Double Gated Single Molecular Transistor for Charge Detection
DDouble Gated Single Molecular Transistor for Charge Detection
S. J. Ray ∗ CEA, INAC-SPSMS, UMR-E CEA/UJF-Grenoble 1,17 Rue Des Martyrs, F-38054 Grenoble Cedex 9, France
R. Chowdhury
Department of Civil Engineering, Indian Instituteof Technology Roorkee, Roorkee 247 667, India
Abstract
The electrostatic behaviour of an 1,3-Cyclobutadiene (C H ) based Single Molecular Transistor(SMT) has been investigated using the first principle calculation based on Density functionalTheory and non-equilibrium Green’s function approach. While the molecule is placed on topof a dielectric layer (backed by a metallic gate) and weakly coupled between the Source/Drainelectrodes, the charge stability diagram revealed the presence of individual charge states in theCoulomb Blockade regime. This gets affected significantly on addition of an another gate electrodeplaced on the top of the molecule. This modified double-gated geometry allows additional controlof the total energy of the system that is sensitive to the individual charge states of the moleculewhich can be used as a charge sensing technique operational at room temperature. ∗ Electronic address: [email protected] a r X i v : . [ c ond - m a t . m e s - h a ll ] N ov . INTRODUCTION In the area of nanoelectronics, single electron transistor (SET) is well known due to itsquantised nature of transport since its discovery [1] that has found application for sensitivecharge detections [2, 3]. The packing density of the MOSFET devices in the present dayCMOS technology is limited by the gate lengths accessible using various lithography tech-niques and the tunnelling issues. As a result of which the industry is constantly lookingfor useful alternatives in next generation technology to achieve faster switching performanceand speed. SET’s can be useful in this direction due to its small size and low power opera-tion and performance that can be easily integrated towards large scale fabrication in future.While the conventional metallic SET’s were made using a metallic island artificially placedbetween the S/D electrodes, in the recent times growing interest was found in replacingthe metallic island by an organic molecule and hence the area of molecular electronics wasdeveloped that has made significant progress towards developing single molecular devices(SMT) with the organic molecules as the active component of the circuit [5, 6]. Operationof such devices have been in presence for the past years which was first demonstrated byReed et. al [5] using Benzene-1,4-dithiolate as the active molecule. Experimental realisa-tions of such devices were made successfully in Carbon based systems [7, 8], Benzene [12],Oligophenylenevinylene (OPV) [20, 21], Fullerene [9], Dipyridylamide [10] and to designlogic circuits [14] etc. However, understanding the detailed nature of electronic transportin such devices in still under study and has not been well understood in details. In thestrong coupling (SC) limit, the conduction behaviour is usually dominated by the coherentelectron transport that often overestimates the current/conductance and in the weak cou-pling (WC) limit, the sequential nature of transport is governed by the orthodox theory ofCoulomb Blockade that underestimates the value of the energy gap [15]. While the trans-port behaviour is usually estimated semi-empirically using a combination of Non-equilibriumGreen’s function formalism (NEGF) and Density Functional Theory (DFT) [16] in the SClimit, the incoherent transport behaviour in the WC limit was formalised by a recent ap-proach proposed by Kaasberg et. al [17] and Strokobro et. al [12] has introduced this withina DFT framework for the estimation of various energy levels. This approach has been usedcomputationally in the recent times to estimate the charging energy of systems based onBenzene [12, 18], Fullerene [12], Napthalene [13], DNA chain [19] etc. which has found2xcellent agreement with the experimental results.Due to the incoherent nature of transport, a SMT is incredibly sensitivity to its chargestate similar to a SET. While an incoming charge is capacitively coupled to the SMTmolecule, any change in the charge state can be sensed through the charge stability dia-gram. In a conventional SMT, the gate electrode is placed in very close proximity of theisland (or the molecule) to control the chemical potential independently. Here in this presentcase, we have modified this geometry to introduce an additional gate electrode on top ofthe molecule to achieve better electrostatic control over the device and to find its influenceon the energy levels of the molecule and to demonstrate its usefulness as a sensitive chargedetector.
