[Paper Review] Graphene separation and stretching induced by piezoelectric effect of ferroelectric domains: impact on the conductance of graphene channel

Morozovska, Anna N., Kurchak, Anatolii I.+1 more|arXiv (Cornell University)|Jun 1, 2017

Graphene research and applications16 citations

TL;DR

This paper proposes a piezoelectric mechanism in ferroelectric substrates that induces controlled stretching and separation of graphene channels via domain wall motion under gate voltage, significantly enhancing graphene conductance through strain-induced acoustic phonon scattering. The effect enables voltage-tunable conductance modulation and offers a novel, no-etching method for fabricating suspended graphene without additional processing steps.

ABSTRACT

P-N junctions in graphene on ferroelectric have been actively studied, but the impact of piezoelectric effect in ferroelectric substrate with ferroelectric domain walls (FDWs) on graphene characteristics was not considered. Due to the piezo-effect ferroelectric domain stripes with opposite spontaneous polarizations elongate or contract depending on the polarity of voltage applied to the substrate. We show that the alternating piezoelectric displacement of the ferroelectric domain surfaces can lead to the alternate stretching and separation of graphene areas at the steps between elongated and contracted domains. Graphene separation at FDWs induced by piezo-effect can cause unusual effects. In particular, the conductance of graphene channel in a field effect transistor increases essentially, because electrons in the stretched section scatter on acoustic phonons. At the same time the graphene conductance is determined by ferroelectric spontaneous polarization and varies greatly in the presence of FDWs. The revealed piezo-mechanism of graphene conductance control is promising for next generations of graphene-based field effect transistors, modulators, electrical transducers and piezo-resistive elements. Also our results propose the method of suspended graphene fabrication based on piezo-effect in a ferroelectric substrate that does not require any additional technological procedures.

Motivation & Objective

• To investigate the impact of the piezoelectric effect in ferroelectric substrates with 180° domain walls on graphene strain and transport properties.
• To analyze how piezoelectric surface displacement at ferroelectric domain walls leads to graphene separation and stretching.
• To quantify the resulting conductance changes in graphene channels due to strain and suspended regions.
• To propose a new method for fabricating suspended graphene using only the piezoelectric effect, avoiding conventional etching or mechanical processes.
• To establish a theoretical framework linking ferroelectric polarization, gate voltage, and graphene conductance via strain-mediated electron scattering.

Proposed method

• Modeling the vertical piezoelectric displacement of the ferroelectric substrate surface near a 180° domain wall using the decoupling approximation and analytical expressions for displacement based on piezoelectric coefficients (d31, d33) and gate voltage U.
• Deriving the surface displacement profile using Eqs. (1)–(3) from Ref. [34], with simplified forms in Appendix A for perfect contact (d=0).
• Analyzing the mechanical forces at the graphene-ferroelectric interface: elastic tension (F), its normal (Fn) and lateral (FS) components, and the binding force (Fb) between graphene and substrate.
• Establishing the condition for graphene separation when Fn > Fb, leading to a critical length l for suspended regions, derived in Appendix B using force balance and geometric approximations.
• Applying Matiessen’s rule (Eq. C.1) to compute the total conductance of a graphene channel with a suspended section of length l, combining conductivities from bonded (σB) and suspended (σS) regions.
• Using Eq. (C.3) to express conductivity in terms of electron concentration nS and mean free path λB, with λB related to ionized impurity scattering and Fermi energy.

Experimental results

Research questions

• RQ1 How does the piezoelectric effect in ferroelectric substrates with 180° domain walls induce mechanical strain and separation in graphene?
• RQ2 What is the relationship between gate voltage, ferroelectric polarization, and the resulting graphene conductance modulation?
• RQ3 Under what conditions does graphene detach from the substrate at domain wall steps due to piezoelectric stress?
• RQ4 Can the piezoelectric effect be used to fabricate suspended graphene without conventional etching or mechanical processing?
• RQ5 How does strain-induced electron scattering on acoustic phonons affect the conductance of suspended graphene regions?

Key findings

• Piezoelectric displacement of ferroelectric substrates (e.g., PZT) can reach 0.5–1 nm under 1–3 V gate voltage, inducing significant mechanical strain in graphene.
• Graphene separation occurs at domain wall steps when the normal component of elastic tension exceeds the binding force, leading to suspended regions of length l proportional to U² and inversely proportional to Yd, where Y is graphene’s Young’s modulus and d is the interfacial gap.
• Conductance increases significantly in suspended graphene regions due to reduced electron scattering on acoustic phonons, with the inverse conductance dominated by the suspended section when l ≪ L.
• The conductance is strongly modulated by ferroelectric polarization and gate voltage, with the dominant contribution to conductance coming from the suspended section due to enhanced electron mobility.
• The model predicts that for U = 1 V, H = 50 nm, d = 0.5 nm, and PS ≈ 0.5 C/m², the carrier concentration in graphene is primarily determined by the polarization difference across the domain wall.
• A novel, no-etching method for suspended graphene fabrication is proposed, relying solely on the piezoelectric effect in ferroelectric substrates, eliminating the need for chemical or mechanical processing steps.