Adva Baratz and Roi Baer- Non-mechanical conductance switching in a realistic molecular tunnel junction

8/3/2019 Adva Baratz and Roi Baer- Non-mechanical conductance switching in a realistic molecular tunnel junction

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Non-mechanical conductance switching in a realistic

molecular tunnel junctionAdva Baratz

and Roi Baer

*

Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, the Hebrew University of Jerusalem, Jeru-

salem 91904 Israel.

We present a molecular junction composed of a donor (polyacetylene strands) and an acceptor (malononitrile) connected to-gether via a benzene ring and coupled weakly to source and drain electrodes on each side, for which a gate electrode inducesintramolecular charge transfer, switching reversibly the character of conductance. Using density functional theory, we show

the junction displays a single, gate-tunable differential conductance channel in a wide energy range. The gate field must alignparallel to the displacement vector between donors and acceptor to affect their potential difference; for strong enough fields

spontaneous intramolecular electron transfer occurs. This event radically affects conductance, reversing the charge of carri-ers, enabling a spin-polarized current channel. We discuss the physical principles controlling the operation of the junction,and find interplay of quantum interference, charging, Coulomb blockade, and electron-hole binding energy effects. We ex-pect this switching behavior a generic property for similar donor-acceptor systems of sufficient stability.

In recent years, gated molecular junctions, coupled weakly tosource-drain (SD) electrodes, were studied experimentally

and analyzed theoretically. The gate shifts differential con-ductance channels with respect to the chemical potential

(Fermi level) of the metallic leads1-15

and also affects nuclear

configuration by inducing electron transfer from metal elec-

trode to the molecule.16,17

However, to our knowledge, it has

not been widely discussed how to use the gate for inducinginternal change of electronic structure within the junctionitself, without generating significant nuclear reorganization.

A molecular junction that responds readily to such manipula-

tions could be useful for achieving high degree of control andswitching capabilities. It is the purpose of this paper to pre-

sent a conceptual idea towards such an effect, backed up by a

careful theoretical analysis of a specific molecular candidate.

A rich variety of physical processes (i.e. interference, charg-ing energies, electron-hole binding energy, polarizability and

Coulomb blocking) affect the various regimes of transport in

this junction. The resulting system displays a single, highly

tunable, resonance state, supporting a single differential con-ductance channel and an on/off switch for spin polarized cur-

rents.

Our analysis is theoretical and makes use of density function-

al theory (DFT) based on the first-principles-tuned Baer-

Neuhauser-Livshits (BNL*)18,19

range-separated hybrid.20,21

This functional allows for good molecular structure predic-

tion while being especially suitable for conductance calcula-

tions since its orbital energies were found to closely approx-

imate quasiparticle energies a property not available in themore common density functionals (see supplementary mate-rial for comparison of BNL* and B3LYP gaps).

22,23The func-

tional also allows calculation of accurate charge transfer24

aswell as valence

25 excitation energies with linear response

time-dependent density functional theory (TDDFT). All elec-

tronic structure calculations were performed using this BNL*

functional18,19,26

within the 6-31G/6-31+G* basis set and Q-

* Email: [email protected]

CHEM v3.1 package.27

See supplementary material for de-

tails on basis sets, tuning and a comparison to B3LYP.

Figure 1: Schematic depiction of the molecular junction explored in this

paper: two thiol-terminated short trans-polyacetylene (PA) segments

)), acting as meta substituents on the aromatic ring of a2-(3-phenylprop-2-ynylidene) malononitrile molecule. The thiol group facili-

tates bonding to gold metallic source drain electrodes. The PAs are electron

donors determining the ionization potential ( ) of the molecule whilethe MN is an electron acceptor, endowing the electron affinity . Themolecular plane is parallel to x-z and lies above a planar gate electrode paral-

lel to the x-y plane. The latter creates an electric field in the vertical direc-tion. The smallest vertical distance between MN and PA is large ( ), facilitating the high tunability of the fundamental gap by . Asufficiently strong induces spontaneous electron transfer from PA to MN.Due to interference effects, electric current cannot flow through the aromatic

ring from left to right PAs but must go instead through the MN. Thus alsocontrols the differential conductance channel of the junction.

The active part of the molecular junction is composed of the

2-(3-phenylprop-2-ynylidene) malononitrile molecule, wherethe malononitrile group (MN) acts as an electron acceptor,

and two thiol- terminated short trans-polyacetylene (PA)

segments connecting in meta position to the benzene ring

acting as electron donors (Figure 1). Configurational stability

of the junction, hindering bending and rotary distortions, even

under strong gate fields and charge shifts, is achieved by us-

ing conjugated PA segments as donors, and CC triple bond

connecting the acceptor to the aromatic ring, (see supplemen-

tary material for description of stability under gate fields).

z

Rz

xy

Oxide

Gate


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2

Figure 2: Graphical depiction of three frontier orbitals dominating the elec-

tronic properties of the junction. The occupied orbitals 1 and 3 (localized on

the left and right donors) and the unoccupied orbital 2 (localized on the ac-

ceptor). The energy of orbital 1 is slightly higher than that of 3.

