. 4 , there is a peak in the conduc- 15-GNR with a 2.4-nm pore exhibits y-axis (Fig. 2A, Inset) re- tance change for the 15-GNR around 0.1 eV for all four charge fl x A Inset fl fi ection symmetry, but not -axis (Fig. 2 , )re ection sym- con gurations; a similarly shaped peak, but with opposite sign, is metry, as in the shape of the letter “Y.” In contrast, the 5-GNR, located at −0.1 eV. Similarly, one finds for the 23-QPC, as shown in D − 8-QPC, and 23-QPC geometries with a 2.4-nm pore exhibit both Fig. 4 , peaks at 0.15 eV and opposite peaks at 0.15 eV. The y- and x-axis reflection symmetry, as in the shape of the letter reader can notice, however, the different parity between the dif- “X.” These symmetries have an effect on the electronic con- C D ferential conductance curves at low energy in Fig. 4 and ,which ductance in GNRs when the DNA strand is introduced. When C arenegativeforthe8-QPC(Fig.4 ) and positive for the 23-QPC calculating the conductance from the transmission probability, (Fig. 4D). Similar conductance curves for a reduced electron charge note that the transmission probability itself does not represent are included in SI Methods and display the same behavior as the full a particular direction of current flow. In other words, a reflection electron test charge but scaled by a constant factor as expected. about either the x-ory axis of the lattice and its on-site electric potential map leaves the transmission probability, and hence the Electrical Response to DNA Translocation. To demonstrate a poten- conductance, unchanged. When the DNA strand is translocated, tial application of a charge-sensing device exploiting the sensitivity the electric potential maps of successive snapshots look like of geometrically tuned GNRs, we simulated the translocation of A→B→C→D in Fig. 5B, corresponding to the translocation of a strand of DNA through a 2.4-nm pore located at the center one half-pitch of the DNA helix, and for the second half of the (point P above) of the four edge geometries. We translocate a cycle the successive snapshots look like E→D′→C′→B′. The D′, 24-base-pair B-type double-stranded DNA segment consisting C′, and B′ potential maps are effectively the mirror images (y-axis of only adenine–thymine nucleotide base pairs. The DNA is reflected) of D, C, and B, respectively. As a result, assuming the
Fig. 5. (A) Schematic of an AT DNA strand translocating through a pore. (B) Potential maps in the graphene plane due to the DNA molecule at eight succes- sive snapshots throughout one full rotation of the DNA strand.
4of6 | www.pnas.org/cgi/doi/10.1073/pnas.1308885110 Girdhar et al. Downloaded by guest on September 26, 2021 A B position and Fermi level, in concert with each other, can strongly change the magnitude of the electrical sensitivity of the devices. Additionally, for some geometries, such as the 8-QPC (Fig. 6C), a small change in Fermi energy (0.12 to 0.16 eV) results in a threefold change in the magnitude of the conductance (13 to 40 μS) and a threefold increase in the magnitude of conductance variations (0.9 to 2.8 μS). Interestingly, because of the presence of NDTC regions within the investigated Fermi energy range, an increase of Fermi energy may actually decrease the conductance, as in case of the 5-GNR (Fig. 6A). Studies on electrochemical CD activity at the edge of graphene nanopore have been reported recently (34), which can lead to an electrochemical sheet current in graphene of the order of 0.5 nA for a pore diameter of 2.4 nm. Although this is a large electrochemical current, the sensitivity reported here to DNA translocation is much larger than the elec- trochemical current measured, especially at larger Fermi energies. In our simulation, a new nucleotide is within the plane of the nanopore after ∼13 time steps. However, no such periodic modu- lation is visible in the conductance curves of Fig. 6. The reason for this is the strong screening due to the phosphate backbone on the DNA strand. As a result, the conductance variation reflects the po- Fig. 6. Conductance as a function of DNA position (snapshot) for multiple sitional changes of the backbone charges as opposed to the move- Fermi energies, 0.04 eV (solid), 0.08 eV (long dash), 0.12 eV (short dash), and ment of the nucleotide charges themselves. To sequence DNA, one 0.16 eV (dot–dash), as the DNA strand rigidly translocates through a 2.4-nm must be able to detect these nucleotides, either by translocating nanopore pore located at the device center (point P). (A) 5-GNR, (B) 15-GNR, a single strand of DNA to prevent screening of the nucleotides by (C) 8-QPC, and (D) 23-QPC. the