Raman spectroscopy serves as a powerful tool for non-contact temperature measurement, leveraging the intrinsic relationship between phonon behavior and thermal effects in materials. Two primary Raman-based techniques dominate this field: phonon line shift analysis and anti-Stokes/Stokes intensity ratio thermometry. These methods are particularly valuable in microelectronics and combustion studies, where precise thermal monitoring is critical.

Phonon line shifts arise due to the anharmonicity of atomic vibrations in a crystal lattice. As temperature increases, lattice expansion and phonon-phonon interactions alter the interatomic potential, leading to shifts in Raman-active mode frequencies. The frequency shift (Δω) of an optical phonon mode can be empirically modeled as a function of temperature (T) using the following expression:
Δω(T) = ω₀ + A(1 + 2/(e^(ħω₀/2k_BT) - 1)) + B(1 + 3/(e^(ħω₀/3k_BT) - 1) + 3/(e^(ħω₀/3k_BT) - 1)^2)
where ω₀ is the frequency at 0 K, A and B are anharmonic constants, ħ is the reduced Planck constant, and k_B is the Boltzmann constant. In silicon, for example, the first-order optical phonon at 520 cm⁻¹ exhibits a linear redshift of approximately -0.024 cm⁻¹/K near room temperature. This sensitivity enables spatial resolution below 1 µm when combined with confocal microscopy, making it ideal for mapping thermal gradients in integrated circuits.

The anti-Stokes/Stokes ratio method relies on the temperature-dependent population of phonon states. Anti-Stokes scattering involves phonon absorption, while Stokes scattering involves phonon emission. Their intensity ratio (I_AS/I_S) follows the Boltzmann distribution:
I_AS/I_S = (ω_AS/ω_S)^4 * exp(-ħΔω/k_BT)
where ω_AS and ω_S are the anti-Stokes and Stokes frequencies, and Δω is their separation. This ratio provides absolute temperature calibration without requiring reference spectra. For diamond, the 1332 cm⁻¹ phonon mode yields a temperature resolution of ±5 K in the 300-800 K range when using optimized collection optics.

In microelectronics, these techniques address critical thermal management challenges. Phonon line shift mapping reveals hot spots in GaN high-electron-mobility transistors (HEMTs), where localized temperatures can exceed 473 K under RF operation. The method detects interfacial thermal resistance in 3D-stacked memory devices by tracking Si phonon shifts across buried layers. Anti-Stokes/Stokes ratios quantify self-heating in fin field-effect transistors (FinFETs) with 300 nm spatial resolution, identifying channel temperatures 40-60 K above ambient during switching.

Combustion diagnostics employ Raman thermometry to overcome limitations of thermocouples and pyrometry. In premixed methane-air flames, C₂ vibrational bands at 1800-2200 cm⁻¹ provide temperature profiles with ±50 K accuracy at 10 µs temporal resolution. The O₂ vibrational Q-branch near 1550 cm⁻¹ serves as a gas-phase thermometer, with anti-Stokes/Stokes measurements agreeing within 2% of coherent anti-Stokes Raman spectroscopy (CARS) data up to 2000 K. Soot particles in diesel engines are analyzed via their graphitic G-band at 1580 cm⁻¹, where the 5 cm⁻¹ linewidth increase between 500-1000 K correlates with cylinder temperature gradients.

Several factors influence measurement accuracy. Phonon line shifts require careful calibration against known thermal expansion coefficients, as strain effects can mimic temperature changes. In silicon-germanium alloys, the 8 cm⁻¹ frequency difference between Si-Si and Si-Ge modes necessitates deconvolution for accurate thermometry. Anti-Stokes/Stokes measurements demand correction for wavelength-dependent detector sensitivity and optical system throughput. For high-temperature applications above 1000 K, blackbody radiation background must be subtracted from Raman signals.

Recent advancements include time-resolved Raman thermometry with picosecond pulses to study heat dissipation in phase-change memory materials like Ge₂Sb₂Te₅. Dual-wavelength excitation minimizes fluorescence interference in organic semiconductor films, enabling temperature mapping in perovskite solar cells under illumination. Computational methods like principal component analysis improve signal-to-noise ratios for low-intensity measurements in turbulent combustion environments.

The table below summarizes key parameters for selected materials:

Material | Raman Mode (cm⁻¹) | Sensitivity (cm⁻¹/K) | Temp. Range (K)
Silicon | 520 | -0.024 | 100-700
Diamond | 1332 | -0.016 | 300-1200
GaN | 568 | -0.014 | 80-1000
Graphene | G-band 1580 | -0.016 | 300-2000

Ongoing research focuses on extending these techniques to emerging materials. In hexagonal boron nitride (hBN), the E₂g phonon at 1366 cm⁻¹ shows promise for thermal management in 2D heterostructures. Ultra-wide bandgap semiconductors like β-Ga₂O₃ exhibit measurable phonon shifts up to 1000 K despite strong optical absorption. Machine learning algorithms are being developed to automate temperature extraction from complex Raman spectra in multi-component systems.

These Raman thermometry methods provide critical insights without perturbing the measured system. In semiconductor manufacturing, they monitor wafer temperature during rapid thermal processing with ±3 K repeatability. For combustion engines, they enable in-cylinder temperature measurements that optimize fuel injection timing. The continued refinement of these techniques will support thermal analysis in next-generation nanoelectronics and clean energy systems.