We now study charge carriers in the molecule. Consider first

the creation of a hole by removing an electron, a process in-

volving investment of energy, the ionization potential . Inthe quasiparticle picture, the hole has a single-particle wave

function, described as a frontier DFT orbital on one of the

donors (orbitals 1 or 3 ofFigure 2). The energy of the hole,

, is closely approximated by the DFT highest occupiedmolecular orbital (HOMO) energy .

19,22,23 Similarly, we

can add an electron to the molecule, this releases energy ofthe amount equal to the electron affinity, . In the DFT calcu-lation, the electron quasiparticle wave function is orbital 2 in

Figure 2 localized primarily on the MN acceptor. The energy

of the electron, , is closely approximated by the lowestunoccupied molecular orbital (LUMO) energy .

We note that the donor orbitals 1 and 3 are spatially non-

overlapping, with orbital 1 having slightly higher energy.

This non-mixing of these left and right orbitals is due to an

interference effect appearing when the PA segments are con-nected to the benzene ring in the meta positions where they

become electronically decoupled: an hole on the left cannot

flow through the ring into the right side.28-32

As we shall seebelow, this has an important bearing on the differential con-

ductance peaks of the junction.

Now consider how a negatively charged gate electrode in thex-y plane below the molecule affects its electronic structure.

The electrode creates an electric field in the z direction , ora potential difference between the electron on MNand the hole on PA, displaced by a distance and where isthe molecular dielectric constant. Therefore, the gate-field

affects the electron-hole energy gap as:

) )

(1)In Figure 3 (left) we plot the DFT-calculated orbital gap vs. the gate field , showing linear dependence, from which:

(2)An abrupt change in the gap occurs at a certain critical value

of the field . This critical behavior is due to a

spontaneous charge transfer induced by the gate, clearly seen

in Figure 3 (right), where the dipole moment and charge on

the MN acceptor jump discontinuously at . We have care-

fully checked, that if the sulfur atoms are held in place (as

happens when the molecule is connected to the metallic

leads), the geometry of the molecule is only slightly distorted

by this internal electron transfer.

In Mullikens theory,33

the energy of electron transfer from

donor to acceptor is ) ) )

) where

is the energy of Coulomb

attraction between the electron and hole. Charge spontane-

ously transfers from donor to acceptor once )

) so from Figure 3 (left):

) (3)

Using Eqs.(2)-(3) we can estimate the internal dielectric con-

stant and the electron-hole effective z-displacement , the latter is in agreement with the minimal donor-acceptor z-displacement .

Figure 3: BNL*-DFT spin-polarized LUMO-HOMO (quasi-particle) gap and

TDDFT optical gap (left), z-component dipole moment and Mulliken charge

on cyano groups (right) vs. gate field.

In Figure 3 (left) we also plot the optical gap , calculatedfrom linear response TDDFT using the same functional. is the first excitation energy corresponding to a transition

dipole moment pointing in the z direction. Note that de-pends linearly on , predicting strong electro-absorptioneffects for z-polarized light in this junction. It is readily visi-

ble in Figure 3 (left) that the exciton binding energy, namely

the difference 1.7 eV, is nearly constant.That the value of is close to that of of Eq.(3) is nocoincidence as both describe electron-hole attraction energy.

Once , i.e. the field is strong enough to induce charge

transfer, a spin (say) electron moves from one of the donors

(orbitals 1 or 3) into the orbital localized on the acceptor (or-bital 2). Orbital 2, the previous LUMO, now has its energy

spin-dependent: the orbital energy drops abruptly slightlybelow the HOMO level (due to the electron-hole binding en-

ergy discussed above) and it get occupied by an electronwhile the orbital energy shoots up in energy above some of

the other unoccupied levels of the PAs. This latter effect is

due to Coulomb repulsion: the energy to add a secondelec-tron to the acceptor is much higher now, due to the presences

of the first transferred electron. Thus, immediately after the

charge transfer orbital 2 is no longer a frontier orbital: both

1

2 3

0

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1

Gap

(eV)

Gate Field (V/)

b

a

Eeh

Eeb

-14

-12

-10

-8

-6

-4

-2

0

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0 0. 2 0. 4 0. 6 0. 8 1

DipoleMoment(e)

ChargeonAcceptor(e

)

Gate Field (V/)


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3

the and LUMOs are now donor orbitals and as a resultthe and gaps become independent of. Further increaseof the field lowers the energies of both spin components of

orbital 2. The component digs deeper into the occupied

levels but the component energy reduces until it resumes its

role as the LUMO at making the gap onceagain field dependent.

Thus far, we discussed this donor-acceptor system as a mole-cule and not as part of a molecular junction. The junction we

consider is formed by attaching the molecule to left and right

metallic leads of chemical potential . The thiol-terminatedPA segments provide for very weak coupling and the mole-

cule preserves much of its chemical and electronic properties:

its orbitals and its orbital energies slightly shift to sharp dif-

ferential conductance resonance channels. We imagine an

experimental setup where the energy needed to transfer an

electron from the molecule to the metal, i.e. is con-trolled and kept fixed for all values of the gate field (in our

case, ). We assume a symmetric applicationof the bias potential across the leads, where the chemical

potential of the left (right) lead is ( ).In this setup experimental realization of current through aresonance at energy requires a bias of ||.