II. SYSTEM DESCRIPTION AND COMPUTATIONAL RECIPE
In this present work, the active component of the the system under investigation is an1,3-Cyclobutadiene molecule working as the ‘island’ in the SMT devices. The molecule has asquare central structure with 4 Hydrogen atoms placed symmetrically at each corners of theCarbon atoms as illustrated in Fig. 1(a). The small and planar structure of Cyclobutadieneis advantageous in such a device as the influence of electrical polarisation is significantly lessthan the direct gate-molecule coupling that determines the performance of a transistor. Forthe single and double gated SMT [11] as illustrated in Fig. 1(b),(d), the molecule was placedsymmetrically between the source (S) and drain (D) electrodes on top of a dielectric slabwith the molecular plane lying parallel to the dielectric surface. For the single gated device,the dielectric layer is of thickness ( d b ) = 3.7 ˚A and with a dielectric constant of 10 ε whichis connected to a metallic backgate electrode of thickness 1 ˚A as illustrated in Fig. 1(b).In the case of the double gated device (see Fig. 1(d)), an additional top gate of thickness 1˚A was introduced to the device between the top part of the Source/Drain(S/D) electrodesconnected to the top of an additional dielectric slab of thickness ( d t ) = 4 ˚A . The spatialseparation between the molecule and both the dielectric layers is ∼ ζ polarised (DZP) basis set.Considering the metal electrodes as equipotential surfaces, Neumann boundary conditionswere used while solving the Poisson’s equation assuming the perpendicular component ofthe electric field stays at zero at the interfaces, details of which could be found here [12].The island-S/D electrode separation was chosen to be large enough so that calculationscan be performed in the weak coupling limit as it is possible to estimate the molecularenergy states accurately when incoming electron gets sufficiently enough time to stabiliseon the molecule, hence carrying no information about its initial or final states. In such adevice, electronic transport is only possible when an electron can be moved from the highestoccupied molecular orbital (HOMO) level to the lowest occupied molecular orbital (LUMO)level and the minimum energy needed for this is called as the additional energy ( E a ) whichcan be expressed by, E a = ( E n − − E n ) − ( E n − E n +1 ) = ( E n +1 − E n − − E n ) (1)where n is the number of electrons in the neutral state of the molecule. III. RESULTS AND DISCUSSION
In Fig. 2(a), the total energy of the molecule in the SMT environment has been estimatedfor different charge states ( q ) as function of the backgate voltage ( V bg ) for a fixed top-gatevoltage V tg = -8V. A part of the total energy ( E tot ) is contributed by the metallic reservoirpotential (= qW ) where W is the work function of the metal electrode, which for the presentcase of Au electrode is 5.28 eV. For all the charge states, E tot showed monotonic dependencewith the gate excitation. For the positive charge states, the total energy gets reduced atnegative gate voltages and the situation is opposite for negative charge states where positivegate voltage reduces E tot . This happens due to the stabilisation of the positive charge statesat V bg < V bg > V bg >
0, the LUMO level goes below the Fermi level ( E F ) ofthe electrode and this allows the transfer of an additional electron to the molecule andit becomes more negatively charged. However for V bg <
0, the HOMO level gets shiftedtowards a higher energy level and in this case, an electron moves from the molecule to theelectrode making it more positively charged.For investigating further dependence of E tot with V bg , the energy can be analytically fittedby a 2 nd order polynomial as, E tot ( q ) = E ( q ) + αqV bg + β ( eV bg ) (2)where coefficients α and β are the fitting parameters which for the present case were es-timated to be α = 0.224 and β = 0.01 eV − . The 2 nd term in the Eqn. 2 is proportionalto q which is due to the strong coupling of the backgate electrode to the molecule and thevalue of α is a measure of the strength of coupling between them. The final term in Eqn. 2indicates the influence of the electrical polarisation of the molecule and is independent ofthe charge states. Since the molecule stays flat parallel to the dielectric surface and hencethe difference of the electric field experienced by different atoms is minimal and this termhas a smaller contribution compared to the 2 nd term as supported by β < α . The valuesof α and β stay almost constant for different charge states and the dependence of E withthe charge states was illustrated in Fig. 2(b). In the absence of any V bg , E decreases withan increase in q initially for q < V tg < q ≥