backbone, or by making the DNA and its backbone undergo nucleotide-specific conformational changes, a topic which we are currently investigating as well as the influence of the thermal DNA potential is reflection symmetric about its own axis (“DNA fluctuations of the DNA molecule on the g-FET conductance. ENGINEERING axis”), the conductance curves corresponding to geometries with only y-axis reflection symmetry should display a half-cycle “mir- Conclusion ” → → ror effect, repeating only after a full A E A rotation, i.e., the We have described above a unique strategy for sensing the mo- ′ conductance should be identical for snapshots D and D , C and lecular structure of biomolecules by using a nanopore in electri- ′ C , etc. On the other hand, because the electric potential maps B cally active monolayer graphene shaped with a lateral constriction and D (and therefore B′ and D′) are identical after an x-axis fl or QPC, using an electrically tunable conductance to optimize re ection, the conductance should mirror after a quarter-cycle detection sensitivity. The suggested measurement has been ana-
translation of the DNA and should repeat itself after a half-cycle BIOPHYSICS AND → → → lyzed theoretically by using a self-consistent model that integrates
(A B C D) in the 5-GNR, 8-QPC, and 23-QPC. ’ COMPUTATIONAL BIOLOGY A–D the nonequilibrium Green s function formalism for calculating Fig. 6 shows the conductance as a function of the snap- electronic transport in the g-QPC with a detailed description of shot number (time) for Fermi energies 0.04, 0.08, 0.12, and 0.16 the electrical potential due to solvent, ions, and molecular charges eV above the Dirac point for each of the four geometries with in the nanopore. In particular, we have demonstrated that gra- a 2.4-nm pore at point P. The lines marked A-B-C-D-E-D′-C′-B′ phene QPCs are capable of detecting DNA molecules trans- correspond to the eight potential maps in Fig. 5B, representing locating through the nanopore, with a sensitivity controlled by the the translation of one full helix of the DNA. As can be seen in graphene carrier concentration. To achieve QPC carrier tunability, Fig. 6B, the 15-GNR displays the half-cycle mirroring behavior described above, only repeating after each full helix translocates we propose a solid-state membrane design made of a graphene through the pore. On the other hand, the 5-GNR, 8-QPC, and QPC sandwiched between two dielectrics to isolate the active 23-QPC conductances shown in Fig. 6 A, C, and D, respectively, display the quarter-cycle mirror effect; lines A–C represent one quarter of the helix, C–E represent the second quarter, etc. The DNA molecule in Fig. 5A contains 24 AT base pairs, which give rise to 2.5 full turns of the double helix. As a result, full trans- location of the DNA molecule should result in 2.5 periods in the conductance curves of the 15-GNR, and 5 periods in the case of 5-GNR, 8-QPC, and 23-QPC, which is indeed the case as shown in Fig. 6. In these latter conductance curves, the peaks of each cycle correspond to potential map A, when the DNA axis is parallel to the y axis, whereas the troughs correspond to potential map C, when the DNA axis is parallel to the x axis. The DNA molecule is not perfectly symmetric, as the bases in a base pair are different nucleotides; additionally, there may be a small discretization asymmetry in the potential map of the DNA. The cumulative effect is a slight difference in the conductance after y fl A C D Fig. 7. Schematic diagram of a four-layer device containing two graphene a -axis re ection, which can be recognized in Fig. 6 , , and . layers (black) to control the translational motion of DNA through the The large conductance variations accompanying DNA trans- nanopore. The top graphene layer (V ) controls the translational speed of location through the pore demonstrate the high sensitivity of C1 the DNA, whereas the second (VC2) controls the lateral confinement of the the device to external charges and their conformation. With a DNA within the nanopore. The third graphene layer (VDS) measures the source–drain bias of 5 mV, the conductance (current) displays sheet current. Finally, a heavily doped back gate (green) lies underneath maximum variations of 0.8–8 μS(4–40 nA) depending on the the sheet current layer to control the carrier concentration. Oxide barriers particular geometry (Fig. 6), well detectable with present tech- (transparent) between different graphene layers provide electrical isolation. nology. These large variations reinforce the idea that angular (See SI Methods for a cross-sectional schematic diagram).