Figure 4: The calculated transmittance function ) through the junction,assuming clamped nuclei, from the zero bias BNL* Hamiltonians (Eq.(4)) at

different gate fields. On the left, a broad energy view of the transmission

channels, from to at several gate fields and on the right azoom into the energy range of 0.5 to 1.7 eV for gate fields, before the charge-

transfer event. The full (dotted) line is the transmission of the () spinstates. The vertical line at -1.1eV is the position of the HOMO energy.

We study the differential conductance of the junction using

Landauers theory, based on the ground-state DFT Hamilto-

nian where the peaks of the transmittance ) (the probabil-ity for an electron of energy to cross the junctionfrom left to right) are directly associated with the differentialconductance channels. In weakly bound junctions these posi-

tion of these peaks are close to the quasiparticle energies

which are close to the orbital energies of our DFT Hamiltoni-

an.21,22

The transmittance ) is thus calculated by:34

) {))} (4)Where ( ) are absorbing potentials

35laid on the left

and right PA segments and )is the Greens function cor-responding to the DFT Hamiltonian (see ref.

30 for further

details and explanations of this method).

The calculated ), is plotted in Figure 4 for several valuesof the gate field . Remarkably, at a very broad energy in-terval ( ) the system displays only a singletransmittance peak (which, under sufficiently large gate field,

may split into two spin-polarized components, as discussedbelow). While there are many occupied and some unoccupied

orbitals associated with the PA strands in this energy range

(e.g. orbitals 1 and 3 in Figure 2), none of them seem to con-

duct current. This is due to the strong destructive interference

effect associated with the connection of the PA strands in a

meta- position on the benzene ring.28-30

The position of the

conductance peak, with respect to the HOMO energy (thevertical line in Figure 4 (left)), is almost exactly equal to the

gap (Figure 3 (left)), indicating that transmission occursthrough the LUMO orbital, i.e. orbital 2 ofFigure 2, mainly

localized on MN - the electron acceptor part of the molecule.

Thus, the ) peak at low fields corresponds to tunneling

transmission of electrons through orbital 2. As a result, thesource-drain voltage needed for reaching this conducting

state is tunable by . This can be seen in the right panel ofFigure 4 zooming into the orange strip region of Figure 4

(left). As the gate field increases (by steps of ) the position of the conductance peak drops bysteps of . This high tunability of differential conduct-ance facilitates a transistor-like operation mode for the junc-

tion, as current is reversibly switched on/off by the gate field.

Figure 5: Expected differential conductance of the molecular junction in

Figure 1 as a function of gate field and source-drain voltage.

As the gate field approaches the critical value , the dif-

ferential conductance resonance splits into two resonances atslightly different energies (Figure 4 (right)), each correspond-

ing to a different value of the z-component of spin. As often

happens in DFT calculations, the breaking of spin symmetry

signals strong correlation effects in the electronic system. At

the critical gate field a catastrophic spin-split occurs: one

spin resonance (say, spin ) shoots down in energy below the

HOMO level (vertical line in Figure 4 (left)), gets occupied

by an electron and becomes a hole conducting channel,

while the other resonance shoots up in energy and becomes

an electron conducting channel. The energy splitting between


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these two spin resonances for gate fields slightly above is

. As explained above, the drastic change of elec-tronic structure happens because of the intramolecular chargetransfer: a electron transfers from one of the frontier orbi t-

als (orbitals 1 or 3 of in Figure 2) of the donors to orbital 2 ofthe acceptor. Since the acceptor now populates an electron,

conductance ofelectrons is blocked due to Coulomb repul-

sion (unless is considerably increased). As the field isfurther increased beyond , the hole differential conduct-ance peak still responds to the field and can be further low-

ered, resulting in highly controllable spin-polarized differen-

tial conductance channel.

In summary, we have presented a molecular junction (Figure

1) with well-separated donor acceptor sites for which proper

orientation with respect to a gate field allows exceptionalcontrol of the conductance and optical properties. The junc-

tion is structurally stable under the strong gate fields. It dis-

plays a single conductance peak at a broad energy range, al-

lowing meticulous control of conductance over a large

source-drain voltage and gate field intervals. The strong elec-

tronic response should render the system less sensitive tostray fields and temperature effects. We summarize the con-ductance properties of the junction in Figure 5, exhibiting

gate control of the differential conductance level, allowing a

transistor-like operation and the switch into a spin-polarized

regime when . Although we here treat a specific sys-

tem, the principle of operation is generic since it is based on

sound physical principles; therefore, other junctions contain-

ing similar design elements should exhibit similar conduct-

ance behavior.

Acknowledgments: We gratefully acknowledge the Israel

Science Foundation for supporting this study under grant no.

1020/10.

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Adva Baratz and Roi Baer- Non-mechanical conductance switching in a realistic molecular tunnel junction