Thermal Characterization of MXene

Project Overview

This work explores the thermal characteristics of MXene thin films ranging from monolayer to few-layers. We use Raman thermometry according to temperature-dependent peak shift, and use the correlation to find the thermal conductivity.

Key Contents

• MXene Preparation – Synthesis
• MXene Dry Transfer
• Temperature-Dependent Raman Calibration
• Complex Refractive Index (n + ik) Extraction
• COMSOL Modeling: 2D (Hankel Transform) Heat-Transfer Model
• Thermal Conductivity Calculation
• Error Analysis

1) MXene Preparation – Synthesis

We prepare MXene (e.g., Ti₃C₂T_x) by selectively etching the A-layer from the MAX phase (Ti₃AlC₂). A LiF/HCl route is used for controlled etching followed by repeated DI-water rinses to ~neutral pH. Intercalation (e.g., Li⁺, DMSO) and mild delamination yield single-/few-layer flakes. Flake concentration is quantified by vacuum filtration and mass difference; oxidation is minimized by cold storage in Ar-purged containers with light protection.

• Quality checks: XRD (c-lattice expansion), AFM (thickness ~1–2 nm per layer), Raman (A_1g, E_g modes), 4-probe sheet resistance.
• Common pitfalls: Over-etching (defect formation), residual salts (insufficient washing), and ambient oxidation (elevated sheet R over time).

2) MXene Dry Transfer

Dry transfer places pre-formed MXene films onto target substrates (e.g., Si/SiO₂, sapphire) without liquid processing on the target. We use a polymer-assisted pickup (PMMA or PDMS stamp), align to lithographic markers, apply gentle heat/pressure, then dissolve/release the support. Surface activation (brief O₂ plasma) is used when higher adhesion is required; transfer is done quickly to limit oxidation.

• Controls: Film areal density via pre-calibrated casting/filtration, post-transfer bake (≤120 °C) to improve contact.
• Verification: Optical/AFM uniformity maps, Raman mapping, and 4-probe continuity checks across the device area.

3) Temperature and Power Dependent Raman Calibration

The Raman thermometer is calibrated by measuring the shift in the Raman peak position as a function of the controlled stage temperature. Laser power is maintained at a low level to minimize self-heating. The temperature coefficient of the Raman shift is defined as χ_T = Δν/ΔT, where ν is the Raman peak position (cm⁻¹) and T is the absolute temperature. This χ_T relation is used to determine the proportionality factor (β) that connects the measured Raman shift to the actual temperature rise. Over a moderate temperature range near room temperature, the relationship is typically linear:

Δω = χ_TΔT

• Procedure: Use a temperature-calibrated heating stage (e.g., 300–500 K). Stabilize at each setpoint, record Raman spectra, fit the characteristic peaks (Lorentzian or Voigt profiles), and extract the temperature slope χ_T.
• Outputs: Slope χ_T with associated uncertainty, linearity range, and goodness-of-fit metrics (R², residuals).

The power-dependent Raman calibration follows a similar procedure, where the laser output power is varied while monitoring the resulting Raman shift. The power coefficient is defined as χ_P = Δν/ΔP, which captures the change in Raman peak position per unit change in absorbed optical power. By combining χ_P with χ_T, the temperature rise induced by laser absorption can be expressed as:

ΔT = Δν/χ_T = (χ_P/χ_T)P_abs

The absorbed power P_abs is obtained from the optical absorption A, calculated using the complex refractive index of the film as A = 1 − R − T, where R and T denote reflectance and transmittance determined via the transfer-matrix model (discussed in the next section).

• Procedure: Vary the laser power using the source controller, collect Raman spectra at each setting, fit the peaks, and determine χ_P.
• Drift control: Use the Si 520.7 cm⁻¹ line as a reference to correct for spectrometer drift; confirm that laser-induced heating is negligible during calibration.
• Outputs: Slope χ_P with uncertainty, linearity range, and fit statistics (R², residuals).

5) Complex Refractive Index (n, k) Extraction

The complex refractive index (n + ik) of MXene thin films is determined by measuring reflectance (R) and transmittance (T) across flakes of varying thicknesses suspended on glass coverslips (~150 μm). Thicknesses are measured independently by AFM for accurate optical modeling.

