(193m) Modeling Electric Double Layer Formation and Strain Induced By a Single-Ion Conducting Polymer on a Two-Dimensional Crystal

Modeling
Electric Double Layer Formation and Strain induced by a Single-ion Conducting
Polymer on a Two-Dimensional Crystal

Aaron Woeppel,
Susan Fullerton-Shirey

Department of
Chemical and Petroleum Engineering, University of Pittsburgh

Current methods using
strain to induce the semiconducting-to-metallic phase transition in two-dimensional
(2D) crystals usually involve mechanical bending of the entire substrate on
which the crystal is deposited. We are taking a new approach to locally strain
2D crystals via field-effect modulation of a single-ion conducting polymer (i.e.,
ionomer), which will enable individual 2D field-effect transistors (FET) to be
strained by applying an ionic gate bias. The mechanism is identical to that
observed in ionic polymer metal composites (IPMCs), where an electrostatic imbalance
is induced because cations, but not anions, are free to diffuse in the
single-ion conductor. Starting with a simple IPMC geometry (electrode/100 nm
ionomer/electrode), we employed finite element modeling to calculate the cation
buildup and resulting electric double layer (EDL) formation at the ionomer/electrode
interface. Because the anions are covalently tethered to the polymer backbone,
the diffusion coefficient of the anions is set to zero, while the diffusion
coefficient of the cations is set to 1 x 10^-8 cm/s. After applying a
1 V bias to one electrode and grounding the other, an EDL is formed within
2 nm of the grounded electrode surface. Likewise, a depletion layer formed
within ~5 nm of the non-grounded electrode surface. At steady state, 90% of the
potential drops within the depletion layer, while the remaining potential drops
at the EDL. The strong electric field induces an ion density of 3 x 10¹⁴
ions/cm² at the ionomer/electrode interface. With a cation diffusion
coefficient of 10^-8 cm²/s and an initial field strength
of 10 mV/nm, complete EDL formation occurred on the timescale of microseconds,
which is consistent with our experimental measurements.  Molecular dynamics
simulations coupled with experiments show that the EDL formation time can be
adjusted by orders of magnitude by modulating the applied field.  We couple the
electrostatics and mechanics to model deformation of the single-ion conductor
in response to the applied field.  Details of the modeling and a brief summary
of our experimental progress on ionomer-gated MoTe₂ FETs will be
presented.

Acknowledgement: 
This work is support in part by the Swanson School of Engineering at the
University of Pittsburgh and Coverstro.

Fig 1: (a) Schematic
of ionomer-gated suspended MoTe₂ FET in the unstrained
semiconducting state (V_G = 0 V) and strained metallic state (V_G
> 0 V). EDL formation at the MoTe₂ crystal/ionomer interface
induces strain in the 2D crystal. (b) Normalized ion concentration and
potential versus distance from non-grounded electrode. A normalized ion
concentration of 0 corresponds to an equal local concentration of cations and
anions. (V= 1.0 V) (c) Cation density in EDL versus time for applied
voltage biases of 1,2, and 3 V. A complete EDL forms on the timescale of
microseconds with a field strength of 10 mV/nm and an ion diffusion coefficient
of 1 x 10^-8 cm²/s.