0. However, the rate of this change in E , dE /dq which can be estimated from the slope as plotted in Fig. 2(c) is linear in q . Thelinear slope indicates that only in the presence of a V tg , adding or removing a charge fromthe molecule at a specific state will have identically opposite influence on the zero-term inenergy.For investigating further dependence of the total energy on V bg and the conduction be-haviour, the charge stability diagrams (also called as Coulomb Diamond plot) have beenplotted in Fig. 3. As the SMT operates in the weak coupling regime, electron transportbetween the S/D electrodes is only possible when the molecular energy levels are accessiblewithin the applied bias ( V d ) window. Details of this conduction regime could be found fromthe charge stability diagram as illustrated in Fig. 3(a) which was calculated for V tg = -8V.5he colourbar on the right represents the number of available energy levels for conduction fordifferent V d and V bg . Experimentally the charge stability diagram is measured by measuringthe source-drain current and the z -axis is represented by the current, conductivity or differ-ential conductance. The diamonds indicate the accessible regions of conduction to separatethe non-conducting and conducting regions for different values of V d and V bg . In Fig. 3(a),the central region of the large diamond surrounded by points ‘A’, ‘B’, ‘C’, ‘D’ marks thekey region of conduction within which sequential tunnelling between different charge statesoccurs in this device. In Fig. 3(b), this region was enlarged to describe the behaviour of theground state excitation of the molecule. The central diamond in Fig. 3(b) corresponds to theneutral charge state of the molecule in its ground state with a hypothetical N electrons in it.Within each of these diamonds, the population does not change on the molecule, however,moving from one of these regions to its left or right will result in changing the population.The charging energy of the ground state can be estimated from the height of the centraldiamond (marked by dotted arrow in Fig. 3(b)) which is 6 .
628 eV and the height of its ‘left’and ‘right’ diamonds are 3 .
428 eV and 2 . C s and C d respectively were estimated from the slopes of the lines ‘AD’ and‘AC’. The slope of the line ‘AD’ is ∼ − C dot − bg /C d and the slope of ‘AC’ = C dot − bg / ( C s + C d )where C dot − bg is the capacitance between the ‘dot’ and the ‘backgate’. The gate capacitanceswere estimated analytically by considering a planar approximation of the gate electrodes ina parallel plate geometry which can be expressed by : C dot − bg = ε (1 + ε r ) A bg /d b and C dot − tg = ε (1 + ε r ) A tg /d t where ε r is the relative permeability of the dielectric layer, C dot − tg
6s the capacitance between the ‘dot’ and the ‘topgate’, d b and d t are the thicknesses ofthe ‘bottom’ and ‘top’ dielectric layers respectively and A bg , A tg are the areas of contactsbetween the ‘bottom’ and ‘top’ gates with their respective dielectric layers in contacts.In Fig. 3(c), a horizontal linescan was taken along the dotted line ‘CD’ as represented inFig. 3(a). The appearance of sharp peaks represent the points when the conduction windowchanges form a certain diamond to the neighbouring one and hence the change of the ‘dot’population by 1 between each of the neighbouring diamonds, from left to right for increasing V bg . At low bias voltage ( V d ), the excitations only occur from the ground state to the firstexcited state which is why the peaks arise at values q = 1 for all values of V bg . Anothervertical line scan taken along ‘AB’ (as illustrated in Fig. 3(d)) showed occurrence of periodicplateaus symmetrically placed on both sides of V d = 0 V. The step like structure arises onlyat finite values of q as a result of charging between different charge states and the chargingenergies can be estimated from the width of the respective steps. In the Coulomb Blockaderegime, the minimum occours at V d = 0 V in the absence of any excitation and subsequentenhancement of V d results in moving to the higher excited states. The occurrence of theplateaus can be understood in details from the differential ( dq/dV d ) charge plot which issimilar to the behaviour observed from the differential conductance (dI/dV) measured in anexperiment as illustrated in the bottom panel of Fig. 3(d). The peak positions observed inFig. 