Reflectance Measurement

A silver mirror of known reflectivity (~99.65%) serves as a reference. Using a beam splitter, the reflected power from the MXene-on-glass sample (P_{R, MX}) is compared to that from the silver mirror (P_{R, Ag}), yielding:

R_{MX / glass} = R_Ag × (P_{R, MX} / P_{R, Ag})

This approach eliminates alignment and power drift errors. Each measurement is repeated at 20 different laser powers to enhance statistical precision.

Transmittance Measurement

The transmittance is measured by placing a power meter below the substrate. First, the incident baseline (T₀) is recorded with no sample. Then, the MXene-on-glass sample is inserted, and transmitted power (T_{MX / glass}) is measured:

T = T_{MX / glass} / T₀

Reflectance and transmittance values from multiple flakes are used to constrain the optical model and extract the most probable refractive index values.

Optical Modeling and Parameter Extraction

A multilayer Transfer Matrix Method (TMM) solver is implemented to simulate R and T as functions of n and k for each flake thickness. The solver sweeps n and k over a defined range and evaluates the Gaussian likelihood:

L(n, k) ∝ exp[ −(R_meas − R_sim)² / (2σ_R²) − (T_meas − T_sim)² / (2σ_T²) ]

The likelihoods from all flakes are multiplied to obtain a joint probability distribution, and the peak of this distribution gives the most probable (n, k) values.

Validation and Application

The extracted optical constants are validated by simulating suspended-film reflectance and transmittance using Fresnel equations, accounting for a small air gap between the MXene and substrate. The resulting (n, k) values are then used to compute the optical absorption:

A = 1 − R − T

This absorption term (A) is subsequently used in the thermal modeling section to determine the absorbed laser power for heat transfer and conductivity analysis.

4) COMSOL Modeling – 2D (Hankel Transform) Heat-Transfer Model

We model axisymmetric heating from a Gaussian beam using transient heat conduction in cylindrical coordinates: ρC ∂T/∂t = k_r(∂²T/∂r² + (1/r)∂T/∂r) + ∂/∂z(k_z ∂T/∂z) + Q(r,z,t). Absorbed power is set by optical modeling (R/T/A from TMM) with a Gaussian profile of radius w₀. Interfacial thermal conductance G is applied at film/substrate boundaries.

• Inputs: Layer thicknesses, k_r/k_z, ρ, C, G, w₀, repetition rate, pulse duration, absorption depth.
• BCs: Adiabatic symmetry at r=0; sufficiently large radial/axial extents to avoid boundary artifacts; substrate bottom isothermal or adiabatic (checked by sensitivity).
• Outputs: ΔT(r,t) at the MXene surface for comparison with Raman-derived temperatures.

For fast parameter sweeps, we validate COMSOL with a Hankel-space semi-analytical solver (Bessel transform in r), enabling quick evaluation of ΔT(0) vs. P_abs, w₀, and G.

5) Thermal Conductivity Calculation

Thermal conductivity is extracted by fitting modeled temperature rises to Raman-derived temperatures across power and/or spatial scans. After converting Raman shifts to ΔT using the calibrated χ, we minimize the residual between experiment and model by varying k (in-plane and, when resolvable, cross-plane) and interfacial G.

• Data: Δω(r,P) → ΔT(r,P) using χ.
• Cost function: minimize ∑_i[ΔT_meas(r_i,P_i) − ΔT_model(r_i,P_i|k,G)]².
• Decoupling strategy: Use thickness/spot-size regimes and frequency content (CW vs. pulsed) to weight sensitivity to in-plane k, cross-plane k, and G.
• Reporting: Best-fit k ± 1σ (from the uncertainty analysis below) and goodness-of-fit metrics.

6) Error Analysis

We propagate uncertainties from optical, thermal, and metrology inputs to the final conductivity. Dominant contributors typically include Raman slope χ, absorbed power P_abs (via R/T/A), beam radius w₀, film thickness, and interface G. Two approaches are used:

• First-order (analytic): σ_k² ≈ ∑(∂k/∂x)² σ_x² over inputs x ∈ {χ, P_abs, w₀, thickness, G, …}.
• Monte Carlo: Sample input distributions (e.g., χ ±2–5%, w₀ ±3%, power meter ±2%, thickness ±5%, G ±20%), refit 10³–10⁴ times, and report the resulting k distribution.

Best practices: Knife-edge beam-waist measurements, spectrometer drift correction via the Si line, repeated low-power Raman checks for non-heating calibration, and oxidation-aware handling to maintain MXene properties across measurements.