Girdhar et al. PNAS Early Edition | 5of6 Downloaded by guest on September 26, 2021 g-layer from the electrolyte as well as suppress mechanical fluc- Electronic Structure of g-QPC Transistor and Electronic Transport. To model tuations of the membrane itself; the design permits simultaneous electronic transport sensitivity through a constriction in a g-QPC, we describe control of the carrier concentration by an external gate as in a FET the electronic properties of the patterned graphene layer through the tight- configuration feasible with today’s semiconductor technology. The binding Hamiltonian (23) (SI Methods): electrically active multilayer membrane device furnishes a start- X X ing design for enhanced performance and multifunctional = † + : : + † : H tij bj ai h c Vi ci ci [3] membranes that use more than one layer of graphene sand-
+ − Health (NIH) Grants 9P41GM104601 and NIH 5 R01 GMO98243-02. The Here, K and Cl are the local ion concentrations, e is the electronic charge, authors also gratefully acknowledge supercomputer time provided by the and c0 is the molar concentration of KCl, which we have set to 1 M. Eq. 1 is Extreme Science and Engineering Discovery Environment (XSEDE) MCA93S028. solved numerically as explained in SI Methods. C.S acknowledges support as a Beckman Graduate Fellow.
1. Branton D, et al. (2008) The potential and challenges of nanopore sequencing. Nat 20. Nelson T, Zhang B, Prezhdo OV (2010) Detection of nucleic acids with graphene nano- Biotechnol 26(10):1146–1153. pores: Ab initio characterization of a novel sequencing device. Nano Lett 10(9):3237–3242. 2. Schloss JA (2008) How to get genomes at one ten-thousandth the cost. Nat Biotechnol 21. Prasongkit J, Grigoriev A, Pathak B, Ahuja R, Scheicher RH (2011) Transverse con- 26(10):1113–1115. ductance of DNA nucleotides in a graphene nanogap from first principles. Nano Lett 3. Schadt EE, Turner S, Kasarskis A (2010) A window into third-generation sequencing. 11(5):1941–1945. Hum Mol Genet 19(R2):R227–R240. 22. Avdoshenko SM, et al. (2013) Dynamic and electronic transport properties of DNA 4. Derrington IM, et al. (2010) Nanopore DNA sequencing with MspA. Proc Natl Acad Sci translocation through graphene nanopores. Nano Lett 13(5):1969–1976. USA 107(37):16060–16065. 23. Castro Neto A, Guinea F, Peres N, Novoselov K, Geim A (2009) The electronic prop- 5. Li J, Gershow M, Stein D, Brandin E, Golovchenko JA (2003) DNA molecules and erties of graphene. Rev Mod Phys 81(1):109–162. configurations in a solid-state nanopore microscope. Nat Mater 2(9):611–615. 24. Brey L, Fertig H (2006) Electronic states of graphene nanoribbons studied with the – 6. Storm AJ, Chen JH, Ling XS, Zandbergen HW, Dekker C (2003) Fabrication of solid- Dirac equation. Phys Rev B 73(23):235411 235415. state nanopores with single-nanometre precision. Nat Mater 2(8):537–540. 25. Han MY, Özyilmaz B, Zhang Y, Kim P (2007) Energy band-gap engineering of gra- – 7. Gracheva M, et al. (2006) Simulation of the electric response of DNA translocation phene nanoribbons. Phys Rev Lett 98(20):206805 206808. through a semiconductor nanopore–capacitor. Nanotech 17(3):622–633. 26. Ezawa M (2006) Peculiar width dependence of the electronic properties of carbon – 8. Gracheva M, Aksimentiev A, Leburton J-P (2006) Electrical signatures of single-stranded nanoribbons. Phys Rev B 73(4):045432 045439. 