Temperature-dependent ellipsometry is a powerful optical characterization technique used to investigate how the optical properties of semiconductors evolve with temperature. By measuring changes in the polarization state of light reflected from a sample, it provides precise information about dielectric functions, bandgap energies, and thermal expansion effects. Unlike room-temperature ellipsometry, this method captures dynamic responses to thermal stress, making it indispensable for studying phase transitions, band structure modifications, and thermal stability in semiconductor materials.
The core principle of ellipsometry lies in analyzing the amplitude ratio (Ψ) and phase difference (Δ) between the p- and s-polarized components of reflected light. These parameters relate directly to the complex refractive index (n + ik) and dielectric function (ε = ε₁ + iε₂) of the material. When temperature is introduced as a variable, thermally induced changes in lattice constants, electronic band structures, and phonon interactions manifest as measurable shifts in Ψ and Δ. For semiconductors, this enables tracking of critical phenomena such as bandgap narrowing, exciton dissociation, and the onset of new phases.
High-temperature ellipsometry setups typically employ resistive heating stages or infrared lamps capable of reaching temperatures exceeding 1000°C in controlled atmospheres. The sample is mounted on a heating element with minimal thermal gradient, often using materials like tungsten or graphite for uniform heat distribution. Optical access is maintained through quartz or sapphire viewports, which remain transparent across a broad spectral range. To minimize radiative heat loss, reflective shields and water-cooled enclosures are integrated. Temperature calibration is critical, achieved using thermocouples or pyrometers with an accuracy of ±1°C. For wide-bandgap semiconductors like GaN or SiC, high-temperature measurements reveal thermally induced strain and defect dynamics, which are crucial for power electronics operating under extreme conditions.
Low-temperature ellipsometry relies on cryostats cooled by liquid nitrogen or helium, enabling studies down to 10K or lower. The sample is placed in a vacuum chamber to prevent condensation, with optical windows made of materials like MgF₂ or ZnSe to maintain transmission at long wavelengths. Temperature stability within ±0.1K is achievable using feedback-controlled cooling systems. Low-temperature measurements are particularly valuable for examining excitonic effects and defect-related transitions, as thermal broadening is minimized. For example, in ZnO, low-temperature ellipsometry resolves discrete exciton peaks that merge into a continuum at higher temperatures, providing insights into electron-phonon coupling.
Bandgap shifts with temperature are a primary focus of temperature-dependent ellipsometry. The Varshni equation describes the temperature dependence of the bandgap (Eg):
Eg(T) = Eg(0) - (αT²)/(T + β)
where Eg(0) is the bandgap at 0K, and α and β are material-specific constants. Ellipsometry directly extracts Eg(T) by tracking critical points in the dielectric function derivative. In wide-bandgap materials like GaN, the bandgap shrinks from 3.50eV at 10K to 3.38eV at 300K due to lattice expansion and electron-phonon renormalization. For AlN, the shift is more pronounced, from 6.25eV at 10K to 6.08eV at 300K, reflecting stronger thermal effects in ultra-wide-bandgap systems.
Phase transitions in semiconductors are another key application. Ferroelectric materials like BaTiO₃ exhibit abrupt changes in the dielectric function near the Curie temperature (120°C for BaTiO₃), detectable as discontinuities in Ψ and Δ. Similarly, the semiconductor-to-metal transition in VO₂ at 68°C is marked by a collapse in the bandgap and a dramatic increase in ε₂. Ellipsometry provides real-time monitoring of these transitions, enabling kinetic studies of nucleation and domain formation.
Thermal expansion coefficients are derived from temperature-dependent ellipsometry by correlating shifts in critical point energies with lattice parameter changes. The relationship ΔEg/ΔT ≈ (dEg/da)(da/dT) links bandgap shifts (ΔEg) to lattice expansion (da/dT). For SiC, the thermal expansion coefficient α = 4.2 × 10⁻⁶ K⁻¹ is confirmed by ellipsometric data, matching X-ray diffraction results. In anisotropic materials like Ga₂O₃, ellipsometry reveals direction-dependent expansion, critical for heterostructure design.
Wide-bandgap semiconductors benefit significantly from temperature-dependent ellipsometry due to their use in high-power and high-frequency devices. GaN-based HEMTs, for instance, experience self-heating during operation, leading to performance degradation. Ellipsometric studies of AlGaN/GaN heterostructures at elevated temperatures quantify the thermal conductivity and interfacial strain that impact electron mobility. Similarly, SiC devices for electric vehicles require precise knowledge of thermal coefficients to ensure reliability under cycling loads. Ellipsometry maps the temperature-dependent dielectric function of 4H-SiC, identifying defect levels that become thermally activated above 200°C.
Challenges in temperature-dependent ellipsometry include calibration drift at extreme temperatures and signal degradation due to sample oxidation or roughening. For high-temperature measurements, maintaining beam alignment is critical as thermal expansion alters optical paths. Solutions include active alignment systems and reference samples with known thermal properties. For low-temperature studies, interference from frost or window birefringence must be mitigated through careful purging and polarization compensation.
Future advancements may integrate ultrafast ellipsometry to resolve transient thermal effects or combine with other in-situ techniques like X-ray scattering. The growing complexity of semiconductor heterostructures demands higher spatial resolution, driving developments in micro-ellipsometry with temperature control. As wide-bandgap materials push into higher voltage and temperature regimes, temperature-dependent ellipsometry remains essential for linking microscopic properties to device performance.