3(d) [bottom panel] represent the values of V d at which charging to an excited stateoccurs in the absence of continuous transport when the tunnelling rate (Γ) is very low.The separation between two neighbouring peaks in Fig. 3(d) [bottom panel] represents thecharging energy of the molecule between subsequent excited states for a given V bg which isnot uniform between all the charge states.To find the systematic dependence of the V tg in such devices, the charging energy ( E ch )for the neutral case in the ground state of the molecule was compared for different valuesof V tg . The minimum in E ch occours at V tg = -8V and it increases with an increase inthe V tg . Reduction of the E ch occurs when the molecule is bought from its gas phase toa SMT environment due to the polarisation of its charge states in the presence of metallicelectrodes. Under the addition a top electrode, this effect gets enhanced and the non-lineardependence of E ch − V bg indicates the influence of additional polarisation in the presence ofthe top electrode and a positive V tg induces additional polarisation to the molecule in itsground state. 7t is to be noted that the vertices of the large diamond enclosed by ‘ABCD’ (see Fig. 3(a))does not stay at the same position with a change of V tg . The position of the line ‘AB’ canbe referenced to investigate this dependence. Since the V bg stays the same for both ‘A’ and‘B’, the x − coordinate which is the value of V bg , can be considered as a reference point. InFig. 4(b), such values of V bg from the line ‘AB’ was plotted as function of V tg which indicatesan almost linear dependence between them. In Fig. 4(b), the dependence between the twogate voltages was plotted to estimate the nature of coupling between them through themolecule. The slope of this line is 1 . d t + 1) / ( d b + 1) = 1.063. The slope ∼ V bg and V tg in Fig. 4(c),(d). For q = 0, the surface is almost symmetrically curved around the red dottedline as illustrated in Fig. 4(c). When the molecule is in a neutral charge state, maximumof the energy occurs due to the polarisation of the molecule when both the gates are atequal values (‘red’ dotted line in Fig. 4(c)) and when they are of opposite signs, total energygets reduced as one of two gate voltages increases the polarisation while the other counterbalances it. For this reason, the minimum of the energy can be found at the two extremes( V tg =+8V, V bg =-8V) and ( V tg =-8V, V bg =+8V) for q = 0. For higher charge states, thesituation changes significantly which can be seen from Fig. 4(d). For q = −
3, the maximumin energy occurs at ( V tg = -8V, V bg = -8V) and minimum on the other end at ( V tg = +8V, V bg = +8V) when the charge state is more stabilised. For q = +3, the situation is opposite whichhas minimum at V tg = -8V, V bg = -8V and maximum at V tg = +8V, V bg = +8V. The natureof the energy surfaces is different for different charge states and starting from any point ofany of these landscapes, energy sharply changes with a change of V bg and V tg which makesit sensitive for detection of an incoming charge state. The steep slope of the energy surfacesindicates that the energy state of the SMT is highly sensitive to a small change of the gatevoltages and this property can be used as a sensitive charge detection technique. Due tothe sequential nature of transport, the change of energy can be translated directly to thechange of current flowing through the device ( I ds ) which in the case of a real experimentaldevice is expected to demonstrate an identical sensitivity. The difference in the nature ofthe energy surfaces for different charge states thus allows to detect an incoming charge state8 apacitance C dot − tg (aF) C dot − bg (aF) C s (aF) C d (aF)Values 2.045 6.002 7.0325 7.0325TABLE I: Junction capacitances for single and double gated devices uniquely in such a device and the addition of a top gate proves to be extremely useful forinvestigating such behaviour. IV. CONCLUSION
In this work, we have performed computational investigation of a SMT with an 1,3-Cyclobutadiene molecule working as the ‘quantum dot’. Unlike the conventional case of asingle gated device, we have found better control of the electrostatics and performance byadding a top gate electrode. The performance of such a device was investigated by calculatingthe energy of the molecule for different gate voltages which were used later to construct thecharge stability diagram to understand the detailed nature of conduction. The molecularenergy states are highly sensitive to the gate voltages that changes significantly for differentcharge states and this unique behaviour can be utilised for using it as a sensitive organiccharge detector. These kinds of single molecular devices could be the ideal candidates forfuture generation nano-electronic devices as charge sensors for faster operational speeds andportability. Unlike the SET devices, these SMT’s are operational at room temperature whichis a genuine advantage of these molecular devices for operational usefulness and industrialapplications.