27. Cervantes-Sodi F, Csanyi G, Piscanec S, Ferrari A (2008) Edge-functionalized and DNA with single base mutations in a nanopore capacitor. Nanotech 17(13):3160–3165. substitutionally doped graphene nanoribbons: Electronic and spin properties. Phys 9. Xie P, Xiong Q, Fang Y, Qing Q, Lieber CM (2012) Local electrical potential detection Rev B 77(16):165427–165439. of DNA by nanowire-nanopore sensors. Nat Nanotechnol 7(2):119–125. 28. Furst J, et al. (2009) Electronic properties of graphene antidot lattices. New J Phys 10. Dekker C (2007) Solid-state nanopores. Nat Nanotechnol 2(4):209–215. 11(9):095020. 11. Ivanov AP, et al. (2011) DNA tunneling detector embedded in a nanopore. Nano Lett 29. Vanevic M, Stojanovic V, Kindermann M (2008) Character of electronic states in graphene 11(1):279–285. antidot lattices: Flat bands and spatial localization. Phys Rev B 80(4):045410–045417. 12. Saha KK, Drndic M, Nikolic BK (2012) DNA base-specific modulation of microampere 30. Baskin A, Král P (2011) Electronic structures of porous nanocarbons. Sci Rep 1(36):36. transverse edge currents through a metallic graphene nanoribbon with a nanopore. 31. Ritter KA, Lyding JW (2009) The influence of edge structure on the electronic prop- – Nano Lett 12(1):50 55. erties of graphene quantum dots and nanoribbons. Nat Mater 8(3):235–242. 13. Sint K, Wang B, Král P (2008) Selective ion passage through functionalized graphene 32. Tapasztó L, Dobrik G, Lambin P, Biró LP (2008) Tailoring the atomic structure of – nanopores. J Am Chem Soc 130(49):16448 16449. graphene nanoribbons by scanning tunnelling microscope lithography. Nat Nano- 14. Garaj S, et al. (2010) Graphene as a subnanometre trans-electrode membrane. Nature technol 3(7):397–401. – 467(7312):190 193. 33. Streetman B, Banerjee S (2005) Solid State Electronic Devices (Prentice Hall, Upper 15. Merchant CA, et al. (2010) DNA translocation through graphene nanopores. Nano Saddle River, NJ). Lett 10(8):2915–2921. 34. Banerjee S, et al. (2013) Electrochemistry at the edge of a single graphene layer in 16. Schneider GF, et al. (2010) DNA translocation through graphene nanopores. Nano a nanopore. ACS Nano 7(1):834–843. Lett 10(8):3163–3167. 35. Gracheva ME, Melnikov DV, Leburton J-P (2008) Multilayered semiconductor mem- 17. Venkatesan BM, et al. (2012) Stacked graphene-Al2O3 nanopore sensors for sensitive branes for nanopore ionic conductance modulation. ACS Nano 2(11):2349–2355. detection of DNA and DNA-protein complexes. ACS Nano 6(1):441–450. 36. Luan B, et al. (2010) Base-by-base ratcheting of single stranded DNA through a solid- 18. Sathe C, Zou X, Leburton J-P, Schulten K (2011) Computational investigation of DNA state nanopore. Phys Rev Lett 104(23):238103–239106. detection using graphene nanopores. ACS Nano 5(11):8842–8851. 37. Melnikov DV, Leburton J-P, Gracheva ME (2012) Slowing down and stretching DNA with 19. Wells DB, Belkin M, Comer J, Aksimentiev A (2012) Assessing graphene nanopores for an electrically tunable nanopore in a p-n semiconductor membrane. Nanotechnology sequencing DNA. Nano Lett 12(8):4117–4123. 23(25):255501–255506.
6of6 | www.pnas.org/cgi/doi/10.1073/pnas.1308885110 Girdhar et al. Downloaded by guest on September 26, 2021