1. What is the Dirac point?

Physically:

In graphene, it is the energy level at which the conduction band and valence band touch, where the density of states is zero. Electrons in graphene behave like massless Dirac fermions near this point. Graphene has a linear dispersion relation near the Dirac point:

E(k)=ℏvF​∣k∣ where vF​ is the Fermi velocity.

Extend to GFET:

In a GFET device, the Dirac point corresponds to the gate voltage at which the number of electrons = holes in the graphene channel(Charge Neutrality Point (CNP)). At this point: the carrier density is minimum, thus channel resistance is maximum, FET current IDS​ reaches a minimum, corresponds to the lowest point in IDS​ ~ VG curve.

The Dirac point is typically located near the gate voltage of 0V when the graphene is undoped (not very often in practice !!!).

Why it matters:

Position of Dirac point indicates intrinsic doping level or environmental effects (e.g. adsorbed water, oxygen, functionalization).

In sensors, shifts in the Dirac point reflect changes in surface charge, molecule binding, or local ion concentration.

Theoretical estimate:

VD​=q*n0​/CG​​+Φ

q: elementary charge = 1.6×10−19 C; n0​: intrinsic doping density or background carrier density (cm−2); CG: gate capacitance per unit area (F/cm2); Φ: built-in potential offset due to work function mismatch, surface dipoles, or trapped charges (V)

2. Parameters that could influence the Dirac point?

Doping

Intrinsic doping from fabrication residues, substrate traps, or process-induced charge; Extrinsic doping from adsorbed gas molecules (e.g., O₂, H₂O, NH₃), or intentionally introduced dopants.

Electrolyte Environment / Ionic Strength

Electrolyte-gated GFETs (e.g., in PBS, NaCl solutions) due to changes in: Debye length, Electric double layer (EDL) capacitance, and Ionic adsorption onto graphene

Like: Higher ionic concentration → enhanced screening → left-shift of VD

Surface Functionalization

Molecules such as ssDNA, proteins, aptamers, antibodies, or chemical linkers can introduce surface charge. These modify the local electric field near the channel and dope the graphene.

Reference Electrode and Gate Stability

In liquid-gated GFETs, unstable reference electrodes (e.g., Ag/AgCl drift or gate leakage) can cause: artificial VD shifts, measurement non-repeatability, which is essential to use a stable reference and minimize leakage.

Metal Contacts/Work Function Mismatch, and Contact Resistance

Metal electrodes (e.g., Au, Ti, Cr) can dope graphene at the contact regions: Au (high work function) → p-type doping; Ti or Al (low work function) → n-type doping

Poor or asymmetric contact resistance between graphene and metal leads: blurs the current minimum, and causes apparent shift or asymmetry in transfer curve. It doesn’t shift the intrinsic VD, but affects how accurately it’s measured.

Channel Geometry (Length & Width)

Short or narrow channels: increase relative influence of contact resistance, and enhance edge effects and disorder

Low W/L ratio → smaller current → lower signal-to-noise

Substrate Effects

Like: SiO₂ can introduce: Fixed charges, Surface dipoles, and Electron traps (e.g., Si–OH groups), which contribute to background electrostatic doping.

3. Relationship between Dirac point shifting and sensing sensitivity?

In GFET-based sensors, the shift in the Dirac point voltage VD​ is often used as the main sensing signal as it directly reflects changes in surface charge or electrostatic environment, which occur when a target molecule binds to the surface of the graphene.

Before sensing: the device has a baseline Dirac point at VD, baseline

Target molecule binds (e.g., DNA, protein, ion): It brings net charge (positive or negative) near the graphene surface, which changes the local carrier density → shifts VD

After binding: The new Dirac point VD, shifted is measured

ΔVD= (VD, shifted−VD, baseline) ,is used as a quantitative readout of the analyte concentration or activity.

Sensitivity S=ΔC/ΔVD​​

ΔVD​ is the Dirac point shift, ΔC is the change in analyte concentration