Acknowledgments
SR acknowledges the support provided through a Research Excellence Grant (REG)within the Joint Research Project “Qu-Ampere” (SIB07) supported by the European Metrol-ogy Research Programme (EMRP). The EMRP is jointly funded by the EMRP participatingcountries within EURAMET and the European Union. [1] M. H. Devoret, D. Esteve, and C. Urbina,
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C CC CH HHH
Back GateTop Gate DrainSource C dot_tg C s C d C dot_bg V tg S ou r ce D r a i n V tg V bg FIG. 1: (a) Schematic of 1,3-Cyclobutadiene molecule, (b) 2D Schematic of the Single gated SMTunder investigation (not upto the scale) with the Cyclobutadiene molecule (referred as the ‘dot’)positioned on top of the dielectric layer and the backgate connected to its back, (c) Junctioncapacitances corresponding to the device in Fig. 1(b), (d) Schematic of the Double gated SMTwith an additional gate connected to the top, (e) Capacitance network for the Double gated SMTand (f) A sample illustration of the distribution of the induced electrostatic potential in differentregions of the device for an equal but opposite values of the two gate voltages at V d = 0 indicatingthe molecule stays in an equipotential (green) region. d E / dq ( V ) -3 -2 -1 0 1 2 3Charge(q) [c] -690-680-670-660 E ( e V ) -3 -2 -1 0 1 2 3Charge(q) [b] -700-690-680-670-660-650 E t o t ( e V ) -8 -4 0 4 8V bg (V) q=-3 q=-2 q=-1 q=0 q=1 q=2 q=3 [a] FIG. 2: (a) Total energy of the molecule in the Double gated SMT as function of V bg for V tg = -8V for different charge states of the molecule. The points are the calculated values and the dottedlines represent the fitted values using Eqn. 2, (b) E estimated from the fits above as a function ofthe charge state q at V tg = -8 V, (c) Differential of the zero-term energy ( dE /dq ) as function of q , showing a linear dependence. The ‘green’ line is the fit to the data points in ‘red’. BC N N+1
N-1 V d ( V ) V bg (V) V d ( V ) V bg (V) D C h a r g e ( q ) -20 0 20V bg (V) bac d E ch C h a r g e ( q ) -20 -10 0 10 20V d (V)-10-50510 dq / d V d FIG. 3: (a) Charge stability diagram estimated for the double gated SMT device for V tg = -8 V.(b) Zoomed version of central region of the large diamond in Fig. 3(a) to highlight the 3 centraldiamonds used for estimating charging energy in the ground state. (c) Line scan taken along ‘CD’and (d) along ‘AB’ as marked in Fig. 3(a), (bottom) Differential charge ( dq/dV g ) as function ofV d . bc d V bg ( V ) -8 -4 0 4 8V tg (V) E c h ( e V ) -8 -4 0 4 8V tg (V) FIG. 4: (a) Charging energy in the neutral case of the molecule in the ground state (as estimated inFig. 3(b)) as function of V tg , (b) Relative location of V bg as function of V tg as estimated from thecoordinate of ‘B’ of the diamond in Fig. 3(a) [see text for details], (c) Energy surface as functionof V tg and V bg for the q = 0 state, The ‘red’ arrow is the line along which two gate voltages stayat identical values, (c) Energy surface as function of V tg and V bg for q = +3 and q = -3 chargestates.= -3 chargestates.